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1. SIMPLIFICATION

UY Al PUT
CLASS NOTES

pr BY ADITYA RANJAN SIR

4. CONCEPT-01

y Bopmas,

This rule is the basic principle of solving
algebraic or numerical expressions.

ae Frag aa a dere aa at EU MA
wl yet fasta 21
Order to solve/Za ti &

V> Vimcwum | Bar

FH
B > Bracket ( hla ) $ 1
C

O > of (a) 3
D > Division (11)

M > Multiplication (UT)
A — Addition (=)

S > Subtraction (YUZTA )

5. COMPLETE COURSE (For all govt. exams ) BY ADITYA RANJAN SIR

Types of Bracket & Solving order

AA A Wa Ud EU AO À MA

(i) — —Minculum/Line/Bar bracket (Tar
TER )

(ii) () — Small bracket (Stet alse )

(iii) {} > Curly bracket (HAT AMA)

(iv) [] > Square bracket (131 AH)

6. COURSE (For all govt. exams ) BY ADITYA RANJAN SIR

NATA 1. Thevalueof9x9+9+9-9x9+9+9x9-
9-9x9is:
9x9+9+9-9x9+9+9x9-9-9x9

sen
mat:

ISSC CPO 27/06/2024 (Shift-03)|
(a) 9 NÉ:
(e) 81 (4) O

A 994 949 x0- Q-

IA

= |

-axq

7. 23-05 = 22:5
18-07 = 11.3
20- .S = 18.5
= One 16.63

8. COMPLETE

COURSE (For all govt. exams ) BY ADITYA RANJAN SIR

2. Simplify the following:
Frerferftern or retenu at:
21-4.9+7+3.9 x 0.4 + 0.9
ISSC CGL 09/09/2024 (Shift-02)
(a) 18.23 (b) 24.12
(c) 26.32 GW 22.76
0.7
21-41 +3.9%04 40.9
ai -
4 0.7 +1.36 +0-90

0.304 24
2274 sl

vv L

9. COMPLETE COURSE (For all govt. exams ) BY ADITYA RANJAN SIR

BopmAS 3. Simplify:/freafafad at area wife
[25 - 48 + 6 + 12 x 2] + 78-[5 +3 of (25-2 x

10)]
(a) 98 (b) 90
( 9 (d) 89
25-ug:, gra
E 94212) +18 - 543 of (25-2 x10)]
= fas.
8+94] + 18- U5+304 5]
_ MER.
119-29

%

10. COMPLETE

COURSE (For all govt. exams )
4.

By ADITYA RANJAN SIR

Simplify
mAs
Bun Fafafad at an ara atl

2.5 x [144 + 198 x (121 x 81 + FEINEN

ISSC CGL 17/07/2023 (Shift-01)
(91180 (b) 175

(c) 185 (d) 190

eri ino a 3
= US vn $

ber] %
ms
180

an

11. COMPLETE COURSE (For all govt. exams ) BY ADITYA RANJAN SIR

5. Simplify. fra & Um Wd Fly, — 60
325 + 276 + [150 - {9 x 9 + (83 - 4 x 15)}]

ISSC CGL 20/07/2023 (Shift-03)

(a) 332 (b) 333
(c) 334 197331
$25+26+ (iso. {4x9 403) J

- 82542164 [iso . 104]

= se ye

256

~ 33)

12. COMPLETE COURSE (For all govt. exams ) BY ADITYA RANJAN SIR

3 2-5+2P=3 6 If (48 + 72 x 3) - [15 +8 x (40 - 32) - 10] + 2P
3 AAA = 6 + 2, then find the value of P?
af (48 + 72 x 3) - (15 + 8 x (40 - 32) - 10) +
2P=6+2, AP um am aif?

