98 + Interview Questions in INDICES IN GENERAL AWARENESS Page 1 InterviewSolution

1.	The box alongside shows the number called Googol. Try to write it as a power of 10.
Answer» According to question box 1 x 10¹⁰⁰

1.

The box alongside shows the number called Googol. Try to write it as a power of 10.

Answer»

According to question box

1 x 10¹⁰⁰

Discussion

2.	Try to write the following numbers in the standard form.i. The diameter of Sun is 1400000000 m. ii. The velocity of light is 300000000 m/sec.
Answer» i. 1400000000 m = 1.4 x 10⁹ m ii. 300000000 m/s = 3.0 x 10⁸ m/sec.

2.

Try to write the following numbers in the standard form.i. The diameter of Sun is 1400000000 m. ii. The velocity of light is 300000000 m/sec.

Answer»

i. 1400000000 m = 1.4 x 10⁹ m

ii. 300000000 m/s = 3.0 x 10⁸ m/sec.

Discussion

3.	Write the following numbers using positive indices:i. (2/7)-2ii. (11/3)-5iii. (1/6)-3iv. (y)-4
Answer» i. (7/2)² ii. (3/11)^-5 iii. 6³ iv. 1/y⁴

3.

Write the following numbers using positive indices:i. (2/7)-2ii. (11/3)-5iii. (1/6)-3iv. (y)-4

Answer»

i. (7/2)²

ii. (3/11)^-5

iii. 6³

iv. 1/y⁴

Discussion

4.	Simplify:i. a6 ÷ a4ii. m5 ÷ m8iii. p3 ÷ p13iv. x10 ÷ x10
Answer» i. a⁶ ÷ a⁴ = a^6-4 = a² ii. m⁵ ÷ m⁸ = m^5-8 = m^-3 iii. p³ ÷ p¹³ = p^{3 - 13} = p^-10 iv. x¹⁰ ÷ x¹⁰ = x^10-10 = x⁰ = 1

4.

Simplify:i. a6 ÷ a4ii. m5 ÷ m8iii. p3 ÷ p13iv. x10 ÷ x10

Answer»

i. a⁶ ÷ a⁴

= a^6-4

= a²

ii. m⁵ ÷ m⁸

= m^5-8

= m^-3

iii. p³ ÷ p¹³

= p^{3 - 13}

= p^-10

iv. x¹⁰ ÷ x¹⁰

= x^10-10

= x⁰

= 1

Discussion

5.	Velocity of light is `30,000,000,000 cm//sec`. Its value by using powers of 10 is ______A. `3xx10^8cm//s`B. `3xx10^9cm//s`C. `3xx10^10cm//s`D. `3xx10^11cm//s`
Answer» Correct Answer - C NA

Discussion

6.	Find the value of `(2^4+2^3)^(2//6)`A. `8(2)^(1//2)`B. `2(3)^(1//3)`C. `64(2)^(1//2)`D. `4(3)^(1//3)`
Answer» Correct Answer - B Given , `(2^4+2^3)^(2)/(6)` `=(2^4+2^3)^(1)/(3)=[2^3(2+1)]^(1//3)` `=2^(3//3)(3)^(1//3)=2(3)^(1//3)` Hence, the correct options is (b) .

Discussion

7.	`(0.000729)^(1/3) = `______A. `0.030`B. `sqrt(0.09)`C. `0.18`D. `0.09`
Answer» Correct Answer - D NA

Discussion

8.	If `a+b+c=0`, then find the value of `(x^(a))^(3)/(x^(-3b)x^(-3c))`
Answer» Correct Answer - B NA

Discussion

9.	Simplifty `(sqrt(144)+sqrt(256))/(3^2-2)`A. 8B. 4C. `-4`D. `-8`
Answer» Correct Answer - B NA

Discussion

10.	If ` a=36`, then find the value of `a^(36^@)-a^(0^36)`.A. 36B. 0C. 1D. 35
Answer» Correct Answer - D NA

Discussion

11.	`(25^2-15^2)^((3)/(2))=` _____A. 4000B. 8000C. 3125D. 1024
Answer» Correct Answer - B Given `(25^2-15^2)^(3//2)` `=[(25+15)(25-15)]^(3//2)` `=[40xx10]^(3//2)=[2^2xx10^2]^(3//2)=(20)^3=8000` Hence, the correct options is (b).

Discussion

12.	`(33^2-31^2)^((5)/(7))=` _____A. 64B. 16C. 32D. 4
Answer» Correct Answer - C `(33^2-31^2)^(5//7)` ` =[(33+31)(33-31)]^(5//7)` `=[64xx2]^(5//7)` `=(2^7)^(5//7) =2^5=32` Hence, the correct options is (c) .

Discussion

13.	If `abc=0`, then find the value of `([(x^(a))^(b)]^(2c))/(x^(abc))`A. 3B. 0C. `-1`D. 1
Answer» Correct Answer - D NA

Discussion

14.	If `abc =0` then find the value of `[(x^a)^b]^c`.A. 1B. aC. bD. c
Answer» Correct Answer - A Gven `abc=0` `[(x^a)^b]^c`. `=(x^a)^(bc)` `=x^(abc)` `=x^0=1` Hence, the correct options is (a).

Discussion

15.	If `a+b+c=0`, then find the value of `sqrt(x^a.x^b.x^c)`.
Answer» Correct Answer - B Given `a+b+c=0`. `sqrt(x^ax^b.x^c)` `=sqrt(x^(a+b+c))=sqrt(x^0)=sqrt(1)=1` Hence, the correct options is (b).

Discussion

16.	If `xyz=0`, then find the value of `[(k^(x))^y]^z-[(k^(y))^z]^x-[(k^(z))^x]^(y)`
Answer» Correct Answer - `-1` NA

Discussion

17.	Simplify `(sqrt(36)+sqrt(64))/(2^3-1)`.A. 1B. 2C. 3D. 4
Answer» Correct Answer - B `(sqrt(36)+sqrt(64))/(2^3-1)` `=(sqrt(6^2)+sqrt(8^2))/(2^3-1)=(6+8)/(8-1)=(14)/(7)=2` Hence, the correct options is (b).

Discussion

18.	Evaluate `a^(n)`.A. 64B. 128C. 32D. 256
Answer» Correct Answer - B (a) Evaluate `(1^(2)+2^(2)+3^(2))` and express it as the exponent of the single number. (b) Simplify and get the result.

Discussion

19.	By what number should `(8//27)^(-3)` be a divided to that the quotient is equal to `(27//8)^(-3)` ?
Answer» Correct Answer - `((3)/(2))^(18)` NA

Discussion

20.	If `a=25` ,then find the value of `a^(25^(0))+a^(0^(25))`.A. 25B. 26C. 24D. 0
Answer» Correct Answer - B Given `a=25`, `a^(25^(0))+a^(0^(25))=a^1+a^0` `=a+1=25+1=26` Hence, the correct options is (b).

Discussion

21.	`(21^(2)-15^(2))^(4/3)=`A. `36 root(3)(6)`B. `1296`C. `root(3)(1296)`D. `(root(3)(6))^(4)`
Answer» Correct Answer - B Recall `(a+b) (a-b)=a^(2)-b^(2)`.

Discussion

22.	By what number should we multiply `3^4` so that the product is equal to `(1)/(27)`?
Answer» Correct Answer - `3^(-7)` NA

Discussion

23.	If `2^(7x-5)=(32)^(x-7)`, then find the value of `(1)/(2^x)`A. `2^17`B. `2^16`C. `2^15`D. None of these
Answer» Correct Answer - C Given `2^(7x-5)=(32)^(x-7)` `rArr 2^(7x-5)=2^(5x-35) (because 32=2^5)` `rArr 7x-5=5x=35` `rArr 2x=-30` `rArr x=-15` `therefore (1)/(2^x)=(1)/(2^-15)=2^15` Hence , the correct option is (c).

Discussion

24.	If `9^(2x-7)=(27)^(x-4)`, then find the value of `3^x`.
Answer» Correct Answer - 9 NA

Discussion

25.	What should be multiplied to `3^(-4)` so that product is 6 ?
Answer» Correct Answer - 486 NA

Discussion

26.	Simplify `(3x^(-2)y^(-3)z^(2)xx5x^(2)xxyxxz^3 )÷x^(3)y^(2)z^(-1)`
Answer» Correct Answer - `15x^(-3)y^(-4)z^(6)` NA

Discussion

27.	Vicky scored x marks in Maths and Rakesh scored `x^3` marks in Maths. The proudct of their marks was 256. Find their marks.
Answer» Correct Answer - 4,64 NA

Discussion

28.	If `xyz=0` , then find the value of `(a^x)^(zy)+(a^y)^(zx)+(a^z)^(xy)`.A. 3B. 2C. 1D. 0
Answer» Correct Answer - A Given `xyz=0` `(a^x)^(zy) +(a^y)^(zx)+(a^z)^(xy)` `=a^(xyz)+a^(xyz)=a^(0)+a^(0)+a^(0)` `1+1+1=3` Hence , the correct option is (a).

