MCQ: Indices and Surds - 3 - SSC CGL MCQ

# MCQ: Indices and Surds - 3 - SSC CGL MCQ

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## 15 Questions MCQ Test Quantitative Aptitude for SSC CGL - MCQ: Indices and Surds - 3

MCQ: Indices and Surds - 3 for SSC CGL 2024 is part of Quantitative Aptitude for SSC CGL preparation. The MCQ: Indices and Surds - 3 questions and answers have been prepared according to the SSC CGL exam syllabus.The MCQ: Indices and Surds - 3 MCQs are made for SSC CGL 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for MCQ: Indices and Surds - 3 below.
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MCQ: Indices and Surds - 3 - Question 1

### If 289 = 17x/5 , then x = ?

Detailed Solution for MCQ: Indices and Surds - 3 - Question 1

Given that , 289 = 17x/5
Use the formula if ax = a y then x = y will be true.
⇒ 17 2 = 17x/5
⇒ x /5 = 2
⇒ x = 10 .

MCQ: Indices and Surds - 3 - Question 2

### If 2p + 3q = 17 and 2p + 2 - 3q + 1 = 5, then, find the value of p and q ?

Detailed Solution for MCQ: Indices and Surds - 3 - Question 2

Apply the law of Fractional Exponents and Laws of Exponents
(am) x (an) = am + n
a-m = 1/am
p0 = 1
and if pX = pY then X will be equal to Y. means X = Y;
(am)n = am x n
(am) x (an) = am + n
am ÷ an = am ? n
Or
am/an = am ? n

Given equation is
2p + 3q = 17 ----------------(i)
2p + 2 - 3q + 1 = 5
⇒ 2p x 22 - 3q x 3 = 5
⇒ 2p x 4 - 3q x 3 = 5
⇒ 4 x 2p - 3 x 3q = 5---------------(ii)
On multiplying Eq. (i) by 3 and adding it, with Eq. (ii), we get

3 x 2p + 3 x 3q = 51
4 x 2p - 3 x 3q = 5
_____________________________
7 x 2p = 56

⇒ 7 x 2p = 7 x 8
⇒ 2p = 8
⇒ 2p = 23
⇒ = 3

On substituting the value of in Eq. (i) . we get
23 + 3q = 17
⇒ 8 + 3q = 17
⇒ 3q = 17 - 8
⇒ 3q = 9
⇒ 3q = 32
⇒ q = 2

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MCQ: Indices and Surds - 3 - Question 3

### 812.5 x 94.5 ÷ 34.8 = 9?

Detailed Solution for MCQ: Indices and Surds - 3 - Question 3

812.5 X 94.5 ÷ 34.8 = 9?
⇒ 812.5 x 94.5 ÷ 34.8 = 9?
Apply the law of Fractional Exponents and Laws of Exponents
(am)n = am x n ----------------1
(am) x (an) = am + n-------------2
am ÷ an = am ? n----------------3
and if pX = pY then X will be equal to Y. means X = Y;----------------4

Apply Law 1
⇒ (92)2.5 x 94.5 ÷ 32 x 2.4 = 9?
⇒ 95 x 94.5 ÷ 92.4 = 9?
Apply law 2 and 3,
⇒ 9(5 + 4.5 - 2.4) = 9?
⇒ 9? = 97.1
Apply the Law 4
∴ = 7.1

MCQ: Indices and Surds - 3 - Question 4

If ( 5 + 2√3 ) / ( 7 + 4√3 ) = a + b√3, then the value of a and b is ?

Detailed Solution for MCQ: Indices and Surds - 3 - Question 4

Given equation is,
( 5 + 2√3 ) / (7 + 4√3 )
Now Multiply and divide by ( 7 - 4√3 ) in above given equation.
By Rationalization, we will get,
[ ( 5 + 2√3 ) / ( 7 + 4√3 ) ] x [ ( 7 - 4√3 ) / ( 7 - 4√3 ) ]
[ ( 5 + 2√3 ) x ( 7 - 4√3 ) ] / [ ( 7 + 4√3 ) x ( 7 - 4√3 ) ]
Apply the formula and multiplication rule of algebra,
( P + Q ) x (R - S ) = P x R - P x S + Q x R - Q x S .................(1)
( a + b ) x ( a - b) = a2 - b2.......................................................(2)

= ( 5 x 7 - 5 x 4√3 + 7 x 2√3 - 2√3 x 4√3 )/ ( 72 - (4√3)2 )
= 35 - 20√3 + 14√3 - 8 x 3 / ( 49 - 16 x 3 )
= ( 35 - 24 - 6√3 )/(49 - 48 )
= 11 - 6√3
∵ ( 5 + 2√3 ) /( 7 + 4√3 ) = a + b√3
∴ a + b√3 = 11 - 6√3
on equating the above equation and we get,
or = 11 and b = - 6

