NIMCET Previous Year Solved Paper 2022
Infomaths
177 views
15 slides
Aug 22, 2023
Slide 1 of 15
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
About This Presentation
NIMCET Previous Year Solved Paper 2022
Infomaths Solved This Nimcet 2022 PVQ.
Infomaths is the best MCA Entrance Coaching Institute in Chandigarh. Prepare for Mca Entrance Exam i.e NIMCET, CUET (JNU, DU, BHU..), MAHCET PU and other university entrance Exams, Ssc Cgl, Bank Po, Iit Jam And Other Gov...
Slide Content
1
PPRREEVVIIOOUUSS YYEEAARR SSOOLLVVEEDD PPAAPPEERRSS
NNIIMMCCEETT AACCTTUUAALL PPAAPPEERR 22002222
MATHS
1. If the angle of elevation of the top of a hill from each
of the vertices A B and C of a horizontal triangle is
α, then the height of the hill is
(a) 1
tan sec
2
bB (b) 1
tan cos
2
b ecA
(c) 1
tan sin
2
cC (d) 1
tan cos
2
a ecA
2. If x
m
y
n
= (x + y)
m+n
, then dy/dx is
(a) xy
xy
(b) xy (c) x/y (d) y/x
3. The value of 3
3 log 5
3
(a) 5
27 (b) 27
5 (c) 9
5 (d) 5
9
4. The value of
2
3 4 2
1
2 2 1
x dx
x x x
(a) 24
21
22 C
xx
(b) 24
21
22 C
xx
(c) 24
1 2 1
2
2
C
xx
(d) None of these
5. If the volume of a parallelopiped whose
adjacent edges are ^ ^ ^
2 3 4 ,a i j k ^ ^ ^
2,b i j k
^ ^ ^
2c i j k is 15, then is
equal to
(a) 1 (b) 5/2 (c) 9/2 (d) 0
6. The area enclosed within the curve |x| + |y| = 2 is
(a) 16 sq. unit (b) 24 sq. unit
(c) 32 sq. unit (d) 8 sq. unit
7. If a < b, then
b
a
x a x b dx is equal to
(a)
2
2
ba (b)
22
2
ba
(c)
33
2
ab (d) (b – a)
2
8. If 2,a i j k 2,b i j k ,c i j k and 7,abc
then the value of are
(a) 2, - 6 (b) 6, - 2 (c) 4, - 2 (d) – 4, 2
9. There are two sets A and B with |A| = m and |B| = n.
If |P(A)| - |P(B)| = 112 then choose the wrong option
(where |A| denotes the cardinality of A, and P(A)
denotes the power set of A)
(a) m + n = 11 (b) 2n – m = 1
(c) 2m – n = 1 (d) 3n – m = 5
10. A particle is at rest at the origin. It moves along the
x-axis with an acceleration x – x
2
, where x is the
distance of the particle at time t. The particle next
comes to rest after it has covered a distance
(a) 1 (b) 1/2 (c) 3/2 (d) 2
11. In a triangle ABC, if the tangent of half the
difference of two angles is equal to one third of the
tangent of half the sum of the angles, then the ratio
of the sides opposite to the angles is
(a) 2 : 1 (b) 1 : 2 (c) 3 : 1 (d) 1 : 1
12. The solutions of the equation 4 cos
2
x + 6 sin
2
x = 5
are
(a) 4
xn
(b) 3
xn
(c) 2
xn
(d) 2
3
xn
13. A straight line through the point A(4, 5) is such that
its intercept between the axes is bisected at A, then
its equation is
(a) 3x + 4y = 20 (b) 3x – 4y + 7 = 0
(c) 5x – 4y = 40 (d) 5x + 4y = 40
14. The domain of the function
1
cosx
fx
x
is
(a) [-1, 0) {1} (b) [-1, 1]
(c) [-1, 1) (d) None of these
15. If the roots of the quadratic equation x
2
+ px + q = 0
are tan 30 and tan 15 respectively, then the value
of 2 + p – q is
(a) 3 (b) 0 (c) 1 (d) 2
16. Which of the following is NOT TRUE?
(a) lim 0
x
x
x
e
(b) 1/
0
1
lim 0
x
xxe
(c) 0
sin
lim 0
12x
x
x
(d) 0
cos
lim 0
12x
x
x
17. Inverse of the function
10 10
10 10
xx
xx
fx
is
(a) log10 (2 – x) (b) 10
11
log
21
x
x
(c)
10
1
log 2 1
2
x (d) 10
12
log
42
x
x
18. The first three moments of a distribution about 2 are
1, 16, -40 respectively. Then mean and variance of
the distribution are
(a) (2, 16) (b) (2, 15) (c) (3, 15) (d) (1, 16)
19. If a1, a2 ….. an, are in Arithmetic Progression with
common difference, d, then the sum (sin d) (cosec a1
. cosec a2 + cosec a2 . cosec a3 + …… + cosec an-1 .
cosec an) is equal to
(a) cot a1 – cot an (b) sin a1 – sin an
(c) cosec a1 – cosec an (d) a1 – an
20. Solution of the equation 1 2 1 2
tan sin 1
2
x x x x
are
(a) 0, 1 (b) 1, - 1 (c) 0, - 1 (d) 0, - 2
21. If cosec - cot = 2, then the value of cosec is
(a) 5
3 (b) 3
5 (c) 4
5 (d) 5
4
PPRREEVVIIOOUUSS YYEEAARR SSOOLLVVEEDD PPAAPPEERRSS
NNIIMMCCEETT AACCTTUUAALL PPAAPPEERR 22002222
MATHS
1. If the angle of elevation of the top of a hill from each
of the vertices A B and C of a horizontal triangle is
α, then the height of the hill is
(a) 1
tan sec
2
bB (b) 1
tan cos
2
b ecA
(c) 1
tan sin
2
cC (d) 1
tan cos
2
a ecA
2. If x
m
y
n
= (x + y)
m+n
, then dy/dx is
(a) xy
xy
(b) xy (c) x/y (d) y/x
3. The value of 3
3 log 5
3
(a) 5
27 (b) 27
5 (c) 9
5 (d) 5
9
4. The value of
2
3 4 2
1
2 2 1
x dx
x x x
(a) 24
21
22 C
xx
(b) 24
21
22 C
xx
(c) 24
1 2 1
2
2
C
xx
(d) None of these
5. If the volume of a parallelopiped whose
adjacent edges are ^ ^ ^
2 3 4 ,a i j k ^ ^ ^
2,b i j k
^ ^ ^
2c i j k is 15, then is
equal to
(a) 1 (b) 5/2 (c) 9/2 (d) 0
6. The area enclosed within the curve |x| + |y| = 2 is
(a) 16 sq. unit (b) 24 sq. unit
(c) 32 sq. unit (d) 8 sq. unit
7. If a < b, then
b
a
x a x b dx is equal to
(a)
2
2
ba (b)
22
2
ba
(c)
33
2
ab (d) (b – a)
2
8. If 2,a i j k 2,b i j k ,c i j k and 7,abc
then the value of are
(a) 2, - 6 (b) 6, - 2 (c) 4, - 2 (d) – 4, 2
9. There are two sets A and B with |A| = m and |B| = n.
If |P(A)| - |P(B)| = 112 then choose the wrong option
(where |A| denotes the cardinality of A, and P(A)
denotes the power set of A)
(a) m + n = 11 (b) 2n – m = 1
(c) 2m – n = 1 (d) 3n – m = 5
10. A particle is at rest at the origin. It moves along the
x-axis with an acceleration x – x
2
, where x is the
distance of the particle at time t. The particle next
comes to rest after it has covered a distance
(a) 1 (b) 1/2 (c) 3/2 (d) 2
11. In a triangle ABC, if the tangent of half the
difference of two angles is equal to one third of the
tangent of half the sum of the angles, then the ratio
of the sides opposite to the angles is
(a) 2 : 1 (b) 1 : 2 (c) 3 : 1 (d) 1 : 1
12. The solutions of the equation 4 cos
2
x + 6 sin
2
x = 5
are
(a) 4
xn
(b) 3
xn
(c) 2
xn
(d) 2
3
xn
13. A straight line through the point A(4, 5) is such that
its intercept between the axes is bisected at A, then
its equation is
(a) 3x + 4y = 20 (b) 3x – 4y + 7 = 0
(c) 5x – 4y = 40 (d) 5x + 4y = 40
14. The domain of the function
1
cosx
fx
x
is
(a) [-1, 0) {1} (b) [-1, 1]
(c) [-1, 1) (d) None of these
15. If the roots of the quadratic equation x
2
+ px + q = 0
are tan 30 and tan 15 respectively, then the value
of 2 + p – q is
(a) 3 (b) 0 (c) 1 (d) 2
16. Which of the following is NOT TRUE?
(a) lim 0
x
x
x
e
(b) 1/
0
1
lim 0
x
xxe
(c) 0
sin
lim 0
12x
x
x
(d) 0
cos
lim 0
12x
x
x
17. Inverse of the function
10 10
10 10
xx
xx
fx
is
(a) log10 (2 – x) (b) 10
11
log
21
x
x
(c)
10
1
log 2 1
2
x (d) 10
12
log
42
x
x
18. The first three moments of a distribution about 2 are
1, 16, -40 respectively. Then mean and variance of
the distribution are
(a) (2, 16) (b) (2, 15) (c) (3, 15) (d) (1, 16)
19. If a1, a2 ….. an, are in Arithmetic Progression with
common difference, d, then the sum (sin d) (cosec a1
. cosec a2 + cosec a2 . cosec a3 + …… + cosec an-1 .
cosec an) is equal to
(a) cot a1 – cot an (b) sin a1 – sin an
(c) cosec a1 – cosec an (d) a1 – an
20. Solution of the equation 1 2 1 2
tan sin 1
2
x x x x
are
(a) 0, 1 (b) 1, - 1 (c) 0, - 1 (d) 0, - 2
21. If cosec - cot = 2, then the value of cosec is
(a) 5
3 (b) 3
5 (c) 4
5 (d) 5
4
2
22. The function
1/
2
1 2 , 0
,
,0
x
xx
fx
ex
is
(a) differentiable at x = 0 (b) continuous at x = 0
(c) discontinuous at x = 0
(d) not differentiable at x = 0
23. If the foci of the ellipse 22
2
1
25
xy
b
and the
hyperbola 22
1
144 81 25
xy
are coincide, then the
value of b
2
is
(a) 25 (b) 16 (c) 64 (d) 49
24. If ,a b c a b c then
(a) a and b are collinear
(b) a and b are perpendicular
(c) a and c are collinear
(d) a and c are perpendicular
25. Suppose that the temperature at a point (x, y) on a
metal plate is T(x, y) = 4x
2
– 4xy + y
2
. An ant,
walking on the plate, traverses a circle of radius 5
centered at the origin. What is the highest
temperature encountered by the ant?
(a) 125 (b) 120 (c) 0 (d) 25
26. The function
2
log 1f x x x is
(a) an even function (b) an odd function
(c) a periodic function
(d) neither an even nor an odd function
27. Angles of elevation of the top of a tower from three
points (collinear) A, B and C on a road leading to the
foot of the tower are 30, 45 and 60 respectively.
The ratio of AB and BC is
(a) 3 :1 (b) 3 : 2 (c) 1 : 2 (d) 2 : 3
28. The mean of 25 observations are found to be 38. It
was later discovered that 23 and 38 were misread at
25 and 36, then the mean is
(a) 32 (b) 36 (c) 38 (d) 42
29. In a Harmonic Progression, p
th
term is q and the q
th
term is p. Then pq
th
term is
(a) 0 (b) 1 (c) pq (d) pq (p + q)
30. A four-digit number is formed using the digits 1, 2,
3, 4, 5 without repetition. The probability that it is
divisible by 3 is
(a) 1/3 (b) 1/4 (c) 1/5 (d) 1/6
31. Let 22a i j k and b be another vector such
that . 14ab and 38a b i j k the vector b =
(a) 5i + j + 2k (b) 5i – j – 2k
(c) 5i + j – 2k (d) 3i + j + 4k
32. A survey is done among a population of 200 people
who like either tea or coffee. It is found that 60% of
the population like tea and 72% of the population
like coffee. Let x be the number of people who like
both tea and coffee. Let m ≤ x ≤ n, then choose the
correct option
(a) n – m = 56 (b) n – m = 28
(c) n – m = 32 (d) n + m = 92
33. The eccentricity of an ellipse, with its centre at the
origin is 1/3. If one of the directrices is x = 9, then
the equation of ellipse is :
(a) 9x
2
+ 8y
2
= 72 (b) 8x
2
+ 9y
2
= 72
(c) 8x
2
+ 7y
2
= 56 (d) 7x
2
+ 8y
2
= 56
34. For a R (the set of all real numbers), a - 1,
1
1 2 .... 1
lim
601 1 2 ....
a a a
a
n
n
n na na na n
.
Then one of the values of a is
(a) 5 (b) 8 (c) -15/2 (d) -17/2
35. Let a be the distance between the lines – 2x + y = 2
and 2x – y = 2, and b be the distance between the
lines 4x – 3y = 5 and 6y – 8x = 1, then
(a) 40 11 5ba (b) 40 2 11ab
(c) 11 2 40ba (d) 11 2 40ab
36. If 1 1 1
1 2 1
1 1 2
Dx
y
for x 0, y 0, then D is
(a) Divisible by x and y
(b) Divisible by x but not by y
(c) Divisible by (1 + x) and (1 + y)
(d) Divisible by (1 + x) but not (1 + y)
37. If 0 < P (A) < 1 and 0 < P(B) < 1, and P(A B) =
P(A) P(B), then
(a) P(B|A) = P(B) – P(A)
(b) P(A
C
– B
C
) = P(A
C
) – P(B
C
)
(c) P (A B)
C
= P(A
C
) P(B
C
)
(d) P(A|B) = P(A) – P(B)
38. Let a, b, c be distinct non-negative numbers. If the
vectors ,ai a j ck i k and ci c j bk lie in a
plane, then c is
(a) The Arithmetic Mean of a and b
(b) The Geometric Mean of a and b
(c) The Harmonic Mean of a and b
(d) Equal to zero
39. The value of 1152
cot cos tan
33
ec
is
(a) 6/17 (b) 3/17 (c) 4/17 (d) 5/17
40. Which term of the series 5 5 1
, , ,........