SSC CPO 03/10/2023 (Shift-3)

(a) 2 (b) 4

(e) 1 are

( Anak) (is+8x8-19] +2P23
> BEER Per >3

13. By ADITYA RANJAN SIR

COMPLETE COURSE (For all govt. exams )
SL + 3 Fe 7. What is the value of/Fafafad a al ua
PAT:
Ss of SE +3 A
8 >69 Br er) 2
—=+4— x +
= Me _ a 8 l6 Me a ar 2 36
= 5
1 1
(a) 27 (b) zos
1 1
a 72 (d) 36
gtx
8 & è- 1427

36

15. COMPLETE COURSE (For all govt. exams ) BY ADITYA RANJAN SIR

8. Simplify the following expression
FU TARA are alfa
ad
25-[16-{14-(18-8+3)}]
\aY16 (b) 18
(c) 15 (d) 20
25-[16- {iy 14]
250]
88: q
qa

16. al
+
ne

of

vp

ol

17. COMPLETE COURSE (For all govt. exams ) BY ADITYA RANJAN SIR

Simplify:

SH) TES.

eee} aba)

= jo- 1831 ISSC CPO 04/10/2023 (Shift-01)| CPO 04/10/2023 (Shift-01)|
3 3 3 8 1
= D-18 -_e ww 0) -5
3 3 3

2 1
() 3 (à) 3

18. COMPLETE COURSE (For all govt. exams ) BY ADITYA RANJAN SIR

= a = 81
AE “eo 10.
B- 4x225

9 25
IfA = "36 B= 9 + [116 + 25) +36], C = [9 +
(16 + 25)] + 36, D = (9 + 16) + (25 + 36), then
which of the following is true?

aña A= 2%, B = 9 + ((16 + 25) +36], C = [9
+ (16 + 25)] + 36, D = (9 + 16) + (25 + 36) À
frafafaa à à Aa Hart a +?

(a) B and D are equal.

(b) C and D are equal.

(c) A and B are equal.

«A and D are equal.

19. (A)
a? + b? = (a + b)? - 2ab
a? + b? = (a — b)? + 2ab
a? — b? = (a + b)(a - b)

20. + (Qtb)*= Q?+b7+2ab

* (a+ = a+ ?_ og, (a8) = (ate) (a-2)

(Q-bY+2ab = 48

21. COMPLETE COURSE (For all govt. exams ) BY ADITYA RANJAN SIR

11. Simplify 52 x 52-48 a
ma AC x 52-48 x 48
SSC Phase-XI 27/06/2023 (Shift-03)

\ (9400 (b) 386

(c) 424 (d) 326

22. By ADITYA RANJAN SIR

COURSE (For all govt. exams )

(12) The value of 1801 x1801 is:

COMPLETE
= (1801)?
= (1800+1)> 1801 x1801 & 4M Am wt
= (1800) +(1%+2x 1800x ı ISSC CPO 09/11/2022 (Shift-02)
(a) 3423601 | e 3243601
(d) 3243106

= 3240000+1+ 3600
(c) 2343601

= 324360]

23. 2
# (101)'= (loot!)
= 10000+1 +200

= 10204
= 10201

# (1001)*= (1000+1)2
00) +1) * Go”
= 1000000 +1 + 2000 2
* (100)? _ 100200]

= 1002004 ¥ 0001 E 0002009
= ( =

24. COMPLETE COURSE (For all govt. exams ) BY ADITYA RANJAN SIR

13. Find the value of (1001+12)(1001-12).
Q + a -
(1001112)1001-12) at ma ara ft
RRB Technician G-III, 29/12/2024 (Shift-02)|
(a) 1000019857
\(by1001857
(e) 1000190857

(d) 100019857
(040) (a-b) ai. &

(100. (12)
100209). Iyy
|WIg5,

coat

25. COMPLETE COURSE (For all govt. exams ) BY ADITYA RANJAN SIR

14. Simplify the following
frafataa a aa atl

4.35 x 4.35 - 2.67 x 2.67

1.68
IRRB Technician G-III, 26/12/2024 (Shift-03)
af 7.02 (b) 6.99
(c) 7.05 (d) 6.96

2

2
IV à de
Tey ar AR
DT

26. COMPLETE COURSE (For all govt. exams ) BY ADITYA RANJAN SIR

58? - 25? 26? -15*

Ae ¿e =. 15. IfA= Dr sy» B= 57-15» then the value
a of 1-2 is:

= Jl = AL

46? - 37°’ 56? - 15? ? B A
- 1-2 an à:
8 A ISSC CGL Tier-II 26/10/2023]
© AL~ 3x20 (a) 2 pr
. (e) 0 (a) -1

27. # (Pe) > cart)
en ¿AREA
* (0% 58) = (o% +b") (a+b*) (a+b) (a-b)

# (a's) (0%) (a+) (0°48) (048) (0-6)
(08) = (3 gy

E)
“(By (Qty) (0-4)

28. COMPLETE COURSE (For all govt. exams ) BY ADITYA RANJAN SIR

16. Simplify the following expression:
Prafatad aise at are aif:

((82)* - 1)

33 x 31x (2° +1)

ISSC Phase-XII 26/06/2024 (Shift-04

(a) 2 (b

= (Gr) Ce > do
RE
PEAK (2) Es

29. 2
(atb) = Q’+b’+20b
(a-b)?= Q’+b?-2ab

an”

©

CS ETS
(0+) +(Q-by= 2048) (CS (0-b)*- Ox904 - ki

30. COMPLETE COURSE (For all govt. exams ) BY ADITYA RANJAN SIR

17. Simpify:
fa at ma athe
a+b ds 8
(379 + 276)? + (379 - 276)?
379 x 379 + 276 x 276
ISSC CHSL 11/08/2023 (Shift-2)
ay (b) 655
(c) 103 (d) 1

CCE;
paid “by: Ÿ (a?
02, eB aus

se

31. COMPLETE COURSE (For all govt. exams ) BY ADITYA RANJAN SIR

18. Simplify the following expression:
erferfige ai at art atta:
(528 + 175) - (525 - 175)?
(525 x 175)
ISSC CPO 27/06/2024 (Shift-03)
(a) 350 (b) 700

(e) 2 \or4

a. VOS
I

32. COMPLETE COURSE (For all govt. exams ) BY ADITYA RANJAN SIR

(25)* + 1250 + 1- (25)?
Simplify: (25) +2541
Hold
(25)* + 1250 +1- (25)?
esprasi1 APA

ISSC CGL 19/09/2024 (Shift-03)|
(a) 602 (b) 601
(e) 603 (d) 604

33. COMPLETE COURSE (For all govt. exams ) BY ADITYA RANJAN SIR

a 20. The value of/1 4431 Hl
2
Q+b+2ab +1 0.325 x 0.325 SFE SITES 0.00885) Goom 0
d?-b? 3 5 x 0.0065 x 3.25 - 7 x 0.175 x 0.025
ISSC CPO 24/11/2020 (Shift-1)
= CS eh se
(0-6) 3 ( igi (b) 3
aed 7
= SÓ + 4 4 (c) O (4) 3
=
Sy 3 3 ISo

34. COMPLETE COURSE (For all govt. exams ) BY ADITYA RANJAN SIR

OP pt 21.
07+ B420b 0.334

(o -b)Lor8) (4.6697 + (2.3317 + ER .667)(2.331) IE (1.6);

(a Ya 7
0.384 =4-k

> (558

The value of (2 334)

© 4.668% 4.669 -

where k=?

4.669 x 4.669 - 9 x PP
(4.669)? + (2.331)? + 14(0.667)(2.331)
-k) @, fai k=?

ISSC CPO 11/12/2019 (Shift-02)|

wl AM (1

MS 0.666 (b) 0.647

(c) 0.467 (d) 0.768
$x 6m) 9
“hom

=(9. 3312

35. a ax à A (0.13)? + (0.217
E e value o! =
4 a (0.39) AE

+3 x (11.52) +9
“e 4)° + 6(2.4)* +3 x (17.28)
wer art RD citer fea à?
(a) 9.7 and 0.8 (b) 0.4 and 0.5
(c} 0.6 and 0.7 (d) 0.5 and 0.6

lies between:

+o <= 2d +d?
QUE nl C8424 + Ca?

See = eh a? dia?

US TO)

y"
ter = Axe a
q A q € Se à Orgy

36. a

? + (0.21)?
22. The value of 0.39% i! aoe
Br RT FEN

(Ay +3 x(11.52)+9 (3)”
ay +6(2.4)" +3 x (17.28) Hes between:
au fra ata fea à?

(a) 0.7 and 0.8 (b) 0.4 and 0.5

iz (c) 0.6 and 0.7 (d) 0.5 and 0.6
RÉ + Assert
LAO rara

rte)
3 (o oR
Fixe: NM -
qe = Ooy

7

37. By ADITYA RANJAN SIR

(B)
a? + b? = (a + b)(a? - ab + b?)
_a? — b? = (a — b)(a? + ab + b?)