Discussion

29.	What should be multiplied to `2^6` so that the products is 1 ?A. 16B. 32C. 64D. 128
Answer» Correct Answer - C Let the required number be `x`. `therefore x xx 2 ^(-6)=1` `rArr x((1)/(2^6))=1` `rArr x=1xx2^6=2^6=64` Hence the correct option is (c).

Discussion

30.	Varun secured x marks in Maths and Rahul secured `x^2` marks in Maths. The product of their marks was 729. Find their marks.A. `3,243`B. `9,81`C. `27,27`D. None of these
Answer» Correct Answer - B Marks secured by Varun =x. Marks secured by Rahul `=x^2`. Given `x.x^2=729`. `x^3=729` `x^3=9^3` `therefore x =9` Marks securd by Varun `=x=9` Marks secured by Rahul `=x^2=9^2=81` Hence , the correct option is (b).

Discussion

31.	`64^(2/3)xx64^(1/3)xx64^((-5)/3)`A. `1/64`B. `1/16`C. 32D. `1/32`
Answer» Correct Answer - B Apply laws of indices.

Discussion

32.	`root(6)(0.004096)=`A. 0.2B. 0.4C. 0.6D. 0.8
Answer» Correct Answer - B Apply prime factorisation.

Discussion

33.	If `(sqrt(3))^(x+y)=9` and `(sqrt(2))^(x-y)=32`, then `2x+y` is _______.A. 1B. 0C. 17D. 11
Answer» Correct Answer - D Given, `(sqrt(3))^(x+y)=9` and `(sqrt(2))^(x-y)=32` `implies 3^((x+y)/2)=3^(2)` and `2^((x-y)/2)=2^(5)` `implies (x+y)/2=2` and `(x-y)/2=5` `implies x+y=4` (1) and `x-y=10` (2) Solving (1) and (2), we get `x=7` and `y=-3` Now, `2x+y=2(7)-3=11`.

Discussion

34.	If `6^(x-y)=36` and `3^(x+y)=729`, then find `x^(2)-y^(2)`.A. 12B. 4C. 24D. 8
Answer» Correct Answer - A `6^(x-y)=36` `6^(x-y)=6^(2)` `:. x-y=2` (1) and `3^(x+y)=3^(6) implies x+y=6` (2) From (1) and (2), `x^(2)-y^(2)=12`.

Discussion

35.	Find the value of `[[a/b]^(sqrt(99)-sqrt(97))]^(sqrt(99)+sqrt(97))`A. `b^(2)/a^(2)`B. `sqrt(b/a)`C. `sqrt(b/a)`D. `a^(2)/b^(2)`
Answer» Correct Answer - D Apply laws of exponents.

Discussion

36.	Find value of `(61^(2)-11^(2))^(3/2)`.A. `50^(3)`B. `216000`C. 3600D. 60
Answer» Correct Answer - B Use the identity `a^(2)-b^(2)=(a+b) (a-b)`

Discussion

37.	If `3^x=9^y=27^(z)=729`, then show that `x+y+z=11`.
Answer» Correct Answer - NA NA

Discussion

38.	If `11^x = 3^y = 99^z`, then `1/x + 1/y + 1/z`A. `2/z-1/y`B. `2/z+1/y`C. `-1/y`D. `0`
Answer» Correct Answer - A (i) Let each of the three given terms be equal to K. (ii) Take the LCM of each term of numerator and denominator. (iii) Simplify using the appropriate laws of indices.

Discussion

39.	If `a^(b^t) = 6561`, then find the least possible value of `(a.b.c)`, where `a, b and c` are integers.A. 24B. 36C. 162D. None of these
Answer» Correct Answer - D (i) Express 6561 as the different ways of exponential forms. (ii) x is of the form `a+b`. (iii) `y` is of the form `a^(2)+ab+b^(2)`.

Discussion

40.	Which is the least among `(3)^25, (9)^12, (27)^3`, and `(81)^2` ?
Answer» Correct Answer - `(81)^2` NA

Discussion

41.	Find the value of `(-1)^(301)+(-1)^(302)+(-1)^(303)+.......+(-1)^(400)`.A. 1B. 101C. 100D. 0
Answer» Correct Answer - D We know `(-1)^x` `=-1`, when x is odd. `=1` , when x is even. `therefore (-1)^(301)+(-1)^(302)+....+(-1)^(400)` `=(-1)+1+(-1)+1+...(100 " terms") =0` Hence, the correct options is (d).

