52 + Interview Questions in SQUARE ROOTS IN GENERAL AWARENESS Page 1 InterviewSolution

1.	1521 trees are planted in a garden in such a way that there are as many trees in each row as there are rows in the garden. Find the number of rows and number of trees in each row.
Answer» Let the no. of trees planted in a garden for each row = x say. No. of rows in the garden = x ∴ Total no. of trees in the garden = x × x = x² According to the sum x² = 1521 x = \(\sqrt{1521}\) = \(\sqrt{39\,\times\,39}\) = 39 ∴ No. of trees for each row = 39 No. of rows in the garden = 39

1.

1521 trees are planted in a garden in such a way that there are as many trees in each row as there are rows in the garden. Find the number of rows and number of trees in each row.

Answer»

Let the no. of trees planted in a garden for each row = x say.

No. of rows in the garden = x

∴ Total no. of trees in the garden = x × x = x²

According to the sum x² = 1521

x = \(\sqrt{1521}\) = \(\sqrt{39\,\times\,39}\) = 39

∴ No. of trees for each row = 39

No. of rows in the garden = 39

Discussion

2.	Kishore told “Every number is a square number”. Krishna told “Every number is a pure number”. In the above two statements who is correct ? A) Kishore B) Krishna C) Both are correct D) Both are false
Answer» D) Both are false

Discussion

3.	\(\sqrt{625}\) + \(\sqrt{441}\) = .............A) 47 B) \(\sqrt{1066}\)C) 46 D) 45
Answer» Correct option is C) 46 Correct option is (C) 46 \(\sqrt{625}+\sqrt{441}\) = 25+21 = 46.

3.

\(\sqrt{625}\) + \(\sqrt{441}\) = .............A) 47 B) \(\sqrt{1066}\)C) 46 D) 45

Answer»

Correct option is C) 46

Correct option is (C) 46

\(\sqrt{625}+\sqrt{441}\) = 25+21 = 46.

Discussion

4.

What will be the units digit of the square of the following numbers?(i) 39 (ii) 297 (iii) 5125 (iv) 7286 (v) 8742

Answer»

Number	Square of the units digit	Units digit of a squared number
i) 39	9² = 9 x 9 = 81	1
ii) 297	7² = 7 x 7 = 49	9
Iii) 5125	5² = 5 x 5 = 25	5
iv) 7286	6² = 6 x 6 = 36	6
v) 8742	2²= 2 x 2 = 4	4

Discussion

5.	The units digit in the square of 431 is ………………… A) 3 B) 7 C) 0 D) 1
Answer» Correct option is D) 1 Correct option is (D) 1 \(\because\) Unit's digit in 431 = 1 \(\therefore\) Unit's digit in \((431)^2=1.\) \((\because\) Cyclicity of 1 is 1)

5.

The units digit in the square of 431 is ………………… A) 3 B) 7 C) 0 D) 1

Answer»

Correct option is D) 1

Correct option is (D) 1

\(\because\) Unit's digit in 431 = 1

\(\therefore\) Unit's digit in \((431)^2=1.\) \((\because\) Cyclicity of 1 is 1)

Discussion

6.

Which of the following numbers are perfect squares?(i) 121 (ii) 136 (iii) 256 (iv) 321 (v) 600

Answer»

Number	Prime factorization	Perfect square numbers Yes/No
i) 121	121 = 11 x 11 = 11²	yes
ii) 136	136 = 8 x 17 = 2 x 2 x 2 x 17	No
iii) 256	256 = 2 x 2 x 2 x 2 x 2 x 2 x 2x 2 = 2⁸= (2⁴)²	yes
iv) 321	321 = 3 x 107	No
v) 600	600 = 120 x 5 = 12 x 10 x 5 = 2 x 2 x 2 x 3 x 5 x 5	No

Discussion

7.	The side of a square is 19 units then its area is ………………… sq. units. A) 312 B) 191 C) 163 D) 361
Answer» Correct option is D) 361 Correct option is (D) 361 Area \(=a^2=19^2=361\) square units.

7.

The side of a square is 19 units then its area is ………………… sq. units. A) 312 B) 191 C) 163 D) 361

Answer»

Correct option is D) 361

Correct option is (D) 361

Area \(=a^2=19^2=361\) square units.