38. x (07463) =(a+ro)(0%+b ias)

+ (GB) = (4) (07+ a)

39. COMPLETE COURSE (For all govt. exams ) BY ADITYA RANJAN SIR

The value of /#1 an €:

a + J (275 x 275 x 275 + 725 x 725 x 725)
ES #b-ab] [d'to'+ae (RTE DS TA E

55 (275% 275 x 278. 725x 725 x 725)
= (CD Cr a) x (@-b) (ob rab X (275 x 275 + 725 x 725 + 725 x 275)

(Peasy Lab Fan) ISSC CPO 29/06/2024 (Shift-02)
= lu lay 450000 (b) 45000
= (O+#)(a+) (e) 450000 (d) -45000
~ 1000x (uso)

~ 4S0009

40. COURSE (For all govt. exams ) BY ADITYA RANJAN SIR

(0.83)° - (0.1)°

d+ ab + b? 24. Simplify: (9 37 +0.083+0.01 ?

(2.83 = ey

- (a) a 2705) Er eo, IH —.
en (0. 83)" + 0.083 + 9-04 à e
fi
= E ISSC CHSL 14/08/2023 (Shift-2)

(a) 0.98 (b) 0.27
(c) 0.93 Nay 0.73
3-83
So
— —

0.13

41. COMPLETE COURSE (For all govt. exams ) BY ADITYA RANJAN SIR

25. Simplify the given expression:
at mi aaa at ara AT:

12.43 x12.43 412.45 +19.87x19.57 x19.57
12.43 x12.43 -12.43 x19.57 + 19.57 19.57

ISSC Phase-XII 24/06/2024 (Shift-03)
(a) 34 (b) 30
Usy 32 (d) 36
ee ,

TO

42. COMPLETE COURSE (For all govt. exams ) BY ADITYA RANJAN SIR

_@+b?
d+- Ob
100 100 100

= _100 (ar) ]

(ar)

= [00x 1000

= 100000

26.

675 x 675 x 675 + 325 x 325 x 325
67.5 x 67.5 + 32.5 x 32.5- 67.5 x 32.5
to:

a b
(678x675 x 675 +6 25% 325 x 325

67.5 x 67.5 + 32.5 x 32,5 - 67,5 x 32.5
T 1Q T lO 0

Eran à pu TA E:

(a) 100 (b) 10,000

(c) 1,000 K{#f 1,00,000

is equal

43. COMPLETE COURSE (For all govt. exams ) BY ADITYA RANJAN SIR

26. _675x675x675+325x325x325 , nal
* 67.5x 67.5+32.5x 32.5- 67.5x 32.5 au

to:
ae + b?

100 nen
67.5 x 67.5)+ G2.5 x 32.5-167.5x 32.5
frafatad à à ter am «3S
(a) 100 (b) 10,000

(c) 1,000 Ngf,00,000

44. COMPLETE COURSE (For all govt. exams ) BY ADITYA RANJAN SIR

(251) +(249)°
25.1 x 25.1 - 624.99 + 24.9 x 24.9
is 5 x 10*, where the value of k is e
a? b

27. The value of

~ AT HM 5 x 10*,

45. By ADITYA RANJAN SIR

(C)
Ilfa+b+c=0
then > a? + b? + c? = 3abc

Otb+c =O

CESSE

46. o: Où DOS 7

fas (374 CCS
ily 3+2-5=0

= BUS)
Y,

47. COMPLETE COURSE (For all govt. exams ) BY ADITYA RANJAN SIR

XL 28. What is the value of/# 4M aa TU
un 0: 0.74 x1.23 x 0.13
OPUS (0.37) + (0.41) —89-39
A m= SSC CPO 11/12/2019 (Shift-01)
a
3
1 à 2
(e) - CE
O37 40.4)

48. By ADITYA RANJAN SIR

COMPLETE COURSE (For all govt. exams )
29. Simplify/am a:
(3.321)° + (2.681)° + (1.245)°

(3.321)? + (2.681)? + (1.245)?

