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InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 51. |
`((a^(x^(4)))/(a^(y^(4))))^((1)/(x^2+y^2))xx((a^(y^(4)))/(a^(z^(4))))^((1)/(y^2+z^2))xx((az^(4))/(a^(x^(4))))^((1)/(z^2+z^2))=`________A. 1B. 2C. 3D. 4 |
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Answer» Correct Answer - A `((a^(x^(4)))/(a^(y^(4))))^((1)/(x^2+y^2))xx(a^(y^(4))/(a^(z^4)))^((1)/(y^2+z^2))xx((a^(z^(1)))/(a^(x^(4))))^((1)/(z^2+x^2))` `=(a^(x^(4)))^((1)/(x^2+y^2))xx(a^(y^(4-z^4)))^((1)/(y^2+z^2))xx(a^(z^(4-x^4)))^((1)/(z^2+x^2))` `=a((x^2-y^2)(x^2+y^2))/(x^3+y^2)xxa((y^2-z^2)(y^2+z^2))/(y^3+z^2)xxa((z^2-x^2)(z^2+x^2))/(z^3+x^2)` `=a^(x^2-y^2+y^2-z^2+z^2-x^2)=a^0=1` Hence , the correct option is (a). |
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| 52. |
If `x^yxxy^x=800`, then find `x-y` (where x and y are positive integers and `xgt y`).A. 2B. 5C. 4D. 3 |
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Answer» Correct Answer - D `x^yxxy^x=800` `rArr x^y xx y^x=25xx32` `rArr 5^2xx2^5=x^yxxy^x(because x gt y)` `rArrx-y=5-2=3` Hence the correct option is (d). |
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| 53. |
`(6sqrt((64)/(125)))^(-2)=`________A. `(5)/(16)`B. `(4)/(5)`C. `(5)/(4)`D. `(16)/(5)` |
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Answer» Correct Answer - C `(6sqrt((64)/125))^(-2)=[((64)/125)^((1)/(6))]^(-2)=((64)/125)^(-(1)/3)=((5^3)/4^3)^((1)/(3))=(5)/(4)` Hence the correct option is (c). |
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| 54. |
If `x^yxxy^x=256`,then find `y^2-x^2` where x and y are positive integers and `x lt y`).A. 15B. 12C. 14D. 16 |
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Answer» Correct Answer - B `x^yxxy^x=256=16xx16=2^4xx4^2` `rArr x^yxxy^x=2^4xx4^2` `rArr x=2` and `y=4 (becauase x lt y)` `therefore y^2=x^2=16 -4=12` Hence, the correct option is (b). |
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| 55. |
Which is the greatest among `2^(156), 4^(79), 128^(23)` and `8^(54)`A. `4^(79)`B. `128^(23)`C. `2^(156)`D. `8^(54)` |
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Answer» Correct Answer - D `4^(79)=(2^(2))^(79)=2^(158)` `128^(23)=(2^(7))^(23)=2^(161)` `8^(54)=(2^(3))^(54)=2^(162)` `8^(54)` is the greatest value. |
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| 56. |
If `x^(200) lt 3^(300)`, then the greatest possible integral value of x.A. 3B. 5C. 4D. 2 |
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Answer» Correct Answer - B (i) Both columns should be expressed as the power of a common component. (ii) `x^(200) lt 3^(300) implies (x^(2))^(100) lt (27)^(100)` (iii) Now check the values for which of the above inequality holds well. |
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| 57. |
If `a lt 0` and n is any odd integer, then the sign of `root(n)(a)` is _______ |
| Answer» Correct Answer - Negative | |
| 58. |
If a |
| Answer» Correct Answer - Does not belong | |
| 59. |
Which of the folowing is the ascending order of `2^(1152), 3^(768), and 5^(384)`A. `5^(384), 3^(768), and 2^(1152)`B. `5^(384), 2^(1152), and 3^(768)`C. `5^(389), 5^(314), and 2^(1152)`D. `2^(1152), 3^(768), and 5^(384)` |