Discussion

8.	A solid with 6 equal square faces on all the surfaces is called …………………..A) Side B) Cube C) Complete cube D) Cuboid
Answer» Correct option is B) Cube

Discussion

9.	1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25 = ……………… A) 132 B) 168 C) 139 D) 169
Answer» Correct option is D) 169 Correct option is (D) 169 \(\because\) 1+3+5+......+ (2n - 1) \(=n^2\) Since, if 2n - 1 = 25 \(\Rightarrow\) \(n=\frac{25+1}2=\frac{26}2=13\) \(\therefore\) 1+3+5+......+25 = \(13^2\) = 169.

9.

1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25 = ……………… A) 132 B) 168 C) 139 D) 169

Answer»

Correct option is D) 169

Correct option is (D) 169

\(\because\) 1+3+5+......+ (2n - 1) \(=n^2\)

Since, if 2n - 1 = 25

\(\Rightarrow\) \(n=\frac{25+1}2=\frac{26}2=13\)

\(\therefore\) 1+3+5+......+25 = \(13^2\) = 169.

Discussion

10.	17 < √x < 18, x = ………………. A) 100 B) 900 C) 300 D) 20
Answer» Correct option is C) 300 Correct option is (C) 300 17 < \(\sqrt x\) < 18 \(\Rightarrow\) 289 < x < 324 (By squaring) In given numbers, only 300 lies between 289 & 324.

10.

17 < √x < 18, x = ………………. A) 100 B) 900 C) 300 D) 20

Answer»

Correct option is C) 300

Correct option is (C) 300

17 < \(\sqrt x\) < 18

\(\Rightarrow\) 289 < x < 324 (By squaring)

In given numbers, only 300 lies between 289 & 324.

Discussion

11.	(24)2 = ……………… A) 512 B) 156 C) 258 D) 256
Answer» Correct option is D) 256 Correct option is (D) 256 \((2^4)^2=16^2=256.\)

11.

(24)2 = ……………… A) 512 B) 156 C) 258 D) 256

Answer»

Correct option is D) 256

Correct option is (D) 256

\((2^4)^2=16^2=256.\)

Discussion

12.	(√a) = ………………A) √a B) 2a C) a/2D) a
Answer» Correct option is D) a

Discussion

13.	35 = ……………. A) 243 B) 81 C) 813 D) 432
Answer» Correct option is A) 243

Discussion

14.	The product of two numbers is 1296. If one number is 16 times the other, find the two numbers?
Answer» Given that the product of two numbers = 1296. Let the second number = x say Then first number = 16 × x = 16x ∴ The product of two numbers = x × 16x= 16x² According to the sum 16x² = 1296 ⇒ x² = \(\frac{1296}{16}\) = 81 ⇒ x² = 81 ⇒ x = \(\sqrt{81}\) = \(\sqrt{9\,\times\,9}\) = 9 ⇒ x = 9 ∴ The first number = 16x = 16 × 9 =144 The second number = x = 9

14.

The product of two numbers is 1296. If one number is 16 times the other, find the two numbers?

Answer»

Given that the product of two numbers = 1296.

Let the second number = x say

Then first number = 16 × x = 16x

∴ The product of two numbers

= x × 16x= 16x²

According to the sum

16x² = 1296

⇒ x² = \(\frac{1296}{16}\) = 81

⇒ x² = 81

⇒ x = \(\sqrt{81}\) = \(\sqrt{9\,\times\,9}\) = 9

⇒ x = 9

∴ The first number = 16x

= 16 × 9 =144

The second number

= x = 9

Discussion

15.	How many cube numbers are there between 1 to 100 ? A) 9 B) 10C) 3 D) 13
Answer» Correct option is C) 3 Correct option is (C) 3 8, 27 & 64 are perfect cube numbers between 1 to 100. \(\therefore\) There is total 3 cube numbers between 1 to 100.

15.

How many cube numbers are there between 1 to 100 ? A) 9 B) 10C) 3 D) 13

Answer»

Correct option is C) 3

Correct option is (C) 3

8, 27 & 64 are perfect cube numbers between 1 to 100.

\(\therefore\) There is total 3 cube numbers between 1 to 100.

Discussion

16.	How many digits are there in the square of 72? A) 4 or 3 B) 3 or 6 C) 2 or 7 D) None
Answer» Correct option is A) 4 or 3 Correct option is (A) 4 or 3 \((72)^2=72\times72\) = 5184 \(\therefore\) 4 digits are in the square of 72.

16.