-3 x 3.321 x 2.681 x 1.245
-(3.321x 2.681) - (2.681 x 1.245) - (1.245 x 3.321)

ISSC CHSL 04/08/2023 (Shift-01)

(a) 6.125 (b) 8.645
(e) 7.247 (d) 10.245

49. (orbe) (ae? tc ab-bc-ac)
(Q+b+c) [co tb+c)?-3(ab +bc-+ac) ]

33, 3
Ob co 3abe (Otb+d) Blarıe)- (a+b+0% J
2

Atb ene >
Gino, (a b) +(b-c)*+(c-a)* J

50. (3.321)° + (2.681)° + (1.245)° 8 x 3.321 x 2.681 x 1.245
(3.32 1)? + (2.681) + (1.245)? -(3.321 x 2.681) — (2.681 x 1.245) — (1.245 x 3.321)
ISSC CHSL 04/08/2023 (Shift-01)
(a) 6.125 (b) 8.645
(sy 7.247 (d) 10.245

3
Hr Babe =
AFB —ab=be - ac

51. COMPLETE

COURSE (For all govt. exams ) BY ADITYA RANJAN SIR

30. Simplify the given expression.

3
(80x 80% 80) + (70 x 70 x 70) + (50 x 50 x 50) - 840000
6400 + 4900 + 2500 - 5600 - 3500 - 4000

feu mu cine at are AÑO

ISSC CHSL 10/08/2023 (Shift-01)
(a) 100 bj 200
(c) 400 (d) 300

3
O°4+6°+3_3ab¢ = (Q+bx) en

Y]
AH ab-be-ar

52. COMPLETE COURSE (For all govt. exams ) BY ADITYA RANJAN SIR

3, 3 31. Simplify the following.
N Patata ar apeiron aa à
a-Obt
ni
ie, a
" 0.05x0 0.05 0.01 0.05 0.015 0.015
- _(a+b)(a 5x5 (0.01x0.01- OB x E x 3:00
25 (a+b? aby SSC CGL 24/07/2023 (Shift-3
= 01013 x | 13 . 13 a
Tos 1000 (a) nih (b) 3510
00,
003
(52

013

54. KH K=0.65555....... so

Ans %-0.55555....... co —O
4104= 5.5555... . eo ——_®
I A= 5.0

AD

56. 12.34
nn. =”

= CAM
>

- -12 210
123-4 = 192 = 23-12
ang > 123 qq0 4% 900
Tupe-3 1.23 1.23 12.34
= 23 = 1234-12
Qn, 103-4 140.23 aa
à ER on
an 1421 aq
% Sl
= lu Yo
jam

57. CONCEPT-03

32. Convert 0.7777......... co into fraction

07 YAA 0.777 7......... com ft À aer
3 7 E
SA 9 (b) 3
2 77
lc) o (d) yy

58. COMPLETE COURSE (For all govt. exams ) BY ADITYA RANJAN SIR

33. Convert 0.535353............ co into fraction
ayımea 0.535353............ co ai fr À act
53 53
(8h 99 (b) 79
53 53
i“ i. (d) 5
= 0.53
25

59. COMPLETE

COURSE (For all govt. exams )

BY ADITYA RANJAN SIR
a 34. Convert it into vulgar fraction
s81-5.582- 0.587

CISF HCM 30/10/2023 (Shift-01
eg 93 97
= ¿Qu la) 167 NA
165 167 165
95 a 22
(<) 367 (4) Tas

165

60. COMPLETE COURSE (For all govt. exams ) BY ADITYA RANJAN SIR

35. Simplify 8.46 in the fractional form.

8.46 8.46 Fl Ur oad A & EU À ae AU
- eus-8 - 638
u aa u“ 838 83
99 (1 99
846 84

te) 5 (d) 59

61. COMPLETE

th

COURSE (For all govt. exams ) BY ADITYA RANJAN SIR

36.
0.0654 48
SSU-6 = 648
900 — Ben
—i6se-—
275
= 18
2138

Correct expression of 0.0654. (the bar
indicates repeating decimal)

0.0654 FT Ret Sims & (m AU Bt pagan

INTPC CBT-2 19/01/2017 (Shift-1)

654 654
(a) 7000 (b) 10000
18 18
275 (d) 277

62. COMPLETE

COURSE (For all govt. exams ) BY ADITYA RANJAN SIR

37. Correct expression of 1.427. (the bar indicates
repeating decimal)

4uon- 44 M427 7 EL ancient & Cae AIRE et ra
—aa0 wal ae):
Bear INTPC CBT-2 17/01/2017 (Shift-3)
= 1
Er 110 1427 157
(a) 1000 110
(e) 1427 157

