MCQ: Square Roots and Cube Roots - 1 - SSC CGL MCQ

# MCQ: Square Roots and Cube Roots - 1 - SSC CGL MCQ

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## 15 Questions MCQ Test SSC CGL Tier 2 - Study Material, Online Tests, Previous Year - MCQ: Square Roots and Cube Roots - 1

MCQ: Square Roots and Cube Roots - 1 for SSC CGL 2024 is part of SSC CGL Tier 2 - Study Material, Online Tests, Previous Year preparation. The MCQ: Square Roots and Cube Roots - 1 questions and answers have been prepared according to the SSC CGL exam syllabus.The MCQ: Square Roots and Cube Roots - 1 MCQs are made for SSC CGL 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for MCQ: Square Roots and Cube Roots - 1 below.
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MCQ: Square Roots and Cube Roots - 1 - Question 1

### (√6 + 1)2 = ? + 2√6

Detailed Solution for MCQ: Square Roots and Cube Roots - 1 - Question 1

? = (√6 + 1)2 − 2√6 = 6 + 1 + 2√6 − 2√6 = 7

MCQ: Square Roots and Cube Roots - 1 - Question 2

### √225 + √2304 = ? − (12)2

Detailed Solution for MCQ: Square Roots and Cube Roots - 1 - Question 2

? = √225 + √2304 + (12)2 = 15 + 48 + 144 = 207

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MCQ: Square Roots and Cube Roots - 1 - Question 3

### The volumes of two cubes are in the ratio 343 : 1331, the ratio of their edges, is

Detailed Solution for MCQ: Square Roots and Cube Roots - 1 - Question 3

Let volume of cubes = a3 and b3

a/b = 7/11
or a : b = 7 : 11

MCQ: Square Roots and Cube Roots - 1 - Question 4

(16)2 − 53 + √169 = (?)2

Detailed Solution for MCQ: Square Roots and Cube Roots - 1 - Question 4

(16)2 − 53 + √169 = (?)2

256 – 125 + 13 = (?)2

144 = (?)2

? = ± 12

MCQ: Square Roots and Cube Roots - 1 - Question 5

10 - x divides ((49)15 -1) completely. What is x?

Detailed Solution for MCQ: Square Roots and Cube Roots - 1 - Question 5

(x- 1) is divisible by x + 1 if n is an even number. (49)15 - 1 = [(72)15 - 1] = (7)30 - 1 which is divisible by 7 + 1 ,8.
10-x=8  so x=2

MCQ: Square Roots and Cube Roots - 1 - Question 6

What should be added to 81x2 + 64y2 to make it a perfect square?

Detailed Solution for MCQ: Square Roots and Cube Roots - 1 - Question 6

81x2=(9x)2
64y2=(8y)2
so term missing 2(9x)(8y)=144xy

MCQ: Square Roots and Cube Roots - 1 - Question 7

What is the sum of first five prime numbers?

Detailed Solution for MCQ: Square Roots and Cube Roots - 1 - Question 7

First five prime numbers are 2, 3, 5, 7, 11. Sum - 28

MCQ: Square Roots and Cube Roots - 1 - Question 8

The smallest number by which 136 must be multiplied so that it becomes a perfect square is

Detailed Solution for MCQ: Square Roots and Cube Roots - 1 - Question 8

Resolve 136 into prime factors and make group of two of each prime factor

136 = 2 × 2 × 2 × 17

136 = (2 × 2) × 2 × 17

We find that 2 and 17 doesn't appear in group of two. So, 136 has to be multiplied with 34 to make it a perfect square.

MCQ: Square Roots and Cube Roots - 1 - Question 9

(64)2 - (36)2 = 20y. What is y?

Detailed Solution for MCQ: Square Roots and Cube Roots - 1 - Question 9

(64)2 - (36)2 = 20 y Using formulae (a + b)(a - b) = a2 - b2
=> (64 + 36)(64 - 36) = 20 y => 100 x 28 = 20 y => y = 5 x 28 = 140

MCQ: Square Roots and Cube Roots - 1 - Question 10

What must be added to 24136 to make it a perfect square?

Detailed Solution for MCQ: Square Roots and Cube Roots - 1 - Question 10

∴ 24136 < (156)2
24136 < 24336
∴ we add 24336 – 24136 = 200
so that it becomes a perfect square

MCQ: Square Roots and Cube Roots - 1 - Question 11

9548 + 7314 = 8362 + x. What is x?

Detailed Solution for MCQ: Square Roots and Cube Roots - 1 - Question 11

9548 + 7314 = 8362 + x ∴ x = 9548 + 7314 - 8362 = 8500

MCQ: Square Roots and Cube Roots - 1 - Question 12

The product of two numbers is 1936. If one number is 4 times the other, the numbers are

Detailed Solution for MCQ: Square Roots and Cube Roots - 1 - Question 12

Let one number = a
∴ Second number = 4a
⇒ 4a × a = 1936
⇒ a2 = 1936/4 = 484
⇒ a2 = 484
⇒ a = 2 × 11 = 22
and 4a = 4 × 22 = 88
∴ Numbers are 22 and 88.

MCQ: Square Roots and Cube Roots - 1 - Question 13

Which of the following number divides 325 + 326 + 327 + 328 completely?

Detailed Solution for MCQ: Square Roots and Cube Roots - 1 - Question 13

325 + 326 + 327 + 328 = 324 x (31 + 32 + 33 + 34) = 324 x (3 + 9 + 27 + 81) = 460 x 120 which is divisible by 30.

MCQ: Square Roots and Cube Roots - 1 - Question 14

Area of a square field is 22500 m2. A man cycles along its boundary at 15 km/ hr. The time will be taken by a man to return to starting point, is

Detailed Solution for MCQ: Square Roots and Cube Roots - 1 - Question 14

Let the side of square field = 'a' m

∴ Area of square field = a2 sq. m

a= 22500 m2

⇒ a = 150 m

Speed of cycling = 15 km / hr

Now, total distance to be covered along the boundary

= 4 × 150 = 600 m

∵ 25/6 m is covered in 1 sec.

∴ 600 m is covered in 600/25×6

=144 sec = 2 min 24 sec.

MCQ: Square Roots and Cube Roots - 1 - Question 15

The largest three digit multiple of 32?

Detailed Solution for MCQ: Square Roots and Cube Roots - 1 - Question 15

999 is the largest three digit number.
On dividing 999 by 32, remainder is 7.
999 - 7 = 992
Therefore, 992 is the largest three digit multiple of 32.

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