Study Material - Jharkhandi Jobs

Chapter 2 : Simplification & Approximation अध्याय 2 : सरलीकरण एवं सन्निकटन

1. Chapter 2 at a Glance

Simplification and Approximation questions test both mathematical accuracy and calculation speed. The strongest approach is not to memorise isolated tricks, but to recognise the structure of an expression and select the shortest valid method.

Complete Chapter Flow:
BODMAS → Brackets & Vinculum → Fractions & Decimals → Powers & Roots → Cancellation & Factorisation → Calculation Shortcuts → Rounding & Approximation → Estimation & Nearest-Value Method → Mixed Problems

Exam Rule:
A shortcut is useful only when it preserves the mathematical value and follows the correct order of operations.

2. BODMAS Rule

BODMAS:
B = Brackets
O = Orders — Powers and Roots
D/M = Division and Multiplication
A/S = Addition and Subtraction

Very Important:
Division does not automatically come before multiplication.
At the same level, division and multiplication are performed from left to right.

Also Remember:
Addition does not automatically come before subtraction.
Addition and subtraction have equal priority and are performed from left to right.

Example:
36÷3×2
=12×2
=24.

3. Use of “Of”

In competitive-exam arithmetic, “of” represents multiplication.

Basic Meaning:
3/4 of 80 = 3/4 × 80 = 60.

Exam Convention:
In traditional aptitude expressions where an explicit “of” forms a clearly intended multiplication block, evaluate that block carefully before combining it with surrounding division or multiplication.

4. Brackets and Nested Expressions

Fundamental Rule:
Solve the innermost grouped expression first and then move outward.

Example:
30 − [12 − {8 − (5−2)}]

5−2=3
8−3=5
12−5=7
30−7=23.

Common Trap:
Do not treat bracket shapes themselves as a universal priority rule. The true principle is innermost first.

5. Vinculum

A vinculum is a horizontal bar that groups the terms lying under it.

Key Rule:
Treat all terms under one vinculum as a single grouped expression.

Example:
20 − 8−3

8−3=5
20−5=15.

Exam Tip:
In printed papers, carefully check exactly how many terms are covered by the vinculum.

6. Minus Sign Before a Bracket

Sign Rules:
−(a+b)=−a−b
−(a−b)=−a+b

Example:
25−(8−13)
=25−(−5)
=25+5
=30.

Exam Trap:
a−(−b)=a+b.

7. Mixed Fractions

Conversion:
a b/c = (ac+b)/c

Example:
3 2/5
=(3×5+2)/5
=17/5.

Common Mistake:
Do not write 3 2/5 as (3+2)/5.

8. Addition and Subtraction of Fractions

Rule:
Fractions with unlike denominators require a common denominator.

Example:
5/6−1/4

=10/12−3/12
=7/12.

Fast Method:
a/b ± c/d = (ad ± bc)/bd
when cross-multiplication is convenient.

9. Multiplication and Division of Fractions

Multiplication:
a/b × c/d = ac/bd

Division:
a/b ÷ c/d = a/b × d/c

Golden Shortcut:
Cancel common factors before multiplication.

Exam Trap:
In fraction division, invert only the divisor.

10. Cancellation Rule

Most Important Rule:
Cancellation occurs between factors, not between terms joined by + or −.

Example:
18/35 × 14/27

18/27=2/3
14/35=2/5

Answer=4/15.

Wrong Thinking:
You cannot cancel a number from only one term of an addition expression.

11. Decimal Addition and Subtraction

Rule:
Align numbers according to the decimal point, not according to their final digits.

Example:
12.5 + 3.075 − 0.62
=12.500 + 3.075 − 0.620
=14.955.

12. Decimal Multiplication

Rule:
Multiply as integers first and then place the decimal according to the total number of decimal places.

Example:
0.24×0.5
=0.120
=0.12.

13. Decimal Division

Rule:
Shift the decimal point in both dividend and divisor by the same number of places until the divisor becomes an integer.

Example:
6.24÷0.8
=62.4÷8
=7.8.

14. Important Fraction-Decimal Equivalents

Fraction	Decimal	Fraction	Decimal
1/2	0.5	1/8	0.125
1/4	0.25	3/8	0.375
3/4	0.75	5/8	0.625
1/5	0.2	7/8	0.875
2/5	0.4	1/10	0.1
3/5	0.6	1/20	0.05
4/5	0.8	1/25	0.04

Exam Shortcut:
These conversions should become mental calculations.

15. Useful Decimal Shortcuts

Remember:
×0.5 = ÷2
÷0.5 = ×2

×0.25 = ÷4
÷0.25 = ×4

×0.125 = ÷8
÷0.125 = ×8

16. Exponent Laws

Core Laws:
a^m×aⁿ=a^m+n

a^m÷aⁿ=a^m−n, a≠0

(a^m)ⁿ=a^mn

(ab)ⁿ=aⁿbⁿ

a⁰=1, a≠0

a⁻ⁿ=1/aⁿ

Exam Trap:
A negative exponent means reciprocal; it does not automatically mean a negative value.

17. Negative Bases and Brackets

Important Difference:
(−3)²=9

but

−3²=−9

Never Forget:
The brackets change the mathematical meaning.

18. Square Roots

Important Relation:
For real a:
√(a²)=|a|

Example:
√144=12
√625=25.

Common Trap:
√(a+b) is generally not equal to √a+√b.

19. Simplifying Square Roots

Method:
Extract the largest perfect-square factor.

Example:
√72
=√(36×2)
=6√2.

Example:
√200
=√(100×2)
=10√2.

20. Like Radicals

Example:
√50+√8
=5√2+2√2
=7√2.

Rule:
Only radicals having the same radical part can be directly combined.

21. Cube Roots

Relation:
∛(a³)=a

Examples:
∛216=6
∛(−125)=−5.

Observation:
Real cube roots are also defined for negative numbers.

22. Perfect-Square and Perfect-Cube Factors

Useful Perfect Squares:
4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 625, 900

Useful Perfect Cubes:
1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1728, 3375, 8000

23. Difference of Squares

Identity:
a²−b²=(a−b)(a+b)

Example:
58²−42²
=(58−42)(58+42)
=16×100
=1600.

Exam Shortcut:
Do not calculate the two squares separately when this identity applies.

24. Numbers Equally Spaced from a Convenient Base

Pattern:
(a−b)(a+b)=a²−b²

Example:
103×97
=(100+3)(100−3)
=10000−9
=9991.

Example:
48×52
=50²−2²
=2496.

25. Common-Factor Shortcut

Identity:
ab+ac=a(b+c)

Example:
37×48+37×52
=37(48+52)
=37×100
=3700.

26. Multiplication by 5, 25 and 125

Fast Conversions:
×5 = ×10÷2
×25 = ×100÷4
×125 = ×1000÷8

Examples:
48×25=1200
64×125=8000.

27. Division by 5, 25 and 125

Fast Conversions:
÷5 = ×2÷10
÷25 = ×4÷100
÷125 = ×8÷1000

Example:
875÷25
=875×4÷100
=35.

28. Multiplication by 9, 99 and 999

Patterns:
9=10−1
99=100−1
999=1000−1

Example:
47×99
=4700−47
=4653.

Example:
83×999
=83000−83
=82917.

29. Multiplication by 11

Example:
43×11
→ 4 (4+3) 3
=473.

Carry Case:
78×11=858, because 7+8=15 and the carry must be handled.

30. Square of a Number Ending in 5

Shortcut:
For a number ending in 5:
Multiply the preceding part n by n+1 and append 25.

Examples:
75²: 7×8=56 → 5625

115²: 11×12=132 → 13225

31. Squares Near 100

Identities:
(a+b)²=a²+2ab+b²
(a−b)²=a²−2ab+b²

Example:
98²
=(100−2)²
=10000−400+4
=9604.

32. Doubling and Halving

Property:
a×b=(2a)×(b/2)

Example:
25×48
=50×24
=100×12
=1200.

33. Telescoping Products

Example:
(1−1/2)(1−1/3)...(1−1/10)

=1/2×2/3×3/4×...×9/10

Intermediate factors cancel.

Answer=1/10.

Exam Shortcut:
Before multiplying a long fraction sequence, look for a cancellation chain.

34. Approximation

Approximation replaces an exact value by a convenient nearby value.

Examples:
49.92≈50
199.7≈200
3.98≈4

Exam Rule:
Approximation is useful only when the required accuracy and option gap permit it.

35. Basic Rounding Rule

Rule:
Next digit 0–4 → retain the required digit.
Next digit 5–9 → increase the required digit by 1.

Examples:
64.32 to one decimal place → 64.3
64.38 to one decimal place → 64.4

36. Rounding Whole Numbers

Examples:
467 to nearest ten → 470
6,847 to nearest hundred → 6,800
36,680 to nearest thousand → 37,000

37. Decimal Places

Rule:
Decimal places are counted immediately from the first digit after the decimal point.

Example:
12.746 to two decimal places → 12.75.

38. Significant Figures

Rules:
• Counting starts from the first non-zero digit.
• Leading zeros are not significant.
• Zeros between non-zero digits are significant.

Example:
0.004586 to 3 significant figures → 0.00459.

Exam Trap:
Do not confuse decimal places with significant figures.

39. Maximum Rounding Error

Rule:
Maximum rounding error = half of the rounding unit.

Examples:
Nearest 1 → maximum error 0.5
Nearest 10 → maximum error 5
Nearest 100 → maximum error 50
Nearest 0.1 → maximum error 0.05

40. Compatible Numbers

Compatible numbers are nearby values that make multiplication or division easy.

Example:
598÷29.9
≈600÷30
=20.

Example:
398×24.9
≈400×25
=10,000.

41. Percentage Estimation

Useful Equivalents:
50%=1/2
25%=1/4
75%=3/4
20%=1/5
12.5%=1/8
33⅓%≈1/3

Example:
24.9% of 803
≈25% of 800
=200.

42. Balanced Estimation

Example:
49.8×20.2
≈50×20
=1000.

Observation:
One factor is rounded upward and the other downward, so some of the estimation error may cancel.

43. Division Estimation

Important Principle:
Choose nearby numerator and denominator values that preserve the approximate ratio.

Example:
799÷39.8
≈800÷40
=20.

Exam Trap:
A small change in the denominator can significantly change the quotient.

44. Option-Gap Analysis

Decision Rule:
Wide option gap → rough estimate may be enough.
Close options → retain more precision.
Extremely close options → exact calculation may be necessary.

Exam Tip:
Do not calculate more accurately than the options require.

45. Order-of-Magnitude Check

Example:
198×51 ≈ 200×50 = 10,000.

Therefore answers near 1,000 or 100,000 are immediately suspicious.

Final Check:
Always ask whether the final answer should be in units, tens, hundreds, thousands or another range.

46. Two-Stage Estimation

Stage 1:
Use rough compatible numbers.

Stage 2:
If two options remain possible, retain one additional digit and refine the estimate.

Example:
149.6×4.02÷19.9
≈150×4÷20
=30.

47. Exact Shortcut Before Approximation

Golden Rule:
Before rounding awkward-looking numbers, check for cancellation, factorisation or an exact identity.

Example:
(59.9²−40.1²)/(59.9+40.1)

=59.9−40.1
=19.8.

48. Mixed-Problem Strategy

Three-Level Method:
Level 1 — Structure: Identify brackets, powers, roots, fractions, decimals and approximation clues.

Level 2 — Simplification: Apply cancellation, identities, convenient conversions and BODMAS.

Level 3 — Verification: Check sign, magnitude and answer options.

49. Common Chapter-Wide Traps

Avoid These Errors:
• Treating D as always before M.
• Treating A as always before S.
• Solving outer brackets before inner brackets.
• Missing a vinculum.
• Forgetting sign reversal after a minus bracket.
• Cancelling terms instead of factors.
• Inverting both fractions during division.
• Misplacing decimal points.
• Confusing −a² with (−a)².
• Assuming √(a+b)=√a+√b.
• Expanding squares when factorisation is shorter.
• Approximating an exact-value question.
• Using rough estimation despite very close options.
• Forgetting BODMAS after approximation.

50. Final 30-Second Revision Formula Sheet

BODMAS:
Brackets → Orders → D/M left to right → A/S left to right

Fractions:
a/b÷c/d = a/b×d/c

Exponents:
a^maⁿ=a^m+n
a^m/aⁿ=a^m−n
(a^m)ⁿ=a^mn

Difference of Squares:
a²−b²=(a−b)(a+b)

Fast Multipliers:
×25=×100÷4
×125=×1000÷8
×99=×100−original number
×999=×1000−original number

Ending in 5 Square:
n5² → n(n+1), then append 25

Approximation:
Check option gap → choose compatible numbers → preserve BODMAS → verify magnitude

Last Exam Reminder:
The fastest method is the shortest correct method, not simply the most complicated shortcut you remember.

51. Verified Previous-Year Questions — Part A

Chapter 2 PYQ Bank:
The following questions cover BODMAS, brackets, vinculum, fractions, decimals, powers, roots and approximation. Solutions are kept concise so that this section can be used for rapid chapter revision.

SSC CGL PYQ BODMAS 24 September 2024 · Tier-I · Shift II

Q1. Simplify: 133 ÷ 19 × 3 − 48 × 2 ÷ 24 + 841 ÷ (45−16)

A. 46
B. 21
C. 12
D. 42

Correct Answer: A. 46

45−16=29.
133÷19×3=7×3=21.
48×2÷24=4.
841÷29=29.

Therefore:
21−4+29=46.

RRB NTPC PYQ Nested Brackets 18 June 2026 · UG CBT-I · Shift III

Q2. Simplify: 156 ÷ [12 + {7 × (15−9) − 28}]

A. 8
B. 10
C. 6
D. 12

Correct Answer: C. 6

15−9=6.
7×6−28=42−28=14.
12+14=26.

Therefore:
156÷26=6.

SSC CHSL PYQ Vinculum & Brackets 15 April 2021 · Tier-I · Shift III

Q3. Simplify: 45 − [36 − {29 − (25 − 7+4)}]

A. 24
B. 22
C. 26
D. 28

Correct Answer: A. 24

Vinculum first:
7+4=11.

25−11=14.
29−14=15.
36−15=21.

Therefore:
45−21=24.

SSC CGL PYQ Fractions & Of 24 August 2021 · Tier-I · Shift II

Q4. Simplify: 7/12 ÷ (1/10 of 2/3) − 5/3 × 9/10 + 5/8 ÷ (3/4 of 2/3)

A. −4
B. 3 23/36
C. 8 1/2
D. 7 29/36

Correct Answer: C. 8 1/2

1/10 of 2/3=1/15 and 3/4 of 2/3=1/2.