10000 (a) 211

63. COMPLETE COURSE (For all govt. exams ) BY ADITYA RANJAN SIR

28168-28 2878 a
aaa | (a) 2999 (b) 25
= 28714 292 a) 24224
aaa 333 4995
= 9 Pg 292
29% 333
“u

33

64. COMPLETE COURSE (For all govt. exams ) BY ADITYA RANJAN SIR

39. Find the Value of x/x # UM aa Hla

0.3 + 0.4 + 0.5 + 0.6 = x

(a) 3 (b) 5
NE (d) 8
34443

2.9 q “=

65. COMPLETE COURSE (For all govt. exams ) BY ADITYA RANJAN SIR

40. The value of 0,56 + 0.43 + 0.89 is

0.56+0.43+0.89 AT Im E

INTPC CBT-1, 23/02/2021 (Shift-01)

(a) 158 aq (by 1.87
Io 1.89 188. (d) 1.88 = 188-1
‘3 aq
36 +43 } 8a = 19
a ag Og +
= (Ra

66. COMPLETE COURSE (For all govt. exams ) BY ADITYA RANJAN SIR

40. The value of 0,56 + 0.43 + 0.89 is

0-565656 pp
0-434343 0.56 +0.43+0.89 HT AI €
—O: 898989 _ INTPC CBT-1, 23/02/2021 (Shift-01)

1-898988 _ _
a (a) 1.98 (b) 1.87

Se 1.89 (d) 1.88

Qng= 1.89

67. COMPLETE COURSE (For all govt. exams ) BY ADITYA RANJAN SIR

41. 3.245+1.234 - 2.12is equal to:
3.245 +1.234-2.12 ama -

ICAR Mains, 08/07/2023 (Shift-3)

2335 (y 2.358 2258-23 (b) 2.437

EIER 9%
(c) 2.243 (d) 2.536
= 3245-32 + 123y-
rn 4-2 - (919-
m ay A
3243 4 1229
A RTS So
= 233 0 o
S335
990

68. COMPLETE COURSE (For all govt. exams ) BY ADITYA RANJAN SIR

41. 3.245+1.234 - 2.12is equal to:
3.245 +1.234-2.12 ama -

ICAR Mains, 08/07/2023 (Shift-3)

(ay 2.358 (b) 2.437
(c) 2.243 (d) 2.536
3-24usysys y
+ 1.2 343434 3
7 2121219 10

26358585 85
= 2.355

69. COMPLETE

COURSE (For all govt. exams )

BY ADITYA RANJAN SIR
193-12 + 39 42. Express the following into vulgar fraction.
a0 qa freafafad at aero fa à aaa atl
_ ni + 39 0.123 + 0.39
~ “Go q IRPF SI 12/12/2024 (Shift-01)
569
- 568 569
~ ae = ST (a) 3100 1100
00 Me
Noo te) 578 579
1100

(4) 1100

70. COMPLETE COURSE (For all govt. exams ) BY ADITYA RANJAN SIR

43. Find the value of @.38) : 0.54.

Re > E Faria ar am ara AO
IRRB JE 18/12/2024 (Shift-02)
= 215 x 907 19 17
e 4a (34745 (b) 337
= pla 26 29
Y (e) 55 (a) 657
238
28.

71. By ADITYA RANJAN SIR

COURSE (For all govt. exams )

COMPLETE

44. Find the value of/# 4M am Fifa

0.2 + 0.3 + 0.32
(a) 0.77 (b) 0.82

(c) 0.86 _(dy 0.87
0.222222
0.333333
0° 3232 30
0- 818187

5 0.9

72. COMPLETE COURSE (For all govt. exams ) BY ADITYA RANJAN SIR

(ares sus 7 193108) iaa value offs an aa alters
qua “400 / 324.786-10.193
108154 3058 (a) 314.59345 (b) 314.59445
= SUEZ _
ore = IGN 314.59345- tre) 314.59445
333 300 STO
= l08isyoo- 33qu
ap + onen S935
33300 - 314s sq
PRES

= \
vote
oo

73. COMPLETE COURSE (For all govt. exams ) BY ADITYA RANJAN SIR

45. Find the value of/a 4M aa fa
324.786 - 10.193

(a) 314.59345 (b) 314.59445
314.59345 (d) 314.59445

0.186186 186

7 _0.193333333

—0-593453Y 837
> 0.508

74. COMPLETE COURSE (For all govt. exams ) BY ADITYA RANJAN SIR

46. If A= 0.312, B = 0.415 and C = 0,309, then
what is the value of A+ B + C?
af? A-0.312,B-0.415 TA C-0.309 €, À
A+B+C @ um fart 2?

