InterviewSolution
Saved Bookmarks
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. |
If A = {x : x is a multiple of 4} and B = {x : x is a multiple of 6}, then A `sub` B consists of all multiple ofA. 4B. 8C. 12D. 16 |
| Answer» Correct Answer - C | |
| 52. |
Power set of the set `A = {phi, {phi}}` isA. AB. `{phi,{phi},A}`C. `{phi,{phi},{{phi}},A}`D. None of these |
| Answer» Correct Answer - C | |
| 53. |
If `n(A) = p and n(B) = q` and no. of subsets of `A` are `48` more than the no. of subsets of `B` then :A. `p=6,q=5`B. `p=6,q=4`C. `p=5,q=6`D. `p=4,q=6` |
| Answer» Correct Answer - D | |
| 54. |
Write all the subsets of B = {p, q} |
|
Answer» {p}, {q}, {p, q} and { } are the subsets of the given set B = {p, q} As the n(B) = 2 then number of all subsets = 2n = 22 = 4 |
|
| 55. |
If `P sube Q` and `Q sube P`, then `"____"` |
| Answer» Correct Answer - `P = Q` | |
| 56. |
State whether the given statement is true or false : (i) if `A sub B and x lin ` then x lin A`. (ii) If `A sube phi` then A = phi ` (iii) If `A,B and C` are three sets such that ` in B and B sub C then A sub C `. (iv) If A, B and C are three sets such that `A sub B and B in C `" then "`A in C`. (v) If A, B and C are three sets such taht ` A cancel(sub) B and B cancel(sub)C` " then " A cancel(sub)C`. (vi) If A, B are sets such that ` x in A and A in B` then `x in B`. |
|
Answer» Correct Answer - (i) True (ii) True (iii) False (iv) False (v) False (vi) False (iii) Let `A = {a}, B = {{a, b}` and C = {{1}, b, c}. Then , `{a} in B` and `B sub C`. But., `{a} cancel(sub) C`. (iv) Let A = {a}, B = {a, b} and C = {{a, b}, c}. Then, `A cancel(sub) B` and `B in C`. But, `A cancel(in)C`. Let A = {a}, B = {b,c} and C = {a, c}. Then, `A cancel(sub)B` and `B cancel(sub)C`. But `A sub C`. Let A = {x}, B = {{x}, y}. Then, `x in A` and `A in B`. But, `x in b`. |
|
| 57. |
If `A= {3,{4,5},6}`, find which of the following statements are true. `(i) {4,5}subeA` `(ii) {4,5} in A` (iii) ` {{4,5 }}sube A ` (iv) `4 in A` ` (v) {3}sube A` (vi) ` {phi}sube A` (vii) `phi sube A` (viii) {3,4,5} sube A ` (ix) {3,6} sube A ` |
|
Answer» Correct Answer - (i) False (ii) True (iii) True (iv) False (v) True (vi) False (vii) True (viii) False (ix) True. |
|
| 58. |
If `A = {2,3,5}`, then the number of subsets of `A` are :A. 3B. 32C. 6D. 8 |
| Answer» Correct Answer - D | |
| 59. |
If `A sube B and B subX`, the the correct option is :A. `A sub X`B. `A sube X`C. `X sub A`D. `X sube A` |
| Answer» Correct Answer - A | |
| 60. |
If `A={x:x in N and 3 le x lt7}`, then `A = ?`A. `{4,5,6,7}`B. `{3,4,5,6}`C. `{4,5,6}`D. None of these |
| Answer» Correct Answer - B | |
| 61. |
Consider the following statements: 1. Parallelism of lines is an equivalence relation. 2. x R y, if x is a father of y, is an equivalence relation. Which of the statements given above is/are correct?A. 1 onlyB. 2 onlyC. Both 1 and 2D. Neither 1 nor 2 |