34 5 is 5
?
13
(a) 12 (b) 11 (c) 10 (d) 9
41. Coordinate of focus of the parabola 4y
2
+ 12x – 20y
+ 67 = 0 is
(a) 5 17
,
42
(b) 17 5
,
24
(c) 17 5
,
42
(d) 5 17
,
24
42. The 10
th
and 50
th
percentiles of the observations 32,
49, 23, 29, 118 respectively are
(a) 21, 32 (b) 23, 32 (c) 23, 33 (d) 22, 31
43. Area of the parallelogram formed by the lines y = 4x,
y = 4x + 1, x + y = 0 and x + y = 1 is
(a) 1/5 (b) 2/5 (c) 5 (d) 10
44. If a1, a2, …… an are any real numbers and n is any
positive integer, then
(a)
2
2
11
nn
ii
ii
n a a
(b)
2
2
11
nn
ii
ii
n a a
(c)
2
2
11
nn
ii
ii
aa
(d) None of these
45. There are two circles in xy-plane whose equations
are x
2
+ y
2
– 2y = 0 and x
2
+ y
2
– 2y – 3 = 0. A point
22. The function
1/
2
1 2 , 0
,
,0
x
xx
fx
ex
is
(a) differentiable at x = 0 (b) continuous at x = 0
(c) discontinuous at x = 0
(d) not differentiable at x = 0
23. If the foci of the ellipse 22
2
1
25
xy
b
and the
hyperbola 22
1
144 81 25
xy
are coincide, then the
value of b
2
is
(a) 25 (b) 16 (c) 64 (d) 49
24. If ,a b c a b c then
(a) a and b are collinear
(b) a and b are perpendicular
(c) a and c are collinear
(d) a and c are perpendicular
25. Suppose that the temperature at a point (x, y) on a
metal plate is T(x, y) = 4x
2
– 4xy + y
2
. An ant,
walking on the plate, traverses a circle of radius 5
centered at the origin. What is the highest
temperature encountered by the ant?
(a) 125 (b) 120 (c) 0 (d) 25
26. The function
2
log 1f x x x is
(a) an even function (b) an odd function
(c) a periodic function
(d) neither an even nor an odd function
27. Angles of elevation of the top of a tower from three
points (collinear) A, B and C on a road leading to the
foot of the tower are 30, 45 and 60 respectively.
The ratio of AB and BC is
(a) 3 :1 (b) 3 : 2 (c) 1 : 2 (d) 2 : 3
28. The mean of 25 observations are found to be 38. It
was later discovered that 23 and 38 were misread at
25 and 36, then the mean is
(a) 32 (b) 36 (c) 38 (d) 42
29. In a Harmonic Progression, p
th
term is q and the q
th
term is p. Then pq
th
term is
(a) 0 (b) 1 (c) pq (d) pq (p + q)
30. A four-digit number is formed using the digits 1, 2,
3, 4, 5 without repetition. The probability that it is
divisible by 3 is
(a) 1/3 (b) 1/4 (c) 1/5 (d) 1/6
31. Let 22a i j k and b be another vector such
that . 14ab and 38a b i j k the vector b =
(a) 5i + j + 2k (b) 5i – j – 2k
(c) 5i + j – 2k (d) 3i + j + 4k
32. A survey is done among a population of 200 people
who like either tea or coffee. It is found that 60% of
the population like tea and 72% of the population
like coffee. Let x be the number of people who like
both tea and coffee. Let m ≤ x ≤ n, then choose the
correct option
(a) n – m = 56 (b) n – m = 28
(c) n – m = 32 (d) n + m = 92
33. The eccentricity of an ellipse, with its centre at the
origin is 1/3. If one of the directrices is x = 9, then
the equation of ellipse is :
(a) 9x
2
+ 8y
2
= 72 (b) 8x
2
+ 9y
2
= 72
(c) 8x
2
+ 7y
2
= 56 (d) 7x
2
+ 8y
2
= 56
34. For a R (the set of all real numbers), a - 1,
1
1 2 .... 1
lim
601 1 2 ....
a a a
a
n
n
n na na na n
.
Then one of the values of a is
(a) 5 (b) 8 (c) -15/2 (d) -17/2
35. Let a be the distance between the lines – 2x + y = 2
and 2x – y = 2, and b be the distance between the
lines 4x – 3y = 5 and 6y – 8x = 1, then
(a) 40 11 5ba (b) 40 2 11ab
(c) 11 2 40ba (d) 11 2 40ab
36. If 1 1 1
1 2 1
1 1 2
Dx
y
for x 0, y 0, then D is
(a) Divisible by x and y
(b) Divisible by x but not by y
(c) Divisible by (1 + x) and (1 + y)
(d) Divisible by (1 + x) but not (1 + y)
37. If 0 < P (A) < 1 and 0 < P(B) < 1, and P(A B) =
P(A) P(B), then
(a) P(B|A) = P(B) – P(A)
(b) P(A
C
– B
C
) = P(A
C
) – P(B
C
)
(c) P (A B)
C
= P(A
C
) P(B
C
)
(d) P(A|B) = P(A) – P(B)
38. Let a, b, c be distinct non-negative numbers. If the
vectors ,ai a j ck i k and ci c j bk lie in a
plane, then c is
(a) The Arithmetic Mean of a and b
(b) The Geometric Mean of a and b
(c) The Harmonic Mean of a and b
(d) Equal to zero
39. The value of 1152
cot cos tan
33
ec
is
(a) 6/17 (b) 3/17 (c) 4/17 (d) 5/17
40. Which term of the series 5 5 1
, , ,........
34 5 is 5
?
13
(a) 12 (b) 11 (c) 10 (d) 9
41. Coordinate of focus of the parabola 4y
2
+ 12x – 20y
+ 67 = 0 is
(a) 5 17
,
42
(b) 17 5
,
24
(c) 17 5
,
42
(d) 5 17
,
24
42. The 10
th
and 50
th
percentiles of the observations 32,
49, 23, 29, 118 respectively are
(a) 21, 32 (b) 23, 32 (c) 23, 33 (d) 22, 31
43. Area of the parallelogram formed by the lines y = 4x,
y = 4x + 1, x + y = 0 and x + y = 1 is
(a) 1/5 (b) 2/5 (c) 5 (d) 10
44. If a1, a2, …… an are any real numbers and n is any
positive integer, then
(a)
2
2
11
nn
ii
ii
n a a
(b)
2
2
11
nn
ii
ii
n a a
(c)
2
2
11
nn
ii
ii
aa
(d) None of these
45. There are two circles in xy-plane whose equations
are x
2
+ y
2
– 2y = 0 and x
2
+ y
2
– 2y – 3 = 0. A point
3
(x, y) is chosen at random inside the larger circle.
Then the probability that the point has been taken
from smaller circle is
(a) 1/3 (b) 2/3 (c) 1/2 (d) 1/4
46. f(x) = x + |x| is continuous for
(a) x (-,) (b) x (-,) – {0}
(c) only x > 0 (d) No value of x
47. The correct expression for cos
-1
(-x) is
(a) /2 – cos
-1
x (b) - cos
-1
x
(c) + cos
-1
x (d) /2 + cos
-1
x
48. If 11
cos cos ,
23
xy
then 9x
2
– 12xycos +4y
2
=
(a) – 36 sin
2
(b) 36 sin
2
(c) 36 cos
2
(d) 36
49. If
22
1,
xy
ab
ab
and x
2
– y
2
= c
2
cut at
right angles, then
(a) a
2
+ b
2
= 2c
2
(b) b
2
– a
2
= 2c
2
(c) a
2
– b
2
= 2c
2
(d) a
2
– b
2
= c
2
50. If , are the roots of x
2
– x – 1 = 0, and An =
n
+
n
, then Arithmetic Mean of An-1 and An is
(a) 2An-1 (b) 1
1
2
n
A
(c) 2An-2 (d) None of these
ANALYTICAL ABILITY AND LOGICAL
REASONING
51. U, V, W, X and T are sitting on a bench. T is sitting
next to U, V is sitting next to W, W is not sitting
with X who is on the left end of the bench. V is in
the second position from the right. T is to the right of
U and X. T and V are sitting together. In which
position T is sitting?
(a) Between U and W (b) Between V and X
(c) Between X and W (d) Between U and V
52. DNN, FQQ, HTT, ……., LZZ
(a) JWW (b) JVV (c) JXX (d) IWW
53. Find the synonym that is most nearly similar in
meaning to the word : DEBACLE
(a) Catastrophe (b) Corker
(c) Opulence (d) Dandy
54. Fill in the blank : HEC, JGE, LIG, NKI, -------
(a) ONM (b) PMK (c) KMP (d) HGF
55. Replace the question mark with an appropriate image
to complete the analogous pair.
(a) (b)
(c) (d)
56. Which of the following is the odd one from the
given alternatives?
(a) Driving (b) Sailing
(c) Diving (d) Swimming
57. Select the pair of words, which are related in the
same way as the capitalized words are related to each
other.
Frugal : Extravagant
(a) Predecessor : Precursor (b) Hermit : Philosopher
(c) Teacher : Philanthropist (d) Criticise : Advocate
58. Identify the sixth number in the series : 6, 11, 21, 36,
56, ?
(a) 52 (b) 81 (c) 82 (d) 21
59. Looking at the portrait of a woman, Manu said, “Her
mother is the wife of my father’s son and I have no
brother and sister.” Whose portrait was Manu
looking at?
(a) His son (b) His daughter
(c) His father (d) His nephew
60. Select the pair of words, which are related in the
same way as the capitalized words are related to each
other.
BUTTERFLY : FREEDOM
(a) chicken : Rooster (b) Self-reliant : Buoyant
(c) Frog : Water (d) Horse : Speed
61. If in a certain language, KOLKOTA is coded as
LPMLPUB, how is MUMBAI coded in that code?
(a) NVNBCJ (b) OVNBBH
(c) NVNCBJ (d) NUNBCH
62. Select the related word from the given alternatives.
MELT : LIQUID : : FREEZE : ?
(a) PUSH (b) CONDENSE
(c) SOLID (d) ICE
63. In the following figure, find the total number of
squares.
(a) 20 (b) 36 (c) 18 (d) 24
64. Which of the following diagrams correctly represents
lions, elephants, and animals?
(a) (b)
(c) (d)
65. Identity the fifth number in the series:
122, 144, 166, 188, ?
(a) 210 (b) 234 (c) 345 (d) 310
66. Fill in the blank : JAK, KBL, LCM, MDN, …….
(a) MEN (b) NEO (c) OEP (d) PEQ
67. Deepak, Rahul, Manoj, and Vinod are brothers. Who
is the heaviest?
I. Rahul is heavier than Deepak and Vinod, but
lighter than Manoj
II. Deepak is lighter than Rahul and Manoj, but
heavier than Vinod.
(a) Either I or II is sufficient.
(x, y) is chosen at random inside the larger circle.
Then the probability that the point has been taken
from smaller circle is
(a) 1/3 (b) 2/3 (c) 1/2 (d) 1/4
46. f(x) = x + |x| is continuous for
(a) x (-,) (b) x (-,) – {0}
(c) only x > 0 (d) No value of x
47. The correct expression for cos
-1
(-x) is
(a) /2 – cos
-1
x (b) - cos
-1
x
(c) + cos
-1
x (d) /2 + cos
-1
x
48. If 11
cos cos ,
23
xy
then 9x
2
– 12xycos +4y
2
=
(a) – 36 sin
2
(b) 36 sin
2
(c) 36 cos
2
(d) 36
49. If
22
1,
xy
ab
ab
and x
2
– y
2
= c
2
cut at
right angles, then
(a) a
2
+ b
2
= 2c
2
(b) b
2
– a
2
= 2c
2
(c) a
2
– b
2
= 2c
2
(d) a
2
– b
2
= c
2
50. If , are the roots of x
2
– x – 1 = 0, and An =
n
+
n
, then Arithmetic Mean of An-1 and An is
(a) 2An-1 (b) 1
1
2
n
A
(c) 2An-2 (d) None of these
ANALYTICAL ABILITY AND LOGICAL
REASONING
51. U, V, W, X and T are sitting on a bench. T is sitting
next to U, V is sitting next to W, W is not sitting
with X who is on the left end of the bench. V is in
the second position from the right. T is to the right of
U and X. T and V are sitting together. In which
position T is sitting?
(a) Between U and W (b) Between V and X
(c) Between X and W (d) Between U and V
52. DNN, FQQ, HTT, ……., LZZ
(a) JWW (b) JVV (c) JXX (d) IWW
53. Find the synonym that is most nearly similar in
meaning to the word : DEBACLE
(a) Catastrophe (b) Corker
(c) Opulence (d) Dandy
54. Fill in the blank : HEC, JGE, LIG, NKI, -------
(a) ONM (b) PMK (c) KMP (d) HGF
55. Replace the question mark with an appropriate image
to complete the analogous pair.
(a) (b)
(c) (d)
56. Which of the following is the odd one from the
given alternatives?
(a) Driving (b) Sailing
(c) Diving (d) Swimming
57. Select the pair of words, which are related in the
same way as the capitalized words are related to each
other.
Frugal : Extravagant
(a) Predecessor : Precursor (b) Hermit : Philosopher
(c) Teacher : Philanthropist (d) Criticise : Advocate
58. Identify the sixth number in the series : 6, 11, 21, 36,
56, ?
(a) 52 (b) 81 (c) 82 (d) 21
59. Looking at the portrait of a woman, Manu said, “Her
mother is the wife of my father’s son and I have no
brother and sister.” Whose portrait was Manu
looking at?
