Surds and Indices - Quantitative Aptitude SSC Notes | EduRev

Quantitative Aptitude for SSC CGL

SSC : Surds and Indices - Quantitative Aptitude SSC Notes | EduRev

The document Surds and Indices - Quantitative Aptitude SSC Notes | EduRev is a part of the SSC Course Quantitative Aptitude for SSC CGL.
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Q 1. What will come in place o f question mark in Surds and Indices - Quantitative Aptitude SSC Notes | EduRev

a. 12
b. 6
c. 16
d. 8

ANSWER: 12 

Explanation:.

Surds and Indices - Quantitative Aptitude SSC Notes | EduRev
Surds and Indices - Quantitative Aptitude SSC Notes | EduRev

Q 2. What is value of (0.000001) ?

a. 0.000001
b. 0.001
c. 1/100
d. 0.1

ANSWER: 1/100

Explanation: 

 Surds and Indices - Quantitative Aptitude SSC Notes | EduRev

If a cube has 6 decimals, then its cube
root will have 6/3 = 2 decimals

Surds and Indices - Quantitative Aptitude SSC Notes | EduRev

Q 3. What will be value of Surds and Indices - Quantitative Aptitude SSC Notes | EduRev(684)2= 467856?  

a. 6.84
b. 0.0684
c. 0.684
d. 0.000684

ANSWER: 6.84 

Explanation: 

I f a square has 4 decimals, then its
square root will have 4/2 = 2 decimals

Surds and Indices - Quantitative Aptitude SSC Notes | EduRev

Q 4. If value of Surds and Indices - Quantitative Aptitude SSC Notes | EduRevis approximately 5.2915, then value ofSurds and Indices - Quantitative Aptitude SSC Notes | EduRev is approximately  

a. 1.2000
b. 0.5687
c. 1.3228
d. 1.4652

ANSWER: 1.3228 

Explanation:  

Surds and Indices - Quantitative Aptitude SSC Notes | EduRev

Q 5. How many zeroes are there in 200010?  

a. 10
b. 30
c. 20
d. 15

ANSWER: 30 

Explanation:  

200010 = 2000 x ... 10 times
2000 = 2 x 1000 i.e it has 3 zeroes.

So that means 3 zeroes x 10 times= 30 zeroes

Q 6. What is value of (36)?  

a. 2
b.Surds and Indices - Quantitative Aptitude SSC Notes | EduRev
c. 1
d.Surds and Indices - Quantitative Aptitude SSC Notes | EduRev

ANSWER: Surds and Indices - Quantitative Aptitude SSC Notes | EduRev

Explanation:  

Surds and Indices - Quantitative Aptitude SSC Notes | EduRev

Q 7. What is value of M in (p/q)2M+2 = (q/p)9-M  

a. 6
b. 5
c. -7/2
d. -11

ANSWER: -11 

Explanation:  

Surds and Indices - Quantitative Aptitude SSC Notes | EduRev

Since the base is same i.e. p/q, we can equate the powers of both
∴ 2M+2 = -(9-M)

∴ 2M+2 = -9+M

∴ M = -11

Q 8. What is value of 22(-2)  

Surds and Indices - Quantitative Aptitude SSC Notes | EduRev

ANSWER: Surds and Indices - Quantitative Aptitude SSC Notes | EduRev

Explanation: 

Surds and Indices - Quantitative Aptitude SSC Notes | EduRev

Q 9. What is value of 2(-2)2  

a. 1/16
b. 1/8
c. 32
d. 16

ANSWER: 16 

Explanation: 

Surds and Indices - Quantitative Aptitude SSC Notes | EduRev Negative number raised to even power gives positive answer

Q 10. There are four expressions given below separated by ‘=’ sign. Which one of the 4 expressions is not the same as the other three?
62 x 6 = (61)3 = 23+33 = 83 - 142 - 102
 

a. (61)3
b. 83 - 142 - 102
c. 23+33
d. All are same

ANSWER: 23+33 

Explanation: 

This is very easy to solve
The first expression is 62 x 6 = 63 = 216.

The second expression is (61)3 = 61 x 3 = 63 = 216
The third expression is 23+33 = 8+27 = 35 = ≠ other two
So answer is Option C

Question 11:  Surds and Indices - Quantitative Aptitude SSC Notes | EduRev = ?

a) 5
b) 6
c) 7
d) None of these
Answer (D) 
Explanation:  
Surds and Indices - Quantitative Aptitude SSC Notes | EduRev
Surds and Indices - Quantitative Aptitude SSC Notes | EduRev
= 14/3

Question 12: Find the value of x in 2|5x - 6| = 83x - 2
a) 2/3
b) 6/7
c) 9/5
d) cannot be determined 
Answer (B) 
Explanation:  
Surds and Indices - Quantitative Aptitude SSC Notes | EduRev
Taking log on both sides we get, 
Surds and Indices - Quantitative Aptitude SSC Notes | EduRev
 |5x – 6| = 3(3x – 2) = 9x – 6
When x > 6/5, |5x – 6| = 5x – 6
Thus, 5x – 6 = 9x – 6
 5x = 9x which is not possible
When x < 6/5, |5x – 6| = 6 – 5x
Thus, 6 – 5x = 9x – 6
14x = 12
 x = 6/7 

Question 13: If log152 729 = x, then what is the value of log81 5625 ? 