|
Answer» Correct Answer - A Statement 1: Let l, m, n are parallel line and R is a relation. `therefore l||l`, then R is reflexive. and l||m and m||l, the R is symmetric. also l||m, m||n implies l||n, then R is transitive. Hence, R is an equivalence relation. Statement 2: x is father of y then x is not the father of x, so relation is not reflexive. Also, x is father of y but y is not father of x, so it is not symmetric. And x is father of y and y is father of z does not imply that x is father of z so, it is not transitive too. So, this is not an equivalence relation. so, only statement 1 is correct. |
|
| 62. |
Observe the given Venn diagram and write the following sets.i. A ii. Biii. A ∪ B iv. Uv. A’ vi. Bvii. (A ∪B )’ |
|
Answer» i. A = {x, y, z, m, n} ii. B = {p, q, r, m, n} iii. A ∪ B = {x, y, z, m, n, p, q, r } iv. U = {x, y, z, m, n, p, q, r, s, t} v. A’ = {p, q, r, s, t} vi. B’ = {x, y, z, s, t} vii. (A ∪ B )’ = {s, t} |
|
| 63. |
From the Venn diagram, A ∪ B = …………….(A) {5, 6} (B) {5, 6, 7, 8} (C) Φ (D) {7,8} |
|
Answer» Correct option is (B) {5, 6, 7, 8} |
|
| 64. |
Let A = {a, b, c}. What is the equivalence relation of smallest cardinality on A? What is the equivalence relation of largest cardinality on A? |
|
Answer» R = {{a, a), (b, b), (c, c)} is this smallest cardinality of A to make it equivalence relation n(R) = 3 R = {(a, a), {a, b), (a, c), (b, c), (b, b), {b, c), (c, a), (c, b), (c, c)} n(R) = 9 is the largest cardinality of R to make it equivalence. |
|
| 65. |
If `A={x:x=3n,n in N} and B={x:x=4n,n in N}`, then find `A cap B`. |
|
Answer» We have `A={x:x in Z and x "is a multiple of " 3}` and `B = {x:x in Z and x " is a multiple of "4}`. `therefore A cap B={x:x in Z and x " is a multiple of both 3 and 4 "}` `={x:x in Z and x " is a multiple of " 12}` `={x:x=12 n, n in Z}`. Hence , `A cap B ={x:x=12 n,n in Z}`. |
|
| 66. |
If n is an integer and if sin`theta` = 1, prove that `theta` = (4n+1)`pi/2` |
|
Answer» `Sin theta = 1 => sin theta = sin (pi/2)` `theta = (pi/2)` Also, we know, `sin theta = sin (2npi+theta)` Here, `n` is an integer. `:. theta = (2npi+(pi/2))` `=> theta = (4npi+pi)/2=>(pi/2)(4n+1)` `:. theta = (4n+1)(pi/2)` |
|
| 67. |
A and B are two mutually exclusive and exhaustive events of a random experiment such that `P(A)=6[P(B)]^2` where P(A) and P(B) denotes probability of A and B respectively. Find P(A) and P(B) |
|
Answer» As, `A` and `B` are mutually exahaustive events, `:. A uu B = S` `:.P(AuuB) = P(S) = 1` As, `A` and `B` are mutually exclusive events, `:. P(AuuB) = P(A)+P(B)`. `=>P(A)+P(B) = 1` `=>6P(B)^2+P(B) - 1 = 0`...(Given that `P(A) = 6P(B)^2`) `=>6P(B)^2+3P(B)-2P(B) - 1 = 0` `=>3P(B)(2P(B)+1)-1(2P(B)+1) = 0` `=>(3P(B)-1)(2P(B)+1) = 0` `=>P(B) = 1/3 and P(B) = -1/2` As, `P(B)` can not be negative, so, `P(B) = 1/3` `:. P(A) = 6(1/3)^2 = 2/3.` |
