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Surds and Indices Quiz 4
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Hi
Direction: Study the following questions carefully and choose the right answer.
Important for :
CGL Tier 2
CGLTier 1
SSC 10+2
1
Given
2
= 1.414 and the value of
8
+ 2
32
– 3
128
+ 4
50
is
A
8.484
B
8.526
C
8.426
D
8.876
» Explain it
Correct Option:
A
8
+ 2
32
– 3
128
+ 4
50
= 2
2
+ 8
2
– 3 × 8
2
+ 4 × 5
2
= (2 + 8 – 24 + 20)
2
= 6
2
= 6 × 1.414 = 8.484
Hence, option A is correct.
1
A
B
C
D
» Explain it
सही विकल्प :
A
A
2
The simplified value of (
3
+ 1)(10 +
12
)(
12
– 2)(5 –
3
) is
A
16
B
88
C
176
D
132
» Explain it
Correct Option:
C
Expression = (
3
+ 1)(10 +
12
)(
12
– 2)(5 –
3
)
= (
3
+ 1)(10 + 2
3
)(2
3
– 2)(5 –
3
)
= (
3
+ 1) × 2(5 +
3
) × 2(
3
– 1)(5 –
3
)
= 4(
3
+ 1)(
3
– 1)(5 –
3
)(5 +
3
)
= 4(3 – 1) (25 – 3)
[(a + b)(a – b) = a
^{2}
– b
^{2}
]
= 4 × 2 × 22 = 176.
Hence, option C is correct.
2
A
B
C
D
» Explain it
सही विकल्प :
C
C
3
If
15
= 3.88, then what is the value of
5 / 3
?
A
1.293
B
1.2934
C
1.29
D
1.295
» Explain it
Correct Option:
A
Given,
15
= 3.88
Now,
5
3
=
5 × 3
3 × 3
=
15
3
=
3.88
= 1.29
3
3
Hence, option A is correct.
3
A
B
C
D
» Explain it
सही विकल्प :
A
A
4
Simplify:
(6.25)
^{1/2}
× (0.0144)
^{1/2}
+ 1
(0.027)
^{1/3}
× (81)
^{1/4}
A
0.14
B
1.4
C
1
D
1.
4
» Explain it
Correct Option:
D
Expression:
(6.25)
^{1/2}
× (0.0144)
^{1/2}
+ 1
(0.027)
^{1/3}
× (81)
^{1/4}
=
(2.5)
^{2×(}
^{1/2)}
× (0.12)
^{2}
^{×(}
^{1/2)}
+ 1
(0.3)
^{3×}
^{1/3}
× (3)
^{4×}
^{(1/4)}
=
2.5 × 0.12 + 1
=
0.3 + 1
(0.3) × (3)
0.9
=
1.3
= 1.4444 = 1.
4
0.9
Hence option D is correct.
4
A
B
C
D
» Explain it
सही विकल्प :
D
D
5
If
3
= 1.732 is given. then the value of
2 + √3
= ?
2 – √3
A
11.732
B
13.928
C
12.928
D
13.925
» Explain it
Correct Option:
B
Given expression =
2 +
3
2 –
3
=
(2 +
3
)(
2 +
3
)
(2 –
3
)(
2 +
3
)
[On rationalising the denominator]
=
(
2 +
3
)
^{2}
=
(2 +
3
)
^{2}
4 – 3
= 2
^{2}
+ (
3
)
^{2}
+ 2 × 2 ×
3
= 4 + 3 + 4
3
= 7 + 4 × 1.732
= 7 + 6.928 = 13.928
Hence, option B is correct.
5
A
B
C
D
» Explain it
सही विकल्प :
B
B
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