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Answer» Correct Answer - B Let us take GCD of `1152,768` , and 384 , which is 384. `therefore 2^1152=(2^3)^384=8^384` `3^768=(3^2)^384=9^(384)` `5^384=(5)^384` `therefore` The asceding order is as follows : `5^384, 8^384, 9^384` i.e., `5^384, 2^1152, and 3^768` Hence, the correct option is (b). |
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| 60. |
Which among `4^(-2),3^(-2),2^(-2)` and `5^(-2)` is the greatest?A. `4^(-2)`B. `3^(-2)`C. `2^(-2)`D. `5^(-2)` |
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Answer» Correct Answer - C `4^(-2),3^(-2),5^(-2)` `rArr (1)/(4^2),(1)/(3^2),(1)/(2^2),(1)/(5^2)` `rArr (1)/(16),(1)/(9),(1)/(4),(1)/(25)` Since , the numerators of the given fractions are same, the fraction which has the least denominator has the greatest value. `therefore (1)/(4)` is the greatest among the given fractions. Hence, the correct option is (c). |
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| 61. |
If `7^((5x-8))xx5^((x+2))=30625`, then find `x`, an integer.A. 4B. 3C. 2D. 1 |
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Answer» Correct Answer - C Prime factorise the number 30625. |
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| 62. |
If `64 gt x^3`, then the greatest possible integer value of x is ____A. 1B. 2C. 3D. 4 |
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Answer» Correct Answer - C `64gt x^3rArr 4^3gt x^3` Clearly, 3 is the greatest possible integer value of x. Hence,the correct option is (c). |
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| 63. |
If `2^n)=1024`, then `2^((n)/(2)+2=`_______A. 64B. 128C. 256D. 512 |
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Answer» Correct Answer - B `2^n=1024=2^10rArrn=10` `2^((n)/(2)+2)= 2^((10)/(2)+2` `=2^5+2=2^7=128` Hence the correct option is (b). |
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| 64. |
A teacher wanted to distribute 2025 chocolates equally among x number of students . If each students gas x chocolates, find x.A. 25B. 35C. 45D. 55 |
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Answer» Correct Answer - C The total number of chocolates to be distributed `= x2025` . The number of students `=x`. The number of chocolates each student gets `=x. therefore 2025 =x xx x ` `2025 =x^2` `rArr x=sqrt(2025)rArr x=45` The number of students in the class `(x)=45`. Hence, the correct option is (c). |
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| 65. |
If `6^n=1296`, then `6^(n-3)` isA. `1/6`B. 6C. 0.6D. Dta insufficient |
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Answer» Correct Answer - B Applt prime factorisation method. |
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| 66. |
`2^3x^(+2)y^(+3)z^(5)xx5^(2)x^(-5)y^(-5)div100x^(-4)y^(-3)z^(-1)=`_______A. `2xyz^(2)`B. `2xy^(2)z`C. `2xyz`D. `2x^(2)yz` |
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Answer» Correct Answer - C `(2^3x^(+2)y^(+3)z^(5)xx5^(2)x^(-5)y^(-5)z^(-5))/(100x^(-4)y^(-3)z^(-1))=(2x^-3.y^(-2))/(x^-4y^-3z^-1)=2xyz` Hence,the correct option is (c). |
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| 67. |
If `sqrt(2)=1.414 and sqrt(7)=2.646`, then find the value of `sqrt(32)+sqrt(252.)`A. `20.839`B. `21.532`C. `19.482`D. `22.231` |
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Answer» Correct Answer - B `sqrt(32)+sqrt(252)` `=4sqrt(2)+6sqrt(7)` `=4xx1.414+6xx2.646` `= 5.656 + 15.876` `=21.532` Hence , the correct option is (b). |