|
| 68. |
Range of `f(x)=tan(pi[x^2-x])/[1+sin(cosx)]`,where [.] denotes greatest integer function. |
|
Answer» Here, we are given `x^2-x` is a greatest integer function. `:.` We can write the given expression, `f(x) = tan(npi)/(1+sin(cosx))`, here `n` is an integer. We know, `tan (npi)` is always `0`. Now, we have to check if the value of `1+sin(cosx)` is `0` or not. Let `1+sin(cosx) = 0` `=>sin(cosx) = -1` `=>cosx = -pi/2` We know, value of `cosx` lies between `-1` and `1`. So, `cosx` can not be `-pi/2`. `:. 1+sin(cosx)` can not be `0`. `:.` Value of the given expression `= tan (npi)/(1+sin(cosx)) = 0` So, option `D` is the correct option. |
|
| 69. |
A and B are two sets having 3 elements in common. If n(A)=5, n(B)=4, then what is `n(AxxB)` equal to ? |
|
Answer» Correct Answer - D Here, n(A) = 5 and n(B) = 4 `therefore n(AxxB)=5xx4=20 " "[because n(A)=m, n(B)=nimpliesn(AxxB)=mn]` |
|
| 70. |
If `log_(10)2, log_(10)(2^(x)-1) and log_(10)(2^(x)+3)` are three consecutive terms of an A.P, then the value of x isA. 1B. `log_(5)2`C. `log_(2)5`D. `log_(10)5` |
|
Answer» Correct Answer - C `log_(10)2, log_(10)(2^(x)-1) and log_(10)(2^(x)+3)` are in A.P. Hence, common difference will be same. `therefore log_(10)(2^(x)-1)-log_(10)2=log(2^(x)+3)-log_(10)(2^(x)-1)` `therefore log_(10)((2^(x)-1)/(2))=log_(10)((2^(x)+3)/(2^(x)-1))` `implies(2^(x)-1)/(2)=(2^(x)+3)/(2^(x)-1)` `(2^(x)-1)^(2)=2(2^(x)+3)` `2^(2x)-2^(x+1)+1=2^(x+1)+6` `2^(2x)-2^(x+2)=5` Let `2^(x)=y`, then `y^(2)-4y-5=0` `y^(2)-5y+y-5=0` `y(y-5)+1(y-5)=0` `y=-1, y=5` `"Therefore, "2^(x)=5` `x=log_(2)5`. |
|
| 71. |
If A = P ({1, 2}), where P denotes the power set, then which one of the following statements is correct?(a) {1, 2} ⊂ A (b) 1∈Α (c) ϕ ∉ A (d) {1, 2}∈Α |
|
Answer» (d) {1, 2} ∈ A Given, A = P ({1, 2}), then A = [ ϕ, {1}, {2}, {1, 2}] ⇒ {1, 2} ∈ A |
|
| 72. |
Let X be the set of all persons living in a city. Persons x, y in X are said to be related as `xlty` if y is at least 5 years older than x. Which one of the following is correct?A. The relation is an equivalence relation on X.B. The relation is transitive but neither reflexive nor symmetricC. The relation is reflexive but neither transitive nor symmetricD. The relation is symmetric but neither transitive nor reflexive |
|
Answer» Correct Answer - B Given that `xlty if y ge x +5` For Reflexive: `x cancellt x` Hence, relation is not reflexive. For Symmetry: if `xlty`, then `y cancellt x` Hence, relation is not symmetry. For Transitive: if `x lt y and y lt z`, then `x lt z` Hence, relation is transitive. |
|
| 73. |
Out of 32 persons, 30 invest in National Savings Certificates and 17 invest in Shares. What is the number of persons who invest in both?(a) 13 (b) 15 (c) 17 (d) 19 |
|
Answer» (b) 15 Use n (A ∪ B) = n (A) + n (B) – n (A ∩ B) |
|
| 74. |