Therefore:
7/12÷1/15 − 5/3×9/10 + 5/8÷1/2
=35/4 − 3/2 + 5/4
=40/4−6/4
=34/4
=17/2 = 8 1/2.

SSC CHSL PYQ BODMAS 1 July 2024 · Tier-I · Shift I

Q5. Simplify: 3 + 28 ÷ 35 × 15 + 4 − 3 × 4

A. 26
B. 10
C. 7
D. 64

Correct Answer: C. 7

28÷35×15
=4/5×15
=12.

Also 3×4=12.

Therefore:
3+12+4−12=7.

SSC CHSL PYQ Bracket Operations 1 July 2024 · Tier-I · Shift III

Q6. Simplify: (36÷6)÷3 + (18÷9)×4 − (12÷6)×(5÷2)

A. 10
B. 15
C. 21
D. 5

Correct Answer: D. 5

(36÷6)÷3=6÷3=2.
(18÷9)×4=2×4=8.
(12÷6)×(5÷2)=2×2.5=5.

Therefore:
2+8−5=5.

SSC CHSL PYQ Fractions & Of 5 July 2024 · Tier-I · Shift II

Q7. Simplify:

([1/2 ÷ (3/4 of 5/6)] ÷ [1/2 ÷ 3/4 × 5/6]) + (2+2×2)/(2÷2×2)

A. 4
B. 121/25
C. 111/25
D. 75/36

Correct Answer: C. 111/25

3/4 of 5/6=5/8.
So 1/2÷5/8=4/5.

Also:
1/2÷3/4×5/6=5/9.

Thus first part:
(4/5)÷(5/9)=36/25.

Second part:
(2+4)/(1×2)=6/2=3.

Total:
36/25+3=111/25.

SSC CHSL PYQ BODMAS & Of 2 July 2024 · Tier-I · Shift II

Q8. Simplify: (3−3×3+3÷3+3×5) × 2 of 5 + (2+2÷2+2×2−2)

A. 105
B. 102
C. 106
D. 100

Correct Answer: A. 105

First bracket:
3−9+1+15=10.

2 of 5=10.
So first part=10×10=100.

Second bracket:
2+1+4−2=5.

Total=105.

SSC CGL PYQ Mixed Fractions 18 September 2024 · Tier-I · Shift I

Q9. Simplify: [(5 1/2 − 3 1/3) of 1 5/13 + 1 − 2 × 3 5/2 ÷ 2 3/4]

A. 0
B. 11/2
C. −2
D. 3 1/2

Correct Answer: A. 0

5 1/2−3 1/3
=11/2−10/3
=13/6.

1 5/13=18/13, so:
13/6×18/13=3.

3 5/2=11/2 and 2 3/4=11/4.
Therefore:
2×11/2÷11/4=4.

Hence:
3+1−4=0.

SSC MTS PYQ Fractions & Of 13 September 2023 · Shift II

Q10. Simplify: (5/3 + 6/5 ÷ 18/5) of 5/12 − (5/6 ÷ 5/12) of 5/12 + 2/3 of 3/2

A. 1
B. 5/6
C. 6/5
D. 0

Correct Answer: A. 1

6/5÷18/5=1/3.
So first bracket=5/3+1/3=2.
First part=2×5/12=5/6.

5/6÷5/12=2, so second part=2×5/12=5/6.

2/3 of3/2=1.

Therefore:
5/6−5/6+1=1.

SSC MTS PYQ Decimal BODMAS 6 September 2023 · Shift I

Q11. Simplify: 45 − 22÷2 + 12 + 70÷35 + 0.4÷0.8 + 1.5÷3 + 1

A. 50
B. 50.5
C. 48.5
D. 54.5

Correct Answer: A. 50

22÷2=11
70÷35=2
0.4÷0.8=0.5
1.5÷3=0.5.

Therefore:
45−11+12+2+0.5+0.5+1
=50.

SSC MTS PYQ Surds & Mixed Fractions 8 September 2023 · Shift II

Q12. Simplify:

[24√45 − 16√20 + √245 − 47√5] ÷ [3 1/5 + 1 2/5 − 2 1/6 − 2 1/5 − 5 2/5 + 3 1/6]

A. 0
B. 3
C. 1
D. 2

Correct Answer: A. 0

√45=3√5, √20=2√5 and √245=7√5.

Numerator:
72√5−32√5+7√5−47√5=0.

The denominator simplifies to −2, which is non-zero.

Therefore:
0÷(−2)=0.

SSC MTS PYQ Square Root 3 May 2023 · Shift II

Q13. Find the value of √[((13²−8²)×5)+4].

A. 23
B. 26
C. 24
D. 22

Correct Answer: A. 23

13²−8²
=169−64
=105.

105×5+4=529.

Therefore:
√529=23.

RRB Group D PYQ Square Root of Decimal 30 August 2022 · Shift III

Q14. Find the value of √1.0201.

A. 10.1
B. 101
C. 1.01
D. 1.02

Correct Answer: C. 1.01

1.0201=10201/10000.

101²=10201 and 100²=10000.

Therefore:
√1.0201=101/100=1.01.

RRB NTPC PYQ Cube Root 26 July 2021 · CBT-I · Shift I

Q15. Between which two consecutive integers does ∛150 lie?

A. 6 and 7
B. 4 and 5
C. 7 and 8
D. 5 and 6

Correct Answer: D. 5 and 6

5³=125 and 6³=216.

Since:
125<150<216,

therefore:
5<∛150<6.

So ∛150 lies between 5 and 6.

SSC MTS PYQ Powers 22 July 2022 · Shift I

Q16. Find the missing value: 2 × 324 × ? = 9² × 22² × 6

A. 359
B. 364
C. 363
D. 366

Correct Answer: C. 363

?=(9²×22²×6)/(2×324).

Since 324=18²:
9²/18²=1/4.

Therefore:
?=(22²×6)/(4×2)
=484×6/8
=484×3/4
=363.

RRB Group D PYQ Exponent Laws 8 December 2025 · Shift III

Q17. Simplify:

[8²¹ ÷ 4²⁸ × 2⁵] ÷ [(4¹⁴)^1/7 × 8²]

A. 2
B. 4
C. 8
D. 16

Correct Answer: B. 4

Write everything with base 2:
8²¹=2⁶³, 4²⁸=2⁵⁶.
(4¹⁴)^1/7=2⁴ and 8²=2⁶.

Therefore:
2^{63−56+5−4−6}
=2²
=4.

RRB Group D PYQ Exponent Factorisation 1 December 2025 · Shift I

Q18. Simplify: [5^3x+4 + 125^x+1] ÷ [125^x+1 − 5^3x+2]

A. 8
B. 7.5
C. 5
D. 10

Correct Answer: B. 7.5

125^x+1=5^3x+3.

Take 5^3x+2 common from numerator and denominator:

=[5²+5]/[5−1]
=(25+5)/4
=30/4
=7.5.

SSC MTS PYQ Approximation 6 July 2022 · Shift III

Q19. Which option is closest to the value of 305.03 ÷ 61.09 × 11.47?

A. 57
B. 47
C. 12
D. 63

Correct Answer: A. 57

305.03÷61.09 is approximately 5.

Therefore:
5×11.47≈57.35.

The closest option is 57.

RRB Group D PYQ Nearest-Value Approximation 5 September 2022 · Shift I

Q20. Find the closest approximate value of: 4.49 ÷ 1.49 − 3.33 × 3 + 4.49

A. −2.5
B. −4.5
C. 4.5
D. 2.5

Correct Answer: A. −2.5

4.49÷1.49≈3.01.
3.33×3=9.99.

Therefore:
3.01−9.99+4.49
≈−2.49.

Closest option=−2.5.

52. Verified Previous-Year Questions — Part B

Chapter 2 PYQ Bank — Q21 to Q40:
This section gives greater emphasis to advanced simplification, approximation, nearest-value techniques, decimal operations, powers, roots, identities and mixed calculations.

SSC CGL PYQ Fractions & Cancellation 18 August 2021 · Tier-I · Shift III

Q21. Simplify: 441 ÷ [270 ÷ 3/7 + (17 ÷ 1/3) − (8 1/2 − 5/2)]

A. 29/75
B. 49/75
C. 39/75
D. 19/75

Correct Answer: B. 49/75

270÷3/7=630.
17÷1/3=51.
8 1/2−5/2=17/2−5/2=6.

Bracket=630+51−6=675.

Therefore:
441/675=49/75.

RRB Group D PYQ Nearest-Value Estimation 30 September 2022 · Shift I

Q22. Find the closest approximate value of: 2.33 − 4.12 + 6.13 × 11.3

A. 106
B. 64
C. 39
D. 43

Correct Answer: B. 64

Use convenient approximations:
2.33≈2, 4.12≈4, 6.13≈6 and 11.3≈11.

Therefore:
2−4+6×11
=−2+66
=64.

RRB Group D PYQ Compatible Numbers 26 August 2022 · Shift I

Q23. Find the closest approximate value of: 44.999 ÷ 8.998 + 23.996 ÷ 11.998 − 7.009 + 8.002 × 1.998

A. 28
B. 16
C. 20
D. 24

Correct Answer: B. 16

Approximate:
45÷9 + 24÷12 −7 +8×2

=5+2−7+16
=16.

RRB Group D PYQ Nearest-Option Method 15 September 2022 · Shift II

Q24. Find the closest approximate value of: 17.99 − 16.02 + 19.89 × 8.19

A. 122
B. 330
C. 42
D. 162

Correct Answer: D. 162

17.99≈18, 16.02≈16, 19.89≈20 and 8.19≈8.

Therefore:
18−16+20×8
=2+160
=162.

RRB NTPC PYQ Approximation with Powers 17 June 2022 · CBT-II Level 3 · Shift III

Q25. Find the closest approximate value of: 5.01 + (3.01 × 1.99²) × 4 + 6.01 ÷ 2.03

A. 56
B. 65
C. 57
D. 52

Correct Answer: A. 56

Approximate:
5.01≈5, 3.01≈3, 1.99≈2, 6.01≈6 and 2.03≈2.

Then:
5+(3×2²)×4+6÷2
=5+48+3
=56.

RRB NTPC PYQ Percentage Approximation 16 June 2022 · CBT-II Level 2 · Shift I

Q26. Find the closest value of ? in: 44.97% of 226 + 55.03 × 4.98 − ? = 140

A. 25
B. 237
C. 508
D. 120

Correct Answer: B. 237

44.97%≈45%, 55.03≈55 and 4.98≈5.

45% of226≈102 and 55×5=275.

So:
102+275−?≈140
?≈377−140
=237.

RRB NTPC PYQ Identity & Approximation 8 January 2021 · CBT-I · Shift I

Q27. Find the approximate value of: (2.697+0.498)² − (2.697−0.498)²

A. 2.00
B. 5.37
C. 2.199
D. 3.195

Correct Answer: B. 5.37

Use:
(a+b)²−(a−b)²=4ab.

=4×2.697×0.498
=5.372424.

Therefore approximate value=5.37.

RRB Group D PYQ Decimal Approximation 30 August 2022 · Shift II

Q28. Find the closest approximate value of: 17.89 − 0.0123 + 2.21 × 3.63

A. 42
B. 15
C. 26
D. 36

Correct Answer: C. 26

2.21×3.63=8.0223.

Therefore:
17.89−0.0123+8.0223
=25.9.

Closest option=26.

RRB Group D PYQ Roots & Approximation 22 August 2022 · Shift I

Q29. Find the closest approximate value of: (√360 + 12 ÷ 6 × 3 − √170) ÷ 2

A. 6
B. 4
C. 8
D. 5

Correct Answer: A. 6

√360≈18.97 and √170≈13.03.
12÷6×3=6.

Therefore:
(18.97+6−13.03)÷2
=11.94÷2
≈6.

RRB Group D PYQ Roots & BODMAS 29 August 2022 · Shift III

Q30. Find the closest approximate value of: (√142 + 52 ÷ 26 × 5 − √80) × 2

A. 32
B. 30
C. 20
D. 26

Correct Answer: D. 26

√142≈11.9 and √80≈8.9.
52÷26×5=10.

Therefore:
(11.9+10−8.9)×2
=13×2
=26.

RRB Group D PYQ Mixed Decimal Approximation 18 September 2022 · Shift II

Q31. Find the closest approximate option for: 48.9 × 3.95 − 2.97 + 17.86

A. 125
B. 140
C. 211
D. 250

Correct Answer: C. 211

The exact value is approximately 208.045.

Among the given options, 211 is the closest.

RRB Group D PYQ BODMAS Approximation 14 September 2022 · Shift III

Q32. Find the closest approximate value of: 5.18 × 4 + 2.06 × 5 − 10 ÷ 2 + 1

A. 15
B. 40
C. 26
D. 30

Correct Answer: C. 26

Using convenient approximations:
5.18≈5 and 2.06≈2.

Then:
5×4+2×5−10÷2+1
=20+10−5+1
=26.

RRB Group D PYQ Mixed Approximation 22 September 2022 · Shift I

Q33. Find the closest approximate value of: 104.96 + 120.96 + 103.16 − 12.89 × 2.04 + 124.93 ÷ 5.1

A. 330
B. 340
C. 328
D. 334

Correct Answer: C. 328

The expression evaluates to approximately 327.3.

Therefore the closest available option is 328.

RRB Group D PYQ Fast Approximation 2 September 2022 · Shift I

Q34. Find the closest approximate value of: 4.98 × 2 + 1.96 × 4 − 8 ÷ 2 + 1

A. 20
B. 12
C. 18
D. 15

Correct Answer: D. 15

4.98≈5 and 1.96≈2.

Therefore:
5×2+2×4−8÷2+1
=10+8−4+1
=15.

RRB NTPC PYQ Mixed Fractions & Cancellation 21 June 2025 · Graduate CBT-I · Shift II

Q35. Simplify: 2 2/9 × 2 2/3 × 567 + 8 3/4

A. 3372.15
B. 3364.35
C. 3368.75
D. 3347.25

Correct Answer: C. 3368.75

2 2/9=20/9, 2 2/3=8/3 and 8 3/4=35/4.

20/9×8/3×567
=20×8×21
=3360.

35/4=8.75.

Total=3368.75.