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| 68. |
The value of `(9^(2)+40^(2))^(3/2)=`A. 41B. 1681C. 68921D. `1/68921` |
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Answer» Correct Answer - C Write the expression as a single number. |
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| 69. |
If `sqrt(2)=1.414 and sqrt(7)=2.646`, find the value of `(sqrt(2)+1)^2+(sqrt(7)+1)^2`. The following stpes are involved in solving the above problem. Arrrange them in sequenatial order. (A) `19.120` (B) `11+2xx4.060=11+8-120` (C) `11+2(sqrt(2)+sqrt(7))=11+2(1.414+2.646)` (D) `(sqrt(2)+sqrt(1))^2+(sqrt(7)+1)^2=2+1+2sqrt(2)+7+1+2sqrt(7)`.A. ABCDB. DACBC. DBCAD. DCBA |
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Answer» Correct Answer - D (D), (C), (B), and (A) is the required sequential order. Hecne , the correct option is (d). |
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| 70. |
If `(2x^2-y^2)^4=256 and (x^2+y^2)^5=243`, then find `x^4-y^4` The following steps are involved in solving the above problem. Arragne then in sequential order. (A) `(x^2-y^2)^4=256=4^4 and (x^2+y^2)^5=3^5` (B) `x^4-y^4=12` (C) `(x^2-y^2)(x^2+y^2)=4xx3`(D) `x^2-y^2=4 and x^2+y^2=3`A. ADCDB. ABCDC. ADBCD. ACDB |
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Answer» Correct Answer - A (A),(D),(C) and (B) is the required sequentail order. Hence the correct option is (a). |
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| 71. |
`[(8^(@)-7^(@))(8^(@)+7^(@))]^(0^(7^(8)))=`A. 1B. 0C. Not definedD. None of these |
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Answer» Correct Answer - C Apply the laws of indices. |
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| 72. |
`81^(1/4)xx9^(3//2)xx27^(- 4/3)=`A. 1B. 3C. 9D. `1/3` |
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Answer» Correct Answer - A Prime factorise the numbers. |
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| 73. |
Find the value of `sqrt(18)+sqrt(12)`, if `sqrt(12)=1.414` and `sqrt(3)=1.732`. The following are the steps involved in solving the above problem. Arrange that in sequential order. (A) `4.242+3.464=7.706` (B) `3sqrt(2)+2sqrt(3)` (C) `sqrt(18)+sqrt(12)=sqrt(3^(2)xx2)+sqrt(2^(2)xx3)` (D) `3(1.414)+2(1.732)`A. CBADB. CABDC. CADBD. CBDA |
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Answer» Correct Answer - D (C), (B), (D) and (A) are the sequential order from the first to the last. |
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| 74. |
`[((a^(0)+b^(0))(a^(0)-b^(0)))/(a^(2)-b^(2))]^(0^(+^(5)))" "("where "a ne 0 and b ne 0)` is |
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Answer» Correct Answer - D Given, `[((a^(0)+b^(0))(a^(0)-b^(0)))/(a^(2)-b^(2))]` `[((1+1)(1-1))/(a^(2)-b^(2))]^(0)=0^(0)` It is not defined. |
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| 75. |
Value of `(125/343)^(2/3)=`A. `5/7`B. `7/5`C. `25/49`D. `49/25` |
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Answer» Correct Answer - C Factorise the numbers. |
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| 76. |
If `(81)^(x)=1/((125)^(y))` and `x, y` are integers, then find the value of `12xy`. |
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Answer» Correct Answer - A Factorise the numbers. |