(a) His son (b) His daughter
(c) His father (d) His nephew
60. Select the pair of words, which are related in the
same way as the capitalized words are related to each
other.
BUTTERFLY : FREEDOM
(a) chicken : Rooster (b) Self-reliant : Buoyant
(c) Frog : Water (d) Horse : Speed
61. If in a certain language, KOLKOTA is coded as
LPMLPUB, how is MUMBAI coded in that code?
(a) NVNBCJ (b) OVNBBH
(c) NVNCBJ (d) NUNBCH
62. Select the related word from the given alternatives.
MELT : LIQUID : : FREEZE : ?
(a) PUSH (b) CONDENSE
(c) SOLID (d) ICE
63. In the following figure, find the total number of
squares.
(a) 20 (b) 36 (c) 18 (d) 24
64. Which of the following diagrams correctly represents
lions, elephants, and animals?
(a) (b)
(c) (d)
65. Identity the fifth number in the series:
122, 144, 166, 188, ?
(a) 210 (b) 234 (c) 345 (d) 310
66. Fill in the blank : JAK, KBL, LCM, MDN, …….
(a) MEN (b) NEO (c) OEP (d) PEQ
67. Deepak, Rahul, Manoj, and Vinod are brothers. Who
is the heaviest?
I. Rahul is heavier than Deepak and Vinod, but
lighter than Manoj
II. Deepak is lighter than Rahul and Manoj, but
heavier than Vinod.
(a) Either I or II is sufficient.
4
(b) Data is both the statements together are not
sufficient
(c) Statement I alone is sufficient, but statement II
alone is not sufficient
(d) Statement II alone is sufficient, but statement I
alone is not sufficient
68. Today is Wednesday. What would be the dady after
61 days?
(a) Monday (b) Saturday
(c) Sunday (d) Tuesday
69. Choose the word opposite in meaning to the given
word : MITIGATE
(a) Tranquilize (b) Intensify
(c) Alleviate (d) Abate
Directions (Qs. No. 70-72): In each question below are
given two statements followed by two conclusion
numbered I and II. You have to take the given two
statements to be true even if they seem to be at variance
from commonly known facts. Read the conclusion and
then decide which of the following given conclusions
logically follows from the two given statements,
disregarding commonly known facts.
70. Statements : No women teacher play. Some women
teachers are athletes.
Conclusions:
I. Male athletes can play.
II. Some athletes can play.
(a) Only conclusion II follows
(b) Only conclusion I follows
(c) either I or II follows
(d) Neither I nor II follows
71. Statements : All mangoes are golden in colour. No
golden-coloured things are cheap.
Conclusions: I. All mangoes are cheap.
II. Golden-coloured mangoes are not cheap.
(a) Only conclusion II follows
(b) Only conclusion I follows
(c) either I or II follows
(d) Neither I nor II follows
72. Statements : All young scientists are open-minded.
No open-minded men are superstitious.
Conclusion :
I. No scientist is superstitious.
II. No young people are superstitious.
(a) Neither I nor II follows
(b) Only conclusions I follows
(c) Either I or II follows
(d) Only conclusions II follows
73. Find out the wrong number in the FOLLOWING
series.
2, 5, 10, 17, 26, 38, 50, 65
(a) 26 (b) 38 (c) 65 (d) 50
74. Find out the wrong number in the FOLLOWING
series.
30, –5, –45, –90, –145, –195, –255.
(a) –145 (b) –255 (c) –5 (d) –195.
75. Six books are labelled A, B, C, D, E and F are placed
side by side. Books B, C, E and F have green covers
while others have yellow covers. Book A, B and D
are new while the rest are old volumes. Book A, B
and C are law reports while the rest are medical
extracts. Which two books are old medical extracts
and have green covers?
(a) C and D (b) C and E (c) B and C (d) E and F
Direction (Qs. 76-78):
The following questions are based on the pie-charts given
below: Percentage-wise distribution of students studying
in Arts and Commerce in seven different institutions
Different institutions – A, B, C, D, E, F and G.
Total number of students studying Arts = 3800.
Total number of students studying commerce = 4200
76. What is the total number of students studying Arts in
Institutes A and G together?
(a) 1206 (b) 1126 (c) 1026 (d) 1226
77. How many students from Institute B study Arts and
Commerce?
(a) 1180 (b) 1208 (c) 1018 (d) 1108
78. The ratio of the number of students studying Arts to
that studying Commerce in institute E is:
(a) 19 : 27 (b) 19 : 16 (c) 19 : 28 (d) 27 : 14
79. Statement: Many shops in the local market have
extended their shops and occupied most part of the
footpath in front of their shops.
Cause of Action:
I. The civic authority should immediately activate
a task force to clear all the footpaths
encroached by the shop owners.
II. The civic authority should charge hefty penalty
to the shop owners for occupying the footpath.
III. The civic authority should setup a monitoring
system so that encroachments do not recur in
future.
(a) I and II follow (b) All I, II and III follows
(c) II and III follows (d) None follows
80. Statement : There is a significant increase in the
number of patients affected by some disease in a city
Course of action :
I. Municipal Corporation of the city should take
immediate action
II. This problem should be raised in the UNESCO.
III. Hospitals in the city should be equipped properly
for the treatment of the patients.
(a) I and III follow (b) I and II follow
(c) All follow (d) Only III follow
Direction (Qs. 81-85):
Comprehension:
Direction: Read the following information carefully
and answer the questions.
Five Dramas A, B, C, D and E have to be staged in 6
hour where 1 hour needs to be given per drama.
(b) Data is both the statements together are not
sufficient
(c) Statement I alone is sufficient, but statement II
alone is not sufficient
(d) Statement II alone is sufficient, but statement I
alone is not sufficient
68. Today is Wednesday. What would be the dady after
61 days?
(a) Monday (b) Saturday
(c) Sunday (d) Tuesday
69. Choose the word opposite in meaning to the given
word : MITIGATE
(a) Tranquilize (b) Intensify
(c) Alleviate (d) Abate
Directions (Qs. No. 70-72): In each question below are
given two statements followed by two conclusion
numbered I and II. You have to take the given two
statements to be true even if they seem to be at variance
from commonly known facts. Read the conclusion and
then decide which of the following given conclusions
logically follows from the two given statements,
disregarding commonly known facts.
70. Statements : No women teacher play. Some women
teachers are athletes.
Conclusions:
I. Male athletes can play.
II. Some athletes can play.
(a) Only conclusion II follows
(b) Only conclusion I follows
(c) either I or II follows
(d) Neither I nor II follows
71. Statements : All mangoes are golden in colour. No
golden-coloured things are cheap.
Conclusions: I. All mangoes are cheap.
II. Golden-coloured mangoes are not cheap.
(a) Only conclusion II follows
(b) Only conclusion I follows
(c) either I or II follows
(d) Neither I nor II follows
72. Statements : All young scientists are open-minded.
No open-minded men are superstitious.
Conclusion :
I. No scientist is superstitious.
II. No young people are superstitious.
(a) Neither I nor II follows
(b) Only conclusions I follows
(c) Either I or II follows
(d) Only conclusions II follows
73. Find out the wrong number in the FOLLOWING
series.
2, 5, 10, 17, 26, 38, 50, 65
(a) 26 (b) 38 (c) 65 (d) 50
74. Find out the wrong number in the FOLLOWING
series.
30, –5, –45, –90, –145, –195, –255.
(a) –145 (b) –255 (c) –5 (d) –195.
75. Six books are labelled A, B, C, D, E and F are placed
side by side. Books B, C, E and F have green covers
while others have yellow covers. Book A, B and D
are new while the rest are old volumes. Book A, B
and C are law reports while the rest are medical
extracts. Which two books are old medical extracts
and have green covers?
(a) C and D (b) C and E (c) B and C (d) E and F
Direction (Qs. 76-78):
The following questions are based on the pie-charts given
below: Percentage-wise distribution of students studying
in Arts and Commerce in seven different institutions
Different institutions – A, B, C, D, E, F and G.
Total number of students studying Arts = 3800.
Total number of students studying commerce = 4200
76. What is the total number of students studying Arts in
Institutes A and G together?
(a) 1206 (b) 1126 (c) 1026 (d) 1226
77. How many students from Institute B study Arts and
Commerce?
(a) 1180 (b) 1208 (c) 1018 (d) 1108
78. The ratio of the number of students studying Arts to
that studying Commerce in institute E is:
(a) 19 : 27 (b) 19 : 16 (c) 19 : 28 (d) 27 : 14
79. Statement: Many shops in the local market have
extended their shops and occupied most part of the
footpath in front of their shops.
Cause of Action:
I. The civic authority should immediately activate
a task force to clear all the footpaths
encroached by the shop owners.
II. The civic authority should charge hefty penalty
to the shop owners for occupying the footpath.
III. The civic authority should setup a monitoring
system so that encroachments do not recur in
future.
(a) I and II follow (b) All I, II and III follows
(c) II and III follows (d) None follows
80. Statement : There is a significant increase in the
number of patients affected by some disease in a city
Course of action :
I. Municipal Corporation of the city should take
immediate action
II. This problem should be raised in the UNESCO.
III. Hospitals in the city should be equipped properly
for the treatment of the patients.
(a) I and III follow (b) I and II follow
(c) All follow (d) Only III follow
Direction (Qs. 81-85):
Comprehension:
Direction: Read the following information carefully
and answer the questions.
Five Dramas A, B, C, D and E have to be staged in 6
hour where 1 hour needs to be given per drama.
5
1. A break of 1 hour has to be taken in third or
four hour.
2. Drama show cannot be started with A and
cannot end in C
3. D has to follow B immediately with no break in
between.
4. A cannot be done immediately after D.
5. A has to precede E immediately with no break
in between.
81. Which hour is a break hour?
(a) 5th (b) 2nd (c) 3rd (d) 4th
82. Which is the drama to be staged first?
(a) B (b) None (c) D (d) A
83. Which is the drama staged immediately after the
break?
(a) A (b) B (c) D (d) None of these
84. Which drama is staged immediately after D?
(a) E (b) None (c) C (d) B
85. Which drama is staged immediately after E?
(a) A (b) E (c) None (d) C
86. The greatest number which on dividing 1657 and
2037 leaves remainders 6 and 5 respectively is
(a) 127 (b) 235 (c) 305 (d) 123
87. At what time, in minutes, between 3 o’clock and 4
o’clock both the needles will coincide each other?
(a) 1
5
11 (b) 4
12
11 (c) 4
13
11 (d) 4
16
11
88. 1. A is the brother of B.
2. C is the father of A.
3. D is brother of E.
4. E is the daughter of B.
Then, the uncle of D is?
(a) E (b) A (c) B (d) C
89. Running at the same constant rate, 6 identical
machines can produce a total of 270 bottles per
minute. At this rate, how many bottles could 10 such
machines produce in 4 minutes?
(a) 648 (b) 2700 (c) 10800 (d) 1800
90. A person’s present age two-fifth of the age of his
mother. After 8 years, he will be one-half of the age
of his mother. What is the present age of the mother?
(a) 40 (b) 30 (c) 50 (d) 60
COMPUTER
91. Suppose the largest n bit number requires, ‘d’ digits
in decimal representation. Which of the following
relations between ‘n’ and ‘d’ approximately correct.
(a) d = 2
n
(b) n = 2
d
(c) d < n log10 2 (d) d > n log10 2
92. ‘Floating point representation’ is used to represent
(a) Boolean Values (b) Integers
(c) Whole numbers (d) Real numbers
93. Which of the following is equivalent to the Boolean
expression : ..X Y X Y X Y
(a) XY (b) XY (c) XY (d) XY
94. The Boolean expression AB + AB' + A'C + AC is
unaffected by the value of the Boolean variable
(a) B (b) None of these
(c) A (d) C
95. Write the simplified form of the Boolean expression
(A + C) (AD +AD') + AC + C:
(a) A + C (b) A' + C
(c) A + C' (d) A + D
96. If a processor clock is rated as 2500 million
cycles per second, then its clock period is
(a) 2.50 × 10
–10
sec (b) 4.00 × 10
–10
sec
(c) 1.00 × 10
–10
sec (d) None of these
97. The minimum number of NAND gates required for
implementing of Boolean expression, AB ABC ABC
is
(a) 1 (b) 0 (c) 2 (d) 3
98. FFFF will be the last memory location in a memory
is size
(a) 1 k (b) 16 k (c) 32 k (d) 64 k
99. The maximum and minimum value represented in
signed 16 bit 2’s complement representations are
(a) 0 and 65535 (b) –32768 and 32767
(c) –16384 and 16383 (d) 0 and 32767
100. If a signal passing through a gate is inhibited by
sending a low into one of the inputs, and the output
is high, the gate is a(n):
(a) NOR (b) AND
(c) NAND (d) OR
ENGLISH
101. Fill in the blanks with the correct option.
Technical writing demands _______ use of
language.
(a) Dramatic (b) Factual
(c) Figurative (d) Poetic
102. Select the correct form of verb/subject verb
agreement.
The principal, along with his assistants, _________
the meeting.
(a) attend (b) are attending
(c) attending (d) is attending
103. Select correct articles.
He is ........ M.A. with PhD and teaches in ......
university.
(a) a, an (b) a, the
(c) the, the (d) an, the
104. Choose the correct alternative
The county cleared this path and paved it with
packed gravel, so they have a peaceful place to hike
and bike.
Which of the following alternatives to the underlined
portion would NOT be acceptable?
(a) path, paving (b) path and then paved
(c) path before paving (d) path paved
105. “Bite and bullet” means
(a) to analyse your faults
(b) to accept something that is difficult or unpleasant
(c) to stop a conflict
(d) to become mad
106. What can you call a person who leads an
unconventional style or living?
(a) Cynic (b) Agnostic
(c) Bohemian (d) Altruist
107. Fill in the blank with the most appropriate option.
Kedar ________ this project for a month and now he
is about to join a new project.