If `log_(3)[log_(3)[log_(3)x]]=log_(3)3`, then what is the value of x?A. 3B. 27C. `3^(9)`D. `3^(27)` |
|
Answer» Correct Answer - D Consider `log_(3)[log_(3)[log_(3)x]]=log_(3)3` `implies log_(3)[log_(3)x]=3` `implies log_(3)x=3^(3)` `implies log_(3)x=27impliesx=3^(27)` |
|
| 75. |
For what value (s) of x is `log_(10){999+sqrt(x^(2)-3x+3)}=3`? |
|
Answer» Correct Answer - D Given equation is : `log_(10){999+sqrt(x^(2)-3x+3)}=3` `implies999+sqrt(x^(2)-3x+3)=10^(3)=1000` `implies sqrt(x^(2)-3x+3)=1` `impliesx^(2)-3x+3=1` `x^(2)-3x+2=0` `impliesx^(2)-2x-x+2=0` `implies x(x-2)-1(x-2)=0` `implies (x-1)(x-2)=0` `implies x=1,2`. |
|
| 76. |
Out of 32 persons, 30 invest in National Savings Certificates and 17 invest in shares. What is the number of persons who invest in both?A. 13B. 15C. 17D. 19 |
|
Answer» Correct Answer - B Let N = National savings certificates S = Shares Total no. of persons = 32 No. of persons who invest in National savings certificates = 30 No. of persons who invest in shares = 17 Therefore `n(NuuS)=32, n(N) =30, n(S)=17` We know that, `n(NuuS)=n(N)+n(S)-n(NnnS)` `implies32=30+17-n(NnnS)` `impliesn(NnnS)=47-32=15` |
|
| 77. |
The relation `R={(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)}` on a set A={1, 2, 3} isA. reflexive, transitive but not symmetricB. reflexive, symmetric but not transitiveC. symmetric, transitive but not reflexiveD. reflexive but neither symmetic nor transitive |
|
Answer» Correct Answer - A Let R={(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)} Reflexive Since, IR 1, 2R2, 3R3 in the set R `therefore` R is reflexive relation. Symmetric Since 1R2 but 2 is not related to 1 in R `therefore` R is not symmetric relation. Transitive 1R2, 2R3 implies 1R3 `therefore` R is not transitive relation. Hence, R is reflexive and transitive only. |
|
| 78. |
Let `f:RrarrR` be defined by `f(x)=|x|//x,xne0, f(0)=2`. What is the range of f?A. {1,2}B. {1,-1}C. {-1,1,2}D. {1} |
|
Answer» Correct Answer - C Let `f:RrarrR` be defined as `f(x)=(|x|)/(x),xne0`. Also, f(0)=2 ie. Value of function at x=0 is 2. Consider, `f(x)={{:((x)/(x)=1ifxgt0),((-x)/(x)=-1ifxlt0):}` because we have `|x|={{:("x,",xge0),("-x,",xlt0):}` Thus, Range of f(x) = {1, -2} |
|
| 79. |
What is the range of the function `y=. x^2/(1+x^2)` where `x in RR?`A. [0,1)B. [0,1]C. (0,1)D. (0,1] |
|
Answer» Correct Answer - A Function `y=(x^(2))/(1+x^(2))x inR` `{:(x=0,y=0),("x=1, -1",y=(1)/(2)),("x=2, -2",y=(4)/(5)),("x=3, -3",y=(9)/(10)),(.,.),(.,.),(.,.):}` Clearly `0leylt1` `impliesy in,[0,1)` Hence Range of y=[0,1) |
|
| 80. |
The range `f(x)=cos2x-sin2x` contains the setA. [2, 4]B. `[-1, 1]`C. `[-sqrt(2), sqrt(2)]`D. `(-sqrt(2),2)` |
|