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| 77. |
If `x=sqrt(81)`, then find the value of `(x^5+x^4)/(x^3)` |
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Answer» Correct Answer - 90 NA |
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| 78. |
If `sqrt(2)=1. 414and sqrt(3)=1. 732` ,find the value of `sqrt(50)+2sqrt(48)` ? |
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Answer» (a) Express `sqrt(50)` and `sqrt(48)` as products of a rational number and `sqrt(2)` or `sqrt(3)`. (b) Use `sqrt(50)=5sqrt(2)` and `sqrt(48)=4sqrt(3)`. (c) Substitute the values of `sqrt(2)` and `sqrt(3)` and simplify. |
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| 79. |
The property be which `'(xy)^(n)=x^(n)xxy^(n)'` is known as ________ property. |
| Answer» Correct Answer - Power of a product | |
| 80. |
If `8^(x^y)=4096` where x and y are positve integers and `x ne 1` , then show that either `x=y or x gt y`. |
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Answer» Correct Answer - NA NA |
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| 81. |
`(x^(-1)-y^(-1))/(z)+(y^(-1)-z^(-1))/(x)+(z^(-1)-x^(-1))/(y)=`_______A. 1B. -1C. 0D. 2 |
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Answer» Correct Answer - C `(x^-1-y^-1)/(z) +(y^(-1)-z^(-1))/(x)+(z^(-1)-x^(-1))/(y)` `((1)/(x)-(1)/(y))/(z)+((1)/(y)-(1)/(z))/(x)+((1)/(z)-(1)/(x))/(y)` `(y-x)/(xyz)+(z-y)/(xyz)+(x-z)/(xyz)` `=(y-x+z-y+x-z)/(xyz)=(0)/(xyz)=0` Hence, the correct option is (c). |
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| 82. |
`((a)/(b))^(x+y+z)div[(sqrt(a/b))^(-x)xx(sqrta/b)^(-y)xx(sqrt(a/b))^(-z)]=`________.A. `[a^3//b^3]^(x+y+z) `B. `[a^2//b^2]^(x+y+z)`C. `[a//b]^(x+y+z)//2`D. `[a//b]^3(x+y+z)//2` |
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Answer» Correct Answer - D `((a)/(b))^(x+y+z)div[(sqrt(a/b))^(-x)xx(sqrta/b)^(-y)xx(sqrt(a/b))^(-z)]` `=((a)/(b))^(x+y+z)div[(a/b)^(-(x)/(2))xx(a/b)^(-(y)/(2))xx(a/b)^(-(z)/(2))]` `=((a)/(b))^(x+y+z)div[(a/b)^(-((x+y+z)/(2)))]` `=(a/b)^((3(x+y+z))/(2))` Hence the correct option is (d). |
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| 83. |
Simplify `[(2)/(5)]^(4)((25)/(8))^(3)((125)/(4))^2` |
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Answer» Correct Answer - `(5^8)/(2^9)` NA |
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| 84. |
Find the value of `(0.000064)^(5/6) div (0.00032)^(6/5)`A. 0.2B. 0.4C. 5D. 2.5 |
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Answer» Correct Answer - C Factorise the numbers. |
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| 85. |
If `x^((5+a)^2)xx x^((5-a)^2)=x^(40)` then find `a^2`. |
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Answer» Correct Answer - 1 NA |
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| 86. |
Which is greater between `3^48` and `2^72` ? |
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Answer» Correct Answer - `3^48` NA |
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| 87. |
The following steps are involved in finding the value of `((x^a)/(x^b))((x^b)/(x^c))((x^c)/(x^a))`. Arrange them in sequential order. (A) `x^0=1` (B) `x^(a-b+b-c+c-a)` (C) `((x^a)/(x^b))((x^b)/(x^c))((x^c)/(x^a))=x^(a-b).x^(b-c).x^(c-a)`A. CBAB. ACBC. BCAD. CAB |