(a) guided (b) has been guiding
(c) guiding (d) guides
Direction (Qs. 108-110):
Read the following passage carefully and answer the
questions:
1. A break of 1 hour has to be taken in third or
four hour.
2. Drama show cannot be started with A and
cannot end in C
3. D has to follow B immediately with no break in
between.
4. A cannot be done immediately after D.
5. A has to precede E immediately with no break
in between.
81. Which hour is a break hour?
(a) 5th (b) 2nd (c) 3rd (d) 4th
82. Which is the drama to be staged first?
(a) B (b) None (c) D (d) A
83. Which is the drama staged immediately after the
break?
(a) A (b) B (c) D (d) None of these
84. Which drama is staged immediately after D?
(a) E (b) None (c) C (d) B
85. Which drama is staged immediately after E?
(a) A (b) E (c) None (d) C
86. The greatest number which on dividing 1657 and
2037 leaves remainders 6 and 5 respectively is
(a) 127 (b) 235 (c) 305 (d) 123
87. At what time, in minutes, between 3 o’clock and 4
o’clock both the needles will coincide each other?
(a) 1
5
11 (b) 4
12
11 (c) 4
13
11 (d) 4
16
11
88. 1. A is the brother of B.
2. C is the father of A.
3. D is brother of E.
4. E is the daughter of B.
Then, the uncle of D is?
(a) E (b) A (c) B (d) C
89. Running at the same constant rate, 6 identical
machines can produce a total of 270 bottles per
minute. At this rate, how many bottles could 10 such
machines produce in 4 minutes?
(a) 648 (b) 2700 (c) 10800 (d) 1800
90. A person’s present age two-fifth of the age of his
mother. After 8 years, he will be one-half of the age
of his mother. What is the present age of the mother?
(a) 40 (b) 30 (c) 50 (d) 60
COMPUTER
91. Suppose the largest n bit number requires, ‘d’ digits
in decimal representation. Which of the following
relations between ‘n’ and ‘d’ approximately correct.
(a) d = 2
n
(b) n = 2
d
(c) d < n log10 2 (d) d > n log10 2
92. ‘Floating point representation’ is used to represent
(a) Boolean Values (b) Integers
(c) Whole numbers (d) Real numbers
93. Which of the following is equivalent to the Boolean
expression : ..X Y X Y X Y
(a) XY (b) XY (c) XY (d) XY
94. The Boolean expression AB + AB' + A'C + AC is
unaffected by the value of the Boolean variable
(a) B (b) None of these
(c) A (d) C
95. Write the simplified form of the Boolean expression
(A + C) (AD +AD') + AC + C:
(a) A + C (b) A' + C
(c) A + C' (d) A + D
96. If a processor clock is rated as 2500 million
cycles per second, then its clock period is
(a) 2.50 × 10
–10
sec (b) 4.00 × 10
–10
sec
(c) 1.00 × 10
–10
sec (d) None of these
97. The minimum number of NAND gates required for
implementing of Boolean expression, AB ABC ABC
is
(a) 1 (b) 0 (c) 2 (d) 3
98. FFFF will be the last memory location in a memory
is size
(a) 1 k (b) 16 k (c) 32 k (d) 64 k
99. The maximum and minimum value represented in
signed 16 bit 2’s complement representations are
(a) 0 and 65535 (b) –32768 and 32767
(c) –16384 and 16383 (d) 0 and 32767
100. If a signal passing through a gate is inhibited by
sending a low into one of the inputs, and the output
is high, the gate is a(n):
(a) NOR (b) AND
(c) NAND (d) OR
ENGLISH
101. Fill in the blanks with the correct option.
Technical writing demands _______ use of
language.
(a) Dramatic (b) Factual
(c) Figurative (d) Poetic
102. Select the correct form of verb/subject verb
agreement.
The principal, along with his assistants, _________
the meeting.
(a) attend (b) are attending
(c) attending (d) is attending
103. Select correct articles.
He is ........ M.A. with PhD and teaches in ......
university.
(a) a, an (b) a, the
(c) the, the (d) an, the
104. Choose the correct alternative
The county cleared this path and paved it with
packed gravel, so they have a peaceful place to hike
and bike.
Which of the following alternatives to the underlined
portion would NOT be acceptable?
(a) path, paving (b) path and then paved
(c) path before paving (d) path paved
105. “Bite and bullet” means
(a) to analyse your faults
(b) to accept something that is difficult or unpleasant
(c) to stop a conflict
(d) to become mad
106. What can you call a person who leads an
unconventional style or living?
(a) Cynic (b) Agnostic
(c) Bohemian (d) Altruist
107. Fill in the blank with the most appropriate option.
Kedar ________ this project for a month and now he
is about to join a new project.
(a) guided (b) has been guiding
(c) guiding (d) guides
Direction (Qs. 108-110):
Read the following passage carefully and answer the
questions:
6
You might think you’ve experienced VR, and you
might have been pretty impressed. Particularly, if
you’re a gamer, there are some great experiences to
be had out there (or rather, in there) today. But over
the next few year, in VR as in all fields of
technology, we’re going to see things that make what
is cutting-edge today look like space lnvaders. And
although the games will be amazing, the effects of
this transformation will be far broader, touching on
our work, education, and social lives.
Today’s most popular VR applications involve
taking total control of user’s sense (sight and
hearing, particularly) to create a totally immersive
experience that places the user in a fully virtual
environment that feels pretty realistic. Climb up
something high and look down, and you’re likely to
get a sense of vertigo. If you see an object moving
quickly towards your head, you’ll feel an urge to
duck out of the way.
Very soon, VR creators will extend this sensory
hijacking to our other facilities – for example, touch
and smell – to deepen that sense of immersion. At
the same time, the devices we use to visit these
virtual worlds will become cheaper and lighter,
removing the friction that can currently be a barrier.
I believe extended reality (XR) – a term that covers
virtual reality (VR), augmented reality (AR), and
mixed reality (MR) – will be one of the most
transformative tech trends of the next five years. It
will be enabled and augmented by other tech trends,
including super-fast networking, that will let us
experience VR as a cloud service just like we
currently consume music and movies. And artificial
intelligence (Al) will provide us with more
personalized virtual worlds to explore, even giving
us realistic virtual characters to share our
experiences with.
108. The passage states all the following about VR
applications except.
(a) Vertigo is a major feature of all Al applications
(b) VR applications takes control of the user’s
senses
(c) VR applications creates a virtual environment
that feels pretty realistic
(d) Future Al will allow us to share our experiences
with realistic virtual characters
109. ‘Duck out of something’ means
(a) To fall down
(b) To meet with an accident
(c) To avoid doing something
(d) To hit something hard
110. Select an antonym for the word ‘argument’ from the
options given below:
(a) Aggrandize (b) Reinforce
(c) Inflate (d) Curtail
111. Which of the phrases given below should replace the
phrase printed in bold to make the sentence
grammatically correct.
He is addicted to smoke.
(a) used to smoke (b) addicted to smoking
(c) addicted with smoking (d) addict of smoke
112. Select the one which best expresses the same
sentence in indirect/direct speech:
He said, “I am glad to be here this evening.”
(a) He said that he was glad to be there that evening
(b) He says he was glad to be here his evening
(c) He asked he is glad to be here this evening
(d) He said he was glad to be here this evening.
113. Choose the synonym.
LIBERAL
(a) Reactionary (b) Generous
(c) Sober (d) Affectionate
114. Identify the word that is similar in meaning to the
underlined word.
Raghu make adulatory remarks about the waiter
who served the food.
(a) Derogatory (b) Ironic
(c) Slanderous (d) Complimentary
115. Select the word which means the same as the
following:
To read something carefully
(a) Presume (b) Perverse
(c) Persiflage (d) Peruse
116. Choose the antonym:
BOLD
(a) Nervous (b) Coy (c) Timid (d) Fearful
117. Fill in the blanks with the correct preposition
Jagdish is waiting for me _______ the campus.
(a) On (b) At (c) In (d) Out
118. Choose the correct alternative with the correct choice
given below each statement.
You are to conform __________ the rules of the
institute.
(a) to (b) with (c) of (d) on
119. Read the following sentence to find if there is any
error in any part:
If I were him / I would teach / him a lesson / No
error
(a) No error (b) If I were him
(c) I would teach (d) him a lesson
120. Fill in the blank.
Neither Peter nor I _________ responsible for this
blunder.
(a) am (b) are (c) is (d) were
NIMCET-2022 ANSWERS
1 2 3 4 5 6 7 8 9 10
d d b c c d d a c c
11 12 13 14 15 16 17 18 19 20
a a d a c d b c a c
21 22 23 24 25 26 27 28 29 30
d a b d c b a c b c
31 32 33 34 35 36 37 38 39 40
a a b d a c c b a b
41 42 43 44 45 46 47 48 49 50
c b a b d a b b c b
51 52 53 54 55 56 57 58 59 60
d a a b d a d b b b
61 62 63 64 65 66 67 68 69 70
c c d a a b c a b d
71 72 73 74 75 76 77 78 79 80
a a b a d c c a b a
81 82 83 84 85 86 87 88 89 90
c a d c c a d b d a
91 92 93 94 95 96 97 98 99 100
d d a a a b b d b b
101 102 103 104 105 106 107 108 109 110
b d d d b c b a c d
111 112 113 114 115 116 117 118 119 120
b a b d d c a a a a
You might think you’ve experienced VR, and you
might have been pretty impressed. Particularly, if
you’re a gamer, there are some great experiences to
be had out there (or rather, in there) today. But over
the next few year, in VR as in all fields of
technology, we’re going to see things that make what
is cutting-edge today look like space lnvaders. And
although the games will be amazing, the effects of
this transformation will be far broader, touching on
our work, education, and social lives.
Today’s most popular VR applications involve
taking total control of user’s sense (sight and
hearing, particularly) to create a totally immersive
experience that places the user in a fully virtual
environment that feels pretty realistic. Climb up
something high and look down, and you’re likely to
get a sense of vertigo. If you see an object moving
quickly towards your head, you’ll feel an urge to
duck out of the way.
Very soon, VR creators will extend this sensory
hijacking to our other facilities – for example, touch
and smell – to deepen that sense of immersion. At
the same time, the devices we use to visit these
virtual worlds will become cheaper and lighter,
removing the friction that can currently be a barrier.
I believe extended reality (XR) – a term that covers
virtual reality (VR), augmented reality (AR), and
mixed reality (MR) – will be one of the most
transformative tech trends of the next five years. It
will be enabled and augmented by other tech trends,
including super-fast networking, that will let us
experience VR as a cloud service just like we
currently consume music and movies. And artificial
intelligence (Al) will provide us with more
personalized virtual worlds to explore, even giving
us realistic virtual characters to share our
experiences with.
108. The passage states all the following about VR
applications except.
(a) Vertigo is a major feature of all Al applications
(b) VR applications takes control of the user’s
senses
(c) VR applications creates a virtual environment
that feels pretty realistic
(d) Future Al will allow us to share our experiences
with realistic virtual characters
109. ‘Duck out of something’ means
(a) To fall down
(b) To meet with an accident
(c) To avoid doing something
(d) To hit something hard
110. Select an antonym for the word ‘argument’ from the
options given below:
(a) Aggrandize (b) Reinforce
(c) Inflate (d) Curtail
111. Which of the phrases given below should replace the
phrase printed in bold to make the sentence
grammatically correct.
He is addicted to smoke.
(a) used to smoke (b) addicted to smoking
(c) addicted with smoking (d) addict of smoke
112. Select the one which best expresses the same
sentence in indirect/direct speech:
He said, “I am glad to be here this evening.”
(a) He said that he was glad to be there that evening
(b) He says he was glad to be here his evening
(c) He asked he is glad to be here this evening
(d) He said he was glad to be here this evening.
113. Choose the synonym.
LIBERAL
(a) Reactionary (b) Generous
(c) Sober (d) Affectionate
114. Identify the word that is similar in meaning to the
underlined word.
Raghu make adulatory remarks about the waiter
who served the food.
(a) Derogatory (b) Ironic
(c) Slanderous (d) Complimentary
115. Select the word which means the same as the
following:
To read something carefully
(a) Presume (b) Perverse
(c) Persiflage (d) Peruse
116. Choose the antonym:
BOLD
(a) Nervous (b) Coy (c) Timid (d) Fearful
117. Fill in the blanks with the correct preposition
Jagdish is waiting for me _______ the campus.
(a) On (b) At (c) In (d) Out
118. Choose the correct alternative with the correct choice
given below each statement.
You are to conform __________ the rules of the
institute.
(a) to (b) with (c) of (d) on
119. Read the following sentence to find if there is any
error in any part:
If I were him / I would teach / him a lesson / No
error
(a) No error (b) If I were him
(c) I would teach (d) him a lesson
120. Fill in the blank.
Neither Peter nor I _________ responsible for this
blunder.
