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
3^{8} + 3^{9} = 3^{8} ⋅ (1 + 3) = 4 ⋅ 3^{8}
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 L^{3}. If the length is tripled, it becomes (3L)^{3}, and 3^{3} = 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: 11^{100} − 11^{99}
A. 10⋅11^{99}
B. 11^{99}
C. 11^{98}
D. 10⋅11^{98}
Answer: Option A
Explanation: 11^{100} − 11^{99} = 11⋅11^{99 }− 1⋅11^{99} = (11 − 1)⋅11^{99} = 10⋅11^{99}
11. If x^{2} = 8, what is x^{4}?
A. 16
B. 32
C. 64
D. 124
Answer: Option C
Explanation:
12. Solve:
A. 10/99
B. 10^{7}/99
C. 100/99
D. 10^{7}
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:
215 videos139 docs151 tests

1. What are the different types of roots? 
2. How do roots absorb water and nutrients? 
3. What is the function of roots in plants? 
4. Can roots grow in different directions? 
5. How do roots contribute to soil health? 

Explore Courses for UPSC exam