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Answer» Correct Answer - A (C),(B), and (A), is the required sequential oreder. Hence, the correct options is (a). |
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| 88. |
`3^4x^3y^6z^4xx27x^(-2)z^(-6)div81xy^(2)z^(-3)=`______A. `27xy`B. `27yz`C. `27 xz`D. `27xyz` |
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Answer» Correct Answer - B `(3^4x^3y^6z^4xx27x^(-2)z^(-6))/(81xy^(2)z^(-3))=(27xy^(3)z^(-2))/(xy^2z^(-3))=27yx` Hence, the correct option is (b). |
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| 89. |
If `(2)^(2x-2)-(8)^(y-1)=(16)^(x-2.5)`, then find the sum of x and y.A. 8B. 7C. 9D. 6 |
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Answer» Correct Answer - B `(2)^(2x-2)=(8)^(y-1)=(16)^(x-2.5)` `rArr (2)^(2x-2)=2^(3y-3)=2^(4x-10)` `rArr(2)^(2x-2)=2^(4x-10)` `2x-2=4x-10` `rArr x=4` `rArr 2^(3y-3)=2^(2xx4-2)=2^(8-2)=2^6` `rArr 3y-3=6` `rArr=3` `therefore` The sum of x and y is 7. Hence, the correct option is (b). |
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| 90. |
If `(xy)^a=z,(yz)^a=x, and (xz)^a=y`, then what is the value of a? (None of x,y and z is either 0 or 1.)A. 1B. `(1)/(2)`C. `(3)/(2)`D. 0 |
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Answer» Correct Answer - B if `(xy)^a=z` `*yz)^a=x` `(xz)^a=y` On multiplying Eqs. (1) , (2) , (3), we get `(xyz)^2a=xyz` `rArr (xyz)^2a=(xyz)^1` `rArr (xyz)^2a=(xyz)^1` `rArr 2a=1rArr a=(1)/(2)` Hence, the correct option is (b). |
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| 91. |
Find the value of `(-(2)/(3))^2/(-(2)/(3))^3+((-(4)/(9)))/((2)/(3))^2`A. `-(1)/(2)`B. `(3)/(2)`C. `-(5)/(2)`D. `(1)/(2)` |
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Answer» Correct Answer - C `(-(2)/(3))^2/(-(2)/(3))^3+((-(4)/(9)))/((2)/(3))^2` `=(-(2)/(3))^2/((2)/(3))^3-((2)/(3))^(2)/((2)/(3))^2` `=(1)/((2)/(3))^(3-2)-1 ` `=-(3)/(2)-1=-(5)/(2)` Hence the correct option is (c). |
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| 92. |
Which of the following is the descending order of `(4)^26,(64)^9, and (256)^7` ? |
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Answer» Correct Answer - C `(4)^26=(2^2)26=(2)^52` `(64)^9=(2^6)^9=2^54` `(256)^7=(2^8)^7=2^56` `therefore (256)^7gt (64)^9gt (4)^26` Hence the correct option is (c). |
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| 93. |
Simplify `((125)/(216))^((2)/(3))xx((36)/(5))^(+2)div((25)/(6))^(-2)` |
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Answer» Correct Answer - `5^4` NA |
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| 94. |
(1) If `5^(n+2)=625 ,f i n d[(n+3)]^(1/3)`:(2) If `(32/243)^n=8/27 ,f i n d((n+0. 4)/1024)^(-n)` |
| Answer» Correct Answer - (i) 5 (ii) 64 | |
| 95. |
Simplify `(p^(a)/p^(b))^(c)xx(p^(b)/p^(c))xx(p^(c)/p^(a))` |
| Answer» Correct Answer - 1 | |
| 96. |
(i) Simplify `(2^(2/3)-2^((-2)/3))(2^(4/3)+1+2^((-4)/3))` (ii) `[(root(6)(7))^(2)+(root(6)(7))^(-2)][(root(6)(7))^(4)-1+(root(6)(7))^(-4)]` |
| Answer» Correct Answer - (i) `15/4` (ii) `50/7` | |
| 97. |
Evaluate the following. (i) fifth root of `243` (ii) Seventh root of `(0.0000128)` |
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Answer» Correct Answer - (i) 3 (ii) 0.2 |
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| 98. |
If `16200=2^(a)xx3^(b)xx^(c)`, then find a, b, c. |
| Answer» Correct Answer - `a=3, b=4` and `c=2` | |