1211 1043
(a) 1100 ) 1100
1097 1141
0-3121212 (©) 1100 1100
UIs 10312- 103 =
ISIS 2312-103 310289 114
2: 3099909 a0 89657 Toa

072726
> 1035

75. COMPLETE

COURSE (For all govt. exams )

By ADITYA RANJAN SIR

47. Find the value of/# 4M am fa

22.4uuuyy y
+ 11-56167 67
~ 33. §99999 q
O °41214219

= 041

22.4 + 11.567 - 33.59

(a) 0.412

AN 0.412

ISSC CGL TIER - II 11/09/2019

(b) 0.31
(d) 0.32

76. COMPLETE COURSE (For all govt. exams ) BY ADITYA RANJAN SIR

Baro 47. Find the value of/# um aa alsa
No Bor 4 22.4 + 11657 - 3368
E
ansz 0. — el, 0.412 bj 0.31
No) 6.412 u 0.32
2 points
My AY À
> $e Digtts WR SR
' u LL u

a
we,

77. COMPLETE COURSE (For all govt. exams ) BY ADITYA RANJAN SIR

48. Find the value of/# 4m aa AHÍ
0.57 - 0.432 + 0.35

a}0.494 "TH 0.498
N9 0.498 (d) 0.494
0.87515

+ 0.35555
> 0-43232

90-4989 8
= TS

78. COMPLETE COURSE (For all govt. exams ) BY ADITYA RANJAN SIR

49. Find the value of/@ 4M aM Aa
0.47 + 0.503 - 0.39 x 0.8
ed

ISSC CGL TIER - II 13/09/2019

(a) 0.615 (b) 0.615
(c) 0.625 \laf 0.625 =

y
43 +48 - 36 xe
_ % a Go y
- + 49g
% “da
. "214408 . 61g
% To

Se]
990

79. COMPLETE COURSE (For all govt. exams ) BY ADITYA RANJAN SIR

Find the value of/# 4M aa AA

HY 0.56 - 0.723 + 0.39 x 0.7

ISSC CGL TIER - II 12/09/2019]

(a) 0.154 (b) 0.154
(c) 0.158 (d) 0.158

80. COMPLETE COURSE (For all govt. exams ) BY ADITYA RANJAN SIR

51. Find the value of/# 4M aa fd
(2.4 x 0.6 x 3 x 0.16) x [0.27 x (0.83 + 0.16) |

ISSC CGL TIER - II 15/11/2020

(a) 0.81 (b) 0.11
Me 11 = 12 (4) 1.36
x

81. © 2.34
0
Sol? -1+082 Ans —2+0-34
= - 0-68
= 71-66
~ 4.
to.
O82

82. COMPLETE COURSE (For all govt. exams ) BY ADITYA RANJAN SIR

52. 2.75+3.78
(2) 1.03 —_yros3 (Pl 153
(9h 4.53 3-47 (d) 5.53
-2+0-15 - 340.78

2 - 541.53
= -3.44

83. COMPLETE COURSE (For all govt. exams ) BY ADITYA RANJAN SIR

= - 5
53. If O.ab+0.ba= 9? find the value of a + b.

o
1

Qb-Q +ba-

D 3 aft 0.aB+ 0.ba = ©, à a + b ar ma am aff
> 004 A bide 5 ws "e
So 3 e) 7 (d) 8
? Wlan) -s
#7 Ku
ye x10+4ÿx1
AE = A ID 41042
Mb: Ox10 by)
© (ath

84. By ADITYA RANJAN SIR

AY = 7. 54. 15 Oxy =<, find x? + y? =?
ag 14
aie ME
aña O.xy=— , qa xP + y2 =?
343 meer
(a) 36 (b) 44
ry? = 6242 (sy 45 (d) 55
= 3649

=45

85. Comparison of Fractions

y Base Method [Le Method)

XD Différence Method

DA ross Muktipticasion Ore
Approximation

86. # Base [Lim Method +

u

a + E
lem (2,5,19)= 15

he ars ms à
Guns
20.0

SS IS

87. EE di ea Method |

Ines

88. jagaprg=hs

©

E o BK A

55.