RRB Group D PYQ Decimal BODMAS 22 December 2025 · Shift I

Q36. Simplify: 0.7 × 72 ÷ 14 + 6.25 − 8.34 × 0.15 + 5.95

A. 21.549
B. 12.526
C. 14.823
D. 14.549

Correct Answer: D. 14.549

0.7×72÷14=3.6.
8.34×0.15=1.251.

Therefore:
3.6+6.25−1.251+5.95
=15.8−1.251
=14.549.

RRB NTPC PYQ Identity & Cancellation 7 March 2021 · CBT-I · Shift I

Q37. Simplify: (4.2×4.2 − 1.9×1.9) ÷ (2.3×6.1)

A. 3
B. 2
C. 1
D. 4

Correct Answer: C. 1

Numerator:
4.2²−1.9²
=(4.2−1.9)(4.2+1.9)
=2.3×6.1.

The denominator is also 2.3×6.1.

Therefore value=1.

RRB Group D PYQ Balanced Approximation 20 September 2022 · Shift III

Q38. Find the closest approximate value of: 239.99 × 20.01 − 99.99 × 30.01

A. 1805
B. 1815
C. 1800
D. 1810

Correct Answer: C. 1800

239.99≈240, 20.01≈20, 99.99≈100 and 30.01≈30.

Therefore:
240×20−100×30
=4800−3000
=1800.

RRB Group D PYQ Percentage Approximation 11 October 2022 · Shift II

Q39. Find the closest approximate value of: 20.01% of 320.002 + 121.99

A. 162
B. 186
C. 154
D. 174

Correct Answer: B. 186

20.01% of320.002 is approximately 64.

121.99≈122.

Therefore:
64+122≈186.

SSC MTS PYQ Advanced Approximation 11 February 2026 · Shift II

Q40. Find the approximate value of:

(76.91×143.97)/(7.07×12.01) − (3.93²×√195.88)/(6.93×8.03^1/3)

A. 145
B. 105
C. 116
D. 98

Correct Answer: C. 116

Approximate:
76.91≈77, 143.97≈144, 7.07≈7, 12.01≈12,
3.93≈4, √195.88≈14, 6.93≈7 and 8.03^1/3≈2.

First term:
77×144÷(7×12)=132.

Second term:
4²×14÷(7×2)=16.

Therefore:
132−16=116.

53. Practice MCQs — Batch 1

Chapter 2 Mixed Practice Bank — Q1 to Q20:
This batch combines BODMAS, brackets, fractions, decimals, powers, roots, cancellation, identities, calculation shortcuts, percentages and approximation.

Practice MCQ

Q1. Simplify: 72 ÷ 8 × 3 + 5² − 7

A. 41
B. 43
C. 45
D. 47

Correct Answer: C. 45

72÷8×3=9×3=27.
5²=25.

Therefore:
27+25−7=45.

Practice MCQ

Q2. Simplify: [48 ÷ (9−3) + 2³] × 2

A. 24
B. 28
C. 30
D. 32

Correct Answer: D. 32

9−3=6.
48÷6=8 and 2³=8.

Bracket=8+8=16.
16×2=32.

Practice MCQ

Q3. Simplify: 3/4 of 96 + 2.5 × 8 − √121

A. 77
B. 79
C. 81
D. 83

Correct Answer: C. 81

3/4 of96=72.
2.5×8=20.
√121=11.

Therefore:
72+20−11=81.

Practice MCQ

Q4. Simplify: (1.25 + 3/4) ÷ 0.5

A. 3
B. 4
C. 5
D. 6

Correct Answer: B. 4

3/4=0.75.

1.25+0.75=2.
2÷0.5=4.

Practice MCQ

Q5. Simplify: (62²−38²) ÷ (62+38)

A. 20
B. 22
C. 24
D. 26

Correct Answer: C. 24

Use:
a²−b²=(a−b)(a+b).

Therefore:
(62−38)(62+38)/(62+38)
=62−38
=24.

Practice MCQ

Q6. Simplify: 84 ÷ 7 + 0.125 × 64 + ∛216

A. 24
B. 26
C. 28
D. 30

Correct Answer: B. 26

84÷7=12.
0.125=1/8, so 0.125×64=8.
∛216=6.

Total=12+8+6=26.

Practice MCQ

Q7. Find the closest approximate value of: 49.7 × 19.8 + 100.2 ÷ 5.01

A. 900
B. 1000
C. 1100
D. 1200

Correct Answer: B. 1000

49.7≈50 and 19.8≈20.
100.2≈100 and 5.01≈5.

Estimated value:
50×20+100÷5
=1000+20
=1020.

Among the given options, 1000 is the closest. The exact value is also about 1004.

Practice MCQ

Q8. Simplify: 25% of 480 + 3/5 of 150 − 32

A. 168
B. 174
C. 178
D. 182

Correct Answer: C. 178

25% of480=120.
3/5 of150=90.

Therefore:
120+90−32=178.

Practice MCQ

Q9. Simplify: 5³ × 5⁻¹ ÷ 5

A. 1
B. 5
C. 25
D. 125

Correct Answer: B. 5

5³×5⁻¹÷5¹
=5³⁻¹⁻¹
=5¹
=5.

Practice MCQ

Q10. Simplify: √288 − √32

A. 4√2
B. 6√2
C. 8√2
D. 10√2

Correct Answer: C. 8√2

√288=√(144×2)=12√2.
√32=√(16×2)=4√2.

Therefore:
12√2−4√2=8√2.

Practice MCQ

Q11. Simplify: (2 1/2 + 1.75) × 4 − 3²

A. 6
B. 8
C. 10
D. 12

Correct Answer: B. 8

2 1/2=2.5.
2.5+1.75=4.25.

4.25×4=17 and 3²=9.

17−9=8.

Practice MCQ

Q12. Simplify: 0.6 ÷ 0.15 + 2.4 × 1.25

A. 6
B. 7
C. 8
D. 9

Correct Answer: B. 7

0.6÷0.15=4.
2.4×1.25=3.

Therefore:
4+3=7.

Practice MCQ

Q13. Find the value of: 47 × 99 + 16 × 125

A. 6553
B. 6603
C. 6653
D. 6703

Correct Answer: C. 6653

47×99
=47×(100−1)
=4700−47
=4653.

16×125=2000.

Therefore:
4653+2000=6653.

Practice MCQ

Q14. Find the value of: 103 × 97 + 48 × 52

A. 12,387
B. 12,437
C. 12,487
D. 12,537

Correct Answer: C. 12,487

103×97
=(100+3)(100−3)
=10000−9
=9991.

48×52
=(50−2)(50+2)
=2500−4
=2496.

Total:
9991+2496=12,487.

Practice MCQ

Q15. Approximately find: 19.9% of 501 + 24.8% of 399

A. 180
B. 190
C. 200
D. 210

Correct Answer: C. 200

19.9%≈20% and 501≈500.
20% of500=100.

24.8%≈25% and 399≈400.
25% of400=100.

Approximate total=200.

Practice MCQ

Q16. Simplify: [2⁵ + √196] ÷ ∛64

A. 10
B. 11
C. 11 1/2
D. 12

Correct Answer: C. 11 1/2

2⁵=32.
√196=14.
∛64=4.

Therefore:
(32+14)÷4
=46/4
=23/2 = 11 1/2.

Practice MCQ

Q17. Simplify: 1/2 ÷ (3/4 of 2/3) + 5/6

A. 7/6
B. 3/2
C. 11/6
D. 13/6

Correct Answer: C. 11/6

3/4 of2/3
=3/4×2/3
=1/2.

Therefore:
1/2÷1/2=1.

1+5/6=11/6.

Practice MCQ

Q18. Simplify: (75²−25²) ÷ (75−25)

A. 50
B. 75
C. 100
D. 125

Correct Answer: C. 100

a²−b²=(a−b)(a+b).

Therefore:
(75−25)(75+25)/(75−25)
=75+25
=100.

Practice MCQ

Q19. Find the value of: 23 × 999 − 230 × 99

A. 187
B. 197
C. 207
D. 217

Correct Answer: C. 207

230×99=23×10×99=23×990.

Therefore:
23×999−23×990
=23(999−990)
=23×9
=207.

Practice MCQ

Q20. Find the closest approximate value of: 299.8 × 4.02 ÷ 19.9

A. 50
B. 60
C. 70
D. 80

Correct Answer: B. 60

299.8≈300, 4.02≈4 and 19.9≈20.

Therefore:
300×4÷20
=1200÷20
=60.

54. Practice MCQs — Batch 2

Chapter 2 Mixed Practice Bank — Q21 to Q40:
This batch continues the chapter-wide practice of simplification and approximation with progressively mixed exam-style calculations.

Practice MCQ

Q21. Simplify: 150 − [36 ÷ (9−3) + 4²]

A. 124
B. 126
C. 128
D. 130

Correct Answer: C. 128

9−3=6, so 36÷6=6 and 4²=16. The bracket is 22; hence 150−22=128.

Practice MCQ

Q22. Round 5,876 to the nearest hundred.

A. 5,800
B. 5,900
C. 6,000
D. 5,870

Correct Answer: B. 5,900

The tens digit is 7, so the hundreds digit increases from 8 to 9. Therefore 5,876 rounds to 5,900.

Practice MCQ

Q23. Round 0.006384 to three significant figures.

A. 0.00630
B. 0.00638
C. 0.00639
D. 0.00640

Correct Answer: B. 0.00638

The first three significant digits are 6, 3 and 8. The next digit is 4, so the third significant digit remains unchanged. Answer=0.00638.

Practice MCQ

Q24. Simplify: (−4)² − 4²

A. −32
B. 0
C. 16
D. 32

Correct Answer: B. 0

(−4)²=16 and 4²=16. Therefore 16−16=0.

Practice MCQ

Q25. Simplify: (1 1/2 + 1 1/4) ÷ 1/2

A. 9/2
B. 5
C. 11/2
D. 6

Correct Answer: C. 11/2

1 1/2=3/2 and 1 1/4=5/4. Their sum is 11/4. Dividing by 1/2 gives 11/4×2=11/2.

Practice MCQ

Q26. Simplify: √98 + √8

A. 7√2
B. 8√2
C. 9√2
D. 10√2

Correct Answer: C. 9√2

√98=7√2 and √8=2√2. Hence 7√2+2√2=9√2.

Practice MCQ

Q27. Find the value of ∛343.

A. 5
B. 6
C. 7
D. 8

Correct Answer: C. 7

Since 7³=343, ∛343=7.

Practice MCQ

Q28. Find the value of 84 × 25.

A. 2,000
B. 2,050
C. 2,100
D. 2,200

Correct Answer: C. 2,100

Use ×25=×100÷4. Thus 84×25=8400÷4=2100.

Practice MCQ

Q29. Find the value of 6,250 ÷ 125.

A. 40
B. 45
C. 50
D. 55

Correct Answer: C. 50

Use ÷125=×8÷1000. Thus 6250×8÷1000=50.

Practice MCQ

Q30. Find the value of 36 × 99.

A. 3,464
B. 3,564
C. 3,664
D. 3,764

Correct Answer: B. 3,564

36×99=36×(100−1)=3600−36=3564.

Practice MCQ

Q31. Find the value of 85².

A. 7,125
B. 7,225
C. 7,325
D. 7,425

Correct Answer: B. 7,225

Multiply 8×9=72 and append 25. Thus 85²=7225.

Practice MCQ

Q32. Find the value of 98 × 102.

A. 9,896
B. 9,996
C. 10,004
D. 10,096

Correct Answer: B. 9,996

(100−2)(100+2)=100²−2²=10000−4=9996.

Practice MCQ

Q33. Find the value of (1−1/2)(1−1/3)(1−1/4)...(1−1/12).

A. 1/10
B. 1/11
C. 1/12
D. 1/13

Correct Answer: C. 1/12

The product becomes 1/2×2/3×3/4×...×11/12. Intermediate factors cancel, leaving 1/12.

Practice MCQ

Q34. Find the closest approximate value of 79.8 × 12.1.

A. 900
B. 960
C. 1,000
D. 1,080

Correct Answer: B. 960

79.8≈80 and 12.1≈12. Therefore 80×12=960.

Practice MCQ

Q35. Approximately find: 24.9% of 803 + 50.1% of 198.

A. 250
B. 275
C. 300
D. 325

Correct Answer: C. 300

24.9%≈25% of 800=200 and 50.1%≈50% of 200=100. Total≈300.

Practice MCQ

Q36. If 3.5 × 8 + ? ÷ 2 = 40, find ?.

A. 20
B. 22
C. 24
D. 26

Correct Answer: C. 24

3.5×8=28. Thus ?÷2=12, so ?=24.

Practice MCQ

Q37. Simplify: 0.75 × 48 + 2.4 ÷ 0.6 − 1.25 × 8

A. 28
B. 30
C. 32
D. 34

Correct Answer: B. 30

0.75×48=36, 2.4÷0.6=4 and 1.25×8=10. Therefore 36+4−10=30.

Practice MCQ

Q38. Simplify: 27 × 46 + 27 × 54

A. 2,600
B. 2,650
C. 2,700
D. 2,750

Correct Answer: C. 2,700

Take 27 common: 27(46+54)=27×100=2700.

Practice MCQ

Q39. Simplify: 2⁷ × 2⁻³ ÷ 2²

A. 2
B. 4
C. 8
D. 16

Correct Answer: B. 4

2⁷⁻³⁻²=2²=4.

Practice MCQ

Q40. Simplify: 96 ÷ 8 × 3 − 4² + 5

A. 21
B. 23
C. 25
D. 27

Correct Answer: C. 25

96÷8×3=36 and 4²=16. Therefore 36−16+5=25.

55. Practice MCQs — Batch 3

Chapter 2 Mixed Practice Bank — Q41 to Q60:
This batch combines exact simplification, roots, identities, calculation shortcuts, rounding and approximation.

Practice MCQ

Q41. Simplify: [64 ÷ (12−4) + √144] × 3

A. 54
B. 57
C. 60
D. 63

Correct Answer: C. 60

12−4=8, 64÷8=8 and √144=12. Thus (8+12)×3=60.

Practice MCQ

Q42. Simplify: 7/8 of 160 − 0.25 × 80

A. 110
B. 120
C. 130
D. 140

Correct Answer: B. 120

7/8 of160=140 and 0.25×80=20. Hence 120.

Practice MCQ

Q43. Simplify: (2.75 + 1 1/4) ÷ 0.8

A. 4
B. 5
C. 6
D. 7

Correct Answer: B. 5

1 1/4=1.25. Thus (2.75+1.25)÷0.8=4÷0.8=5.