a) Surds and Indices - Quantitative Aptitude SSC Notes | EduRev
b) Surds and Indices - Quantitative Aptitude SSC Notes | EduRev
c) Surds and Indices - Quantitative Aptitude SSC Notes | EduRev
d) Surds and Indices - Quantitative Aptitude SSC Notes | EduRev
Answer (A) 
Explanation:  log125 729
= log5 9
= x
Surds and Indices - Quantitative Aptitude SSC Notes | EduRev
Surds and Indices - Quantitative Aptitude SSC Notes | EduRev
Surds and Indices - Quantitative Aptitude SSC Notes | EduRev
= Surds and Indices - Quantitative Aptitude SSC Notes | EduRev 

Question 14: Find the number of digits in the number 240127 when written in base 7. 
a) 117
b) 181
c) 98
d) 109 

Answer (D) 
Explanation: 
The formula for finding the number of digits in a number ‘m’ in base ‘n’ is: 
[logn(m)] + 1 , where [A] is greatest integer less than or equal to A. 
2401 = 74
Surds and Indices - Quantitative Aptitude SSC Notes | EduRev
Thus, the answer is D. 

Question 15: What is the value of  Surds and Indices - Quantitative Aptitude SSC Notes | EduRev
a) -2
b) -1
c) 0
d) None of these

Answer (A) 
Explanation:
Surds and Indices - Quantitative Aptitude SSC Notes | EduRev
 Surds and Indices - Quantitative Aptitude SSC Notes | EduRev

Question 16: If  32x+3-244*3x = -9, then which of the following statements is true? 
a) ‘x’ is a positive number
b) ‘x’ is a negative number
c) ‘x’ can be either a positive number or a negative number
d) None of the above

Answer (C) 
Explanation:
The equation can be written as follow: 
Surds and Indices - Quantitative Aptitude SSC Notes | EduRev
Let 3x = t
⇒ 27t2 - 244t + 9 = 0
⇒ 27t2 - 243t-t + 9 = 0
⇒ 27t(t - 9)-1(t - 9) = 0
 t = 9 or t = 1/27
⇒ 3x = 32 or 3x = 3-3
So, x = 2 or x = -3
So, ‘x’ can be either a positive number or a negative number. Option c) is the correct answer 

Question 17: If x,y are natural numbers, log8+log5 = log(x+y)+log(x-y) and log8+log11 = log(x-y)+log(1+xy), then find the value of (x3 - y3)
a) 325
b) 316
c) 643
d) 602 

Answer (B)
Explanation:
log(x+y)(x-y) = log40
(x+y)(x-y) = 40
x+y = 10 and x-y = 4 or x+y = 20 and x-y = 2
x = 7 and y = 3 or x = 11 and y = 9.
log88 = log(x-y)(1+xy)
x = 7 and y = 3 satisfy the equation. 

(x3 - y3) = 73 - 33 = 316 

Question 18: If log16 5 = x and log3 = y, find the value of log3 6 in terms of x and y?
a)  Surds and Indices - Quantitative Aptitude SSC Notes | EduRev
b) Surds and Indices - Quantitative Aptitude SSC Notes | EduRev
c) Surds and Indices - Quantitative Aptitude SSC Notes | EduRev
d) 1 + 4xy
Answer (A) 
Explanation:

log16 5 = x
Surds and Indices - Quantitative Aptitude SSC Notes | EduRev
log5 3 = y
Surds and Indices - Quantitative Aptitude SSC Notes | EduRev

We have to find the value of log3 6

= 1+ Surds and Indices - Quantitative Aptitude SSC Notes | EduRev
= 1+ Surds and Indices - Quantitative Aptitude SSC Notes | EduRev
= 1+1/4xy = Surds and Indices - Quantitative Aptitude SSC Notes | EduRev


Question 19: Find the value of log1010 + log10102 + ..... +log1010n

a) Surds and Indices - Quantitative Aptitude SSC Notes | EduRev
b) Surds and Indices - Quantitative Aptitude SSC Notes | EduRev
c) Surds and Indices - Quantitative Aptitude SSC Notes | EduRev
d) Surds and Indices - Quantitative Aptitude SSC Notes | EduRev
Answer (B) 
Explanation:
Surds and Indices - Quantitative Aptitude SSC Notes | EduRev
Surds and Indices - Quantitative Aptitude SSC Notes | EduRev
Surds and Indices - Quantitative Aptitude SSC Notes | EduRev
Surds and Indices - Quantitative Aptitude SSC Notes | EduRev
Surds and Indices - Quantitative Aptitude SSC Notes | EduRev


Question 20: If Surds and Indices - Quantitative Aptitude SSC Notes | EduRev. Find x
a) 512
b) 289
c) 170
d) None of these
Answer (D)  
Explanation:

Surds and Indices - Quantitative Aptitude SSC Notes | EduRev
Surds and Indices - Quantitative Aptitude SSC Notes | EduRev
Surds and Indices - Quantitative Aptitude SSC Notes | EduRev
Surds and Indices - Quantitative Aptitude SSC Notes | EduRev
Surds and Indices - Quantitative Aptitude SSC Notes | EduRev
⇒ x = 28900
Since there is no such option, the correct option to choose is D – None of these.

Logarithms, Surds and Indices questions will be asked in CAT quantitative aptitude section,

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