(a) am (b) are (c) is (d) were
NIMCET-2022 ANSWERS
1 2 3 4 5 6 7 8 9 10
d d b c c d d a c c
11 12 13 14 15 16 17 18 19 20
a a d a c d b c a c
21 22 23 24 25 26 27 28 29 30
d a b d c b a c b c
31 32 33 34 35 36 37 38 39 40
a a b d a c c b a b
41 42 43 44 45 46 47 48 49 50
c b a b d a b b c b
51 52 53 54 55 56 57 58 59 60
d a a b d a d b b b
61 62 63 64 65 66 67 68 69 70
c c d a a b c a b d
71 72 73 74 75 76 77 78 79 80
a a b a d c c a b a
81 82 83 84 85 86 87 88 89 90
c a d c c a d b d a
91 92 93 94 95 96 97 98 99 100
d d a a a b b d b b
101 102 103 104 105 106 107 108 109 110
b d d d b c b a c d
111 112 113 114 115 116 117 118 119 120
b a b d d c a a a a
7
NIMCET-2022 (SOLUTIONS)
1. Ans. (d)
Let h be height of hill and be a angle of elevation
at A, B, C. In this way foot of hill M is circumcentre
of ABC AM = CM = BM = R
Now by sine law
2sin 2sin 2sin
a b c
R
A B C
…(1)
Also tan
h
R
…(2)
h = R tan
Now put 2sin
a
R
A
from (1)
tan
2sin
a
h
A
tan cos
2
a
ecA
2. Ans. (d) Here x
m
y
n
= (x + y)
m+n
Taking log on both sides
m logx + n logy = (m + n) log (x + y)
differentiate w.r.t. x
1
.1
m n dy dy
mn
x y dx x y dx
dy m n n m m n
dx x y y x x y
m x y m n xdy my ny nx ny
dx y x y x x y
dy my nx my nx
dx y x y x x y
dy y
dx x
3. Ans. (b) As 33
3 log 5 log 53
3 3 .3
1
3
log 5 127
27.3 27.5
5
as log
a
x
ax
4. Ans. (c)
2
3 4 2
1
2 2 1
x dx
x x x
=
2
5
24
1
21
2
x
dx
x
xx
=35
24
11
21
2
xx
dx
xx
Put 24
21
2 t
xx
35
44
dx dt
xx
35
11
4
dt
dx
xx
11
2
4 4 2
dt t
tc
t
24
21
2
2
xx
c
5. Ans. (c) As volume of parallelepiped with edges 2 3 4a i j k
, 2 , 2b i j k c i j k is abc
=15 2 3 4
1 2 15
12
2(
2
– 4) – (3 - 8) + (6 - 4) = 15
(2- 9) + 1 (2 - 9) = 0
(2 - 9) ( + 1) = 0 9
2
6. Ans. (d) |x| + |y| = 2 x y = 2
So lines are
x + y = 2, x + y = - 2, x – y = 2, x – y = - 2
It forms a rectangle
As x + y = 2, x + y = - 2
and x – y = - 2, x – y = 2 are two set
of parallel lines and perpendicular to one another .
Length of CD
22
2 0 0 2 8 2 2
BD
22
2 0 0 2 2 2
So area of rectangle 2 2.2 2 8lb sq. unit.
7. Ans. (d) Here a < b
So if a < x < b x – a > 0, x – b < 0
|x – a| = x – a, |x – b| = - (x – b)
b
a
x a x b dx
bb
aa
x a x b dx b a dx
2b
a
b a x b a b a b a
8. Ans. (a) As 7abc
Here ,1, 2 , 1, , 2ab 1,1,1c
abc
12
1 2 7
1 1 1
( + 2) – (3) + 1 (-2 + 2) = 7
2
+ 4 - 12 = 0
2
+ 6 - 2- 12 = 0
( + 6) – 2 ( + 6) = 0
A
((
B
C D
x – y = 2 x – y = - 2
x + y = 2
x + y = - 2
A
B
C
N
M
R
R
h
NIMCET-2022 (SOLUTIONS)
1. Ans. (d)
Let h be height of hill and be a angle of elevation
at A, B, C. In this way foot of hill M is circumcentre
of ABC AM = CM = BM = R
Now by sine law
2sin 2sin 2sin
a b c
R
A B C
…(1)
Also tan
h
R
…(2)
h = R tan
Now put 2sin
a
R
A
from (1)
tan
2sin
a
h
A
tan cos
2
a
ecA
2. Ans. (d) Here x
m
y
n
= (x + y)
m+n
Taking log on both sides
m logx + n logy = (m + n) log (x + y)
differentiate w.r.t. x
1
.1
m n dy dy
mn
x y dx x y dx
dy m n n m m n
dx x y y x x y
m x y m n xdy my ny nx ny
dx y x y x x y
dy my nx my nx
dx y x y x x y
dy y
dx x
3. Ans. (b) As 33
3 log 5 log 53
3 3 .3
1
3
log 5 127
27.3 27.5
5
as log
a
x
ax
4. Ans. (c)
2
3 4 2
1
2 2 1
x dx
x x x
=
2
5
24
1
21
2
x
dx
x
xx
=35
24
11
21
2
xx
dx
xx
Put 24
21
2 t
xx
35
44
dx dt
xx
35
11
4
dt
dx
xx
11
2
4 4 2
dt t
tc
t
24
21
2
2
xx
c
5. Ans. (c) As volume of parallelepiped with edges 2 3 4a i j k
, 2 , 2b i j k c i j k is abc
=15 2 3 4
1 2 15
12
2(
2
– 4) – (3 - 8) + (6 - 4) = 15
(2- 9) + 1 (2 - 9) = 0
(2 - 9) ( + 1) = 0 9
2
6. Ans. (d) |x| + |y| = 2 x y = 2
So lines are
x + y = 2, x + y = - 2, x – y = 2, x – y = - 2
It forms a rectangle
As x + y = 2, x + y = - 2
and x – y = - 2, x – y = 2 are two set
of parallel lines and perpendicular to one another .
Length of CD
22
2 0 0 2 8 2 2
BD
22
2 0 0 2 2 2
So area of rectangle 2 2.2 2 8lb sq. unit.
7. Ans. (d) Here a < b
So if a < x < b x – a > 0, x – b < 0
|x – a| = x – a, |x – b| = - (x – b)
b
a
x a x b dx
bb
aa
x a x b dx b a dx
2b
a
b a x b a b a b a
8. Ans. (a) As 7abc
Here ,1, 2 , 1, , 2ab 1,1,1c
abc
12
1 2 7
1 1 1
( + 2) – (3) + 1 (-2 + 2) = 7
2
+ 4 - 12 = 0
2
+ 6 - 2- 12 = 0
( + 6) – 2 ( + 6) = 0
A
((
B
C D
x – y = 2 x – y = - 2
x + y = 2
x + y = - 2
A
B
C
N
M
R
R
h
8
( + 6) ( - 2) = 0 = - 6, 2
9. Ans. (c) As if |A| = m |P(A)| = 2
m
|B| = n |P(B)| = 2
n
Also |P(A)| - |P(B)| = 112
2
m
– 2
n
= 112 m = 7, n = 4
Satisfies (a), (b), (d) choices
So only (c) choice 2m – n = 1 is wrong.
10. Ans. (c) As .
dv dv dx
a
dt dx dt
dv
av
dx
Here 2
a x x 2dv
v x x
dx
2
vdv x x dx 2 2 3
2 2 3
v x x
As 23
00
23
xx
v 3
2
x
11. Ans. (a) According to given condition
1 1 1 1 1
tan tan tan
2 3 2 3 2
A B A B C
11
tan cot
3 2 2 3 2
CC
…(1)
As we know by NAPIER’s ANALOGY
tan cot
22
A B a b C
ab
…(2)
From (1)
11
tan cot
2 3 2
C
AB
from (1), (2) 1
3
ab
ab
By componendo / dividendo 2 1 3
2 1 3
a
b
2
1
a
b
12. Ans. (a) 4cos
2
x + 6sin
2
x = 5
4cos
2
x + 6(1 – cos
2
x) = 5
1 = 2cos
2
x 2 2 21
cos cos cos
24
xx
4
xn
13. Ans. (d)
As intercept form of straight line is 1
xy
ab
Also as A is mid. point of line BC
4, 5
22
ab
a = 8, b = 10
Required line 1
8 10
xy
5x + 4y = 40
14. Ans. (a) As
/
:0
f g f g
D D D x g x
Here 1
cos
1,1
x
D
D[x] = R
Also [x] 0 x [0, 1)
Required domain = [-1, 1] R – [0, 1)
= [-1, 0) {1}
15. Ans. (c) Here quadratic equation is x
2
+ px + q = 0
and roots are tan30, tan 15
S= Sum = tan30 + tan15 = - p
P= Product = tan30.tan15 = q
1
23
3
Sp …(1)
1
. 2 3
3
Pq …(2)
as tan15 2 3
From (1), (2)
p – q + 2
1 2 3
2 3 2
33
1 2 3
3 1 3 1
3 3 3
3 3 1 1
16. Ans. (d) Only (d) is
00
cos cosh
lim lim
1 2 1 2
hx
x
xh
cos0 1
10
1 2 0 1
17. Ans. (b) 10 10
10 10
xx
xx
y
Apply componendo / dividendo
21 2.10
10
12.10
x
x
x
y
y
2
10
11
10 2 log
11
x yy
x
yy
10
11
log
21
y
x
y
So inverse is 10
11
log
21
x
y
x
18. Ans. (c) Here r
th
moment of distribution is
1
r
ri
xx
n
Have
1
1
21
i
x
n
21
i
x
n
2 1 3
i
x
Mean x
n
Also
2
2
1
2 16
i
x
n
We have to find
2211
3 2 1
ii
xx
nn
21
2 1 2 2
ii
xx
n
(0, b)
C
A
B (a, 0)
(4, 5)
( + 6) ( - 2) = 0 = - 6, 2
9. Ans. (c) As if |A| = m |P(A)| = 2
m
|B| = n |P(B)| = 2
n
Also |P(A)| - |P(B)| = 112
2
m
– 2
n
= 112 m = 7, n = 4
Satisfies (a), (b), (d) choices
So only (c) choice 2m – n = 1 is wrong.
10. Ans. (c) As .
dv dv dx
a
dt dx dt
dv
av
dx
Here 2
a x x 2dv
v x x
dx
2
vdv x x dx 2 2 3
2 2 3
v x x
As 23
00
23
xx
v 3
2
x
11. Ans. (a) According to given condition
1 1 1 1 1
tan tan tan
2 3 2 3 2
A B A B C
11
tan cot
3 2 2 3 2
CC
…(1)
As we know by NAPIER’s ANALOGY
tan cot
22
A B a b C
ab
…(2)
From (1)
11
tan cot
2 3 2
C
AB
from (1), (2) 1
3
ab
ab
By componendo / dividendo 2 1 3
2 1 3
a
b
2
1
a
b
12. Ans. (a) 4cos
2
x + 6sin
2
x = 5
4cos
2
x + 6(1 – cos
2
x) = 5
1 = 2cos
2
x 2 2 21
cos cos cos
24
xx
4
xn
13. Ans. (d)
As intercept form of straight line is 1
xy
ab
Also as A is mid. point of line BC
4, 5
22
ab
a = 8, b = 10
Required line 1
8 10
xy
5x + 4y = 40
14. Ans. (a) As
/
:0
f g f g
D D D x g x
Here 1
cos
1,1
x
D
D[x] = R
Also [x] 0 x [0, 1)
Required domain = [-1, 1] R – [0, 1)
= [-1, 0) {1}
15. Ans. (c) Here quadratic equation is x
2
+ px + q = 0
and roots are tan30, tan 15
S= Sum = tan30 + tan15 = - p
P= Product = tan30.tan15 = q
1
23
3
Sp …(1)
1
. 2 3
3
Pq …(2)
as tan15 2 3
From (1), (2)
p – q + 2
1 2 3
2 3 2
33
1 2 3
3 1 3 1
3 3 3
3 3 1 1
16. Ans. (d) Only (d) is
00
cos cosh
lim lim
1 2 1 2
hx
x
xh
cos0 1
10
1 2 0 1
17. Ans. (b) 10 10
10 10
xx
xx
y
Apply componendo / dividendo
21 2.10
10
12.10
x
x
x
y
y
2
10
11
10 2 log
11
x yy
x
yy
10
11
log
21
y
x
y
So inverse is 10
11
log
21
x
y
x
18. Ans. (c) Here r
th
moment of distribution is
1
r
ri
xx
n
Have
1
1
21
i
x
n
21
i
x
n
2 1 3
i
x
Mean x
n
Also
2
2
1
2 16
i
x
n
We have to find
2211
3 2 1
ii
xx
nn
21
2 1 2 2
ii
xx
n
(0, b)
C
A
B (a, 0)
(4, 5)
9
21 1 2
2 1 2
ii
xx
n n n
= 16 + 1 – 2(1) = 15 variance = 15
19. Ans. (a) Here a1, a2, ……., an are in A.P.,
d = a2 – a1 = a3 – a2 = …. an – an-1
Now sin d(cosec a1 cosec a2 + cosec a2 cosec a3 +
….. + cosec an-1 cosec an)
1 2 2 3 1
sin sin sin
.......
sin sin sin sin sin sin
nn
d dd
a a a a a a
2 1 3 2 1
1 2 2 3 1
sin sin sin
........
sin sin sin sin sin sin
nn
nn
a a a a a a
a a a a a a
2 1 2 1
12
sin cos cos sin
......
sin sin
a a a a
aa
11
1
sin cos cos sin
sin sin
n n n n
nn
a a a a
aa
= (cota1 – cota2) + (cota2 – cot a3) + ……..
+ (cotan-1 – cotan)
=cota1-cotan
20. Ans. (c)
1 1 2
tan 1 sin 1
2
x x x x
Now
11
2
1
tan 1 cos
1
xx
xx
1 1 2
2
1
cos sin 1
21
xx
xx
22
2
1
1 1 1
1
x x x x
xx
x
2
+ x = 0 x(x + 1) = 0 x = 0, - 1
21. Ans. (d) If cosec – cot = 2 …(1)
As (cosec - cot ) (cosec + cot )
= cosec
2
- cot
2
= 1
2(cosec + cot) = 1
1
cos cot
2
ec …(2)
Adding (1), (2)
1 5 5
2cos 2 cos
2 2 4
ec ec
22. Ans. (a) At x = 0
2
11
2
0 0 0
lim lim 1 2 lim 1 2xx
x x x
f x x x
= e
2
Also f(0) = e
2
2
0
lim 0
x
f x f e
cont at x = 0.
Now to check differentiability
0
0
' 0 lim
0
x
f x f
f
x
1
2
0
12
lim
x
x
xe
x
2
3
23
0
11
1
1
1 2 2
2
1 1 1
12
2 ......
3
2 2 2
1 ......
1 2 3
lim
x
xx
xx
x
x x x
x
x
(By binomial expansion
2
1
1 1 .....
2
n nn
x nx x
)
23
23
0
1 1 1 1 2
lim 1 2 .4 8 ....