Practice MCQ

Q44. Simplify: √324 + ∛512 − 2⁴

A. 8
B. 10
C. 12
D. 14

Correct Answer: B. 10

18+8−16=10.

Practice MCQ

Q45. Simplify: (73²−27²) ÷ (73−27)

A. 90
B. 95
C. 100
D. 105

Correct Answer: C. 100

Using difference of squares, the value is 73+27=100.

Practice MCQ

Q46. Simplify: 96 × 125 ÷ 12

A. 800
B. 900
C. 1,000
D. 1,100

Correct Answer: C. 1,000

96×125=12,000 and 12,000÷12=1000.

Practice MCQ

Q47. Find the value of 999 × 54 − 99 × 540.

A. 468
B. 486
C. 504
D. 522

Correct Answer: B. 486

53,946−53,460=486.

Practice MCQ

Q48. Find the value of 125².

A. 15,225
B. 15,425
C. 15,625
D. 15,825

Correct Answer: C. 15,625

12×13=156; append 25 → 15,625.

Practice MCQ

Q49. Find the value of 49 × 51 + 99 × 101.

A. 12,398
B. 12,448
C. 12,498
D. 12,548

Correct Answer: C. 12,498

49×51=2499 and 99×101=9999. Total=12,498.

Practice MCQ

Q50. Find the closest approximate value of: 398.7 ÷ 19.9 + 24.9 × 8.1

A. 200
B. 220
C. 240
D. 260

Correct Answer: B. 220

≈400÷20+25×8=20+200=220.

Practice MCQ

Q51. Round 0.04764 to three significant figures.

A. 0.0475
B. 0.0476
C. 0.0477
D. 0.0480

Correct Answer: B. 0.0476

The next digit after 4, 7 and 6 is 4, so the result is 0.0476.

Practice MCQ

Q52. Round −18.67 to one decimal place.

A. −18.6
B. −18.7
C. −18.8
D. −19.0

Correct Answer: B. −18.7

The hundredths digit is 7, so −18.67 rounds to −18.7.

Practice MCQ

Q53. Simplify: (1/3 + 0.5) × 12

A. 8
B. 9
C. 10
D. 11

Correct Answer: C. 10

1/3+1/2=5/6; 5/6×12=10.

Practice MCQ

Q54. Simplify: 4³ ÷ 2⁴ + √81

A. 11
B. 12
C. 13
D. 14

Correct Answer: C. 13

64÷16+9=4+9=13.

Practice MCQ

Q55. Simplify: √75 − √27

A. √3
B. 2√3
C. 3√3
D. 4√3

Correct Answer: B. 2√3

5√3−3√3=2√3.

Practice MCQ

Q56. Simplify: ∛(−216) + (−3)²

A. −15
B. −3
C. 3
D. 15

Correct Answer: C. 3

−6+9=3.

Practice MCQ

Q57. Find the value of (1−1/2)(1−1/3)...(1−1/15).

A. 1/13
B. 1/14
C. 1/15
D. 1/16

Correct Answer: C. 1/15

The telescoping product leaves 1/15.

Practice MCQ

Q58. Simplify: 37 × 62 + 37 × 38

A. 3,600
B. 3,700
C. 3,800
D. 3,900

Correct Answer: B. 3,700

37(62+38)=37×100=3700.

Practice MCQ

Q59. Find the value of 996 × 1004.

A. 999,884
B. 999,984
C. 1,000,016
D. 1,000,084

Correct Answer: B. 999,984

1000²−4²=1,000,000−16=999,984.

Practice MCQ

Q60. Approximately find: 33.2% of 601 + 12.6% of 799.

A. 250
B. 275
C. 300
D. 325

Correct Answer: C. 300

≈1/3 of600 + 1/8 of800 =200+100=300.

56. Practice MCQs — Batch 4

Chapter 2 Mixed Practice Bank — Q61 to Q80:
This batch combines fractions, decimals, exponents, roots, fast calculation, rounding and estimation.

Practice MCQ

Q61. Simplify: 144 ÷ [18 − (12−6)] + 2³

A. 18
B. 20
C. 22
D. 24

Correct Answer: B. 20

18−6=12, 144÷12=12 and 2³=8. Total=20.

Practice MCQ

Q62. Simplify: 5/6 ÷ (10/9 of 3/4) + 7/8

A. 13/8
B. 15/8
C. 17/8
D. 19/8

Correct Answer: B. 15/8

10/9 of3/4=5/6. Thus the quotient is 1, and 1+7/8=15/8.

Practice MCQ

Q63. Simplify: 0.375 × 64 + 0.625 × 16

A. 30
B. 32
C. 34
D. 36

Correct Answer: C. 34

3/8×64=24 and 5/8×16=10. Total=34.

Practice MCQ

Q64. Simplify: 5⁴ × 5⁻² ÷ 25

A. 1
B. 5
C. 25
D. 125

Correct Answer: A. 1

25=5², so 5⁴⁻²⁻²=5⁰=1.

Practice MCQ

Q65. Simplify: √0.0225 + √2.25

A. 1.55
B. 1.60
C. 1.65
D. 1.70

Correct Answer: C. 1.65

0.15+1.5=1.65.

Practice MCQ

Q66. Simplify: ∛0.008 + ∛27

A. 3.0
B. 3.1
C. 3.2
D. 3.3

Correct Answer: C. 3.2

0.2+3=3.2.

Practice MCQ

Q67. Find the value of 72 × 25 + 32 × 125.

A. 5,400
B. 5,600
C. 5,800
D. 6,000

Correct Answer: C. 5,800

1800+4000=5800.

Practice MCQ

Q68. Simplify: 8,750 ÷ 125 − 375 ÷ 25

A. 45
B. 50
C. 55
D. 60

Correct Answer: C. 55

70−15=55.

Practice MCQ

Q69. Find the value of 97².

A. 9,309
B. 9,409
C. 9,509
D. 9,609

Correct Answer: B. 9,409

(100−3)²=10000−600+9=9409.

Practice MCQ

Q70. Find the value of 115² − 85².

A. 5,000
B. 5,500
C. 6,000
D. 6,500

Correct Answer: C. 6,000

(115−85)(115+85)=30×200=6000.

Practice MCQ

Q71. Find the closest approximate value of: 499.5 × 2.01 + 998 ÷ 49.9

A. 980
B. 1,000
C. 1,020
D. 1,040

Correct Answer: C. 1,020

≈500×2+1000÷50=1000+20=1020.

Practice MCQ

Q72. Round 12.49 to the nearest integer.

A. 11
B. 12
C. 13
D. 14

Correct Answer: B. 12

0.49<0.5, so the nearest integer is 12.

Practice MCQ

Q73. Round 68,749 to the nearest thousand.

A. 68,000
B. 68,700
C. 69,000
D. 70,000

Correct Answer: C. 69,000

The hundreds digit is 7, so round upward to 69,000.

Practice MCQ

Q74. Round 0.0008064 to three significant figures.

A. 0.000805
B. 0.000806
C. 0.000807
D. 0.000810

Correct Answer: B. 0.000806

The next digit after 8,0,6 is 4, so 0.000806.

Practice MCQ

Q75. Simplify: (49.9²−30.1²) ÷ (49.9+30.1)

A. 18.8
B. 19.8
C. 20.8
D. 21.8

Correct Answer: B. 19.8

The expression reduces to 49.9−30.1=19.8.

Practice MCQ

Q76. Approximately find: 19.8% of 251 + 49.9% of 302.

A. 175
B. 190
C. 200
D. 225

Correct Answer: C. 200

≈20% of250 + 50% of300 =50+150=200.

Practice MCQ

Q77. If 2.5 × 6 + ? ÷ 4 = 23, find ?.

A. 24
B. 28
C. 32
D. 36

Correct Answer: C. 32

15+?÷4=23, so ?÷4=8 and ?=32.

Practice MCQ

Q78. Simplify: 3/5 of 75 + 0.4 of 50 + 2³

A. 69
B. 71
C. 73
D. 75

Correct Answer: C. 73

45+20+8=73.

Practice MCQ

Q79. Simplify: (√225 + ∛125) × 2 − 3²

A. 29
B. 31
C. 33
D. 35

Correct Answer: B. 31

(15+5)×2−9=31.

Practice MCQ

Q80. Simplify: 4.8 ÷ 0.12 + 0.25 × 64

A. 52
B. 54
C. 56
D. 58

Correct Answer: C. 56

40+16=56.

57. Practice MCQs — Batch 5

Chapter 2 Mixed Practice Bank — Q81 to Q100:
This final English batch integrates the full Simplification & Approximation chapter.

Practice MCQ

Q81. Simplify: 200 − [48 ÷ {10−(6−2)} + 5²]

A. 163
B. 165
C. 167
D. 169

Correct Answer: C. 167

6−2=4, 10−4=6, 48÷6=8 and 5²=25. Thus 200−33=167.

Practice MCQ

Q82. Simplify: 7/12 of 144 + 1.25 × 16 − √100

A. 90
B. 92
C. 94
D. 96

Correct Answer: C. 94

84+20−10=94.

Practice MCQ

Q83. Simplify: (3 1/3 − 1 5/6) × 6

A. 7
B. 8
C. 9
D. 10

Correct Answer: C. 9

10/3−11/6=3/2; 3/2×6=9.

Practice MCQ

Q84. Simplify: (0.875 + 1/8) × 8

A. 6
B. 7
C. 8
D. 9

Correct Answer: C. 8

0.875=7/8, so the bracket equals 1. Thus answer=8.

Practice MCQ

Q85. Simplify: 3⁵ × 3⁻² ÷ 3²

A. 1
B. 3
C. 9
D. 27

Correct Answer: B. 3

3⁵⁻²⁻²=3=3.

Practice MCQ

Q86. Simplify: √192 − √48

A. 2√3
B. 3√3
C. 4√3
D. 6√3

Correct Answer: C. 4√3

8√3−4√3=4√3.

Practice MCQ

Q87. Simplify: ∛1000 + 10√0.81

A. 17
B. 18
C. 19
D. 20

Correct Answer: C. 19

10+10×0.9=19.

Practice MCQ

Q88. Find the value of 125 × 72 − 25 × 160.

A. 4,500
B. 5,000
C. 5,500
D. 6,000

Correct Answer: B. 5,000

9000−4000=5000.

Practice MCQ

Q89. Find the value of 999 × 101.

A. 99,899
B. 100,899
C. 100,999
D. 101,899

Correct Answer: B. 100,899

999×100+999=100,899.

Practice MCQ

Q90. Find the value of 205 × 195.

A. 39,875
B. 39,925
C. 39,975
D. 40,025

Correct Answer: C. 39,975

200²−5²=40,000−25=39,975.

Practice MCQ

Q91. Find the closest approximate value of: 599.7 ÷ 29.98 + 39.9 × 24.95

A. 980
B. 1,000
C. 1,020
D. 1,040

Correct Answer: C. 1,020

≈600÷30+40×25=20+1000=1020.

Practice MCQ

Q92. Round 84,951 to the nearest hundred.

A. 84,900
B. 85,000
C. 85,100
D. 84,950

Correct Answer: B. 85,000

The tens digit is 5, so the number rounds to 85,000.

Practice MCQ

Q93. Round 8.495 to two decimal places.

A. 8.49
B. 8.50
C. 8.51
D. 8.59

Correct Answer: B. 8.50

The third decimal digit is 5, so 8.49 rounds upward to 8.50.

Practice MCQ

Q94. Round 0.009949 to three significant figures.

A. 0.00994
B. 0.00995
C. 0.00996
D. 0.0100

Correct Answer: B. 0.00995

The next digit after 9,9,4 is 9, so the result is 0.00995.

Practice MCQ

Q95. Simplify: (60.2²−39.8²) ÷ (60.2−39.8)

A. 90
B. 95
C. 100
D. 105

Correct Answer: C. 100

The value becomes 60.2+39.8=100.

Practice MCQ

Q96. Simplify: 12.5% of 800 + 33 1/3% of 300

A. 180
B. 190
C. 200
D. 210

Correct Answer: C. 200

1/8 of800=100 and 1/3 of300=100. Total=200.

Practice MCQ

Q97. If ? ÷ 0.25 − 12 = 28, find ?.

A. 8
B. 10
C. 12
D. 14

Correct Answer: B. 10

?÷0.25=40, so 4?=40 and ?=10.

Practice MCQ

Q98. Simplify: [2³ + √144] × 3/4

A. 12
B. 15
C. 18
D. 20

Correct Answer: B. 15

(8+12)×3/4=20×3/4=15.

Practice MCQ

Q99. Find the value of (1−1/3)(1−1/4)...(1−1/10).

A. 1/10
B. 1/5
C. 2/5
D. 1/2

Correct Answer: B. 1/5

2/3×3/4×...×9/10=2/10=1/5.

Practice MCQ

Q100. Find the closest approximate value of: (79.9 × 25.1) ÷ 10.02

A. 180
B. 190
C. 200
D. 210

Correct Answer: C. 200

≈80×25÷10=200.