MCQ: Indices and Surds - 3 - Question 5

Simplify ( 6a-2bc-3/4ab-3c2 ) ÷ ( 5a-3 b2c-1/3ab-2c3 )

Detailed Solution for MCQ: Indices and Surds - 3 - Question 5

Given equation is,
( 6a-2bc-3/4ab-3c2 ) ÷ ( 5a-3 b2c-1/3ab-2c3 )
Apply the algebra law a ÷ b = a x 1/b
= ( 6a-2bc-3/4ab-3c2 ) x ( 3ab-2c3/5a-3 b2c-1 )
= ( 6a-2 bc-3 x 3ab-2c3) / ( 4ab-3c2 x 5a-3b2c-1 )
Apply the law of Fractional Exponents and Laws of Exponents
(am)(an) = am+n
am÷an=am-n
Or
am/an=am-n
= 18a-2 + 1 b1 - 2 c -3 + 3 / 20a1 - 3 b-3 + 2 c2 - 1
= 9a-1b-1c0/ 10a - 2 b-1c1
= ( 9/10 ) a-1 + 2b-1 + 1 c0 - 1
= ( 9/10 ) a1b0 c-1
= ( 9/10 ) ac-1 [∵ b0 = 1]

MCQ: Indices and Surds - 3 - Question 6

The value of 273 × 34 ÷ 310 is equal to :

Detailed Solution for MCQ: Indices and Surds - 3 - Question 6

273 × 34 ÷ 310

= 313 - 10 = 33
= 3 × 3 × 3 = 27

MCQ: Indices and Surds - 3 - Question 7

If 102/5 × 108/5 = 10n, the value of n is :

Detailed Solution for MCQ: Indices and Surds - 3 - Question 7

∵ 102/5 × 108/5 = 10n
⇒ 102/5 + 8/5 = 10n
⇒ 1010/5 = 10n ⇒ 102 = 10n ⇒ n = 2
Hence, the value of n is 2.

MCQ: Indices and Surds - 3 - Question 8

The value of 12x2y4z3 ÷ (2xy2 × 3yz2) will be :

Detailed Solution for MCQ: Indices and Surds - 3 - Question 8

12x2y4z3 ÷ (2xy2 × 3yz2)

MCQ: Indices and Surds - 3 - Question 9

if √4 × 43/2 ÷ 4-3 = 2x, the value of x will be :

Detailed Solution for MCQ: Indices and Surds - 3 - Question 9

√4 × 43/2 ÷ 4-3 = 2x

⇒ 42+3 = 2x
⇒ ( 22 )5 = 2x ⇒ 210 = 2x ⇒ x = 10
∴ Value of x is 10.

MCQ: Indices and Surds - 3 - Question 10

Solve the below equation.
173.5 x 177.3 ÷ 174.2 = 17?

Detailed Solution for MCQ: Indices and Surds - 3 - Question 10

173.5 x 177.3 ÷ 174.2 = 17?
Apply the Laws of Exponents ::
(am) x (an) = am+n
Fractional Exponents ::
am÷ a n=am?n
⇒ 173.5 + 7.3 - 4.2 = 17?
⇒ 176.6 = 17?
? = 6.6

MCQ: Indices and Surds - 3 - Question 11

L√M is surd of order ........, where M is a rational number; L is a positive integer and L√M is irrational.

Detailed Solution for MCQ: Indices and Surds - 3 - Question 11

L√3 = M1/L = Surd of Lth order.

MCQ: Indices and Surds - 3 - Question 12

( 42 x 229 ) ÷ ( 9261)1/3 = ?

Detailed Solution for MCQ: Indices and Surds - 3 - Question 12

Given that, (42 x 229) ÷ (9261)1/3 = ?
As we know that (9621)1/3 = (21 x 21 x 21)1/3 = 213x1/3
∴ 42 x 229 ÷ (213 x )1/3 = ?
∴ 42 x 229 ÷ 21 = ?
∴ 42 x 229 x 1/ 21 = ?
∴ 2 x 229 = ?
∴ ? = 2 x 229
∴ ? = 458

MCQ: Indices and Surds - 3 - Question 13

The expression [(√2)√2]√2 gives

Detailed Solution for MCQ: Indices and Surds - 3 - Question 13

Given expression = [(√2)√2]√2
= (√2)(2)√2/2
= (√2)(2)1/√2
= (2)1/2 x 21/√2
= 2(2/21/√2)
= (2)(2)(1/√2 - 1)
which denotes a real number but not a rational number .

MCQ: Indices and Surds - 3 - Question 14

The value of

Detailed Solution for MCQ: Indices and Surds - 3 - Question 14

MCQ: Indices and Surds - 3 - Question 15

The value of

Detailed Solution for MCQ: Indices and Surds - 3 - Question 15

## Quantitative Aptitude for SSC CGL

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## Quantitative Aptitude for SSC CGL

314 videos|170 docs|185 tests