How many digits are there in the square of 72? A) 4 or 3 B) 3 or 6 C) 2 or 7 D) None

Answer»

Correct option is A) 4 or 3

Correct option is (A) 4 or 3

\((72)^2=72\times72\) = 5184

\(\therefore\) 4 digits are in the square of 72.

Discussion

17.	The side of a square is 72 cm then its perimeter is ……………. cm. A) 298 B) 148 C) 288 D) 188
Answer» Correct option is C) 288 Correct option is (C) 288 Perimeter = 4 \(\times\) side of square = 4 \(\times\) 72 = 288 cm.

17.

The side of a square is 72 cm then its perimeter is ……………. cm. A) 298 B) 148 C) 288 D) 188

Answer»

Correct option is C) 288

Correct option is (C) 288

Perimeter = 4 \(\times\) side of square

= 4 \(\times\) 72 = 288 cm.

Discussion

18.	1, 4, 9, 16, 25 are ………………… numbers. A) Square B) Cube C) Pure D) None
Answer» Correct option is A) Square

Discussion

19.	212 = ………………. A) 144 B) 441 C) 141 D) 191
Answer» Correct option is B) 441

Discussion

20.	(0.2)2 = ………….. A) 0.4 B) 0.004 C) 0.45 D) 0.04
Answer» Correct option is D) 0.04 Correct option is (D) 0.04 \((0.2)^2=(\frac2{10})^2=\frac{2^2}{10^2}=\frac4{100}=0.04\)

20.

(0.2)2 = ………….. A) 0.4 B) 0.004 C) 0.45 D) 0.04

Answer»

Correct option is D) 0.04

Correct option is (D) 0.04

\((0.2)^2=(\frac2{10})^2=\frac{2^2}{10^2}=\frac4{100}=0.04\)

Discussion

21.	\(\sqrt{55}\) is .......................A) not, a square number B) square number C) cube number D) value is 10
Answer» A) not, a square number Correct option is (A) not a perfect square number 55 = 5 \(\times\) 11 Factors 5 & 11 of 55 are not in square form in prime factorisation of 55. \(\therefore\) 55 is not a perfect square number.

21.

\(\sqrt{55}\) is .......................A) not, a square number B) square number C) cube number D) value is 10

Answer»

A) not, a square number

Correct option is (A) not a perfect square number

55 = 5 \(\times\) 11

Factors 5 & 11 of 55 are not in square form in prime factorisation of 55.

\(\therefore\) 55 is not a perfect square number.

Discussion

22.	How many integers are there between 92 and 102 ?A) 16 B) 13 C) 28 D) 18
Answer» Correct option is D) 18 Correct option is (D) 18 \(\because\) Total number of integers between \(n^2\;\&\;(n+1)^2\) is 2n. \(\therefore\) Total number of integers between \(9^2\) & \(10^2\) \(=2\times9=18.\)

22.

How many integers are there between 92 and 102 ?A) 16 B) 13 C) 28 D) 18

Answer»

Correct option is D) 18

Correct option is (D) 18

\(\because\) Total number of integers between \(n^2\;\&\;(n+1)^2\) is 2n.

\(\therefore\) Total number of integers between \(9^2\) & \(10^2\) \(=2\times9=18.\)

Discussion

23.	If √2 = 1.414 then the value of \(\sqrt\frac{200}{49}\) = …………. A) 2.02 B) 20.2 C) 30.2 D) 21.2
Answer» Correct option is A) 2.02 Correct option is (A) 2.02 \(\sqrt{\frac{200}{49}}=\frac{10\sqrt2}7=\frac{14.14}7\) \((\because\sqrt2=1.414)\) = 2.02

23.

If √2 = 1.414 then the value of \(\sqrt\frac{200}{49}\) = …………. A) 2.02 B) 20.2 C) 30.2 D) 21.2

Answer»

Correct option is A) 2.02

Correct option is (A) 2.02

\(\sqrt{\frac{200}{49}}=\frac{10\sqrt2}7=\frac{14.14}7\) \((\because\sqrt2=1.414)\)

= 2.02

Discussion

24.	1112 = ………………….. A) 12341 B) 12321 C) 12312 D) 12221
Answer» Correct option is B) 12321 Correct option is (B) 12321 \(111^2=(100+11)^2\) \(=100^2+2\times100\times11+11^2\) = 10000 + 2200 + 121 = 12321.

24.