1. अध्याय 2 एक नज़र में

Simplification एवं Approximation questions में mathematical accuracy के साथ calculation speed भी महत्वपूर्ण होती है। सबसे अच्छा approach अलग-अलग tricks याद करना नहीं, बल्कि expression की structure पहचानकर shortest valid method चुनना है।

पूरा Chapter Flow:
BODMAS → Brackets एवं Vinculum → Fractions एवं Decimals → Powers एवं Roots → Cancellation एवं Factorisation → Calculation Shortcuts → Rounding एवं Approximation → Estimation एवं Nearest-Value Method → Mixed Problems

Exam Rule:
Shortcut तभी उपयोगी है जब वह mathematical value को सही रखे और operations का correct order follow करे।

2. BODMAS Rule

BODMAS:
B = Brackets
O = Orders — Powers एवं Roots
D/M = Division एवं Multiplication
A/S = Addition एवं Subtraction

बहुत महत्वपूर्ण:
Division हमेशा multiplication से पहले नहीं होती।
Same priority पर division और multiplication left to right solve किए जाते हैं।

इसी प्रकार:
Addition और subtraction की priority समान है तथा इन्हें left to right solve किया जाता है।

उदाहरण:
36÷3×2
=12×2
=24।

3. “Of” का प्रयोग

Basic Meaning:
3/4 of80 = 3/4×80 = 60।

Exam Convention:
Traditional aptitude expressions में स्पष्ट “of” multiplication block को carefully identify करें और surrounding operations के साथ सही क्रम में solve करें।

4. Brackets एवं Nested Expressions

मुख्य नियम:
सबसे पहले innermost grouped expression solve करें और फिर बाहर की ओर बढ़ें।

उदाहरण:
30 − [12 − {8 − (5−2)}]

5−2=3
8−3=5
12−5=7
30−7=23।

Common Trap:
Bracket के shape को independent universal priority न मानें। सही principle innermost first है।

5. Vinculum

मुख्य नियम:
एक ही vinculum के नीचे के सभी terms को एक grouped expression की तरह solve करें।

उदाहरण:
20 − 8−3

8−3=5
20−5=15।

Exam Tip:
Printed paper में ध्यान दें कि vinculum कितने terms के ऊपर है।

6. Bracket के पहले Minus Sign

Sign Rules:
−(a+b)=−a−b
−(a−b)=−a+b

उदाहरण:
25−(8−13)
=25−(−5)
=30।

Exam Trap:
a−(−b)=a+b।

7. Mixed Fractions

Conversion:
a b/c = (ac+b)/c

उदाहरण:
3 2/5
=(3×5+2)/5
=17/5।

8. Fractions का Addition एवं Subtraction

Rule:
Different denominators वाले fractions के लिए common denominator चाहिए।

उदाहरण:
5/6−1/4
=10/12−3/12
=7/12।

Fast Method:
a/b ± c/d = (ad ± bc)/bd

9. Fractions का Multiplication एवं Division

Multiplication:
a/b×c/d=ac/bd

Division:
a/b÷c/d=a/b×d/c

Golden Shortcut:
Multiplication से पहले cancellation करें।

Exam Trap:
Fraction division में केवल divisor को reciprocal में बदलें।

10. Cancellation Rule

सबसे महत्वपूर्ण:
Cancellation factors के बीच होती है, + या − से जुड़े terms के बीच नहीं।

उदाहरण:
18/35×14/27
→2/3×2/5
=4/15।

11. Decimal Addition एवं Subtraction

Rule:
Numbers को decimal point के अनुसार align करें।

उदाहरण:
12.5+3.075−0.62
=14.955।

12. Decimal Multiplication

Rule:
पहले integers की तरह multiply करें और फिर total decimal places के अनुसार decimal point लगाएँ।

उदाहरण:
0.24×0.5=0.12।

13. Decimal Division

Rule:
Dividend एवं divisor दोनों के decimal को समान places shift करके divisor को integer बनाएँ।

उदाहरण:
6.24÷0.8
=62.4÷8
=7.8।

14. महत्वपूर्ण Fraction-Decimal Equivalents

Fraction	Decimal	Fraction	Decimal
1/2	0.5	1/8	0.125
1/4	0.25	3/8	0.375
3/4	0.75	5/8	0.625
1/5	0.2	7/8	0.875
2/5	0.4	1/10	0.1
3/5	0.6	1/20	0.05
4/5	0.8	1/25	0.04

15. महत्वपूर्ण Decimal Shortcuts

याद रखें:
×0.5=÷2
÷0.5=×2

×0.25=÷4
÷0.25=×4

×0.125=÷8
÷0.125=×8

16. Exponent Laws

Core Laws:
a^m×aⁿ=a^m+n
a^m÷aⁿ=a^m−n
(a^m)ⁿ=a^mn
a⁰=1
a⁻ⁿ=1/aⁿ

Exam Trap:
Negative exponent का अर्थ reciprocal है, negative answer नहीं।

17. Negative Base और Brackets

महत्वपूर्ण अंतर:
(−3)²=9
लेकिन
−3²=−9

18. Square Roots

Relation:
Real a के लिए √(a²)=|a|

Examples:
√144=12
√625=25

Exam Trap:
√(a+b) generally √a+√b नहीं होता।

19. Square Root Simplification

उदाहरण:
√72=√(36×2)=6√2

√200=√(100×2)=10√2

20. Like Radicals

उदाहरण:
√50+√8
=5√2+2√2
=7√2।

21. Cube Roots

Relation:
∛(a³)=a

Examples:
∛216=6
∛(−125)=−5

22. Important Perfect Squares एवं Cubes

Perfect Squares:
4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 625, 900

Perfect Cubes:
1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1728, 3375, 8000

23. Difference of Squares

Identity:
a²−b²=(a−b)(a+b)

उदाहरण:
58²−42²
=(58−42)(58+42)
=16×100
=1600।

24. Convenient Base के आसपास Numbers

उदाहरण:
103×97
=(100+3)(100−3)
=9991।

उदाहरण:
48×52
=2500−4
=2496।

25. Common Factor

उदाहरण:
37×48+37×52
=37(48+52)
=37×100
=3700।

26. 5, 25 एवं 125 से Multiplication

Fast Conversions:
×5=×10÷2
×25=×100÷4
×125=×1000÷8

27. 5, 25 एवं 125 से Division

Fast Conversions:
÷5=×2÷10
÷25=×4÷100
÷125=×8÷1000

28. 9, 99 एवं 999 से Multiplication

Patterns:
9=10−1
99=100−1
999=1000−1

उदाहरण:
47×99=4700−47=4653।

29. 11 से Multiplication

उदाहरण:
43×11=473।

Carry Example:
78×11=858।

30. 5 पर समाप्त Number का Square

Shortcut:
5 से पहले वाले part n को n+1 से multiply करें और अंत में25 लगाएँ।

Examples:
75²=5625
115²=13225

31. 100 के पास Squares

उदाहरण:
98²
=(100−2)²
=10000−400+4
=9604।

32. Doubling और Halving

उदाहरण:
25×48
=50×24
=100×12
=1200।

33. Telescoping Products

उदाहरण:
(1−1/2)(1−1/3)...(1−1/10)
=1/2×2/3×...×9/10
=1/10।

34. Approximation

Examples:
49.92≈50
199.7≈200
3.98≈4

Exam Rule:
Approximation तभी करें जब question और option gap इसकी अनुमति दें।

35. Basic Rounding Rule

Rule:
Next digit 0–4 → retained digit unchanged।
Next digit 5–9 → retained digit में1 जोड़ें।

36. Whole Numbers का Rounding

Examples:
467 → nearest ten = 470
6,847 → nearest hundred = 6,800
36,680 → nearest thousand = 37,000

37. Decimal Places

उदाहरण:
12.746 को two decimal places तक round करने पर 12.75।

38. Significant Figures

Rule:
Counting first non-zero digit से शुरू होती है।

उदाहरण:
0.004586 को 3 significant figures तक → 0.00459।

39. Maximum Rounding Error

Rule:
Maximum rounding error = rounding unit का आधा।

Examples:
Nearest1 →0.5
Nearest10 →5
Nearest100 →50
Nearest0.1 →0.05

40. Compatible Numbers

उदाहरण:
598÷29.9
≈600÷30
=20।

उदाहरण:
398×24.9
≈400×25
=10,000।

41. Percentage Estimation

Useful Equivalents:
50%=1/2
25%=1/4
75%=3/4
20%=1/5
12.5%=1/8

उदाहरण:
24.9% of803
≈25% of800
=200।

42. Balanced Estimation

उदाहरण:
49.8×20.2
≈50×20
=1000।

43. Division Estimation

उदाहरण:
799÷39.8
≈800÷40
=20।

Exam Trap:
Denominator को बहुत aggressively round न करें।

44. Option-Gap Analysis

Decision Rule:
Options दूर हों → rough estimate।
Options close हों → अधिक precision।
Options अत्यंत close हों → exact calculation की आवश्यकता हो सकती है।

45. Order-of-Magnitude Check

उदाहरण:
198×51≈200×50=10,000।

इसलिए 1,000 या100,000 जैसा answer तुरंत suspicious होगा।

46. Two-Stage Estimation

Stage 1:
Rough compatible numbers से estimate निकालें।

Stage 2:
यदि दो options possible हों तो अधिक precision के साथ refine करें।

47. Approximation से पहले Exact Shortcut

Golden Rule:
Awkward numbers को round करने से पहले cancellation, factorisation या identity check करें।

उदाहरण:
(59.9²−40.1²)/(59.9+40.1)
=59.9−40.1
=19.8।

48. Mixed-Problem Strategy

Three-Level Method:
Level 1 — Structure: Brackets, powers, roots, fractions, decimals और approximation clues पहचानें।

Level 2 — Simplification: Cancellation, identities, conversions और BODMAS apply करें।

Level 3 — Verification: Sign, magnitude और options check करें।

49. Chapter-Wide Common Traps

इन गलतियों से बचें:
• Division को हमेशा multiplication से पहले करना।
• Addition को हमेशा subtraction से पहले करना।
• Outer bracket पहले solve करना।
• Vinculum miss करना।
• Minus bracket में signs गलत बदलना।
• Terms को cancel करना।
• Fraction division में दोनों fractions invert करना।
• Decimal point गलत place करना।
• −a² और(−a)² को समान मानना।
• √(a+b)=√a+√b मानना।
• Identity available होने पर भी squares separately calculate करना।
• Exact question को approximate करना।
• Close options में rough estimation करना।
• Approximation के बाद BODMAS भूलना।

50. Final 30-Second Revision Formula Sheet

BODMAS:
Brackets → Orders → D/M left to right → A/S left to right

Fraction Division:
a/b÷c/d=a/b×d/c

Exponent Laws:
a^maⁿ=a^m+n
a^m/aⁿ=a^m−n
(a^m)ⁿ=a^mn

Difference of Squares:
a²−b²=(a−b)(a+b)

Fast Multipliers:
×25=×100÷4
×125=×1000÷8
×99=×100−original number
×999=×1000−original number

Ending-in-5 Square:
Preceding part × successor, फिर25 append करें।

Approximation:
Option gap देखें → compatible numbers चुनें → BODMAS रखें → magnitude verify करें।

Final Exam Reminder:
सबसे तेज method वही है जो सबसे कम steps में सही answer दे।

51. सत्यापित Previous-Year Questions — Part A

Chapter 2 PYQ Bank:
इन questions में BODMAS, brackets, vinculum, fractions, decimals, powers, roots तथा approximation का chapter-wide revision शामिल है।

SSC CGL PYQ BODMAS 24 सितंबर 2024 · Tier-I · Shift II

प्रश्न 1. सरल कीजिए: 133 ÷ 19 × 3 − 48 × 2 ÷ 24 + 841 ÷ (45−16)

A. 46
B. 21
C. 12
D. 42

सही उत्तर: A. 46

45−16=29।
133÷19×3=7×3=21।
48×2÷24=4।
841÷29=29।

अतः:
21−4+29=46।

RRB NTPC PYQ Nested Brackets 18 जून 2026 · UG CBT-I · Shift III

प्रश्न 2. सरल कीजिए: 156 ÷ [12 + {7 × (15−9) − 28}]

A. 8
B. 10
C. 6
D. 12

सही उत्तर: C. 6

15−9=6।
7×6−28=42−28=14।
12+14=26।

अतः:
156÷26=6।

SSC CHSL PYQ Vinculum & Brackets 15 अप्रैल 2021 · Tier-I · Shift III

प्रश्न 3. सरल कीजिए: 45 − [36 − {29 − (25 − 7+4)}]

A. 24
B. 22
C. 26
D. 28

सही उत्तर: A. 24

सबसे पहले vinculum:
7+4=11।

25−11=14।
29−14=15।
36−15=21।
45−21=24।

SSC CGL PYQ Fractions & Of 24 अगस्त 2021 · Tier-I · Shift II

प्रश्न 4. सरल कीजिए: 7/12 ÷ (1/10 of 2/3) − 5/3 × 9/10 + 5/8 ÷ (3/4 of 2/3)

A. −4
B. 3 23/36
C. 8 1/2
D. 7 29/36

सही उत्तर: C. 8 1/2

1/10 of2/3=1/15 तथा3/4 of2/3=1/2।

अब:
7/12÷1/15 − 5/3×9/10 + 5/8÷1/2
=35/4−3/2+5/4
=17/2
=8 1/2।

SSC CHSL PYQ BODMAS 1 जुलाई 2024 · Tier-I · Shift I

प्रश्न 5. सरल कीजिए: 3 + 28 ÷ 35 × 15 + 4 − 3 × 4

A. 26
B. 10
C. 7
D. 64

सही उत्तर: C. 7

28÷35×15=12 तथा3×4=12।

अतः:
3+12+4−12=7।

SSC CHSL PYQ Bracket Operations 1 जुलाई 2024 · Tier-I · Shift III

प्रश्न 6. सरल कीजिए: (36÷6)÷3 + (18÷9)×4 − (12÷6)×(5÷2)

A. 10
B. 15
C. 21
D. 5

सही उत्तर: D. 5

(36÷6)÷3=2।
(18÷9)×4=8।
(12÷6)×(5÷2)=5।

अतः:
2+8−5=5।

SSC CHSL PYQ Fractions & Of 5 जुलाई 2024 · Tier-I · Shift II

प्रश्न 7. सरल कीजिए:

([1/2 ÷ (3/4 of 5/6)] ÷ [1/2 ÷ 3/4 × 5/6]) + (2+2×2)/(2÷2×2)

A. 4
B. 121/25
C. 111/25
D. 75/36

सही उत्तर: C. 111/25

3/4 of5/6=5/8।
1/2÷5/8=4/5।

दूसरे denominator में:
1/2÷3/4×5/6=5/9।

इसलिए first part=36/25।

Second part=(2+4)/(1×2)=3।

Total=36/25+3=111/25।

SSC CHSL PYQ BODMAS & Of 2 जुलाई 2024 · Tier-I · Shift II

प्रश्न 8. सरल कीजिए: (3−3×3+3÷3+3×5) × 2 of 5 + (2+2÷2+2×2−2)

A. 105
B. 102
C. 106
D. 100

सही उत्तर: A. 105

पहला bracket:
3−9+1+15=10।

2 of5=10।
इसलिए first part=100।

दूसरा bracket:
2+1+4−2=5।

Total=105।

SSC CGL PYQ Mixed Fractions 18 सितंबर 2024 · Tier-I · Shift I

प्रश्न 9. सरल कीजिए: [(5 1/2 − 3 1/3) of 1 5/13 + 1 − 2 × 3 5/2 ÷ 2 3/4]

