MCQ: Indices and Surds - 1 - SSC CGL MCQ

# MCQ: Indices and Surds - 1 - SSC CGL MCQ

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## 15 Questions MCQ Test Quantitative Aptitude for SSC CGL - MCQ: Indices and Surds - 1

MCQ: Indices and Surds - 1 for SSC CGL 2024 is part of Quantitative Aptitude for SSC CGL preparation. The MCQ: Indices and Surds - 1 questions and answers have been prepared according to the SSC CGL exam syllabus.The MCQ: Indices and Surds - 1 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 - 1 below.
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MCQ: Indices and Surds - 1 - Question 1

### 163/2 + 16 -3/2 = ?

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

163/2 + 16-3/2
Apply the law of Fractional Exponents and Laws of Exponents
am x an = am+n
a-m = 1/am
⇒163/2 + 1/163/2
⇒(161/2)3 + 1/(161/2)3
⇒(42 x 1/2)3 + 1/(42 x 1/2)3
⇒43 + 1/43
⇒ 64 + 1/64
⇒ (64 x 64+ 1)/64
= (4096+1)/64
= 4097/64

MCQ: Indices and Surds - 1 - Question 2

### (16)9 ÷ (16)4 x (16)3 = (16)?

Detailed Solution for MCQ: Indices and Surds - 1 - Question 2

Given that ,(16)9 ÷ (16)4 x (16) 3 = (16)?
Apply the law of Fractional Exponents and Laws of Exponents
(am) x (an) = am + n-------------------1
am ÷ an = am ? n----------------2
⇒ (16)9 ÷ (16)4 x (16) 3 = (16)?
⇒ (16)? = (16)9 + 3 - 4
? = 12 - 4 = 8

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MCQ: Indices and Surds - 1 - Question 3

### If (1/5 )3a = 0.008 Find the value of ( 0.25)a

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

(1/5 )3a = 0.008 = 8/1000 = 1/125 = (1/5 )3
Apply the Algebra Law and Solve the equation.
⇒ 3a = 3
∴ a = 1
∴ ( 0.25 )a = ( 0.25 )1 = 0.25

MCQ: Indices and Surds - 1 - Question 4

1/1 + xb - a + xc - a + 1/1 + xa-b + xc - b + 1/1 + xb - c+ xa - c = ?

Detailed Solution for MCQ: Indices and Surds - 1 - Question 4

? = 1/ ( 1 + xb - a + xc - a ) + 1/ ( 1 + xa - b + xc - b ) + 1 / ( 1 + xb - c + xa - c )
Apply the law of algebra and solve the given equation.
⇒ ? =1/ ( 1 + xb/xa + xc/xa ) + 1/ ( 1+ xa/xb + xc/xb ) + 1/ ( 1 + xb/xc + xa/xc )
⇒ ? = xa/ ( xa+xb+xc ) + xb/ ( xb + xa+ xc ) + xc/ ( xc+xb+xa )
⇒ ? = ( xa + xb + xc ) / ( xa + xb + xc ) = 1

MCQ: Indices and Surds - 1 - Question 5

[(2a2)3]3 [(3a3)2]2 ÷ [(6a6)2]2 is equivalent to :

Detailed Solution for MCQ: Indices and Surds - 1 - Question 5

[(2a2)3]3 [(3a3)2]2 ÷ [(6a6)2]2
= (8a6)3. (9a6)2 ÷ (36a12)2

MCQ: Indices and Surds - 1 - Question 6

The value of 6a3 b3 c2 ÷ 2ab2c is :

Detailed Solution for MCQ: Indices and Surds - 1 - Question 6

6a3 b3 c2 ÷ 2ab2c

= 3a3 - 1 b3 - 2 c2 - 1 = 3a2bc

MCQ: Indices and Surds - 1 - Question 7

(100)0 is equivalent to :

Detailed Solution for MCQ: Indices and Surds - 1 - Question 7

If any given number (suppose x) is a rational number other than zero, then x0 = 1.

MCQ: Indices and Surds - 1 - Question 8

If m = 7 - 4√3, then (√m + 1/√m) = ?