1112 = ………………….. A) 12341 B) 12321 C) 12312 D) 12221

Answer»

Correct option is B) 12321

Correct option is (B) 12321

\(111^2=(100+11)^2\) \(=100^2+2\times100\times11+11^2\)

= 10000 + 2200 + 121

= 12321.

Discussion

25.	1 + 3 + 5 + 7 + 9 = A) 92 B) 72 C) 52 D) 42
Answer» Correct option is C) 5² Correct option is (C) 5² 1 + 3 + 5 + 7 + 9 = \(5^2\) \((\because\) 1+3+5+...+ (2n+1) = \(n^2)\)

25.

1 + 3 + 5 + 7 + 9 = A) 92 B) 72 C) 52 D) 42

Answer»

Correct option is C) 5²

Correct option is (C) 5²

1 + 3 + 5 + 7 + 9 = \(5^2\)

\((\because\) 1+3+5+...+ (2n+1) = \(n^2)\)

Discussion

26.	Which of the following is a perfect cube number ? A) 25B) 64 C) 81 D) 100
Answer» Correct option is B) 64 Correct option is (B) 64 (A) 25 = 5 \(\times\) 5 (not a perfect cube number) (B) 64 = 4 \(\times\) 4 \(\times\) 4 \(=4^3\) is a perfect cube number. (C) 81 = 9 \(\times\) 9 (not a perfect cube number) (D) 100 = 10 \(\times\) 10 (not a perfect cube number)

26.

Which of the following is a perfect cube number ? A) 25B) 64 C) 81 D) 100

Answer»

Correct option is B) 64

Correct option is (B) 64

(A) 25 = 5 \(\times\) 5 (not a perfect cube number)

(B) 64 = 4 \(\times\) 4 \(\times\) 4 \(=4^3\) is a perfect cube number.

(C) 81 = 9 \(\times\) 9 (not a perfect cube number)

(D) 100 = 10 \(\times\) 10 (not a perfect cube number)

Discussion

27.	Which of the following number is called Ramanujans number ? A) 1729 B) 1728C) 1818D) 1719
Answer» Correct option is A) 1729

Discussion

28.	\(\sqrt{10201}\) = ......................A) 1001 B) 101 C) 111 D) 121
Answer» Correct option is B) 101 Correct option is (B) 101 \(\sqrt{10201}\) = \(\sqrt{(101)^2}\) = 101.

28.

\(\sqrt{10201}\) = ......................A) 1001 B) 101 C) 111 D) 121

Answer»

Correct option is B) 101

Correct option is (B) 101

\(\sqrt{10201}\) = \(\sqrt{(101)^2}\) = 101.

Discussion

29.	No. of integers lie between 42 and 52A) 8 B) 10 C ) 9 D) 11
Answer» Correct option is A) 8 Correct option is (A) 8 \(\because\) No. of integers between \(n^2\;\&\;(n+1)^2\) is 2n. \(\therefore\) No. of integers lie between \(4^2\) and \(5^2\) is \(2\times4=8.\)

29.

No. of integers lie between 42 and 52A) 8 B) 10 C ) 9 D) 11

Answer»

Correct option is A) 8

Correct option is (A) 8

\(\because\) No. of integers between \(n^2\;\&\;(n+1)^2\) is 2n.

\(\therefore\) No. of integers lie between \(4^2\) and \(5^2\) is \(2\times4=8.\)

Discussion

30.	(121)2 is a ……………… number. A) prime B) odd C) even D) none
Answer» Correct option is B) odd Correct option is (B) odd Unit's digit of number 121 is 1. \(\therefore\) Unit's digit of number \((121)^2\) is 1 which is not divisible by 2. Thus, \((121)^2\) is an odd number.

30.

(121)2 is a ……………… number. A) prime B) odd C) even D) none

Answer»

Correct option is B) odd

Correct option is (B) odd

Unit's digit of number 121 is 1.

\(\therefore\) Unit's digit of number \((121)^2\) is 1 which is not divisible by 2.

Thus, \((121)^2\) is an odd number.

Discussion

31.	…………….. should be subtracted from 4215 to become a perfect square number.A) 119 B) 120 C) 110 D) 1
Answer» Correct option is A) 119 Correct option is (A) 119 Nearest perfect square which is less than to 4215 is 4096 (square of 64). Difference between them = 4215 - 4096 = 119. Thus, we have to subtract 119 from 4215 to become a perfect square number.

