Practice Questions for Roots

# Practice Questions for Roots | CSAT Preparation - UPSC PDF Download

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

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

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

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

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

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.

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.

Explanation:

10. Evaluate: 11100 − 1199
A. 10⋅1199

B. 1199
C. 1198
D. 10⋅1198

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

Explanation:

12. Solve:

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

13. Solve: (√5 + √4)2
A. 20
B. 9 + 4√5
C. 20 + 4√5
D. 9

Explanation:
First, FOIL:

14.
A.
B.
C.
D.

Explanation:

15. Solve:

A. 0.125
B. 0.25
C. 4
D. 8

Explanation:

The document Practice Questions for Roots | CSAT Preparation - UPSC is a part of the UPSC Course CSAT Preparation.
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## FAQs on Practice Questions for Roots - CSAT Preparation - UPSC

 1. What are the different types of roots?
Ans. There are three main types of roots: taproots, fibrous roots, and adventitious roots. Taproots are thick and have one main root, while fibrous roots are thin and spread out. Adventitious roots grow from stems or leaves.
 2. How do roots absorb water and nutrients?
Ans. Roots have specialized structures called root hairs that increase their surface area for absorption. Through a process called osmosis, water and dissolved nutrients move from areas of high concentration in the soil to areas of low concentration in the root cells.
 3. What is the function of roots in plants?
Ans. Roots have several important functions in plants. They anchor the plant in the ground, provide support and stability, and absorb water and nutrients from the soil. Roots also store food and nutrients for the plant's growth and development.
 4. Can roots grow in different directions?
Ans. Yes, roots can grow in different directions depending on various factors such as gravity, light, and the presence of obstacles. Roots exhibit tropisms, which are growth responses to stimuli, and can grow towards or away from certain stimuli.
 5. How do roots contribute to soil health?
Ans. Roots play a crucial role in maintaining soil health. They help in soil aeration by creating channels for air to enter the soil. Roots also release organic compounds that nourish beneficial soil microorganisms. Additionally, the growth and decay of roots contribute to the organic matter content in the soil, improving its fertility and structure.

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