Detailed Solution for MCQ: Indices and Surds - 1 - Question 8

Given that ,
= 7 - 4√3
Then I/m = 1/7 - 4√3......................(1)
Now multiply and divide with 7 + 4√3 in Eq. (1)
We will get,
1/m = ( 1/7 - 4√3 ) x ( 7 + 4√3 / 7 + 4√3)
1/m = ( 7 + 4√3 )/ ( 7 - 4√3 ) x ( 7 + 4√3
1/m = ( 7 + 4√3 ) / ( 72 - ( 4√3)2 )
1/m = ( 7 + 4√3 ) / ( 49 - 4 x 4 x 3 )
1/m = ( 7 + 4√3 ) /49 - 48
1/m = ( 7 + 4√3 ) / 1
1/m = 7 + 4√3
∴ m + 1/m = 14
⇒ ( m + 1/m ) + 2 = 14 + 2 = 16
∴ (√m + 1/√m)2 = ( m + 1/m )+ 2
⇒ (√m + 1/√m)2 = 16
⇒ (√m + 1/√m)2 = 42
⇒ (√m + 1/√m) = 4

MCQ: Indices and Surds - 1 - Question 9

if a = 2 + √3, then what is the value of (a2 + a -2) ?

Detailed Solution for MCQ: Indices and Surds - 1 - Question 9

Given that, a = 2 + √3
Then, 1/a = 2 - √3 [ by conjugate property ]
Conjugate law is below,
if x = p + √q
then 1/x = p - √q
Apply the law of algebra in above equation.
Now, we have, a2 + a -2
= ( a + 1/a )2 - 2
= ( 2 + √3 + 2 - √3)2 - 2
= (4)2 - 2 = 16 - 2 = 14

MCQ: Indices and Surds - 1 - Question 10

If (p/q)n - 1 = (q/p)n - 3, then the value of n is

Detailed Solution for MCQ: Indices and Surds - 1 - Question 10

Given equation is below
(p/q)n - 1 = (q/p)n - 3
Apply the law of Fractional Exponents and Laws of Exponents
a - m = 1/a m
or
am = 1/a - m
(p/q)n - 1 = (q) - (n - 3) x 1/ (p) - (n - 3)
(p/q)n - 1 = (p) 3 - n x 1/ (q) 3 - n
(p/q)n - 1 = (p/q) 3 - n
if pX = pY then X will be equal to Y. means X = Y;
⇒ n - 1 = 3 - n
⇒ 2n = 4
⇒ n = 2

MCQ: Indices and Surds - 1 - Question 11

[(12)-2]2/[(12)2]-2 = ?

Detailed Solution for MCQ: Indices and Surds - 1 - Question 11

? = [(12)-2]2/[(12)2]-2
Apply the Algebra Law,
(am)n = amn

= (12) - 4/(12) - 4
= 1

MCQ: Indices and Surds - 1 - Question 12

[ (11)3 x (6)2] ÷ (4)3 = ?

Detailed Solution for MCQ: Indices and Surds - 1 - Question 12

? = [ (11)3 x (6)2 ] x 1/43
? = [ 113 x 62 ] x 1/43
Solve the equation by algebra law.
?= [ 1331 x 36 ] x 1/64 =1331 x 36 / 64
? = 748.6875

MCQ: Indices and Surds - 1 - Question 13

(16)–3/4 + 2–3 + (8)–2/3 is equivalent to :

Detailed Solution for MCQ: Indices and Surds - 1 - Question 13

(16)–3/4 + 2–3 + (8)–2/3

MCQ: Indices and Surds - 1 - Question 14

is equivalent to :

Detailed Solution for MCQ: Indices and Surds - 1 - Question 14

MCQ: Indices and Surds - 1 - Question 15

If m and n are natural numbers, the m√n

Detailed Solution for MCQ: Indices and Surds - 1 - Question 15

If and n are natural numbers, then m√n is irrational unless is mth power of an integer.

## Quantitative Aptitude for SSC CGL

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## Quantitative Aptitude for SSC CGL

314 videos|170 docs|185 tests