Answer» Correct Answer - C Let f(x)=cos2x-sin2x `f(x)=(1)/(sqrt(2))[sqrt(2)cos2x-sin2x]` `f(x)=sqrt(2)[(1)/(sqrt(2))cos2x-(1)/(sqrt(2))sin2x]` `f(x)=sqrt(2)[cos.(pi)/(4)cos2x-sin.(pi)/(4)sin2x]` `f(x)=sqrt(2)[cos((pi)/(4)+2x)]` We know, `-1lecos((pi)/(4)+2x)le1` `implies-sqrt(2)lesqrt(2)cos((pi)/(4)+2x)lesqrt(2)` `implies-sqrt(2)lef(x)lesqrt(2)` `therefore " Range of "f(x)=[-sqrt(2),sqrt(2)]` |
|
| 81. |
Which one of the following is correct? The function `F:ArarrR` where `A={x in R,-(pi)/(2)ltxlt(pi)/(2)}` defined by f(x) = tan x.A. InjectiveB. Not injectiveC. BijectiveD. Not bijective |
|
Answer» Correct Answer - A `because` f(x)=tanx f(x) is increasing in the interval `(-(pi)/(2),(pi)/(2))` Hence, f(x) is injective in the interval `(-(pi)/(2),(pi)/(2))` |
|
| 82. |
What is `(1111)_(2)+(1001)_(2)-(1010)_(2)` equal to ?A. `(111)_(2)`B. `(1100)_(2)`C. `(1110)_(2)`D. `(1010)_(2)` |
|
Answer» Correct Answer - C Since, `(1111)_(2)=1xx2^(3)+1xx2^(2)+1xx2^(1)+1xx2^(0)` `=8+4+2+1=15` `(1001)_(2)=1xx2^(3)+0xx2^(2)+0xx2^(1)+1xx2^(0)=8+1=9` `and (1010)_(2)=1xx2^(3)+0xx2^(2)+1xx2^(1)+0xx2^(0)=8+2=10` `therefore (1111)_(2)+(1001)_(2)-(1010)_(2)=15+9-10=14` `therefore (14)_(10)=(1110)_(2)` |
|
| 83. |
What is the value of `((0.101)_(2)^((11)_(2))+(0.011)_(2)^((11)_(2)))/((0.101)_(2)^((10)_(2))-(0.101)_(2)^((01)_(2))(0.011)_(2)^((01)_(2))+(0.011)_(2)^((10)_(2)))`A. `(0.001)_(2)`B. `(0.01)_(2)`C. `(0.1)_(2)`D. `(1)_(2)` |
|
Answer» Correct Answer - D `(0.101)_(2)=2^(-1)xx1+2^(-2)xx0+2^(-3)xx1` `= (1)/(2)+0+(1)/(8)=(5)/(8)` and `(0.011)_(2)=0xx2^(-1)+1xx2^(-2)+1xx2^(-3)` `=0+(1)/(4)+(1)/(8)=(3)/(8)` Also, `(11)_(2)=1xx2^(1)+1xx2^(0)=3` and `(01)_(2)=0xx2^(1)xx1xx2^(0)=1` `therefore ((0.101)_(2)^((11))+(0.011)_(2)^((11)_(2)))/((0.101)_(2)^((10)_(2))-(0.101)_(2)^((01)_(2))(0.011)_(2)^((01))+(0.011)_(2)^((10)_(2)))` `=(((5)/(8))^(3)+((3)/(8))^(3))/(((5)/(8))^(2)-((5)/(8))((3)/(7))+((3)/(8))^(2))=(5)/(8)+(3)/(8)=(8)/(8)=1=(1)_(2)` |
|
| 84. |
If `S={x:x^2+1=0,x` is real}, then S isA. `{-1}`B. {0}C. {1}D. an empty set |
|
Answer» Correct Answer - D `S={x : x^(2)+1=0, x: 5" real"}` `x^(2)+1=0impliesx^(2)=-1impliesx=sqrt(-1)rarr` complex number No real numbers. So, S is empty set |
|
| 85. |
Consider the following with regard to a relation R on a set of real numbers defined by xRy if and only if 3x+4y=5 I. 0 R 1 II. `1 R(1)/(2)` III. `(2)/(3)R(3)/(4)` Which of the above are correct?A. I and IIB. I and IIIC. II and III onlyD. I, II and III |
|
Answer» Correct Answer - C Let on the set of real numbers, R is a relation defined by xRy if and only if 3x+4y=5 (I) Put x=0 and y=1, we get LHS=3(0)+4(1)=`4ne5` (=RHS) Hence 0 is not related to 1. (II) Now, Put x=1 and `y=(1)/(2)`, we get `LHS=3(1)+4xx(1)/(2)=5=5(=RHS)` Hence 1 is related to `(1)/(2)`. (III) Similarly, `(2)/(3)` is related to `(3)/(4)`. Hence, both statements II and III are correct. |
|
| 86. |