31.

…………….. should be subtracted from 4215 to become a perfect square number.A) 119 B) 120 C) 110 D) 1

Answer»

Correct option is A) 119

Correct option is (A) 119

Nearest perfect square which is less than to 4215 is 4096 (square of 64).

Difference between them = 4215 - 4096 = 119.

Thus, we have to subtract 119 from 4215 to become a perfect square number.

Discussion

32.	\(\sqrt{2\frac{14}{25}}\) = .................√2(14/25) = .......................A) 8/7B) 8/5C) 5/8D) 1/3
Answer» Correct option is B) 8/5 Correct option is (B) 8/5 \(\sqrt{2\frac{14}{25}}=\sqrt{\frac{2\times25+14}{25}}=\sqrt{\frac{50+14}{25}}=\sqrt{\frac{64}{25}}\) \(=\sqrt{\frac{8^2}{5^2}}=\frac{8}{5}.\)

32.

\(\sqrt{2\frac{14}{25}}\) = .................√2(14/25) = .......................A) 8/7B) 8/5C) 5/8D) 1/3

Answer»

Correct option is B) 8/5

Correct option is (B) 8/5

\(\sqrt{2\frac{14}{25}}=\sqrt{\frac{2\times25+14}{25}}=\sqrt{\frac{50+14}{25}}=\sqrt{\frac{64}{25}}\) \(=\sqrt{\frac{8^2}{5^2}}=\frac{8}{5}.\)

Discussion

33.	\(\sqrt{169}\) + \(\sqrt{25}\) = ...................A) 18 B) 19C) 13 D) 12
Answer» Correct option is A) 18 option A is the correct one Correct option is (A) 18 \(\sqrt{169}+\sqrt{25}=\sqrt{13^2}+\sqrt{5^2}\) = 13+5 = 18.

33.

\(\sqrt{169}\) + \(\sqrt{25}\) = ...................A) 18 B) 19C) 13 D) 12

Answer»

Correct option is A) 18

option A is the correct one

Correct option is (A) 18

\(\sqrt{169}+\sqrt{25}=\sqrt{13^2}+\sqrt{5^2}\) = 13+5 = 18.

Discussion

34.	In the expansion of 311 the units digit is …………….. A) 3 B) 7 C) 10D) 16
Answer» Correct option is B) 7 Correct option is (B) 7 \(\because3^4=3^2\times3^2=9\times9=81\) Unit's digit in \(3^4\) = 1 \(\therefore\) Unit digit's in \(3^{11}=3^4\times3^4\times3^3\) \(=1\times1\times7=7\) \((\because\) Unit's digit in \(3^4\) = 1 & unit's digit in \(3^3\) = 7 \((\because3^3=27))\)

34.

In the expansion of 311 the units digit is …………….. A) 3 B) 7 C) 10D) 16

Answer»

Correct option is B) 7

Correct option is (B) 7

\(\because3^4=3^2\times3^2=9\times9=81\)

Unit's digit in \(3^4\) = 1

\(\therefore\) Unit digit's in \(3^{11}=3^4\times3^4\times3^3\)

\(=1\times1\times7=7\)

\((\because\) Unit's digit in \(3^4\) = 1 & unit's digit in \(3^3\) = 7 \((\because3^3=27))\)

Discussion

35.	In 1, 8, □ 64, □ = ……………. A) 27 B) 25 C) 26 D) 10
Answer» Correct option is A) 27

Discussion

36.	\(\sqrt\frac{0.01}{0.81} =..........................\)A) 1/5B) 1/2 C) 1/9D) 9
Answer» Correct option is C) 1/9 Correct option is (C) 1/9 \(\sqrt{\frac{0.01}{0.81}}=\sqrt{\frac1{81}}=\frac{\sqrt1}{\sqrt{81}}\) = \(\frac{1}{9}\).

36.

\(\sqrt\frac{0.01}{0.81} =..........................\)A) 1/5B) 1/2 C) 1/9D) 9

Answer»

Correct option is C) 1/9

Correct option is (C) 1/9

\(\sqrt{\frac{0.01}{0.81}}=\sqrt{\frac1{81}}=\frac{\sqrt1}{\sqrt{81}}\) = \(\frac{1}{9}\).

