Practice Questions for Roots | CSAT Preparation - UPSC PDF Download

A. 24
B. 12
C. 48
D. 36
Answer: Option A
Explanation:

 

A. 2.24
B. 1.24
C. 1.34
D. 2.34
Answer: Option D
Explanation:


3. If   , then what will be the value of
A. 21.66
B. 13.41
C. 22.35
D. 44.7
Answer: Option D
Explanation:

 
4. The cube root of 0.000729 is
A. 0.09
B. 0.9
C. 0.21
D. 0.11
Answer: Option A
Explanation:

5. What is the least perfect square which is divisible by each of 21, 36 and 66?
A. 213444
B. 214434
C. 214344
D. 231444
Answer: Option A
Explanation:
LCM of 21, 36, 66 = 2772
ie, all multiples of 2772 are divisible by 21, 36 and 66
Prime factorization of 2772 is,
2772 = 2 × 2 × 3 × 3 × 7 × 11
ie, to make it a perfect square, we have to multiply it by 7 and 11
Hence, required number = 2772 × 7 × 11 = 213444

6. In the sequence 1, 3, 9, 27, 81, … , each term after the first is three times the previous term. What is the sum of the 9th and 10th terms in the sequence?
A. 6(3)⁹
B. 6(3)⁸
C. (3)¹⁰
D. 4(3)⁸
Answer: Option D
Explanation:
We can rewrite the sequence as (3)⁰, (3)¹, (3)², (3)³, (3)⁴, … ,
and we can see that the 9th term in the sequence is (3)⁸ and the 10th term in the sequence is (3)⁹. Therefore, the sum of the 9th and 10th terms would be
3⁸ + 3⁹ = 3⁸ ⋅ (1 + 3) = 4 ⋅ 3⁸

7.
A. 2
B. 64
C. 4
D. 32
Answer: Option A
Explanation: This can either be done by brute force (slow) or by recognizing the properties of roots and exponents (fast).  Roots are simply fractional exponents:  etc. so they can be done in any order.
So we see a cube root, we can immediately cancel that with the exponent of 3. taking us from here:    We now simplify

8. If the side length of a cube is tripled, how does the volume of the cube change?
A. Volume becomes 27 times larger.
B. Not enough information is given.
C. Volume becomes 9 times larger.
D. Volume becomes 3 times larger.
Answer: Option A
Explanation: The equation for the volume of a cube is L³.  If the length is tripled, it becomes (3L)³, and 3³ = 27, so the volume increases by 27 times the original size.

9. Simplify this expression as much as possible:

A.
B.
C.
D. 
Answer: Option D
Explanation: 


10. Evaluate: 11¹⁰⁰ − 11⁹⁹
A. 10⋅11⁹⁹
B. 11⁹⁹
C. 11⁹⁸
D. 10⋅11⁹⁸
Answer: Option A
Explanation: 11¹⁰⁰ − 11⁹⁹ = 11⋅11⁹⁹ − 1⋅11⁹⁹ = (11 − 1)⋅11⁹⁹ = 10⋅11⁹⁹

11. If x² = 8, what is x⁴?
A. 16
B. 32
C. 64
D. 124
Answer: Option C
Explanation:

12. Solve:

A. 10/99
B. 10⁷/99
C. 100/99
D. 10⁷
Answer: Option D
Explanation:


13. Solve: (√5 + √4)²
A. 20
B. 9 + 4√5
C. 20 + 4√5
D. 9
Answer: Option B
Explanation:
First, FOIL:


14. 
A.
B.
C.
D. 
Answer: Option C
Explanation:


15. Solve: 

A. 0.125
B. 0.25
C. 4
D. 8
Answer: Option D
Explanation: