BANK & INSURANCE (SIMPLIFICATION SURDS & INDICES)

Total Questions: 50

31. x³ − 149.996×1.5 = (5.01)²×8.99 + 177.2% of (9.99)³

Correct Answer: (b) 13
Solution:

Let's approximate:
x³ − 150 × 1.5 ≈ 5² × 9 + 177% of 10³
=> x³ - 225 ≈ 25 × 9 + 1.77 × 1000
=> x³ - 225 ≈ 225 + 1770
=> x³ ≈ 225 + 1770 + 225
=> x³ ≈ 2220
=> x ≈ 13.04 (∛2220 ≈ 13.04)
=> x ≈ 13

32. 128.01x + √1681 = 11.99³ + 168.99

Correct Answer: (a) 14.5
Solution:

√1681 = 41

11.99³ ≈ 12³ = 1728

RHS ≈ 1728 + 168.99 = 1896.99

128.01x + 41 ≈ 1896.99 ⇒ 128.01x ≈ 1855.99

x ≈ 1855.99 ÷ 128.01 ≈ 14.5

33. [√{³√(7.99)+6.96} − 3.89×(6.99+√(225.1)×5.96) + 13] = ?

Correct Answer: (c)−372
Solution:

³√7.99 ≈ 2, so √(2+6.96)=√8.96 ≈ 3

3.89 ≈ 4, 6.99 ≈ 7, √225.1 ≈ 15, 5.96 ≈ 6

Inside ( ) ≈ 7 + 15×6 = 97

3.89×(…) ≈ 4×97 = 388

Result ≈ 3 − 388 + 13 = −372

34. [(9.99)² × √288.96] − [14 − 6×7 + √168.59 + (11.02)²] = ?

Correct Answer: (d) 1594
Solution:

 (9.99)² ≈ 100

√288.96 ≈ 17  ⇒ first bracket ≈ 100 × 17 = 1700

14 − 6×7 = 14 − 42 = −28

√168.59 ≈ 13 and (11.02)² ≈ 121

Second bracket ≈ −28 + 13 + 121 = 106

Result ≈ 1700 − 106 = 1594

35. √728.4601 × 4.99 − 370 + [16.01 × √625.01] = ?

Correct Answer: (a) 165
Solution:

√728.4601 ≈ 26.99 (since 26.99² = 728.4601)

26.99 × 4.99 ≈ 134.68

√625.01 ≈ 25.00

16.01 × 25.00 ≈ 400.25

Total ≈ 134.68 − 370 + 400.25 ≈ 164.93 ≈ 165

36. 4⁸ ÷ 256 × 64 ÷ 4³ × 4 = 16 × 4^?

Correct Answer: (b) 3
Solution:

4⁸ = 65536

65536 ÷ 256 = 256

256 × 64 = 16384

16384 ÷ 4³(=64) = 256

256 × 4 = 1024

RHS = 16 × 4^? = 4² × 4^? = 4^(?+2)

1024 = 4⁵ ⇒ ?+2 = 5 ⇒ ? = 3

37. 21² + ?² − 3² = 45% of 180 + 80 × 8

Correct Answer: (d) 17
Solution:

45% of 180 = 81

80 × 8 = 640 ⇒ RHS = 721

21² = 441 and 3² = 9

441 + ?² − 9 = 721 ⇒ ?² + 432 = 721

?² = 289 ⇒ ? = 17

38. (2 × 3)³ ÷ (4 × 9)² × (27 × 8)² = (6)^?

Correct Answer: (c) 5
Solution:

(2×3)=6 ⇒ (2×3)³ = 6³

(4×9)=36 = 6² ⇒ (4×9)² = (6²)² = 6⁴

(27×8)=216 = 6³ ⇒ (27×8)² = (6³)² = 6⁶

So LHS = 6³ ÷ 6⁴ × 6⁶ = 6^(3−4+6) = 6⁵

Answer: 5

39. Q32. (0.1)⁹⁴ ÷ 0.001^64 = (0.1?)²

Correct Answer: (b) −49
Solution:

(0.1)⁹⁴ ÷ (0.001)^64 = (0.1?)²
=> (0.1)⁹⁴ ÷ (0.1³)^64 = (0.1?)²
=> (0.1)⁹⁴ ÷ (0.1)^192 = (0.1?)²
=> (0.1)^(94 - 192) = (0.1?)²
=> (0.1)^(-98) = (0.1?)²
=> (0.1?)² = (0.1)^(-98)
=> 0.1? = 0.1^(-49)
=> ? = -49

40. 23 × √16 + 540 ÷ √1296 − 27 × 4 = ?

Correct Answer: (a) −1
Solution:

√16 = 4

√1296 = 36

23×4 + 540÷36 − 108 = 92 + 15 − 108 = −1

Answer: −1