Discussion

37.	\(\sqrt{4^4 \times \, 5^4}\) = ............................A) 4 B) 4 × 5 C) 42 × 52 D) 4 × 5
Answer» Correct option is C) 4² × 5² Correct option is (C) 4² × 5² \(\sqrt{4^4\times5^4}=(4^4\times5^4)^\frac12\) \(=(4^4)^\frac12\times(5^4)^\frac12=4^2\times5^2.\)

37.

\(\sqrt{4^4 \times \, 5^4}\) = ............................A) 4 B) 4 × 5 C) 42 × 52 D) 4 × 5

Answer»

Correct option is C) 4² × 5²

Correct option is (C) 4² × 5²

\(\sqrt{4^4\times5^4}=(4^4\times5^4)^\frac12\) \(=(4^4)^\frac12\times(5^4)^\frac12=4^2\times5^2.\)

Discussion

38.	\(\sqrt\frac{25}{64}\) = .......................A) 5/9B) 5/8C) 15/31D) 5/4
Answer» Correct option is B) 5/8 Correct option is (B) 5/8 \(\sqrt{\frac{25}{64}}=\sqrt{\frac{5^2}{8^2}}\) \(=\frac{\sqrt{5^2}}{\sqrt{8^2}}=\frac{5}{8}.\)

38.

\(\sqrt\frac{25}{64}\) = .......................A) 5/9B) 5/8C) 15/31D) 5/4

Answer»

Correct option is B) 5/8

Correct option is (B) 5/8

\(\sqrt{\frac{25}{64}}=\sqrt{\frac{5^2}{8^2}}\) \(=\frac{\sqrt{5^2}}{\sqrt{8^2}}=\frac{5}{8}.\)

Discussion

39.	√1 = …………… A) 0 B) 1 C) 6 D) 4
Answer» Correct option is B) 1

Discussion

40.	How many integers are in between the squares of 25, 26 …………………..? A) 50 B) 60 C) 70 D) 100
Answer» Correct option is A) 50 Correct option is (A) 50 Total number of integers between \(n^2\;\&\;(n+1)^2\) is 2n. \(\therefore\) Total number of integers between the squares of 25 and 26 \(=2\times25=50.\)

40.

How many integers are in between the squares of 25, 26 …………………..? A) 50 B) 60 C) 70 D) 100

Answer»

Correct option is A) 50

Correct option is (A) 50

Total number of integers between \(n^2\;\&\;(n+1)^2\) is 2n.

\(\therefore\) Total number of integers between the squares of 25 and 26 \(=2\times25=50.\)

Discussion

41.	The following numbers are not perfect squares. Give reasons? (i) 257 (ii) 4592(iii) 2433 (iv) 5050 (v) 6098
Answer» i) 257 → The units digit of the number is 7. So it is not a perfect square number. ii) 4592 → The units digit of the number is 2. So it is not a perfect square number. iii) 2433 → The units digit of the number is 3. So, it is not a perfect square number. iv) 5050 → The last two digits of the number are not two zero’s. So, it is not a perfect square number. v) 6098 → The units digit of the number is 8. So It is not a perfect square number.

41.

The following numbers are not perfect squares. Give reasons? (i) 257 (ii) 4592(iii) 2433 (iv) 5050 (v) 6098

Answer»

i) 257 → The units digit of the number is 7. So it is not a perfect square number.

ii) 4592 → The units digit of the number is 2. So it is not a perfect square number.

iii) 2433 → The units digit of the number is 3. So, it is not a perfect square number.

iv) 5050 → The last two digits of the number are not two zero’s. So, it is not a perfect square number.

v) 6098 → The units digit of the number is 8. So It is not a perfect square number.

Discussion

42.

Find whether the square of the following numbers are even or odd? (i) 431(ii) 2826(iii) 8204 (iv) 17779(v) 99998

Answer»

Number	Units digit of square of a number	Even / Odd
(i) 431	1² = 1	1 , odd
(ii) 2826	6² = 36	6, odd
(iii) 8204	4² = 16	6 , even
(iv)17779	9²= 81	1 , odd
(v) 99998	8² = 64	4 , even

Discussion

43.	Which of the following number is doesn’t lie in the units place of a square number ? A) 1 B) 4 C) 3 D) 5
Answer» Correct option is C) 3

Discussion

44.	How many numbers lie between the square of the following numbers (i) 25; 26 (ii) 56; 57 (iii) 107;108
Answer» The numbers lie between the square of the numbers are: 1) 25,26 → 2 x 25=50 ii) 56, 57 → 2 x 56 = 112 iii) 107, 108 → 2 x 107 = 214

44.

