Surds and Indices questions for CGL Tier 2,
CGL Tier 1 and SSC 10+2
Surds and indices quiz 1
Directions: Study the following questions carefully and choose the right
answer:
1. The value of (256)5/4 is:
A. 512 B. 984
C. 1024 D. 1032
( ) ( ) ( )
( ) ( ) ( )
A. 102 B. 105
C. 107 D. None of these
3. (2.4 × 103) ÷ (8 × 10–2) = ?
A. 3 x 10–5 B. 3 x 104
C. 3 x 105 D. 30
( ) ( )
( ) ( )
A. 3/4 B. 2/3
C. 4/9 D. 1/8
5. (1000)7 ÷ 1018 = ?
A. 10 B. 100
C. 1000 D. 10000
6. 49 × 49 × 49 × 49 = 7?
A. 4 B. 7
C. 8 D. 16
7. The value of (8–25 – 8–26) is:
A. 7 × 8 – 25 B. 7 × 8 – 26
C. 8 × 8 – 26 E. 8 × 8 – 25
8. (64)–1/2 – (32)–4/5 = ?
A. 1/8 B. 3/8
C. 1/16 D. 3/16
9. (18)3.5 ÷ (27)3.5 × 63.5 = 2?
A. 3.5 B. 4.5
C. 6 D. 7
( ) ( )
( ) ( ) ( )
A. 3/7 B. 7/3
C. 10/7 D. 16/7
Correct answers:
1 2 3 4 5 6 7 8 9 10
C A B C C C B C D A
Explanations:
1). From the given equation:
(256) 5/4
= (44) 5/4
= 4(4 × 5/4)
= 45
= 1024.
Hence, option C is correct.
2). Given expression =
1 1 1
−2/3 + −3/4 +
(216) (256) (32)−1/5
1 1 1
= 3×(–2/3) + 4×(–3/4) + 5×(–1/5)
6 4 2
1 1 1
= –2 + –3 +
6 4 2–1
= (62 + 43 + 21)
= (36 + 64 + 2)
= 102.
Hence, option A is correct.
3). Given equation
= (2.4 × 103) ÷ (8 × 10–2)
2.4 × 103
then,
8 × 10– 2
24 ×102
=
8 × 10– 2
= (3 × 104)
Hence, option B is correct.
4). Given equation:
1 –2/3 1 –4/3
( ) ÷ ( ) = ?
216 27
(216)(2/3) ÷ (27)(4/3)
(216)2/3 (63)×(2/3)
= = .
(27)4/3 (33)×(4/3)
62 36 4
= 4= =
3 81 9
Hence, option C is correct.
5). Given equation = (1000)7 ÷ 1018 .
(1000)7 (103)7 10(3 × 7)
⇒ ⇒ ⇒ .
(10)18 (10)18 (10)18
⇒ 1021 = 10(21 - 18) ⇒ 103 = 1000.
(10)18
Hence, option C is correct.
6). From the given equation:
49 × 49 × 49 × 49
⇒ (72 × 72 × 72 × 72)
⇒ 7(2 + 2+ 2+ 2)
⇒ 78
So, the correct answer is 8.
Hence, option C is correct.
7). From the given equation:
8–25 – 8–26
1 1
= ( 25 − 26)
8 8
(8 − 1)
=
826
= 7 × 8−26
Hence, option B is correct.
8). From the given equation:
(64)–1/2 − (32)–4/5
⇒ (82)–1/2 − {(2)5}–4/5.
⇒ 82 x (−1/2) −(2)5 x (−4)/5
⇒ 8−1 − (2)−4
1 1
⇒ − 4
8 (2)
1 1
⇒( − )
8 16
1
=
16
Hence, option C is correct.
9). In this question as we need to find the power of base 2 given in
R.H.S, it's clear that factors other than 2 will be cancelled out on
calculation in L.H.S.
Therefore, we can solve this question just by picking 2 is as bases
with their powers in L.H.S.
(18)3.5 ÷ (27)3.5 × 63.5 = 2x
↓ ↓
3.5 3.5
(2 × 9) ÷ (27) × (2 × 3)3.5= 2x
↓ Neglecting bases other than 2 ↓
3.5
(2) × (2)3.5 = 2x
⇒ 23.5 + 3.5 = 2x
⇒ 27 = 2x ⇒ x = 7.
Hence, option D is correct.
10). From the given equation:
(243)0.13 x (243)0.07
70.25 x (49)0.075 x (343)0.2
(243)(0.13+0.07)
= 0.25
7 x (72)0.075x (73)0.2
(243)0.2
70.25 x (7)(2x0.075) x (7)(3x0.2)
(35)0.2
= 0.25 0.15 0.6
7 x7 x7
3(5x0.2)
=
7(0.25+0.15+0.6)
31 3
= 1 =
7 7
Hence, option A is correct.