Which fraction among the following is the
least?

Prafatan à à mar fit wae Bret à?

2. Ed

1171 tery
8

(a) 33 (

ISSC CGL MAINS (08/08/2022)
5
11

7
ll 37 (d) 2

89. 55.

Which fraction among the following is the
least?

EN fr aa a À

Wwe

(a) 13

SSC CGL MAINS (08/08/2022)

(ce) 37 (d) 72

90. 56.

Find the greatest of the following fractions.
Prafatad fast à à wae ast first ara aif

CRPF HCM 23/02/2023 (Shift - 01

13 ») 15
(a) 21 (b) Io

ws À aj E
(As (d) 1

91. 57. Which of the following is the largest fraction?
Em à à ai ast Fra an a à?

8 6

N y De se
4 13

(e) 5 (d) 35

92. COMPLETE COURSE (For all govt. exams ) BY ADITYA RANJAN SIR

Lem (2,4,7)= 28 y
FU | LCM METHOD |
4 L G 58. Find the greatest among

44 ,20 ,24 Qu) fratatad fast À à wae at first ara AO
28 28 28 28

inl
2

& ©
7

Aja
Alo

NFS

(b)

(c)

Ia la

Ajo Nie

93. COMPLETE

COURSE (For all govt. exams )

By ADITYA RANJAN SIR

59. Find the smallest among
Frac à à amar Ra wae Biar à?
19 24 Ye

2 27 97 2 8 q, 16
3’9 9

2 8
(a) 3 b) 5

10 a
de (a)

9

94. ñ el
+ Dh e mod action

Proper (NCD) _Improper (ND D)
5
L;
© 4 © Ford

HI 404

ur 20 een

95. _ PROPER FRACTIONS |

Numerator of the fraction is less then
denominator or we can say value of the
fraction is less than 1.

aw a AA EX à Bel a aa A AT HA 1 a
aaa

12 4 7 12
2’3’ 5’ 11° 23 °°:

96. COMPLETE

COURSE (For all govt. exams ) BY ADITYA RANJAN SIR

To compare/qrt & few:

Step 1: Take the difference of N’ and D: of each
of the fractions. /weim fut RH sist mat ET aT
Ha At el

Step 2: Difference must be same. If the given
difference is not same, make them same by
taking LCM of each difference. / 37 WAM ET
AÑO afe stat EA EA Wels stat AT aT.
FIERT SA AM wT Cl

Step 3: Fraction with smaller N’ will be least
and fraction with greater N’ will be greatest./
SA VAR wa A ait are fu wad wet au
afan sist are first wae ast eit

97. By ADITYA RANJAN SIR

Ex: Compare ue ar

¿a

t Ss

Sam 623)
u EXT à 6232

98. COMPLETE

COURSE (For all govt. exams )

BY ADITYA RANJAN SIR
Ex: The greatest value among the fractions
waa así ait mad Bier fr ara I
L

pales
7’3 4
y

5 So 30

2x2

99. COMPLETE COURSE (For all govt. exams ) BY ADITYA RANJAN SIR

60. What is difference between the largest and the
105 147 96 154 8 11

5 7
A > e Bi 31,
«(a u( 1& Al smallest fractions among 9'11'15 and 17°
q nN
Ss

LES
A

ai à à
Lom (4,7,6)= 84 ak — À à waa ag ait aaa oe

9711715 17
a u-e ra a am an à?
‘he 7 1S ICRPF HCM 24/02/2023 (Shift - 02)
= _l6S~ 136 29 8
gee NOW aes ES
~ 2
ES + a 27
S () 45 (os

100. COMPLETE COURSE (For all govt. exams ) BY ADITYA RANJAN SIR

What is the difference of the largest and
Huy smallest of the given fractions?

dm fa à à cad at at aa et fs a ait

an +?
5536
11’7’8’11
SSC CHSL 13/03/2023 (Shift-O1))
(a) az (b) =
56 56

1 a ©
CE (d) 56