How many numbers lie between the square of the following numbers (i) 25; 26 (ii) 56; 57 (iii) 107;108

Answer»

The numbers lie between the square of the numbers are:

1) 25,26 → 2 x 25=50

ii) 56, 57 → 2 x 56 = 112

iii) 107, 108 → 2 x 107 = 214

Discussion

45.	If a, b, c are Pythagorean triplets then which of the following is true ?A) a2 – b2 = c B) a2 + b2 = c C) b = c2 – a2 D) a2 > b2 + c2
Answer» B) a² + b² = c

Discussion

46.	If there are no common factors other than’ 1′ among a, b, c then the triplet is called a ………………….A) Primitive B) Secondary C) Triplet D) None
Answer» Correct option is A) Primitive

Discussion

47.	Identify Pythagorean Triplet. A) 1, 2, 7 B) 8, 9, 6 C) 3, 4, 6 D) 6, 8, 10
Answer» Correct option is D) 6, 8, 10 Correct option is (D) 6, 8, 10 (A) \(1^2+2^2=1+4=5\neq7^2\) \(\therefore\) (1, 2, 7) is not a Pythagorean triplet. (B) \(8^2+9^2\neq6^2\) \(\therefore\) (8, 9, 6) is not a Pythagorean triplet. (C) \(3^2+4^2=9+16=25\neq6^2\) \(\therefore\) (3, 4, 6) is not a Pythagorean triplet. (D) \(6^2+8^2=36+64=100=10^2\) \(\therefore\) (6, 8, 10) is a Pythagorean triplet.

47.

Identify Pythagorean Triplet. A) 1, 2, 7 B) 8, 9, 6 C) 3, 4, 6 D) 6, 8, 10

Answer»

Correct option is D) 6, 8, 10

Correct option is (D) 6, 8, 10

(A) \(1^2+2^2=1+4=5\neq7^2\)

\(\therefore\) (1, 2, 7) is not a Pythagorean triplet.

(B) \(8^2+9^2\neq6^2\)

\(\therefore\) (8, 9, 6) is not a Pythagorean triplet.

(C) \(3^2+4^2=9+16=25\neq6^2\)

\(\therefore\) (3, 4, 6) is not a Pythagorean triplet.

(D) \(6^2+8^2=36+64=100=10^2\)

\(\therefore\) (6, 8, 10) is a Pythagorean triplet.

Discussion

48.	= ……………… A) 0.0112 B) 0.11 C)0.112 D) 0.114
Answer» Correct option is B) 0.11

Discussion

49.	(-2)3 = …………….. A) 8B)\(\frac{1}{8}\)C) \(\frac{1}{3^2}\)D) -8
Answer» Correct option is D) -8

Discussion

50.	= ……………… A) 0.5 B) 0.2 C) 0.7 D) 0.45
Answer» Correct option is B) 0.2

Discussion

Explore topic-wise InterviewSolutions in .

1521 trees are planted in a garden in such a way that there are as many trees in each row as there are rows in the garden. Find the number of rows and number of trees in each row.

Kishore told “Every number is a square number”. Krishna told “Every number is a pure number”. In the above two statements who is correct ? A) Kishore B) Krishna C) Both are correct D) Both are false

\(\sqrt{625}\) + \(\sqrt{441}\) = .............A) 47 B) \(\sqrt{1066}\)C) 46 D) 45

What will be the units digit of the square of the following numbers?(i) 39 (ii) 297 (iii) 5125 (iv) 7286 (v) 8742

The units digit in the square of 431 is ………………… A) 3 B) 7 C) 0 D) 1

Which of the following numbers are perfect squares?(i) 121 (ii) 136 (iii) 256 (iv) 321 (v) 600

The side of a square is 19 units then its area is ………………… sq. units. A) 312 B) 191 C) 163 D) 361

A solid with 6 equal square faces on all the surfaces is called …………………..A) Side B) Cube C) Complete cube D) Cuboid

1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25 = ……………… A) 132 B) 168 C) 139 D) 169

17 &lt; √x &lt; 18, x = ………………. A) 100 B) 900 C) 300 D) 20

(24)2 = ……………… A) 512 B) 156 C) 258 D) 256

(√a) = ………………A) √a B) 2a C) a/2D) a

35 = ……………. A) 243 B) 81 C) 813 D) 432

The product of two numbers is 1296. If one number is 16 times the other, find the two numbers?