A. 0
B. 11/2
C. −2
D. 3 1/2

सही उत्तर: A. 0

5 1/2−3 1/3=13/6।

1 5/13=18/13।
इसलिए 13/6×18/13=3।

3 5/2=11/2 तथा2 3/4=11/4।
2×11/2÷11/4=4।

अतः:
3+1−4=0।

SSC MTS PYQ Fractions & Of 13 सितंबर 2023 · Shift II

प्रश्न 10. सरल कीजिए: (5/3 + 6/5 ÷ 18/5) of 5/12 − (5/6 ÷ 5/12) of 5/12 + 2/3 of 3/2

A. 1
B. 5/6
C. 6/5
D. 0

सही उत्तर: A. 1

6/5÷18/5=1/3।
इसलिए पहला bracket=2।
First part=5/6।

5/6÷5/12=2।
Second part=5/6।

2/3 of3/2=1।

अतः:
5/6−5/6+1=1।

SSC MTS PYQ Decimal BODMAS 6 सितंबर 2023 · Shift I

प्रश्न 11. सरल कीजिए: 45 − 22÷2 + 12 + 70÷35 + 0.4÷0.8 + 1.5÷3 + 1

A. 50
B. 50.5
C. 48.5
D. 54.5

सही उत्तर: A. 50

22÷2=11
70÷35=2
0.4÷0.8=0.5
1.5÷3=0.5।

अतः:
45−11+12+2+0.5+0.5+1=50।

SSC MTS PYQ Surds & Mixed Fractions 8 सितंबर 2023 · Shift II

प्रश्न 12. सरल कीजिए:

[24√45 − 16√20 + √245 − 47√5] ÷ [3 1/5 + 1 2/5 − 2 1/6 − 2 1/5 − 5 2/5 + 3 1/6]

A. 0
B. 3
C. 1
D. 2

सही उत्तर: A. 0

√45=3√5, √20=2√5 तथा√245=7√5।

Numerator:
72√5−32√5+7√5−47√5=0।

Denominator=−2।

अतः:
0÷(−2)=0।

SSC MTS PYQ Square Root 3 मई 2023 · Shift II

प्रश्न 13. √[((13²−8²)×5)+4] का मान ज्ञात करें।

A. 23
B. 26
C. 24
D. 22

सही उत्तर: A. 23

13²−8²=169−64=105।

105×5+4=529।

√529=23।

RRB Group D PYQ Square Root of Decimal 30 अगस्त 2022 · Shift III

प्रश्न 14. √1.0201 का मान ज्ञात करें।

A. 10.1
B. 101
C. 1.01
D. 1.02

सही उत्तर: C. 1.01

1.0201=10201/10000।

101²=10201 तथा100²=10000।

अतः:
√1.0201=1.01।

RRB NTPC PYQ Cube Root 26 जुलाई 2021 · CBT-I · Shift I

प्रश्न 15. ∛150 किन दो consecutive integers के बीच स्थित है?

A. 6 और7
B. 4 और5
C. 7 और8
D. 5 और6

सही उत्तर: D. 5 और6

5³=125 तथा6³=216।

125<150<216।

इसलिए:
5<∛150<6।

अतः answer=5 और6।

SSC MTS PYQ Powers 22 जुलाई 2022 · Shift I

प्रश्न 16. Missing value ज्ञात करें: 2 × 324 × ? = 9² × 22² × 6

A. 359
B. 364
C. 363
D. 366

सही उत्तर: C. 363

?=(9²×22²×6)/(2×324)।

324=18² और9²/18²=1/4।

अतः:
?=484×6/8
=484×3/4
=363।

RRB Group D PYQ Exponent Laws 8 दिसंबर 2025 · Shift III

प्रश्न 17. सरल कीजिए:

[8²¹ ÷ 4²⁸ × 2⁵] ÷ [(4¹⁴)^1/7 × 8²]

A. 2
B. 4
C. 8
D. 16

सही उत्तर: B. 4

सभी terms को base2 में लिखें:
8²¹=2⁶³
4²⁸=2⁵⁶
(4¹⁴)^1/7=2⁴
8²=2⁶।

अतः:
2^{63−56+5−4−6}=2²=4।

RRB Group D PYQ Exponent Factorisation 1 दिसंबर 2025 · Shift I

प्रश्न 18. सरल कीजिए: [5^3x+4 + 125^x+1] ÷ [125^x+1 − 5^3x+2]

A. 8
B. 7.5
C. 5
D. 10

सही उत्तर: B. 7.5

125^x+1=5^3x+3।

Numerator एवं denominator से5^3x+2 common लें।

Expression:
=(5²+5)/(5−1)
=30/4
=7.5।

SSC MTS PYQ Approximation 6 जुलाई 2022 · Shift III

प्रश्न 19. 305.03 ÷ 61.09 × 11.47 का closest approximate value कौन-सा है?

A. 57
B. 47
C. 12
D. 63

सही उत्तर: A. 57

305.03÷61.09 लगभग5 है।

इसलिए:
5×11.47≈57.35।

Nearest option=57।

RRB Group D PYQ Nearest-Value Approximation 5 सितंबर 2022 · Shift I

प्रश्न 20. 4.49 ÷ 1.49 − 3.33 × 3 + 4.49 का closest approximate value ज्ञात करें।

A. −2.5
B. −4.5
C. 4.5
D. 2.5

सही उत्तर: A. −2.5

4.49÷1.49≈3.01।
3.33×3=9.99।

अतः:
3.01−9.99+4.49≈−2.49।

Closest option=−2.5।

52. सत्यापित Previous-Year Questions — Part B

Chapter 2 PYQ Bank — प्रश्न 21 से 40:
इस भाग में advanced simplification, approximation, nearest-value method, decimal operations, powers, roots, identities तथा mixed calculations पर अधिक focus रखा गया है।

SSC CGL PYQ Fractions & Cancellation 18 अगस्त 2021 · Tier-I · Shift III

प्रश्न 21. सरल कीजिए: 441 ÷ [270 ÷ 3/7 + (17 ÷ 1/3) − (8 1/2 − 5/2)]

A. 29/75
B. 49/75
C. 39/75
D. 19/75

सही उत्तर: B. 49/75

270÷3/7=630।
17÷1/3=51।
8 1/2−5/2=6।

Bracket=630+51−6=675।

अतः:
441/675=49/75।

RRB Group D PYQ Nearest-Value Estimation 30 सितंबर 2022 · Shift I

प्रश्न 22. 2.33 − 4.12 + 6.13 × 11.3 का closest approximate value ज्ञात करें।

A. 106
B. 64
C. 39
D. 43

सही उत्तर: B. 64

2.33≈2, 4.12≈4, 6.13≈6 तथा11.3≈11।

अतः:
2−4+6×11
=−2+66
=64।

RRB Group D PYQ Compatible Numbers 26 अगस्त 2022 · Shift I

प्रश्न 23. 44.999 ÷ 8.998 + 23.996 ÷ 11.998 − 7.009 + 8.002 × 1.998 का closest approximate value ज्ञात करें।

A. 28
B. 16
C. 20
D. 24

सही उत्तर: B. 16

Approximate expression:
45÷9+24÷12−7+8×2

=5+2−7+16
=16।

RRB Group D PYQ Nearest-Option Method 15 सितंबर 2022 · Shift II

प्रश्न 24. 17.99 − 16.02 + 19.89 × 8.19 का closest approximate value ज्ञात करें।

A. 122
B. 330
C. 42
D. 162

सही उत्तर: D. 162

17.99≈18, 16.02≈16, 19.89≈20 तथा8.19≈8।

अतः:
18−16+20×8
=2+160
=162।

RRB NTPC PYQ Approximation with Powers 17 जून 2022 · CBT-II Level 3 · Shift III

प्रश्न 25. 5.01 + (3.01 × 1.99²) × 4 + 6.01 ÷ 2.03 का closest approximate value ज्ञात करें।

A. 56
B. 65
C. 57
D. 52

सही उत्तर: A. 56

5.01≈5, 3.01≈3, 1.99≈2, 6.01≈6 तथा2.03≈2।

अब:
5+(3×2²)×4+6÷2
=5+48+3
=56।

RRB NTPC PYQ Percentage Approximation 16 जून 2022 · CBT-II Level 2 · Shift I

प्रश्न 26. 44.97% of 226 + 55.03 × 4.98 − ? = 140 में ? का closest value ज्ञात करें।

A. 25
B. 237
C. 508
D. 120

सही उत्तर: B. 237

44.97%≈45%, 55.03≈55 तथा4.98≈5।

45% of226≈102 तथा55×5=275।

इसलिए:
102+275−?≈140
?≈237।

RRB NTPC PYQ Identity & Approximation 8 जनवरी 2021 · CBT-I · Shift I

प्रश्न 27. (2.697+0.498)² − (2.697−0.498)² का approximate value ज्ञात करें।

A. 2.00
B. 5.37
C. 2.199
D. 3.195

सही उत्तर: B. 5.37

Identity:
(a+b)²−(a−b)²=4ab।

=4×2.697×0.498
=5.372424।

Approximate value=5.37।

RRB Group D PYQ Decimal Approximation 30 अगस्त 2022 · Shift II

प्रश्न 28. 17.89 − 0.0123 + 2.21 × 3.63 का closest approximate value ज्ञात करें।

A. 42
B. 15
C. 26
D. 36

सही उत्तर: C. 26

2.21×3.63=8.0223।

17.89−0.0123+8.0223=25.9।

Closest option=26।

RRB Group D PYQ Roots & Approximation 22 अगस्त 2022 · Shift I

प्रश्न 29. (√360 + 12 ÷ 6 × 3 − √170) ÷ 2 का closest approximate value ज्ञात करें।

A. 6
B. 4
C. 8
D. 5

सही उत्तर: A. 6

√360≈18.97 तथा√170≈13.03।
12÷6×3=6।

अतः:
(18.97+6−13.03)÷2
≈6।

RRB Group D PYQ Roots & BODMAS 29 अगस्त 2022 · Shift III

प्रश्न 30. (√142 + 52 ÷ 26 × 5 − √80) × 2 का closest approximate value ज्ञात करें।

A. 32
B. 30
C. 20
D. 26

सही उत्तर: D. 26

√142≈11.9 तथा√80≈8.9।
52÷26×5=10।

अतः:
(11.9+10−8.9)×2
=13×2
=26।

RRB Group D PYQ Mixed Decimal Approximation 18 सितंबर 2022 · Shift II

प्रश्न 31. 48.9 × 3.95 − 2.97 + 17.86 का closest approximate option ज्ञात करें।

A. 125
B. 140
C. 211
D. 250

सही उत्तर: C. 211

Expression का value लगभग208.045 है।

दिए गए options में 211 सबसे निकट है।

RRB Group D PYQ BODMAS Approximation 14 सितंबर 2022 · Shift III

प्रश्न 32. 5.18 × 4 + 2.06 × 5 − 10 ÷ 2 + 1 का closest approximate value ज्ञात करें।

A. 15
B. 40
C. 26
D. 30

सही उत्तर: C. 26

5.18≈5 तथा2.06≈2।

5×4+2×5−10÷2+1
=20+10−5+1
=26।

RRB Group D PYQ Mixed Approximation 22 सितंबर 2022 · Shift I

प्रश्न 33. 104.96 + 120.96 + 103.16 − 12.89 × 2.04 + 124.93 ÷ 5.1 का closest approximate value ज्ञात करें।

A. 330
B. 340
C. 328
D. 334

सही उत्तर: C. 328

Expression का value लगभग327.3 है।

Nearest available option=328।

RRB Group D PYQ Fast Approximation 2 सितंबर 2022 · Shift I

प्रश्न 34. 4.98 × 2 + 1.96 × 4 − 8 ÷ 2 + 1 का closest approximate value ज्ञात करें।

A. 20
B. 12
C. 18
D. 15

सही उत्तर: D. 15

4.98≈5 तथा1.96≈2।

5×2+2×4−8÷2+1
=10+8−4+1
=15।

RRB NTPC PYQ Mixed Fractions & Cancellation 21 जून 2025 · Graduate CBT-I · Shift II

प्रश्न 35. सरल कीजिए: 2 2/9 × 2 2/3 × 567 + 8 3/4

A. 3372.15
B. 3364.35
C. 3368.75
D. 3347.25

सही उत्तर: C. 3368.75

2 2/9=20/9, 2 2/3=8/3 तथा8 3/4=35/4।

20/9×8/3×567=3360।
35/4=8.75।

Total=3368.75।

RRB Group D PYQ Decimal BODMAS 22 दिसंबर 2025 · Shift I

प्रश्न 36. सरल कीजिए: 0.7 × 72 ÷ 14 + 6.25 − 8.34 × 0.15 + 5.95

A. 21.549
B. 12.526
C. 14.823
D. 14.549

सही उत्तर: D. 14.549

0.7×72÷14=3.6।
8.34×0.15=1.251।

अतः:
3.6+6.25−1.251+5.95
=15.8−1.251
=14.549।

RRB NTPC PYQ Identity & Cancellation 7 मार्च 2021 · CBT-I · Shift I

प्रश्न 37. सरल कीजिए: (4.2×4.2 − 1.9×1.9) ÷ (2.3×6.1)

A. 3
B. 2
C. 1
D. 4

सही उत्तर: C. 1

Numerator:
4.2²−1.9²
=(4.2−1.9)(4.2+1.9)
=2.3×6.1।

Denominator भी2.3×6.1 है।

अतः answer=1।

RRB Group D PYQ Balanced Approximation 20 सितंबर 2022 · Shift III

प्रश्न 38. 239.99 × 20.01 − 99.99 × 30.01 का closest approximate value ज्ञात करें।

A. 1805
B. 1815
C. 1800
D. 1810

सही उत्तर: C. 1800

239.99≈240, 20.01≈20, 99.99≈100 तथा30.01≈30।

अतः:
240×20−100×30
=4800−3000
=1800।

RRB Group D PYQ Percentage Approximation 11 अक्टूबर 2022 · Shift II

प्रश्न 39. 20.01% of 320.002 + 121.99 का closest approximate value ज्ञात करें।

A. 162
B. 186
C. 154
D. 174

सही उत्तर: B. 186

20.01% of320.002 लगभग64 है।
121.99≈122।

अतः:
64+122≈186।

SSC MTS PYQ Advanced Approximation 11 फरवरी 2026 · Shift II

प्रश्न 40. Approximate value ज्ञात करें:

(76.91×143.97)/(7.07×12.01) − (3.93²×√195.88)/(6.93×8.03^1/3)