Discussion

42.	Find the value of `3^4[(2/3)^2+(2/3)-(2/(3))^3]`A. 86B. 66C. 68D. 88
Answer» Correct Answer - B `3^4[(2/3)^2+(2/3)-(2/(3))^3]` `=3^4,(2^2)/(3^2)+3^4.(2)/(3)-3^4.(2^3)/(3^3)` `=36+54-24=66` Hence the correct optin is (b).

Discussion

43.	If `3^x=6561`, then `3^(x-3)` is ____A. 81B. 243C. 729D. 27
Answer» Correct Answer - B `3x=6561 =(81)^2=(3^4)=3^8` `rArr x=8` `3^x-3=3^8-3=3^5=243` Hence, the correct options is (b).

Discussion

44.	`2^(3^(2))=` ____A. 64B. 32C. 256D. 512
Answer» Correct Answer - D `2^(2^(2))=2^9=512`

Discussion

45.	If `(9)^(2x+4)=(243)^(2x-3.2)` , then x =_______A. 12B. 10C. 8D. 4
Answer» Correct Answer - D Given , `(9)^(2x+4)=(243)^(2x-3.2)` `rArr (3)^(4x+8)=(3)^(10x-16)` `rArr 4x+8=10x-16` `rArr 6x=24rArr x=4` Hence the correct option is (d).

Discussion

46.	`(2^3)^4=` _____A. `(2^(4^(3)))`B. `(2^(3^(4)))`C. `(2^(4))^(3)`D. None of these
Answer» Correct Answer - C `(2^3)^4=2^12=(2^4)^3` Hence ,the correct option is (c).

Discussion

47.	`3^(2^(0^(5)))=`_____
Answer» Correct Answer - C `0^5=0 and 2^0=1` `therefore3^(2^(0^(5)))=3^1=3` Hence,the correct option is (c).

Discussion

48.	In `2x^5`, base is ____A. 2B. 2xC. xD. 5
Answer» Correct Answer - C Base is x. Hence, the correct options is (c) .

Discussion

49.	`200000000=` _____
Answer» Correct Answer - A `200000000=2xx10^8` Hence ,the correct option is (a).

Discussion

50.	If `2^(2n-3)=2048` , then `(4n+3n^2)=` _____.A. 175B. 25C. 125D. 75
Answer» Correct Answer - A Given, `2^(2n-)=2048` `rArr (2^2n)/(8)=2^11` `rArr 2^2n=2^11 xx2^3=2^14` `rArr n=7` `therefore (4n+3n^2)` `=(4xx7+3xx7^2)=175`. Hence , the correct option is (a).

Discussion

Explore topic-wise InterviewSolutions in .

The box alongside shows the number called Googol. Try to write it as a power of 10.

Try to write the following numbers in the standard form.i. The diameter of Sun is 1400000000 m. ii. The velocity of light is 300000000 m/sec.

Write the following numbers using positive indices:i. (2/7)-2ii. (11/3)-5iii. (1/6)-3iv. (y)-4

Simplify:i. a6 ÷ a4ii. m5 ÷ m8iii. p3 ÷ p13iv. x10 ÷ x10

Velocity of light is `30,000,000,000 cm//sec`. Its value by using powers of 10 is ______A. `3xx10^8cm//s`B. `3xx10^9cm//s`C. `3xx10^10cm//s`D. `3xx10^11cm//s`

Find the value of `(2^4+2^3)^(2//6)`A. `8(2)^(1//2)`B. `2(3)^(1//3)`C. `64(2)^(1//2)`D. `4(3)^(1//3)`

`(0.000729)^(1/3) = `______A. `0.030`B. `sqrt(0.09)`C. `0.18`D. `0.09`

If `a+b+c=0`, then find the value of `(x^(a))^(3)/(x^(-3b)x^(-3c))`

Simplifty `(sqrt(144)+sqrt(256))/(3^2-2)`A. 8B. 4C. `-4`D. `-8`

If ` a=36`, then find the value of `a^(36^@)-a^(0^36)`.A. 36B. 0C. 1D. 35

`(25^2-15^2)^((3)/(2))=` _____A. 4000B. 8000C. 3125D. 1024

`(33^2-31^2)^((5)/(7))=` _____A. 64B. 16C. 32D. 4

If `abc=0`, then find the value of `([(x^(a))^(b)]^(2c))/(x^(abc))`A. 3B. 0C. `-1`D. 1

If `abc =0` then find the value of `[(x^a)^b]^c`.A. 1B. aC. bD. c

If `a+b+c=0`, then find the value of `sqrt(x^a.x^b.x^c)`.