.2 3
x
x x x
xx
xx
2
22
1 ......
12
2 3 2 3
0
21 2 2 2
1 1 2 ...
2 3 2 3
lim
x
x
xx
x
= finite value
23. Ans. (b) Foci of Ellipse and Hyperbola are
coinciding.
For 22
2
1
25
xy
b
b
2
= a
2
(1 – e
2
)
b
2
= a
2
– a
2
e
2
b
2
= 25 – a
2
e
2
…(1)
For Hyperbola 22
1
144 81 25
xy
b
2
= a
2
(e
2
– 1) b
2
= a
2
e
2
– a
2
2 2 2 281 144 225
9
25 25 25
a e a e … (2)
Put (2) in (1) b
2
= 25 – 9 b
2
= 16
24. Ans. (d) As 11
sin a b c a b c n
1 is angle between ab and c but ab is to
both ,ab and if c is also to a from choice (d)
ab and c are parallel 0a b c
IIly 22
sina b c a b c n
Again 2 is angle between a and bc
but bc to both ,bc
Also if a is to c a and bc are parallel so
are parallel 0a b c
25. Ans. (c) T(x, y) = 4x
2
– 4xy + y
2
Also circle of radius 5 centred at origin
(x – 0)
2
+ (y – 0)
2
= 5
2
x
2
+ y
2
= 25
11xx
1xx
21 1 2
2 1 2
ii
xx
n n n
= 16 + 1 – 2(1) = 15 variance = 15
19. Ans. (a) Here a1, a2, ……., an are in A.P.,
d = a2 – a1 = a3 – a2 = …. an – an-1
Now sin d(cosec a1 cosec a2 + cosec a2 cosec a3 +
….. + cosec an-1 cosec an)
1 2 2 3 1
sin sin sin
.......
sin sin sin sin sin sin
nn
d dd
a a a a a a
2 1 3 2 1
1 2 2 3 1
sin sin sin
........
sin sin sin sin sin sin
nn
nn
a a a a a a
a a a a a a
2 1 2 1
12
sin cos cos sin
......
sin sin
a a a a
aa
11
1
sin cos cos sin
sin sin
n n n n
nn
a a a a
aa
= (cota1 – cota2) + (cota2 – cot a3) + ……..
+ (cotan-1 – cotan)
=cota1-cotan
20. Ans. (c)
1 1 2
tan 1 sin 1
2
x x x x
Now
11
2
1
tan 1 cos
1
xx
xx
1 1 2
2
1
cos sin 1
21
xx
xx
22
2
1
1 1 1
1
x x x x
xx
x
2
+ x = 0 x(x + 1) = 0 x = 0, - 1
21. Ans. (d) If cosec – cot = 2 …(1)
As (cosec - cot ) (cosec + cot )
= cosec
2
- cot
2
= 1
2(cosec + cot) = 1
1
cos cot
2
ec …(2)
Adding (1), (2)
1 5 5
2cos 2 cos
2 2 4
ec ec
22. Ans. (a) At x = 0
2
11
2
0 0 0
lim lim 1 2 lim 1 2xx
x x x
f x x x
= e
2
Also f(0) = e
2
2
0
lim 0
x
f x f e
cont at x = 0.
Now to check differentiability
0
0
' 0 lim
0
x
f x f
f
x
1
2
0
12
lim
x
x
xe
x
2
3
23
0
11
1
1
1 2 2
2
1 1 1
12
2 ......
3
2 2 2
1 ......
1 2 3
lim
x
xx
xx
x
x x x
x
x
(By binomial expansion
2
1
1 1 .....
2
n nn
x nx x
)
23
23
0
1 1 1 1 2
lim 1 2 .4 8 ....
.2 3
x
x x x
xx
xx
2
22
1 ......
12
2 3 2 3
0
21 2 2 2
1 1 2 ...
2 3 2 3
lim
x
x
xx
x
= finite value
23. Ans. (b) Foci of Ellipse and Hyperbola are
coinciding.
For 22
2
1
25
xy
b
b
2
= a
2
(1 – e
2
)
b
2
= a
2
– a
2
e
2
b
2
= 25 – a
2
e
2
…(1)
For Hyperbola 22
1
144 81 25
xy
b
2
= a
2
(e
2
– 1) b
2
= a
2
e
2
– a
2
2 2 2 281 144 225
9
25 25 25
a e a e … (2)
Put (2) in (1) b
2
= 25 – 9 b
2
= 16
24. Ans. (d) As 11
sin a b c a b c n
1 is angle between ab and c but ab is to
both ,ab and if c is also to a from choice (d)
ab and c are parallel 0a b c
IIly 22
sina b c a b c n
Again 2 is angle between a and bc
but bc to both ,bc
Also if a is to c a and bc are parallel so
are parallel 0a b c
25. Ans. (c) T(x, y) = 4x
2
– 4xy + y
2
Also circle of radius 5 centred at origin
(x – 0)
2
+ (y – 0)
2
= 5
2
x
2
+ y
2
= 25
11xx
1xx
10
2 2 2
, 4 4 25 25T x y x x x x
22
, 25 3 4 25T x y x x x
2
2
42
6 4 25
2 25
xxdT
xx
dx x
2
2
2
4
6 4 25
25
x
xx
x
22
2
25
64
25
xx
x
x
=0
22
6 25 4 25 2 0x x x
22
6 25 4 25 2x x x
2
2 2 2
36 25 16 25 2x x x
2
2 2 2
9 25 4 25 2x x x
225x
2
– 9x
4
= 4(625 + 4x
4
– 100x
2
)
25x
4
– 625x
2
+ 2500 = 0
x
4
– 25x
2
+ 100 = 0
(x
2
– 20) (x
2
– 5) = 0 x
2
= 20, 5
At x
2
= 5 dT
dx
changes sign from +ve to –ve
x
2
= 5 is a point of maxima
Also x
2
+ y
2
= 25 y
2
= 20
Now T(x, y) = 4x
2
– 4xy + y
2
4.5 4 5 20 20 = 40 – 40 = 0
26. Ans. (b) It’s an odd function
As f(x) + f(-x)
22
log 1 log 1x x x x
2
2 2 2 2
log 1 log 1 log1 0x x x x
f(x) + f(-x) = 0 f(-x) = - f(x)
f(x) is an odd function.
27. Ans. (a)
In OCD, tan 60 3
h
z
3
h
z …(1)
In OBD ,tan 45 1
h
yz
y + z = h …(2)
In OAD, 1
tan30
3
h
x y z
3x y z h …(3)
Put (2) in (3) 31xh
Put (1) in (2) 31
33
h
y h h
31
3 :1
31
3
h
AB x
BC y
h
28. Ans. (c) 25
1
25 38
i
i
x
Incorrect sum = 950
Incorrect sum-Incorrect values
+correct values
New Mean =
n
950 25 36 23 38
25
=38
29. Ans. (b) In H.P.,
If Tp = q, Tq = p Tpq = 1 (results)
30. Ans. (c)
Now is divisible by 3 if
Sum of digits of that no is divisible by 3.
As we have to make 4 digit no. out of 1, 2, 3, 4, 5
If we leave 3, we have 1, 2, 4, 5
Here sum = 12 divisible by 3
So nos. with help of 1, 2, 4, 5 are 4 out of total 5
Required probability 41
55
31. Ans. (a) From choices
. 14, 3 4a b a b i j k
Only (a) choice 52i j k satisfies both
32. Ans. (a) Here
60
200 120
100
nT
72
200 144
100
nC
n (T C) = 200, n (T C) = x
As n(T) + n(C) – n(T C) n(T C) min (n(T), n(C))
120 + 144 – 200 n(T C) 120
64 n(T C) 120
Given m x n n – m = 120 – 64 = 56
33. Ans. (b)
Ellipse with centre at origin (0, 0) is 22
22
1
xy
ab
Here 1
3
e and directrices a
x
e
9 9 3
1
3
aa
a
e
2
9a …(1)
Also b
2
= a
2
(1 – e
2
) 2
1
91
3
b
2
= 8 …(2)
A B C
30 45 60
D
h
2 2 2
, 4 4 25 25T x y x x x x
22
, 25 3 4 25T x y x x x
2
2
42
6 4 25
2 25
xxdT
xx
dx x
2
2
2
4
6 4 25
25
x
xx
x
22
2
25
64
25
xx
x
x
=0
22
6 25 4 25 2 0x x x
22
6 25 4 25 2x x x
2
2 2 2
36 25 16 25 2x x x
2
2 2 2
9 25 4 25 2x x x
225x
2
– 9x
4
= 4(625 + 4x
4
– 100x
2
)
25x
4
– 625x
2
+ 2500 = 0
x
4
– 25x
2
+ 100 = 0
(x
2
– 20) (x
2
– 5) = 0 x
2
= 20, 5
At x
2
= 5 dT
dx
changes sign from +ve to –ve
x
2
= 5 is a point of maxima
Also x
2
+ y
2
= 25 y
2
= 20
Now T(x, y) = 4x
2
– 4xy + y
2
4.5 4 5 20 20 = 40 – 40 = 0
26. Ans. (b) It’s an odd function
As f(x) + f(-x)
22
log 1 log 1x x x x
2
2 2 2 2
log 1 log 1 log1 0x x x x
f(x) + f(-x) = 0 f(-x) = - f(x)
f(x) is an odd function.
27. Ans. (a)
In OCD, tan 60 3
h
z
3
h
z …(1)
In OBD ,tan 45 1
h
yz
y + z = h …(2)
In OAD, 1
tan30
3
h
x y z
3x y z h …(3)
Put (2) in (3) 31xh
Put (1) in (2) 31
33
h
y h h
31
3 :1
31
3
h
AB x
BC y
h
28. Ans. (c) 25
1
25 38
i
i
x
Incorrect sum = 950
Incorrect sum-Incorrect values
+correct values
New Mean =
n
950 25 36 23 38
25
=38
29. Ans. (b) In H.P.,
If Tp = q, Tq = p Tpq = 1 (results)
30. Ans. (c)
Now is divisible by 3 if
Sum of digits of that no is divisible by 3.
As we have to make 4 digit no. out of 1, 2, 3, 4, 5
If we leave 3, we have 1, 2, 4, 5
Here sum = 12 divisible by 3
So nos. with help of 1, 2, 4, 5 are 4 out of total 5
Required probability 41
55
31. Ans. (a) From choices
. 14, 3 4a b a b i j k
Only (a) choice 52i j k satisfies both
32. Ans. (a) Here
60
200 120
100
nT
72
200 144
100
nC
n (T C) = 200, n (T C) = x
As n(T) + n(C) – n(T C) n(T C) min (n(T), n(C))
120 + 144 – 200 n(T C) 120
64 n(T C) 120
Given m x n n – m = 120 – 64 = 56
33. Ans. (b)
Ellipse with centre at origin (0, 0) is 22
22
1
xy
ab
Here 1
3
e and directrices a
x
e
9 9 3
1
3
aa
a
e
2
9a …(1)
Also b
2
= a
2
(1 – e
2
) 2
1
91
3
b
2
= 8 …(2)
A B C
30 45 60
D
h
11
Ellipse is 22
22
1
xy
ab
22
1
98
xy
8x
2
+ 9y
2
= 72
34. Ans. (d)
1
1 2 .... 1
lim
601 1 2 ....
a a a
a
n
n
n na na na n
1
1
12
.....
lim
1 1 2
. 1 .....
a a a
a
a
n
a
n
n
n n n
n
n n a a a
n n n n
1
12
.....
lim
1 1 2
1 .....
a a a
a
n
n
n n n
n
a a a
n n n n
1
1 1 2
.....
lim
1 1 1 2
1 .....
a a a
a
n
n
n n n n
n
a a a
n n n n n
1
1
1
1
lim
11
1
a
n
r
a
nn
r
r
nn
r
a
n n n
1 1
1
0
12
0
0
1
11
1
22
a
a x
x dx
aa
x
aaxa x dx
21
1 2 1 60aa
(a + 1) (2a + 1) = 120
2a
2
+ 3a – 119 = 0 2a
2
+ 17a – 14a – 119 = 0
2a(a – 7) +17 (a – 7) = 0
(a – 7) (2a + 17) = 0 a = 7, - 17/2
35. Ans. (a) Here lines are – 2x + y = 2 2x – y = - 2
and 2x – y = 2
and distance between these two is a
22
22 4
21 5
a
…….(1)
other two lines are 4x – 3y = 5
and 6y – 8x = 1 1
43
2
xy
22
5
112
1043
b
………(2)
From (1) and (2)11 5 40ab
36. Ans. (c) D=1 1 1
1 2 1
1 1 2
x
y
1 0 0
1 1 0 1 1
1 0 1
x x y
y
Divisible by (1 + x), (1 + y)
37. Ans. (c) Here P(A B) = P(A) . P(B)
A, B are independent events A
c
, B
c
are also
independent.
Now (c) choice implies
P(A B)
c
= P(A
c
B
c
) = P(A
c
). P(B
c)
as A
c
, B
c
are
independent.
38. Ans. (b) If vectors ,,ai a j ck i k ci c j bk
are in same plane.
1 0 1 0
aac
c c b
a(-c) – 1 (ab – c
2
) + c(a) = 0
ab = c
2
a, c, b in G.P. c is G.M. of a, b.
39. Ans. (a)
1152
cot cos tan
33
ec
Now 1153
cos tan
34
ec
1152
cot cos tan
33
ec
1132
cot tan tan
43
1
32
43
cot tan
32
1.
43
11
98
1712
cot tan cot tan
6 6
12
16
cot cot
17
6
17
40. Ans. (b) As sequence is 5 5 5 5
, , ,...... ,
3 4 5 13
It’s 11
th
term.
41. Ans. (c) Here PARABOLA is
4y
2
+ 12x – 20y + 67 = 0
4y
2
– 20y = - 12x – 67.