A. 145
B. 105
C. 116
D. 98

सही उत्तर: C. 116

Approximate करें:
76.91≈77, 143.97≈144, 7.07≈7, 12.01≈12,
3.93≈4, √195.88≈14, 6.93≈7 तथा8.03^1/3≈2।

First term:
77×144÷(7×12)=132।

Second term:
4²×14÷(7×2)=16।

अतः:
132−16=116।

53. Practice MCQs — Batch 1

Chapter 2 Mixed Practice Bank — प्रश्न 1 से 20:
इस batch में BODMAS, brackets, fractions, decimals, powers, roots, cancellation, identities, calculation shortcuts, percentages तथा approximation का मिश्रित अभ्यास शामिल है।

Practice MCQ

प्रश्न 1. सरल कीजिए: 72 ÷ 8 × 3 + 5² − 7

A. 41
B. 43
C. 45
D. 47

सही उत्तर: C. 45

72÷8×3=9×3=27 तथा 5²=25। अतः 27+25−7=45।

Practice MCQ

प्रश्न 2. सरल कीजिए: [48 ÷ (9−3) + 2³] × 2

A. 24
B. 28
C. 30
D. 32

सही उत्तर: D. 32

9−3=6, 48÷6=8 और 2³=8। इसलिए bracket=16 तथा 16×2=32।

Practice MCQ

प्रश्न 3. सरल कीजिए: 3/4 of 96 + 2.5 × 8 − √121

A. 77
B. 79
C. 81
D. 83

सही उत्तर: C. 81

3/4 of96=72, 2.5×8=20 तथा √121=11। अतः 72+20−11=81।

Practice MCQ

प्रश्न 4. सरल कीजिए: (1.25 + 3/4) ÷ 0.5

A. 3
B. 4
C. 5
D. 6

सही उत्तर: B. 4

3/4=0.75। इसलिए 1.25+0.75=2 और 2÷0.5=4।

Practice MCQ

प्रश्न 5. सरल कीजिए: (62²−38²) ÷ (62+38)

A. 20
B. 22
C. 24
D. 26

सही उत्तर: C. 24

a²−b²=(a−b)(a+b)। इसलिए expression=62−38=24।

Practice MCQ

प्रश्न 6. सरल कीजिए: 84 ÷ 7 + 0.125 × 64 + ∛216

A. 24
B. 26
C. 28
D. 30

सही उत्तर: B. 26

84÷7=12, 0.125×64=8 तथा ∛216=6। Total=26।

Practice MCQ

प्रश्न 7. 49.7 × 19.8 + 100.2 ÷ 5.01 का closest approximate value ज्ञात करें।

A. 900
B. 1000
C. 1100
D. 1200

सही उत्तर: B. 1000

49.7≈50, 19.8≈20, 100.2≈100 तथा 5.01≈5। अनुमानित value≈1020 है; दिए गए options में 1000 सबसे निकट है।

Practice MCQ

प्रश्न 8. सरल कीजिए: 25% of 480 + 3/5 of 150 − 32

A. 168
B. 174
C. 178
D. 182

सही उत्तर: C. 178

25% of480=120 तथा 3/5 of150=90। अतः 120+90−32=178।

Practice MCQ

प्रश्न 9. सरल कीजिए: 5³ × 5⁻¹ ÷ 5

A. 1
B. 5
C. 25
D. 125

सही उत्तर: B. 5

5³⁻¹⁻¹=5¹=5।

Practice MCQ

प्रश्न 10. सरल कीजिए: √288 − √32

A. 4√2
B. 6√2
C. 8√2
D. 10√2

सही उत्तर: C. 8√2

√288=12√2 तथा √32=4√2। अतः difference=8√2।

Practice MCQ

प्रश्न 11. सरल कीजिए: (2 1/2 + 1.75) × 4 − 3²

A. 6
B. 8
C. 10
D. 12

सही उत्तर: B. 8

2 1/2=2.5। 2.5+1.75=4.25; 4.25×4=17। फिर 17−9=8।

Practice MCQ

प्रश्न 12. सरल कीजिए: 0.6 ÷ 0.15 + 2.4 × 1.25

A. 6
B. 7
C. 8
D. 9

सही उत्तर: B. 7

0.6÷0.15=4 तथा 2.4×1.25=3। अतः answer=7।

Practice MCQ

प्रश्न 13. 47 × 99 + 16 × 125 का मान ज्ञात करें।

A. 6553
B. 6603
C. 6653
D. 6703

सही उत्तर: C. 6653

47×99=4653 तथा 16×125=2000। Total=6653।

Practice MCQ

प्रश्न 14. 103 × 97 + 48 × 52 का मान ज्ञात करें।

A. 12,387
B. 12,437
C. 12,487
D. 12,537

सही उत्तर: C. 12,487

103×97=9991 तथा 48×52=2496। Total=12,487।

Practice MCQ

प्रश्न 15. लगभग मान ज्ञात करें: 19.9% of 501 + 24.8% of 399

A. 180
B. 190
C. 200
D. 210

सही उत्तर: C. 200

19.9%≈20% of500=100 तथा 24.8%≈25% of400=100। Total≈200।

Practice MCQ

प्रश्न 16. सरल कीजिए: [2⁵ + √196] ÷ ∛64

A. 10
B. 11
C. 11 1/2
D. 12

सही उत्तर: C. 11 1/2

32+14=46 तथा ∛64=4। इसलिए 46÷4=11 1/2।

Practice MCQ

प्रश्न 17. सरल कीजिए: 1/2 ÷ (3/4 of 2/3) + 5/6

A. 7/6
B. 3/2
C. 11/6
D. 13/6

सही उत्तर: C. 11/6

3/4 of2/3=1/2। अतः 1/2÷1/2=1 और 1+5/6=11/6।

Practice MCQ

प्रश्न 18. सरल कीजिए: (75²−25²) ÷ (75−25)

A. 50
B. 75
C. 100
D. 125

सही उत्तर: C. 100

Difference of squares से expression=75+25=100।

Practice MCQ

प्रश्न 19. 23 × 999 − 230 × 99 का मान ज्ञात करें।

A. 187
B. 197
C. 207
D. 217

सही उत्तर: C. 207

230×99=23×990। अतः 23(999−990)=23×9=207।

Practice MCQ

प्रश्न 20. 299.8 × 4.02 ÷ 19.9 का closest approximate value ज्ञात करें।

A. 50
B. 60
C. 70
D. 80

सही उत्तर: B. 60

299.8≈300, 4.02≈4 तथा 19.9≈20। अतः 300×4÷20=60।

54. Practice MCQs — Batch 2

Chapter 2 Mixed Practice Bank — प्रश्न 21 से 40:
इस batch में nested brackets, rounding, significant figures, exponents, roots, decimal calculations तथा approximation पर मिश्रित अभ्यास है।

Practice MCQ

प्रश्न 21. सरल कीजिए: 150 − [36 ÷ (9−3) + 4²]

A. 124
B. 126
C. 128
D. 130

सही उत्तर: C. 128

9−3=6, 36÷6=6 तथा 4²=16। Bracket=22। इसलिए 150−22=128।

Practice MCQ

प्रश्न 22. 5,876 को nearest hundred तक round करें।

A. 5,800
B. 5,900
C. 6,000
D. 5,870

सही उत्तर: B. 5,900

Tens digit 7 है, इसलिए hundreds digit बढ़ेगा। Answer=5,900।

Practice MCQ

प्रश्न 23. 0.006384 को three significant figures तक round करें।

A. 0.00630
B. 0.00638
C. 0.00639
D. 0.00640

सही उत्तर: B. 0.00638

पहले three significant digits 6,3,8 हैं और next digit 4 है। इसलिए answer=0.00638।

Practice MCQ

प्रश्न 24. सरल कीजिए: (−4)² − 4²

A. −32
B. 0
C. 16
D. 32

सही उत्तर: B. 0

(−4)²=16 तथा 4²=16। अतः 16−16=0।

Practice MCQ

प्रश्न 25. सरल कीजिए: (1 1/2 + 1 1/4) ÷ 1/2

A. 9/2
B. 5
C. 11/2
D. 6

सही उत्तर: C. 11/2

3/2+5/4=11/4। अब 11/4÷1/2=11/4×2=11/2।

Practice MCQ

प्रश्न 26. सरल कीजिए: √98 + √8

A. 7√2
B. 8√2
C. 9√2
D. 10√2

सही उत्तर: C. 9√2

√98=7√2 तथा √8=2√2। Total=9√2।

Practice MCQ

प्रश्न 27. ∛343 का मान ज्ञात करें।

A. 5
B. 6
C. 7
D. 8

सही उत्तर: C. 7

7³=343। इसलिए ∛343=7।

Practice MCQ

प्रश्न 28. 84 × 25 का मान ज्ञात करें।

A. 2,000
B. 2,050
C. 2,100
D. 2,200

सही उत्तर: C. 2,100

×25=×100÷4। इसलिए 84×25=8400÷4=2100।

Practice MCQ

प्रश्न 29. 6,250 ÷ 125 का मान ज्ञात करें।

A. 40
B. 45
C. 50
D. 55

सही उत्तर: C. 50

÷125=×8÷1000। इसलिए 6250×8÷1000=50।

Practice MCQ

प्रश्न 30. 36 × 99 का मान ज्ञात करें।

A. 3,464
B. 3,564
C. 3,664
D. 3,764

सही उत्तर: B. 3,564

36×99=36×(100−1)=3600−36=3564।

Practice MCQ

प्रश्न 31. 85² का मान ज्ञात करें।

A. 7,125
B. 7,225
C. 7,325
D. 7,425

सही उत्तर: B. 7,225

8×9=72 और अंत में25 लगाएँ। उत्तर=7225।

Practice MCQ

प्रश्न 32. 98 × 102 का मान ज्ञात करें।

A. 9,896
B. 9,996
C. 10,004
D. 10,096

सही उत्तर: B. 9,996

(100−2)(100+2)=10000−4=9996।

Practice MCQ

प्रश्न 33. (1−1/2)(1−1/3)(1−1/4)...(1−1/12) का मान ज्ञात करें।

A. 1/10
B. 1/11
C. 1/12
D. 1/13

सही उत्तर: C. 1/12

यह telescoping product है। सभी intermediate factors cancel होकर 1/12 बचता है।

Practice MCQ

प्रश्न 34. 79.8 × 12.1 का closest approximate value ज्ञात करें।

A. 900
B. 960
C. 1,000
D. 1,080

सही उत्तर: B. 960

79.8≈80 तथा12.1≈12। इसलिए 80×12=960।

Practice MCQ

प्रश्न 35. लगभग मान ज्ञात करें: 24.9% of 803 + 50.1% of 198

A. 250
B. 275
C. 300
D. 325

सही उत्तर: C. 300

25% of800=200 तथा 50% of200=100। Total≈300।

Practice MCQ

प्रश्न 36. यदि 3.5 × 8 + ? ÷ 2 = 40 है, तो ? ज्ञात करें।

A. 20
B. 22
C. 24
D. 26

सही उत्तर: C. 24

3.5×8=28। इसलिए ?÷2=12 और ?=24।

Practice MCQ

प्रश्न 37. सरल कीजिए: 0.75 × 48 + 2.4 ÷ 0.6 − 1.25 × 8

A. 28
B. 30
C. 32
D. 34

सही उत्तर: B. 30

36+4−10=30।

Practice MCQ

प्रश्न 38. सरल कीजिए: 27 × 46 + 27 × 54

A. 2,600
B. 2,650
C. 2,700
D. 2,750

सही उत्तर: C. 2,700

27 common लें: 27(46+54)=27×100=2700।

Practice MCQ

प्रश्न 39. सरल कीजिए: 2⁷ × 2⁻³ ÷ 2²

A. 2
B. 4
C. 8
D. 16

सही उत्तर: B. 4

2⁷⁻³⁻²=2²=4।

Practice MCQ

प्रश्न 40. सरल कीजिए: 96 ÷ 8 × 3 − 4² + 5

A. 21
B. 23
C. 25
D. 27

सही उत्तर: C. 25

96÷8×3=36 तथा4²=16। अतः 36−16+5=25।

55. Practice MCQs — Batch 3

Chapter 2 Mixed Practice Bank — प्रश्न 41 से 60:
इस batch में exact simplification, roots, identities, calculation shortcuts, rounding तथा approximation का अभ्यास है।

Practice MCQ

प्रश्न 41. सरल कीजिए: [64 ÷ (12−4) + √144] × 3

A. 54
B. 57
C. 60
D. 63

सही उत्तर: C. 60

12−4=8, 64÷8=8 तथा√144=12। अतः (8+12)×3=60।

Practice MCQ

प्रश्न 42. सरल कीजिए: 7/8 of 160 − 0.25 × 80

A. 110
B. 120
C. 130
D. 140

सही उत्तर: B. 120

7/8 of160=140 तथा0.25×80=20। Difference=120।

Practice MCQ

प्रश्न 43. सरल कीजिए: (2.75 + 1 1/4) ÷ 0.8

A. 4
B. 5
C. 6
D. 7

सही उत्तर: B. 5

1 1/4=1.25। इसलिए (2.75+1.25)÷0.8=4÷0.8=5।

Practice MCQ

प्रश्न 44. सरल कीजिए: √324 + ∛512 − 2⁴

A. 8
B. 10
C. 12
D. 14

सही उत्तर: B. 10

18+8−16=10।

Practice MCQ

प्रश्न 45. सरल कीजिए: (73²−27²) ÷ (73−27)