If `xyz=0`, then find the value of `[(k^(x))^y]^z-[(k^(y))^z]^x-[(k^(z))^x]^(y)`

Simplify `(sqrt(36)+sqrt(64))/(2^3-1)`.A. 1B. 2C. 3D. 4

Evaluate `a^(n)`.A. 64B. 128C. 32D. 256

By what number should `(8//27)^(-3)` be a divided to that the quotient is equal to `(27//8)^(-3)` ?

If `a=25` ,then find the value of `a^(25^(0))+a^(0^(25))`.A. 25B. 26C. 24D. 0

`(21^(2)-15^(2))^(4/3)=`A. `36 root(3)(6)`B. `1296`C. `root(3)(1296)`D. `(root(3)(6))^(4)`

By what number should we multiply `3^4` so that the product is equal to `(1)/(27)`?

If `2^(7x-5)=(32)^(x-7)`, then find the value of `(1)/(2^x)`A. `2^17`B. `2^16`C. `2^15`D. None of these

If `9^(2x-7)=(27)^(x-4)`, then find the value of `3^x`.

What should be multiplied to `3^(-4)` so that product is 6 ?

Simplify `(3x^(-2)y^(-3)z^(2)xx5x^(2)xxyxxz^3 )÷x^(3)y^(2)z^(-1)`

Vicky scored x marks in Maths and Rakesh scored `x^3` marks in Maths. The proudct of their marks was 256. Find their marks.

If `xyz=0` , then find the value of `(a^x)^(zy)+(a^y)^(zx)+(a^z)^(xy)`.A. 3B. 2C. 1D. 0

What should be multiplied to `2^6` so that the products is 1 ?A. 16B. 32C. 64D. 128

Varun secured x marks in Maths and Rahul secured `x^2` marks in Maths. The product of their marks was 729. Find their marks.A. `3,243`B. `9,81`C. `27,27`D. None of these

`64^(2/3)xx64^(1/3)xx64^((-5)/3)`A. `1/64`B. `1/16`C. 32D. `1/32`

`root(6)(0.004096)=`A. 0.2B. 0.4C. 0.6D. 0.8

If `(sqrt(3))^(x+y)=9` and `(sqrt(2))^(x-y)=32`, then `2x+y` is _______.A. 1B. 0C. 17D. 11

If `6^(x-y)=36` and `3^(x+y)=729`, then find `x^(2)-y^(2)`.A. 12B. 4C. 24D. 8

Find the value of `[[a/b]^(sqrt(99)-sqrt(97))]^(sqrt(99)+sqrt(97))`A. `b^(2)/a^(2)`B. `sqrt(b/a)`C. `sqrt(b/a)`D. `a^(2)/b^(2)`

Find value of `(61^(2)-11^(2))^(3/2)`.A. `50^(3)`B. `216000`C. 3600D. 60

If `3^x=9^y=27^(z)=729`, then show that `x+y+z=11`.

If `11^x = 3^y = 99^z`, then `1/x + 1/y + 1/z`A. `2/z-1/y`B. `2/z+1/y`C. `-1/y`D. `0`

If `a^(b^t) = 6561`, then find the least possible value of `(a.b.c)`, where `a, b and c` are integers.A. 24B. 36C. 162D. None of these

Which is the least among `(3)^25, (9)^12, (27)^3`, and `(81)^2` ?

Find the value of `(-1)^(301)+(-1)^(302)+(-1)^(303)+.......+(-1)^(400)`.A. 1B. 101C. 100D. 0

Find the value of `3^4[(2/3)^2+(2/3)-(2/(3))^3]`A. 86B. 66C. 68D. 88

If `3^x=6561`, then `3^(x-3)` is ____A. 81B. 243C. 729D. 27

`2^(3^(2))=` ____A. 64B. 32C. 256D. 512

If `(9)^(2x+4)=(243)^(2x-3.2)` , then x =_______A. 12B. 10C. 8D. 4

`(2^3)^4=` _____A. `(2^(4^(3)))`B. `(2^(3^(4)))`C. `(2^(4))^(3)`D. None of these

`3^(2^(0^(5)))=`_____

In `2x^5`, base is ____A. 2B. 2xC. xD. 5

`200000000=` _____

If `2^(2n-3)=2048` , then `(4n+3n^2)=` _____.A. 175B. 25C. 125D. 75