How many cube numbers are there between 1 to 100 ? A) 9 B) 10C) 3 D) 13

How many digits are there in the square of 72? A) 4 or 3 B) 3 or 6 C) 2 or 7 D) None

The side of a square is 72 cm then its perimeter is ……………. cm. A) 298 B) 148 C) 288 D) 188

1, 4, 9, 16, 25 are ………………… numbers. A) Square B) Cube C) Pure D) None

212 = ………………. A) 144 B) 441 C) 141 D) 191

(0.2)2 = ………….. A) 0.4 B) 0.004 C) 0.45 D) 0.04

\(\sqrt{55}\) is .......................A) not, a square number B) square number C) cube number D) value is 10

How many integers are there between 92 and 102 ?A) 16 B) 13 C) 28 D) 18

If √2 = 1.414 then the value of \(\sqrt\frac{200}{49}\) = …………. A) 2.02 B) 20.2 C) 30.2 D) 21.2

1112 = ………………….. A) 12341 B) 12321 C) 12312 D) 12221

1 + 3 + 5 + 7 + 9 = A) 92 B) 72 C) 52 D) 42

Which of the following is a perfect cube number ? A) 25B) 64 C) 81 D) 100

Which of the following number is called Ramanujans number ? A) 1729 B) 1728C) 1818D) 1719

\(\sqrt{10201}\) = ......................A) 1001 B) 101 C) 111 D) 121

No. of integers lie between 42 and 52A) 8 B) 10 C ) 9 D) 11

(121)2 is a ……………… number. A) prime B) odd C) even D) none

…………….. should be subtracted from 4215 to become a perfect square number.A) 119 B) 120 C) 110 D) 1

\(\sqrt{2\frac{14}{25}}\) = .................√2(14/25) = .......................A) 8/7B) 8/5C) 5/8D) 1/3

\(\sqrt{169}\) + \(\sqrt{25}\) = ...................A) 18 B) 19C) 13 D) 12

option A is the correct one

In the expansion of 311 the units digit is …………….. A) 3 B) 7 C) 10D) 16

In 1, 8, □ 64, □ = ……………. A) 27 B) 25 C) 26 D) 10

\(\sqrt\frac{0.01}{0.81} =..........................\)A) 1/5B) 1/2 C) 1/9D) 9

\(\sqrt{4^4 \times \, 5^4}\) = ............................A) 4 B) 4 × 5 C) 42 × 52 D) 4 × 5

\(\sqrt\frac{25}{64}\) = .......................A) 5/9B) 5/8C) 15/31D) 5/4

√1 = …………… A) 0 B) 1 C) 6 D) 4

How many integers are in between the squares of 25, 26 …………………..? A) 50 B) 60 C) 70 D) 100

The following numbers are not perfect squares. Give reasons? (i) 257 (ii) 4592(iii) 2433 (iv) 5050 (v) 6098

Find whether the square of the following numbers are even or odd? (i) 431(ii) 2826(iii) 8204 (iv) 17779(v) 99998

Which of the following number is doesn’t lie in the units place of a square number ? A) 1 B) 4 C) 3 D) 5

How many numbers lie between the square of the following numbers (i) 25; 26 (ii) 56; 57 (iii) 107;108

If a, b, c are Pythagorean triplets then which of the following is true ?A) a2 – b2 = c B) a2 + b2 = c C) b = c2 – a2 D) a2 &gt; b2 + c2

If there are no common factors other than’ 1′ among a, b, c then the triplet is called a ………………….A) Primitive B) Secondary C) Triplet D) None

Identify Pythagorean Triplet. A) 1, 2, 7 B) 8, 9, 6 C) 3, 4, 6 D) 6, 8, 10

= ……………… A) 0.0112 B) 0.11 C)0.112 D) 0.114

(-2)3 = …………….. A) 8B)\(\frac{1}{8}\)C) \(\frac{1}{3^2}\)D) -8

= ……………… A) 0.5 B) 0.2 C) 0.7 D) 0.45

17 < √x < 18, x = ………………. A) 100 B) 900 C) 300 D) 20

If a, b, c are Pythagorean triplets then which of the following is true ?A) a2 – b2 = c B) a2 + b2 = c C) b = c2 – a2 D) a2 > b2 + c2