Assertion (A) : `{x in R|x^(2)lt0}` is not a set. Here R is the correct of real numbers. Reason (R ) : For every real number `x, x^(2)gt0`.A. Both A and R are individually true, and R is the correct explanation of A.B. Both A and R are individually true but R is not the correct explanation of A.C. A is true but R is falseD. A is false but R is true |
|
Answer» Correct Answer - A Since `x^(2)lt0` is not possible for real number. A is true. Since `x^(2)gt0` for `AA x in R`. Both (A) and (R ) are true and (R ) is the correct explanation of (A). |
|
| 87. |
Which one of the following real valued functions is never zero?A. Polynomial functionB. Trigonometric functionC. Logarithmic functionD. Exponential function |
|
Answer» Correct Answer - D When `f(x)=e^(x)` `f(x)ne0, AAx in R` implies An exponential function is never zero. |
|
| 88. |
The remainder and the quotient of the binary division `(101110)_2 -: (110)_2` respectivelyA. `(111)_(2) and (100)_(2)`B. `(100)_(2) and (111)_(2)`C. `(101)_(2) and (101)_(2)`D. `(100)_(2) and (100)_(2)` |
|
Answer» Correct Answer - B `(101110)_(2)=1xx2^(5)+0xx2^(4)+1xx2^(3)+1xx2^(2)+1xx2^(1)+0xx2^(0)` `=32+0+8+4+2+0` `=(46)_(10)` Similarly, `(110)_(2)=1xx2^(2)+1xx2^(1)+0xx2^(0)` `=4+2` `=(6)_(10)` Quotient = 7 Remainder = 4 `(7)_(10)=(111)_(2) and (4)_(10)=(100)_(2)` |
|
| 89. |
Consider the following statements `1. phiin{phi}" 2."{phi}subephi` Which of the statements given above is/are correct?A. 1 onlyB. 2 onlyC. Both 1 and 2D. Neither 1 nor 2 |
|
Answer» Correct Answer - D Both statements are incorrect. |
|
| 90. |
If `2^(x)=3^(y)=12^(z)`, then what is `(x+2y)//(xy)` equal to ?A. zB. `(1)/(z)`C. 2zD. `(z)/(2)` |
|
Answer» Correct Answer - B Given that `2^(x)=3^(y)=12^(z)=k` Taking `log_(2)` on both the sides `x=log_(2)k, y=log_(3)k and z=log_(12)k` `(x+2y)/(xy)=(log_(2)k+2log_(3)k)/(log_(2)klog_(3)k)` `=(1)/(log_(3)k)+(2)/(log_(2)k)` `=log_(k)3+2log_(k)2=log_(k)3+log_(k)4` `log_(k)12=(1)/(log_(12)k)=(1)/(z)` |
|
| 91. |
Which one of the following is correct? The real number `root3(2+sqrt(5))+root3(2-sqrt(5))` is :A. an integerB. a rational number but not an integerC. an irrational numberD. none of the above |
|
Answer» Correct Answer - B The given number `root(3)(2+sqrt(5))+root(3)(2-sqrt(5))` can be written as : `=(2+sqrt(5))^(1//3)+(2-sqrt(5))^(1//3)` `2^(1//3)[1+(1)/(2)sqrt(5)]^(1//3)+2^(1//3)[1-(1)/(2)sqrt(5)]^(1//3)` `=2^(1//3)[1+(1)/(6)sqrt(5)+...+1-(1)/(6)sqrt(5)+...]` Thus the given number is a rational number but not an integer. |
|
| 92. |
What is the product of the binary numbers 1001.01 and 11.1?A. `101110.011`B. `100000.011`C. `101110.101`D. `100000.101` |
|
Answer» Correct Answer - B `1001.01=1xx2^(3)+1xx2^(0)+1xx2^(-2)`, corresponding to number of base 10. `=8+1+(1)/(4)=(37)/(4)=9.25` and `11.1=1xx2^(1)+1xx2^(0)+1xx2^(-1)` `=2+1+(1)/(2)=(7)/(2)=3.5` Corresponding to the number of base 10. `therefore 1001.01xx11.1=9.25xx3.5=32.375` From decimal to binary `(32)_(10)=(100000)` and `(.375)_(10)=0.25+0.125` `=(1)/(4)+(1)/(8)=1xx2^(-2)+1xx2^(-3)=(0.011)_(2)` `therefore (32.375)_(10)=(100000.011)_(2)` |