4(y
2
– 5y) = - 12x – 67
2 25
4 5 12 67 25
4
y y x
= - 12x - 42
2
5
4
2
y
42
12
12
x
2
57
3
22
yx
It’s of type Y
2
= 4a X 4a = - 3 a = - 3/4
4
3
5
Ellipse is 22
22
1
xy
ab
22
1
98
xy
8x
2
+ 9y
2
= 72
34. Ans. (d)
1
1 2 .... 1
lim
601 1 2 ....
a a a
a
n
n
n na na na n
1
1
12
.....
lim
1 1 2
. 1 .....
a a a
a
a
n
a
n
n
n n n
n
n n a a a
n n n n
1
12
.....
lim
1 1 2
1 .....
a a a
a
n
n
n n n
n
a a a
n n n n
1
1 1 2
.....
lim
1 1 1 2
1 .....
a a a
a
n
n
n n n n
n
a a a
n n n n n
1
1
1
1
lim
11
1
a
n
r
a
nn
r
r
nn
r
a
n n n
1 1
1
0
12
0
0
1
11
1
22
a
a x
x dx
aa
x
aaxa x dx
21
1 2 1 60aa
(a + 1) (2a + 1) = 120
2a
2
+ 3a – 119 = 0 2a
2
+ 17a – 14a – 119 = 0
2a(a – 7) +17 (a – 7) = 0
(a – 7) (2a + 17) = 0 a = 7, - 17/2
35. Ans. (a) Here lines are – 2x + y = 2 2x – y = - 2
and 2x – y = 2
and distance between these two is a
22
22 4
21 5
a
…….(1)
other two lines are 4x – 3y = 5
and 6y – 8x = 1 1
43
2
xy
22
5
112
1043
b
………(2)
From (1) and (2)11 5 40ab
36. Ans. (c) D=1 1 1
1 2 1
1 1 2
x
y
1 0 0
1 1 0 1 1
1 0 1
x x y
y
Divisible by (1 + x), (1 + y)
37. Ans. (c) Here P(A B) = P(A) . P(B)
A, B are independent events A
c
, B
c
are also
independent.
Now (c) choice implies
P(A B)
c
= P(A
c
B
c
) = P(A
c
). P(B
c)
as A
c
, B
c
are
independent.
38. Ans. (b) If vectors ,,ai a j ck i k ci c j bk
are in same plane.
1 0 1 0
aac
c c b
a(-c) – 1 (ab – c
2
) + c(a) = 0
ab = c
2
a, c, b in G.P. c is G.M. of a, b.
39. Ans. (a)
1152
cot cos tan
33
ec
Now 1153
cos tan
34
ec
1152
cot cos tan
33
ec
1132
cot tan tan
43
1
32
43
cot tan
32
1.
43
11
98
1712
cot tan cot tan
6 6
12
16
cot cot
17
6
17
40. Ans. (b) As sequence is 5 5 5 5
, , ,...... ,
3 4 5 13
It’s 11
th
term.
41. Ans. (c) Here PARABOLA is
4y
2
+ 12x – 20y + 67 = 0
4y
2
– 20y = - 12x – 67.
4(y
2
– 5y) = - 12x – 67
2 25
4 5 12 67 25
4
y y x
= - 12x - 42
2
5
4
2
y
42
12
12
x
2
57
3
22
yx
It’s of type Y
2
= 4a X 4a = - 3 a = - 3/4
4
3
5
12
focus is (a, 0) X = a, Y = 0
X = -3/4, Y = 0
7 3 5
,0
2 4 2
xy 17 5
,
42
xy
17 5
,
42
42. Ans. (b) Here data is 32, 49, 23, 29, 118
In ascending order 23, 29, 32, 49, 118
1
100
th
k
n
Pk
term
10
51
10 .6
100
P
th item which is 23.
50
16
50 50 3
100 100
n
P
rd item. = 32.
43. Ans. (a) Here parallel lines of parallelogram are
y = 4x and y = 4x + 1
4x – y = 0, 4x – y + 1 = 0 and x + y = 0, x + y = 1
As area of parallelogram with parallel sides
a1x + b1y + c1 = 0, a1x + b1y + d1 = 0
a2x + b2y + c2 = 0, a2x + b2y + d2 = 0
is
1 1 2 2
1 2 2 1
c d c d
a b a b
So in our case = Area 1 0 1 0 1
4 1 5
44. Ans. (b) By result ; m [0, 1]
1 2 1 2
........ ....
m
m m m
nn
a a a a a a
nn
Take m = 2
2
2 2 2
1 2 1 2
........ ....
nn
a a a a a a
nn
2
2
11
nn
ii
ii
n a a
45. Ans. (d) Here circles be x
2
+y
2
–2y = 0 with centre (0,
1), r = 1 as (x – 0)
2
+ (y – 1)
2
= 1
x
2
+ y
2
– 2y – 3 = 0 with centre (0, 1), r = 2
as (x – 0)
2
+ (y – 1)
2
= 4 = 2
2
Now area of larger circle is .2
2
= 4
and area of smaller circle is .1
2
=
If point (x, y) is taken from smaller circle.
favourable cases / region =
Out of total = 4 required prob. 1
44
46. Ans. (a) y = x + |x| is continuous for all x as sum of
two continuous functions is always continuous.
47. Ans. (b)
11
cos cosxx
48. Ans. (b) As 11
cos cos
23
xy
22
1
cos 1 1
2 3 2 3
x y x y
22
1
49
cos
66
xy
xy
22
49
cos
6
xy x y
22
6cos 4 9xy x y
22
6cos 4 9xy x y
2 2 2 2 2
12cos 36cos 4 9x y xy x y
2 2 2 2
9 4 36x y x y
2 2 2 2
9 4 12 cos 36 36cos 36sinx y xy
49. Ans. (c) Here curves are
22
2 2 2
1,
xy
x y c
ab
Now m1 = slope of first curve
21
2 . 0
x y dy
a a b b dx
22
0
x y dy
dxab
2
1 2
.
dy x b
m
dx ya
…(1)
IIly for second curve x
2
– y
2
= c
2
2 2 0
dy
xy
dx
2
dy x x
m
dx y y
…(2)
If two curves cut at 90
m1m2 = - 1 2
2
.1
x b x
yya
22
22
xa
yb
…(3)
Now first equation is
b
2
x
2
+ a
2
y
2
= a
2
b
2
…(4)
and second equation is x
2
– y
2
= c
2
b
2
x
2
– b
2
y
2
= b
2
c
2
…(5)
Multiply (4) by c
2
, (5) by (a
2
)
c
2
b
2
x
2
+ a
2
c
2
y
2
= a
2
b
2
c
2
and a
2
b
2
x
2
– a
2
b
2
y
2
= a
2
b
2
c
2
Subtract (c
2
b
2
– a
2
b
2
)x
2
+ (a
2
c
2
+ a
2
b
2
)y
2
= 0
Put 2
22
2
a
xy
b
in above
2
2 2 2 2 2 2 2 2 2 2
2
0
a
c b a b y a c a b y
b
(a
2
c
2
– a
4
) + (a
2
c
2
+ a
2
b
2
) = 0
(0, 3)
(0, 1)
(0, 0)
(0, -1)
focus is (a, 0) X = a, Y = 0
X = -3/4, Y = 0
7 3 5
,0
2 4 2
xy 17 5
,
42
xy
17 5
,
42
42. Ans. (b) Here data is 32, 49, 23, 29, 118
In ascending order 23, 29, 32, 49, 118
1
100
th
k
n
Pk
term
10
51
10 .6
100
P
th item which is 23.
50
16
50 50 3
100 100
n
P
rd item. = 32.
43. Ans. (a) Here parallel lines of parallelogram are
y = 4x and y = 4x + 1
4x – y = 0, 4x – y + 1 = 0 and x + y = 0, x + y = 1
As area of parallelogram with parallel sides
a1x + b1y + c1 = 0, a1x + b1y + d1 = 0
a2x + b2y + c2 = 0, a2x + b2y + d2 = 0
is
1 1 2 2
1 2 2 1
c d c d
a b a b
So in our case = Area 1 0 1 0 1
4 1 5
44. Ans. (b) By result ; m [0, 1]
1 2 1 2
........ ....
m
m m m
nn
a a a a a a
nn
Take m = 2
2
2 2 2
1 2 1 2
........ ....
nn
a a a a a a
nn
2
2
11
nn
ii
ii
n a a
45. Ans. (d) Here circles be x
2
+y
2
–2y = 0 with centre (0,
1), r = 1 as (x – 0)
2
+ (y – 1)
2
= 1
x
2
+ y
2
– 2y – 3 = 0 with centre (0, 1), r = 2
as (x – 0)
2
+ (y – 1)
2
= 4 = 2
2
Now area of larger circle is .2
2
= 4
and area of smaller circle is .1
2
=
If point (x, y) is taken from smaller circle.
favourable cases / region =
Out of total = 4 required prob. 1
44
46. Ans. (a) y = x + |x| is continuous for all x as sum of
two continuous functions is always continuous.
47. Ans. (b)
11
cos cosxx
48. Ans. (b) As 11
cos cos
23
xy
22
1
cos 1 1
2 3 2 3
x y x y
22
1
49
cos
66
xy
xy
22
49
cos
6
xy x y
22
6cos 4 9xy x y
22
6cos 4 9xy x y
2 2 2 2 2
12cos 36cos 4 9x y xy x y
2 2 2 2
9 4 36x y x y
2 2 2 2
9 4 12 cos 36 36cos 36sinx y xy
49. Ans. (c) Here curves are
22
2 2 2
1,
xy
x y c
ab
Now m1 = slope of first curve
21
2 . 0
x y dy
a a b b dx
22
0
x y dy
dxab
2
1 2
.
dy x b
m
dx ya
…(1)
IIly for second curve x
2
– y
2
= c
2
2 2 0
dy
xy
dx
2
dy x x
m
dx y y
…(2)
If two curves cut at 90
m1m2 = - 1 2
2
.1
x b x
yya
22
22
xa
yb
…(3)
Now first equation is
b
2
x
2
+ a
2
y
2
= a
2
b
2
…(4)
and second equation is x
2
– y
2
= c
2
b
2
x
2
– b
2
y
2
= b
2
c
2
…(5)
Multiply (4) by c
2
, (5) by (a
2
)
c
2
b
2
x
2
+ a
2
c
2
y
2
= a
2
b
2
c
2
and a
2
b
2
x
2
– a
2
b
2
y
2
= a
2
b
2
c
2
Subtract (c
2
b
2
– a
2
b
2
)x
2
+ (a
2
c
2
+ a
2
b
2
)y
2
= 0
Put 2
22
2
a
xy
b
in above
2
2 2 2 2 2 2 2 2 2 2
2
0
a
c b a b y a c a b y
b
(a
2
c
2
– a
4
) + (a
2
c
2
+ a
2
b
2
) = 0
(0, 3)
(0, 1)
(0, 0)
(0, -1)
13
2a
2
c
2
= a
4
– a
2
b
2
2c
2
= a
2
– b
2
50. Ans. (b) As , are roots of x
2
– x – 1 = 0
+ = 1, = - 1
As An+1 =
n+1
+
n+1
= (
n
+
n
) ( + ) - (
n-1
+
n-1
)
= An( + ) - (An-1)
as An =
n
+
n
, An-1 =
n-1
+
n-1
= An(1) + 1(An-1) = An + An-1 An+1 = An + An-1
A.M. of An, An-1 11
22
n n n
A A A
51. Ans. (d) VTU OR UTV,
VW OR WV,
(XWX)
X U T V W
Hence, T is sitting between U and V.
52. Ans. (a)
+3 +3 +3 +3
D N N, F Q Q, H T T,…J W W, L Z Z
+2 +2 +2 +2
53. Ans. (a) The exact synonym of the given word
'Debacle' is 'Catastrophe'. Debacle: a complete
failure, especially because of bad planning and
organization.
Example: The collapse of the company was
described as the greatest financial debacle in US
history. Catastrophe: a sudden event that causes
very great trouble or destruction. Example: They
were warned of the ecological catastrophe to come.
By reading the above definitions we can infer that
the correct answer is Option (a).
54. Ans. (b)
H E C, T G E, L I G, N K I, P M K
55. Ans. (d)
56. Ans. (a) All words except ‘driving’ are related to
movement activities that are related to water bodies,
while driving cannot be done on water bodies.
Hence, ‘driving’ is the odd one out.
Word Meaning
Driving
Operate and control the direction and
speed of a motor vehicle.
Diving
The sport or activity of swimming or
exploring under water.
Sailing The action of sailing in a ship or boat.
Swimming
The sport or activity of propelling
oneself through water using the
limbs.
57. Ans. (d)
58. Ans. (b)
6, 11, 21, 36, 56, 81
59. Ans. (b)
60. Ans. (b) We know that Round the world, butterflies
are seen as the departed souls of our ancestors.
Indigenous people recognize the chrysalis as the soul
trapped inside the body.
The emergence of the adult butterfly symbolizes the
freedom of the soul upon death.
Hence, Both Butterfly and Freedom are inter-related.
The same way 'Self-reliant' is related to the word
'Buoyant'.
Both are of similar meaning.
Therefore, the correct answer is Option (b).
61. Ans. (c)
K O L K O T A
+1 +1 +1 +1 +1 +1 +1
L P M L P U B
Similarly
M U M B A I
+1 +1 +1 +1 +1 +1
N V N C B J
62. Ans. (c) First is the process of formation of the
second.