A. 90
B. 95
C. 100
D. 105

सही उत्तर: C. 100

Difference of squares से value=73+27=100।

Practice MCQ

प्रश्न 46. सरल कीजिए: 96 × 125 ÷ 12

A. 800
B. 900
C. 1,000
D. 1,100

सही उत्तर: C. 1,000

96×125=12000 तथा12000÷12=1000।

Practice MCQ

प्रश्न 47. 999 × 54 − 99 × 540 का मान ज्ञात करें।

A. 468
B. 486
C. 504
D. 522

सही उत्तर: B. 486

999×54=53946 तथा99×540=53460। Difference=486।

Practice MCQ

प्रश्न 48. 125² का मान ज्ञात करें।

A. 15,225
B. 15,425
C. 15,625
D. 15,825

सही उत्तर: C. 15,625

12×13=156 और अंत में25 लगाएँ। Answer=15,625।

Practice MCQ

प्रश्न 49. 49 × 51 + 99 × 101 का मान ज्ञात करें।

A. 12,398
B. 12,448
C. 12,498
D. 12,548

सही उत्तर: C. 12,498

49×51=2499 तथा99×101=9999। Total=12,498।

Practice MCQ

प्रश्न 50. 398.7 ÷ 19.9 + 24.9 × 8.1 का closest approximate value ज्ञात करें।

A. 200
B. 220
C. 240
D. 260

सही उत्तर: B. 220

लगभग 400÷20+25×8=20+200=220।

Practice MCQ

प्रश्न 51. 0.04764 को three significant figures तक round करें।

A. 0.0475
B. 0.0476
C. 0.0477
D. 0.0480

सही उत्तर: B. 0.0476

First three significant digits 4,7,6 हैं और next digit4 है। Answer=0.0476।

Practice MCQ

प्रश्न 52. −18.67 को one decimal place तक round करें।

A. −18.6
B. −18.7
C. −18.8
D. −19.0

सही उत्तर: B. −18.7

Hundredths digit7 है, इसलिए answer=−18.7।

Practice MCQ

प्रश्न 53. सरल कीजिए: (1/3 + 0.5) × 12

A. 8
B. 9
C. 10
D. 11

सही उत्तर: C. 10

1/3+1/2=5/6 और 5/6×12=10।

Practice MCQ

प्रश्न 54. सरल कीजिए: 4³ ÷ 2⁴ + √81

A. 11
B. 12
C. 13
D. 14

सही उत्तर: C. 13

64÷16+9=4+9=13।

Practice MCQ

प्रश्न 55. सरल कीजिए: √75 − √27

A. √3
B. 2√3
C. 3√3
D. 4√3

सही उत्तर: B. 2√3

√75=5√3 तथा√27=3√3। Difference=2√3।

Practice MCQ

प्रश्न 56. सरल कीजिए: ∛(−216) + (−3)²

A. −15
B. −3
C. 3
D. 15

सही उत्तर: C. 3

∛(−216)=−6 तथा(−3)²=9। इसलिए answer=3।

Practice MCQ

प्रश्न 57. (1−1/2)(1−1/3)...(1−1/15) का मान ज्ञात करें।

A. 1/13
B. 1/14
C. 1/15
D. 1/16

सही उत्तर: C. 1/15

Telescoping cancellation के बाद 1/15 बचता है।

Practice MCQ

प्रश्न 58. सरल कीजिए: 37 × 62 + 37 × 38

A. 3,600
B. 3,700
C. 3,800
D. 3,900

सही उत्तर: B. 3,700

37(62+38)=37×100=3700।

Practice MCQ

प्रश्न 59. 996 × 1004 का मान ज्ञात करें।

A. 999,884
B. 999,984
C. 1,000,016
D. 1,000,084

सही उत्तर: B. 999,984

(1000−4)(1000+4)=1000000−16=999,984।

Practice MCQ

प्रश्न 60. लगभग मान ज्ञात करें: 33.2% of 601 + 12.6% of 799

A. 250
B. 275
C. 300
D. 325

सही उत्तर: C. 300

33.2%≈1/3 of600=200 तथा12.6%≈1/8 of800=100। Total≈300।

56. Practice MCQs — Batch 4

Chapter 2 Mixed Practice Bank — प्रश्न 61 से 80:
इस batch में fractions, decimals, exponents, roots, fast calculation, rounding तथा estimation का chapter-wide अभ्यास है।

Practice MCQ

प्रश्न 61. सरल कीजिए: 144 ÷ [18 − (12−6)] + 2³

A. 18
B. 20
C. 22
D. 24

सही उत्तर: B. 20

12−6=6, 18−6=12, 144÷12=12 तथा2³=8। Total=20।

Practice MCQ

प्रश्न 62. सरल कीजिए: 5/6 ÷ (10/9 of 3/4) + 7/8

A. 13/8
B. 15/8
C. 17/8
D. 19/8

सही उत्तर: B. 15/8

10/9 of3/4=5/6। इसलिए 5/6÷5/6=1 और 1+7/8=15/8।

Practice MCQ

प्रश्न 63. सरल कीजिए: 0.375 × 64 + 0.625 × 16

A. 30
B. 32
C. 34
D. 36

सही उत्तर: C. 34

0.375=3/8 और0.625=5/8। इसलिए 24+10=34।

Practice MCQ

प्रश्न 64. सरल कीजिए: 5⁴ × 5⁻² ÷ 25

A. 1
B. 5
C. 25
D. 125

सही उत्तर: A. 1

25=5²। इसलिए 5⁴⁻²⁻²=5⁰=1।

Practice MCQ

प्रश्न 65. सरल कीजिए: √0.0225 + √2.25

A. 1.55
B. 1.60
C. 1.65
D. 1.70

सही उत्तर: C. 1.65

√0.0225=0.15 तथा√2.25=1.5। Sum=1.65।

Practice MCQ

प्रश्न 66. सरल कीजिए: ∛0.008 + ∛27

A. 3.0
B. 3.1
C. 3.2
D. 3.3

सही उत्तर: C. 3.2

∛0.008=0.2 तथा∛27=3। Total=3.2।

Practice MCQ

प्रश्न 67. 72 × 25 + 32 × 125 का मान ज्ञात करें।

A. 5,400
B. 5,600
C. 5,800
D. 6,000

सही उत्तर: C. 5,800

72×25=1800 तथा32×125=4000। Total=5800।

Practice MCQ

प्रश्न 68. सरल कीजिए: 8,750 ÷ 125 − 375 ÷ 25

A. 45
B. 50
C. 55
D. 60

सही उत्तर: C. 55

8750÷125=70 तथा375÷25=15। Difference=55।

Practice MCQ

प्रश्न 69. 97² का मान ज्ञात करें।

A. 9,309
B. 9,409
C. 9,509
D. 9,609

सही उत्तर: B. 9,409

(100−3)²=10000−600+9=9409।

Practice MCQ

प्रश्न 70. 115² − 85² का मान ज्ञात करें।

A. 5,000
B. 5,500
C. 6,000
D. 6,500

सही उत्तर: C. 6,000

(115−85)(115+85)=30×200=6000।

Practice MCQ

प्रश्न 71. 499.5 × 2.01 + 998 ÷ 49.9 का closest approximate value ज्ञात करें।

A. 980
B. 1,000
C. 1,020
D. 1,040

सही उत्तर: C. 1,020

लगभग 500×2+1000÷50=1000+20=1020।

Practice MCQ

प्रश्न 72. 12.49 को nearest integer तक round करें।

A. 11
B. 12
C. 13
D. 14

सही उत्तर: B. 12

Decimal part 0.49 है, जो0.5 से कम है। Answer=12।

Practice MCQ

प्रश्न 73. 68,749 को nearest thousand तक round करें।

A. 68,000
B. 68,700
C. 69,000
D. 70,000

सही उत्तर: C. 69,000

Hundreds digit7 है, इसलिए answer=69,000।

Practice MCQ

प्रश्न 74. 0.0008064 को three significant figures तक round करें।

A. 0.000805
B. 0.000806
C. 0.000807
D. 0.000810

सही उत्तर: B. 0.000806

First three significant digits 8,0,6 हैं और next digit4 है। Answer=0.000806।

Practice MCQ

प्रश्न 75. सरल कीजिए: (49.9²−30.1²) ÷ (49.9+30.1)

A. 18.8
B. 19.8
C. 20.8
D. 21.8

सही उत्तर: B. 19.8

Difference of squares से value=49.9−30.1=19.8।

Practice MCQ

प्रश्न 76. लगभग मान ज्ञात करें: 19.8% of 251 + 49.9% of 302

A. 175
B. 190
C. 200
D. 225

सही उत्तर: C. 200

20% of250=50 तथा50% of300=150। Total≈200।

Practice MCQ

प्रश्न 77. यदि 2.5 × 6 + ? ÷ 4 = 23 है, तो ? ज्ञात करें।

A. 24
B. 28
C. 32
D. 36

सही उत्तर: C. 32

2.5×6=15। इसलिए ?÷4=8 और ?=32।

Practice MCQ

प्रश्न 78. सरल कीजिए: 3/5 of 75 + 0.4 of 50 + 2³

A. 69
B. 71
C. 73
D. 75

सही उत्तर: C. 73

45+20+8=73।

Practice MCQ

प्रश्न 79. सरल कीजिए: (√225 + ∛125) × 2 − 3²

A. 29
B. 31
C. 33
D. 35

सही उत्तर: B. 31

(15+5)×2−9=40−9=31।

Practice MCQ

प्रश्न 80. सरल कीजिए: 4.8 ÷ 0.12 + 0.25 × 64

A. 52
B. 54
C. 56
D. 58

सही उत्तर: C. 56

4.8÷0.12=40 तथा0.25×64=16। Total=56।

57. Practice MCQs — Batch 5

Chapter 2 Mixed Practice Bank — प्रश्न 81 से 100:
यह final batch पूरे Simplification & Approximation chapter के concepts को integrate करता है।

Practice MCQ

प्रश्न 81. सरल कीजिए: 200 − [48 ÷ {10−(6−2)} + 5²]

A. 163
B. 165
C. 167
D. 169

सही उत्तर: C. 167

6−2=4, 10−4=6, 48÷6=8 तथा5²=25। इसलिए 200−33=167।

Practice MCQ

प्रश्न 82. सरल कीजिए: 7/12 of 144 + 1.25 × 16 − √100

A. 90
B. 92
C. 94
D. 96

सही उत्तर: C. 94

7/12 of144=84, 1.25×16=20 तथा√100=10। इसलिए 84+20−10=94।

Practice MCQ

प्रश्न 83. सरल कीजिए: (3 1/3 − 1 5/6) × 6

A. 7
B. 8
C. 9
D. 10

सही उत्तर: C. 9

10/3−11/6=3/2। फिर 3/2×6=9।

Practice MCQ

प्रश्न 84. सरल कीजिए: (0.875 + 1/8) × 8

A. 6
B. 7
C. 8
D. 9

सही उत्तर: C. 8

0.875=7/8। इसलिए 7/8+1/8=1 और 1×8=8।

Practice MCQ

प्रश्न 85. सरल कीजिए: 3⁵ × 3⁻² ÷ 3²

A. 1
B. 3
C. 9
D. 27

सही उत्तर: B. 3

3⁵⁻²⁻²=3¹=3।

Practice MCQ

प्रश्न 86. सरल कीजिए: √192 − √48

A. 2√3
B. 3√3
C. 4√3
D. 6√3

सही उत्तर: C. 4√3

√192=8√3 तथा√48=4√3। Difference=4√3।

Practice MCQ

प्रश्न 87. सरल कीजिए: ∛1000 + 10√0.81

A. 17
B. 18
C. 19
D. 20

सही उत्तर: C. 19

∛1000=10 तथा√0.81=0.9। इसलिए 10+10×0.9=19।

Practice MCQ

प्रश्न 88. 125 × 72 − 25 × 160 का मान ज्ञात करें।

A. 4,500
B. 5,000
C. 5,500
D. 6,000

सही उत्तर: B. 5,000

125×72=9000 तथा25×160=4000। Difference=5000।

Practice MCQ

प्रश्न 89. 999 × 101 का मान ज्ञात करें।

A. 99,899
B. 100,899
C. 100,999
D. 101,899

सही उत्तर: B. 100,899

999×101=999×100+999=99,900+999=100,899।

Practice MCQ

प्रश्न 90. 205 × 195 का मान ज्ञात करें।

A. 39,875
B. 39,925
C. 39,975
D. 40,025

सही उत्तर: C. 39,975

(200+5)(200−5)=200²−5²=40000−25=39,975।

Practice MCQ

प्रश्न 91. 599.7 ÷ 29.98 + 39.9 × 24.95 का closest approximate value ज्ञात करें।

A. 980
B. 1,000
C. 1,020
D. 1,040

सही उत्तर: C. 1,020

लगभग 600÷30+40×25=20+1000=1020।

Practice MCQ

प्रश्न 92. 84,951 को nearest hundred तक round करें।

A. 84,900
B. 85,000
C. 85,100
D. 84,950

सही उत्तर: B. 85,000

Tens digit5 है, इसलिए hundreds place round-up होगा। Answer=85,000।

Practice MCQ

प्रश्न 93. 8.495 को two decimal places तक round करें।

A. 8.49
B. 8.50
C. 8.51
D. 8.59

सही उत्तर: B. 8.50

Third decimal digit5 है। इसलिए 8.49 round-up होकर 8.50 होगा।

Practice MCQ

प्रश्न 94. 0.009949 को three significant figures तक round करें।

A. 0.00994
B. 0.00995
C. 0.00996
D. 0.0100

सही उत्तर: B. 0.00995

पहले three significant digits 9,9,4 हैं और next digit9 है। इसलिए answer=0.00995।

Practice MCQ

प्रश्न 95. सरल कीजिए: (60.2²−39.8²) ÷ (60.2−39.8)

A. 90
B. 95
C. 100
D. 105

सही उत्तर: C. 100

Difference of squares से value=60.2+39.8=100।

Practice MCQ

प्रश्न 96. सरल कीजिए: 12.5% of 800 + 33 1/3% of 300

A. 180
B. 190
C. 200
D. 210

सही उत्तर: C. 200

12.5%=1/8, इसलिए 800/8=100। 33 1/3%=1/3, इसलिए 300/3=100। Total=200।

Practice MCQ

प्रश्न 97. यदि ? ÷ 0.25 − 12 = 28 है, तो ? ज्ञात करें।

A. 8
B. 10
C. 12
D. 14

सही उत्तर: B. 10

?÷0.25=40। चूँकि ÷0.25=×4, इसलिए 4?=40 और ?=10।

Practice MCQ

प्रश्न 98. सरल कीजिए: [2³ + √144] × 3/4

A. 12
B. 15
C. 18
D. 20

सही उत्तर: B. 15

(8+12)×3/4=20×3/4=15।

Practice MCQ

प्रश्न 99. (1−1/3)(1−1/4)...(1−1/10) का मान ज्ञात करें।

A. 1/10
B. 1/5
C. 2/5
D. 1/2

सही उत्तर: B. 1/5

2/3×3/4×...×9/10 में intermediate terms cancel होकर 2/10=1/5 बचता है।

Practice MCQ

प्रश्न 100. (79.9 × 25.1) ÷ 10.02 का closest approximate value ज्ञात करें।

A. 180
B. 190
C. 200
D. 210

सही उत्तर: C. 200

79.9≈80, 25.1≈25 तथा10.02≈10। इसलिए 80×25÷10=200।