MCQ: Indices and Surds - 2 - SSC CGL MCQ

MCQ: Indices and Surds - 2 - SSC CGL MCQ

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15 Questions MCQ Test Quantitative Aptitude for SSC CGL - MCQ: Indices and Surds - 2

MCQ: Indices and Surds - 2 for SSC CGL 2024 is part of Quantitative Aptitude for SSC CGL preparation. The MCQ: Indices and Surds - 2 questions and answers have been prepared according to the SSC CGL exam syllabus.The MCQ: Indices and Surds - 2 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 - 2 below.
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MCQ: Indices and Surds - 2 - Question 1

If a2x + 2 = 1,where a is a positive real number other than 1, then x = ?

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

Given that, a2x + 2 = 1
Apply the algebra Law,
p0 = 1

⇒ a2x + 2 = a0
Apply the algebra law
pX = pY then X will be equal to Y. means X = Y;

⇒ 2x + 2 = 0
⇒ x = -2/2 = -1

MCQ: Indices and Surds - 2 - Question 2

If {(24)1/2}? = 256, find the value of '?'.

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

Given that, (24x 1/2)? = 256
Apply the law of Fractional Exponents and Laws of Exponents
⇒ (22)? = 28
⇒ 22 x ? = 28
⇒ 2 x ? = 8
∴ ? = 8/2 = 4

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MCQ: Indices and Surds - 2 - Question 3

Third power of 4 is equivalent to :

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

Third power of 4 = 43 = 4 × 4 × 4 = 64

MCQ: Indices and Surds - 2 - Question 4

What is the difference between the third power of 2 and the second power of 3?

Detailed Solution for MCQ: Indices and Surds - 2 - Question 4

Third power of 2 = 23 = 2 × 2 × 2 = 8
And second power of 3 = 32 = 3 × 3 = 9
∴ Difference = 9 – 8 = 1

MCQ: Indices and Surds - 2 - Question 5

Find the value of m - n, if ( 9n x 32 x (3-n/2)-2 - (27)n ) / ( 33m x 23 ) = 1/27 ?

Detailed Solution for MCQ: Indices and Surds - 2 - Question 5

( 9n x 32 x (3-n/2)-2 - (27)n ) / ( 33m x 23 ) = 1/27
⇒ ( 32n x 32 x 3n - 33n) / ( 33m x 23 ) = 1/27
⇒ ( 32n + n x 32 - 33n) / ( 33m x 23 )= 1/27
⇒ ( 33n x 32 - 33n) / ( 33m x 23 ) = 1/27
⇒ 33n( 32 - 1) / ( 33m x 8 ) = 1/27
⇒ 33n( 9 - 1) / (33m x 8 ) = 1/27
⇒ ( 33n x 8 ) / (33m x 8 ) = 1/27
⇒ 33n / 33m = 1/27
⇒ 33n - 3m = 1/33
⇒ 33( n - m ) = 3-3
3(n - m) = -3
or n - m = -1
or m - n = 1

MCQ: Indices and Surds - 2 - Question 6

If 16 x 8n + 2 = 2m, then m is equal to

Detailed Solution for MCQ: Indices and Surds - 2 - Question 6

Given that 16 x 8n + 2 = 2m

Apply the law of Fractional Exponents and Laws of Exponents
if a multiply three times a x a x a then
a x a x a = a3
if a multiply two times a x a then
a x a = a2
if a multiply n times a x a x a x....up to n times, then
a x a x a x a ......up to n times = an
⇒ (2)4 x 23 x (n+2) = 2m
⇒ (2)4 x 23n+6 = 2m
aman = am+n
⇒ (2)(4 + 3n + 6) = 2m
⇒ (2)(3n + 10) = 2m
if pX = pY then X will be equal to Y. means X = Y;
On comparing, we get
3n + 10 = m
⇒ m = 3n + 10;

MCQ: Indices and Surds - 2 - Question 7

If x - 1 + 2 x + 1 = 320, then find the value of x ?

Detailed Solution for MCQ: Indices and Surds - 2 - Question 7

∵ 2x - 1 + 2x + 1 = 320
Apply the law of Algebra
⇒ 2x - 1(1 + 2 2 ) = 320
⇒ 2x - 1(1 + 4 ) = 320
⇒ 2x - 1 x 5 = 320
⇒ 2x - 1 = 64 = 2 x 2 x 2 x 2 x 2 x 2
⇒ 2x - 1 = 26
if pX = pY then X will be equal to Y. means X = Y;
⇒ x - 1 = 6
∴ x = 7

MCQ: Indices and Surds - 2 - Question 8

Find the value of (10)200 ÷ (10)196 .