63. Ans. (d)
A B C D E
J I H G F
No. of squares No. of squares
= 4 2 + 3 1 = 11 = 5 + 4 + 4=13
Total number of squares = 11 + 13 = 24
64. Ans. (a)
65. Ans. (a)
122, 144, 166, 188, 210
+
3
+
3
+
3
+
3
+
2
+
2
+
2
+
2 +
2
+
2
+
2
+
2
+
2
+
2
+
2
+
2
+
5
+10 +15 +20 +25
+2
2
+22 +22 +22
-
+
Portrait
-
Manu
+
+
Lions Elephants
Animals
2a
2
c
2
= a
4
– a
2
b
2
2c
2
= a
2
– b
2
50. Ans. (b) As , are roots of x
2
– x – 1 = 0
+ = 1, = - 1
As An+1 =
n+1
+
n+1
= (
n
+
n
) ( + ) - (
n-1
+
n-1
)
= An( + ) - (An-1)
as An =
n
+
n
, An-1 =
n-1
+
n-1
= An(1) + 1(An-1) = An + An-1 An+1 = An + An-1
A.M. of An, An-1 11
22
n n n
A A A
51. Ans. (d) VTU OR UTV,
VW OR WV,
(XWX)
X U T V W
Hence, T is sitting between U and V.
52. Ans. (a)
+3 +3 +3 +3
D N N, F Q Q, H T T,…J W W, L Z Z
+2 +2 +2 +2
53. Ans. (a) The exact synonym of the given word
'Debacle' is 'Catastrophe'. Debacle: a complete
failure, especially because of bad planning and
organization.
Example: The collapse of the company was
described as the greatest financial debacle in US
history. Catastrophe: a sudden event that causes
very great trouble or destruction. Example: They
were warned of the ecological catastrophe to come.
By reading the above definitions we can infer that
the correct answer is Option (a).
54. Ans. (b)
H E C, T G E, L I G, N K I, P M K
55. Ans. (d)
56. Ans. (a) All words except ‘driving’ are related to
movement activities that are related to water bodies,
while driving cannot be done on water bodies.
Hence, ‘driving’ is the odd one out.
Word Meaning
Driving
Operate and control the direction and
speed of a motor vehicle.
Diving
The sport or activity of swimming or
exploring under water.
Sailing The action of sailing in a ship or boat.
Swimming
The sport or activity of propelling
oneself through water using the
limbs.
57. Ans. (d)
58. Ans. (b)
6, 11, 21, 36, 56, 81
59. Ans. (b)
60. Ans. (b) We know that Round the world, butterflies
are seen as the departed souls of our ancestors.
Indigenous people recognize the chrysalis as the soul
trapped inside the body.
The emergence of the adult butterfly symbolizes the
freedom of the soul upon death.
Hence, Both Butterfly and Freedom are inter-related.
The same way 'Self-reliant' is related to the word
'Buoyant'.
Both are of similar meaning.
Therefore, the correct answer is Option (b).
61. Ans. (c)
K O L K O T A
+1 +1 +1 +1 +1 +1 +1
L P M L P U B
Similarly
M U M B A I
+1 +1 +1 +1 +1 +1
N V N C B J
62. Ans. (c) First is the process of formation of the
second.
63. Ans. (d)
A B C D E
J I H G F
No. of squares No. of squares
= 4 2 + 3 1 = 11 = 5 + 4 + 4=13
Total number of squares = 11 + 13 = 24
64. Ans. (a)
65. Ans. (a)
122, 144, 166, 188, 210
+
3
+
3
+
3
+
3
+
2
+
2
+
2
+
2 +
2
+
2
+
2
+
2
+
2
+
2
+
2
+
2
+
5
+10 +15 +20 +25
+2
2
+22 +22 +22
-
+
Portrait
-
Manu
+
+
Lions Elephants
Animals
14
66. Ans. (b)
J A K, K B L, L C M, M D N, N E O
67. Ans. (c) I. Manoj > Rahul > Deepak, Vinod
II. Manoj, Rahul > Deepak > Vinod
So, clearly can see that statement I alone is sufficient
to answer the question.
68. Ans. (a)
Wednesday 3
+ 61
= 64
7 R = 1 Monday
69. Ans. (b) 'Mitigate' is a verb which means 'to reduce
or to diminish'. Option B - to become greater, more
serious, or more extreme, or to make something do
this:
Therefore, the most appropriate antonym for
'Mitigate' is Option B - Intensify.
70. Ans. (d)
From Venn Diagram we can clearly see that neither I
nor II follows.
71. Ans. (a)
From Venn Diagram, we can see that only II follows.
72. Ans. (a)
From Venn Diagram, it is clear that neither I nor II
follows.
73. Ans. (b) 37
2, 5, 10, 17, 26, 38, 50, 65
+3 +5 +7 +9 +12 +12 +15
+11 +13
Hence 38 is wrong number.
74. Ans. (a) 30
30 - 35 = -5
-5 - 40 = -45
-45 - 45 = -90
-90 - 50 = -140
-140 - 55 = -195
-195 - 60 = -255
Hence, -145 is wrong. -140 should have come in
place of -145
75. Ans. (d) Green cover = B, C, E, F
Yellow cover = A and D
New volumes = A, B, D
Old volumes = C, E, F
Law reports = A, B, C
Medical extracts = D, E, F
Clearly, E and F are the two old medical extracts
with green covers.
Directions (Solutions 76-78) :
100% 3800 1% 38
Institutes Students studying Arts
A 15% 15 38
B 8% 8 38
C 17% 17 38
D 21% 21 38
E 14% 14 38
F 13% 13 38
G 12% 12 38
100% 4200 1% 42
Institutes Students studying Arts
A 12% 12 42
B 17% 17 42
C 15% 15 42
D 14% 14 42
E 18% 18 42
F 13% 13 42
G 11% 11 42
76. Ans. (c) No. of students studying arts in institutes A
and G together = 15% + 12%
= 27% 38 = 1026
77. Ans. (c) No. of students from institute B studying
Arts and commerce
= 8 38 + 17 42 = 304 + 714 = 1018
78. Ans. (a) Arts : Commerce
E 14 38 : 18 42
19 : 27
79. Ans. (b) All of the given options stand true and
therefore option (b) is the right answer
80. Ans. (a) I and III follows.
Woman
Teacher
+
1
+
1
+
1
+
1 +
1
+
1
+
1
+
1
+
1
+
1
+
1
+
1
Athletes
Mangoes
Golden
Cheap
Young
scientists
Open
minded
Superstitious
Play
66. Ans. (b)
J A K, K B L, L C M, M D N, N E O
67. Ans. (c) I. Manoj > Rahul > Deepak, Vinod
II. Manoj, Rahul > Deepak > Vinod
So, clearly can see that statement I alone is sufficient
to answer the question.
68. Ans. (a)
Wednesday 3
+ 61
= 64
7 R = 1 Monday
69. Ans. (b) 'Mitigate' is a verb which means 'to reduce
or to diminish'. Option B - to become greater, more
serious, or more extreme, or to make something do
this:
Therefore, the most appropriate antonym for
'Mitigate' is Option B - Intensify.
70. Ans. (d)
From Venn Diagram we can clearly see that neither I
nor II follows.
71. Ans. (a)
From Venn Diagram, we can see that only II follows.
72. Ans. (a)
From Venn Diagram, it is clear that neither I nor II
follows.
73. Ans. (b) 37
2, 5, 10, 17, 26, 38, 50, 65
+3 +5 +7 +9 +12 +12 +15
+11 +13
Hence 38 is wrong number.
74. Ans. (a) 30
30 - 35 = -5
-5 - 40 = -45
-45 - 45 = -90
-90 - 50 = -140
-140 - 55 = -195
-195 - 60 = -255
Hence, -145 is wrong. -140 should have come in
place of -145
75. Ans. (d) Green cover = B, C, E, F
Yellow cover = A and D
New volumes = A, B, D
Old volumes = C, E, F
Law reports = A, B, C
Medical extracts = D, E, F
Clearly, E and F are the two old medical extracts
with green covers.
Directions (Solutions 76-78) :
100% 3800 1% 38
Institutes Students studying Arts
A 15% 15 38
B 8% 8 38
C 17% 17 38
D 21% 21 38
E 14% 14 38
F 13% 13 38
G 12% 12 38
100% 4200 1% 42
Institutes Students studying Arts
A 12% 12 42
B 17% 17 42
C 15% 15 42
D 14% 14 42
E 18% 18 42
F 13% 13 42
G 11% 11 42
76. Ans. (c) No. of students studying arts in institutes A
and G together = 15% + 12%
= 27% 38 = 1026
77. Ans. (c) No. of students from institute B studying
Arts and commerce
= 8 38 + 17 42 = 304 + 714 = 1018
78. Ans. (a) Arts : Commerce
E 14 38 : 18 42
19 : 27
79. Ans. (b) All of the given options stand true and
therefore option (b) is the right answer
80. Ans. (a) I and III follows.
Woman
Teacher
+
1
+
1
+
1
+
1 +
1
+
1
+
1
+
1
+
1
+
1
+
1
+
1
Athletes
Mangoes
Golden
Cheap
Young
scientists
Open
minded
Superstitious
Play
15
Solutions (81 to 85):
Days Dramas
1 B
2 D
3 Break
4 C
5 A
6 E
81. Ans. (c) 82. Ans. (a) 83. Ans. (d)
84. Ans. (c) 85. Ans. (c)
86. Ans. (a) Required number
= H.C.F. of (1657−6) and (2037−5)
= H.C.F. of 1651 and 2032
1651=13×127 and 2032=2×2×2×2×127
Common factor 127
Required number = 127
87. Ans. (d)
2
30
11
MH
2
30 3
11
M
180
11
4
= 16
11 min part 3.
88. Ans. (b)
C
+
|
A B
|
E
-
D
+
From diagram , we can see A is the uncle of D.
89. Ans. (d) 6 3 10 4
270 x
x = 1800
90. Ans. (a) Person : his mother
3
Present 2 : 5
+ 8 +8
(1 : 2) 3
1 3
Person : His mother
Present (2 : 5) 8 = 40
+ 1 +1 1 8 yrs
After 8 years 3 : 6
Present age of mother = 40 yrs
91. Ans. (d) 10
d
> 2
7
Take log both sides log1010
d
> log102
n
d > nlog102
92. Ans. (d)
93. Ans. (a)
x y x y x y
x y x y x y
= xy xy xy
x y y xy 1yy
x xy = x y xy
94. Ans. (a) AB + AB' + A'C + AC
A(B + B') + C(A' + A)
A + C independent of B
95. Ans. (a) (A + C) (AD + AD') + AC + C
(A + C) (A(D + D') + C(A + 1)
(A + C) (A) + C = AA + AC + C =A + C(A + 1)
=A + C
96. Ans. (b) Clock Period 1
cycle per second
10
10
6
1 100 10
4 10
2525 10
97. Ans. (b) 98. Ans. (d) 99. Ans. (b)
100. Ans. (b) 101. Ans. (b) 102. Ans. (d)
103. Ans. (d) 104. Ans. (d) 105. Ans. (b)
106. Ans. (c) 107. Ans. (b) 108. Ans. (a)
109. Ans. (c) 110. Ans. (d) 111. Ans. (b)
112. Ans. (a) 113. Ans. (b) 114. Ans. (d)
115. Ans. (d) 116. Ans. (c) 117. Ans. (a)
118. Ans. (a) 119. Ans. (a) 120. Ans. (a)
Solutions (81 to 85):
Days Dramas
1 B
2 D
3 Break
4 C
5 A
6 E
81. Ans. (c) 82. Ans. (a) 83. Ans. (d)
84. Ans. (c) 85. Ans. (c)
86. Ans. (a) Required number
= H.C.F. of (1657−6) and (2037−5)
= H.C.F. of 1651 and 2032
1651=13×127 and 2032=2×2×2×2×127
Common factor 127
Required number = 127
87. Ans. (d)
2
30
11
MH
2
30 3
11
M
180
11
4
= 16
11 min part 3.
88. Ans. (b)
C
+
|
A B
|
E
-
D
+
From diagram , we can see A is the uncle of D.
89. Ans. (d) 6 3 10 4
270 x
x = 1800
90. Ans. (a) Person : his mother
3
Present 2 : 5
+ 8 +8
(1 : 2) 3
1 3
Person : His mother
Present (2 : 5) 8 = 40
+ 1 +1 1 8 yrs
After 8 years 3 : 6
Present age of mother = 40 yrs
91. Ans. (d) 10
d
> 2
7
Take log both sides log1010
d
> log102
n
d > nlog102
92. Ans. (d)
93. Ans. (a)
x y x y x y
x y x y x y
= xy xy xy
x y y xy 1yy
x xy = x y xy
94. Ans. (a) AB + AB' + A'C + AC
A(B + B') + C(A' + A)
A + C independent of B
95. Ans. (a) (A + C) (AD + AD') + AC + C
(A + C) (A(D + D') + C(A + 1)
(A + C) (A) + C = AA + AC + C =A + C(A + 1)
=A + C
96. Ans. (b) Clock Period 1
cycle per second
10
10
6
1 100 10
4 10
2525 10
97. Ans. (b) 98. Ans. (d) 99. Ans. (b)
100. Ans. (b) 101. Ans. (b) 102. Ans. (d)
103. Ans. (d) 104. Ans. (d) 105. Ans. (b)
106. Ans. (c) 107. Ans. (b) 108. Ans. (a)
109. Ans. (c) 110. Ans. (d) 111. Ans. (b)
112. Ans. (a) 113. Ans. (b) 114. Ans. (d)
115. Ans. (d) 116. Ans. (c) 117. Ans. (a)
118. Ans. (a) 119. Ans. (a) 120. Ans. (a)
Download
Download Slideshow Get the original presentation fileQuick Actions
Statistics
- Views 177
- Slides 15
- Age 834 days
Related Slideshows
32
figurative-language power point.pptththtrht
acecamero20
20 views
22
Figurative-Language-powerpoint.pptgttgth
acecamero20
22 views
44
Plasma proteins functions electroforesis - Copy.pptx
DratoshKatiyar
20 views
2
FORMATO 4. PLANTEAMIENTO DEL PROBLEMA. 4 Oct. 2022.ppt
LuisLopez350618
17 views
4
Cristiano Ronaldo jugador portugués, la leyenda
laparchizacorp
18 views
10
🎮✨ Top 10 Most Used Software Tools by Indie Game Developers (2025 Edition)
cheapersgamecomcare
18 views