|
| 93. |
Among the following equations, which are linear 1. `2x+y-z=5` 2. `pix+y-ez=log3` 3. `3^(x)+2y=7` 4. `sinx-y-5z=4` Select the correct answer using the code given belowA. 1 onlyB. 1 and 2 onlyC. 3 and 4D. 1, 2 and 4 |
|
Answer» Correct Answer - B An equation of the form ax+by+cz=d, where a, b, c, d are real number, not all zero, is linear. `implies2x+y-z=5` and `pix+y-ez` log 3 are linear. |
|
| 94. |
The multiplication of the number `(10101)_(2) " by "(1101)_(2)` yields which one of the following ?A. `(100011001)_(2)`B. `(100010001)_(2)`C. `(110010011)_(2)`D. `(100111001)_(2)` |
|
Answer» Correct Answer - B `because (10101)_(2)=2^(4)xx1+0xx2^(3)+1xx2^(2)+0xx2+1xx2^(0)` `=16+4+1=21` and `(1101)_(2)=1xx2^(3)+1xx2^(2)+0xx2^(1)+1xx2^(0)` `=8+4+1=13` `therefore (10101)_(2)xx(1101)_(2)=21xx13` `=273=256+16+1=2^(8)+2^(4)+2^(0)` So, there will be 1 at `9^(th), 5^(th)` and first place from right and zero at other places So, `(273)_(10)=(100010001)_(2)` |
|
| 95. |
S = { 3, \(\pi\) , √2, - 5, 3 + √7, 2/7} . Which of the following is a sub-set of ‘S’ containing all irrational numbers ?(A) {3, \(\pi\), 2/7 , - 5, 3 + √7}(B) {3, + \(\pi\), √2, \(\pi\)}(C) {3, \(\pi\), √2}(D) {3, - 5, 2/7} |
|
Answer» Correct option is (B) {3 + √7,√2 , π} |
|
| 96. |
In a committee, 50 people speak Hindi, 20 speak English and 10 speak both Hindi and English . How many speak at least one of these two languages ? |
|
Answer» Correct Answer - 60 `n(AcupB)= n(A) +n(B) -n(A cap B) =(50 +20-10)=60`. |
|
| 97. |
If `n(A)=x, n(B)=2[n(A)], n(A uu B)=2017` and `n(A nn B)=1007`. Find the value of `x`. |
|
Answer» Correct Answer - 1008 Given `n(A)=x, n(B)=2[n(A)]=2x` `n(A uu B)=2017, n(A nn B)=1007` `n(A uu B)=n(A)+n(B)-n(A nn B)` `2017=x+2x-1007` `3x=3024` `x=1008` |
|
| 98. |
If `A={x : x in N, 2015 lt x lt 2017} B={x : x in N, x+1=2017}`, then `A-B=` ________.A. `phi`B. `{2016}`C. `{2015, 2016, 2017}`D. `{1, 2, 3, ... 2017}` |
|
Answer» Correct Answer - A `A={2016}` `B={2016}` `A-B={ }` (or) `phi` Hence, the correct option is (a). |
|
| 99. |
If `A={x : x in N, x" is an additive inverse of "2017}` and `B={x : x in N, x" is a multiplicative inverse of "2017}`. Then `Auu B=` ________.A. `phi`B. `{-2017, 1/2017}`C. `1`D. `{2017, (-1)/2017}` |
|
Answer» Correct Answer - A Additive inverse of 2017 is -2017 but `-2017 notin N` `:. A={ }` Multiplicative inverse of 2017 is `1/2017`, but `1/2017 notin N` `:. B={ }` `A uu B={ }` Hence, the correct option is (a). |
|
| 100. |
If A is collection of natural numbers which are less than 2 and `B={x : x in N, x" is neither prime nor composite"}` then `A nn B=` ________.A. `phi`B. `{1}`C. `N`D. None of these |
|
Answer» Correct Answer - B `A={1}` `B={1}` `A nn B={1}` Hence, the correct option is (b). |
|