Detailed Solution for MCQ: Indices and Surds - 2 - Question 8

Given equation is
(10)200 ÷ (10)196
Apply the law of Algebra
am ÷ an = am ? n

= (10)200 - 196
= 104
= 10000

MCQ: Indices and Surds - 2 - Question 9

Evaluate ( 0.00032)2/5

Detailed Solution for MCQ: Indices and Surds - 2 - Question 9

Given that
(0.00032)2/5 = (32/100000)2/5
Solve the equation by algebra Law
= (25/105)2/5
= {(2/10)5}2/5
= (2/10)5x2/5
= (1/5)2 = 1/25

MCQ: Indices and Surds - 2 - Question 10

Value of ? in expression
78.9 ÷ (343)1.7 x (49)4.8 = 7? is

Detailed Solution for MCQ: Indices and Surds - 2 - Question 10

78.9 ÷ (343)1.7 x (49)4.8 = 7?
Apply the law of Fractional Exponents and Laws of Exponents
(am)(an) = am+n
am÷an=am?n
am/an=am?n
(am)n = amn
78.9 ÷ (343)1.7 x (49)4.8 = 7?
⇒ 78.9 ÷ (73)1.7 x (72)4.8 = 7?
⇒ 78.9 ÷ 75.1 x 79.6 = 7?
⇒ 78.9 - 5.1 + 9.6 = 7?
⇒ 718.5 - 5.1 = 7?
∴ ? = 13.4

MCQ: Indices and Surds - 2 - Question 11

If 3x - 3x-1 = 18, then xx is equal to

Detailed Solution for MCQ: Indices and Surds - 2 - Question 11

∵ 3x - 3x - 1 = 18
⇒ 3x - 1(3 - 1) = 18
⇒ 3x - 1(2) = 18
⇒ 3x - 1 = 18/2
⇒ 3x - 1 = 9
⇒ 3x - 1 = 32
Apply the Algebra law,
If aX = aY then X will be equal to Y.
means X = Y;
⇒ x - 1 = 2
⇒ x = 3
Then xx = (3)3 = 27

MCQ: Indices and Surds - 2 - Question 12

If 2x - 1 + 2x + 1 = 2560, find the value of x.

Detailed Solution for MCQ: Indices and Surds - 2 - Question 12

2x - 1 + 2x + 1 = 2560
2x - 1 + 2x - 1 + 2 = 2560
Apply the Law of Algebra
2x - 1 + 2x - 1 x 2 2 = 2560
⇒ 2x - 1 ( 1 + 22 ) = 2560
⇒ 2x - 1 = 2560/5 = 512 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
⇒ 2x - 1 = 29
x - 1 = 9
∴ = 9 + 1 = 10

MCQ: Indices and Surds - 2 - Question 13

if ax = b, by= c and xyz = 1, then what is the value of cz ?

Detailed Solution for MCQ: Indices and Surds - 2 - Question 13

Given, xyz = 1, ax = b, by = c
Now, b = ax
Apply the law of algebra .
Take the power y of both side equation.
⇒ by= axy
Take the power z of both side equation.
⇒ byz = axyz
⇒ ( by )z = axyz
Replace the by with c and xyz with as per given equation,
⇒ cz = a

MCQ: Indices and Surds - 2 - Question 14

Find the quotient when (a-1 - 1) is divided by (a - 1).

Detailed Solution for MCQ: Indices and Surds - 2 - Question 14

Given equation is
a-1 - 1
Apply the law of Fractional Exponents and Laws of Exponents
x-y = 1/xy
⇒ a-1 - 1 = 1/a - 1
⇒ a-1 - 1 = (1 - a)/a
Now divide by a - 1 in above equation,
⇒ ( a-1 - 1 ) ÷ (a - 1) = (1 - a)/a ÷ (a - 1)
⇒ ( a-1 - 1 ) ÷ (a - 1) = (1 - a)/a x 1/ (a - 1)
⇒ ( a-1 - 1 ) ÷ (a - 1) = -1x (a - 1)/a x 1/ (a - 1)
⇒ ( a-1 - 1 ) ÷ (a - 1) = -1/a
∴ Required quotient = -1/a.

MCQ: Indices and Surds - 2 - Question 15

What is the value of a5 × a7?

Detailed Solution for MCQ: Indices and Surds - 2 - Question 15

a5 × a= a5 + 7 = a12

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