InterviewSolution
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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.
| 1. |
If `3^(x)=4^(x-1)`, then `x=`A. `(2log_(3)2)/(2log_(3)2-1)`B. `(2)/(2-log_(2)3)`C. `(1)/(1-log_(4)3)`D. `(2log_(2)3)/(2log_(2)3-1)` |
| Answer» Correct Answer - A::B::C | |
| 2. |
The value of `6+log_(3/2)(1/(3sqrt2)sqrt(4-1/(3sqrt2)sqrt(4-1/(3sqrt2)sqrt(4-1/(3sqrt2).....))))` is |
| Answer» Correct Answer - `4` | |
| 3. |
Solve the following equations : `(i) log_(x)(4x-3)=2` `(ii) log_2)(x-1)+log_(2)(x-3)=3` `(iii) log_(2)(log_(8)(x^(2)-1))=0` `(iv) 4^(log_(2)x)-2x-3=0` |
| Answer» Correct Answer - `(i) 3` `(ii) 5` `(iii) +-3` `(iv)3` | |
| 4. |
Solve for `x` `(i) 2^(|x+1|)+2^(|x|)=6` and `x in I` `(ii) x^(2)+x+1+|x-3| le |x^(2)+2x-2|` `(iii) |2x-4|-2|x^(2)+x-3|+2|x-1||x+1|=0` |
| Answer» Correct Answer - `(i) -2,1` `(ii) [3,oo)` `(iii) [-1,1]uu[2,oo)` | |
| 5. |
Let `alphaa n dbeta`be nonzero real numbers such that `2(cosbeta-cosalpha)+cosalphacosbeta=1`. Then which of the following is/are true?`sqrt(3)tan(alpha/2)+tan(beta/2)=0``sqrt(3)tan(alpha/2)-tan(beta/2)=0``t a n""(alpha/2)+sqrt(3)tan(beta/2)=0``t a n""(alpha/2)-sqrt(3)tan(beta/2)=0`A. `sqrt(3)tan((alpha)/(2))-tan((beta)/(2))=0`B. `tan((alpha)/(2))-sqrt(3)tan((beta)/(2))=0`C. `tan((alpha)/(2))+sqrt(3)tan((beta)/(2))=0`D. `sqrt(3)tan((alpha)/(2))+tan((beta)/(2))=0` |
| Answer» Correct Answer - B::C | |
| 6. |
Let `alpha,beta`, are two real solution of equation `(log_(10)x)^2 + log_(10)x^2 = (log_(10))^2 -1,` then` sqrt1/(alpha beta)`equal to`(i) 20 (ii) 3 (iii) 10 (iv) 1`A. `20`B. `3`C. `10`D. `1` |
| Answer» Correct Answer - C | |
| 7. |
If `log_(1/2) ((x^2+6x+9)/(2(x+1)) )< - log_2(x+1)` then complete set of values of x isA. `(-1,1+2sqrt(2))`B. `(1-2sqrt(2),2)`C. `(-1,oo)`D. `(1-2sqrt(2),1+2sqrt(2))` |
| Answer» Correct Answer - A | |
| 8. |
If `A = sin^2x + cos^4 x`, then for all real x :A. `(3)/(4) le A le 1`B. `(13)/(16) le A le 1`C. `1 le A le 2`D. `(3)/(4) le A le (13)/(16)` |
| Answer» Correct Answer - A | |
| 9. |
The solution set of the inequality `|9^x-3^(x+1) + 15| < 2.9^x - 3^x` isA. `(-oo,1)`B. `(1,oo)`C. `(-oo,1]`D. `[2,oo)` |
| Answer» Correct Answer - B | |
| 10. |
Solve the following rational in equalities `(i) ((x-1)(x+2))/((x-3)(x+3)) lt 0` `(ii) ((1-x)^(3)(x+2)^(4))/((x+9)^(2)(x-8))ge0` `(iii) ((x^(2)-3x+1)^(3))/((x-1)(x+2))le0` `(iv) (x(2^(x)-3^(x)))/((x^(2)+x+1)(x-1))gt0` `(v) ((x-1)(x-2)(x-3))/((x+1)(x+2)(x+3)) le1` `(vi) 1 lt (3x^(2)-7x+8)/(x^(2)+1) le2` |
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Answer» Correct Answer - `(i) (-3,-2) uu (1,3)` `(ii) {-2}uu[1,8)` `(iii)(-2,(3-sqrt(5))/(2)]uu(1,(3+sqrt(5))/(2)]` `(iv) (-oo,1)-{0}` `(v) (-3,-2) uu (-1,oo)` `(vi) [1,6]` |
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| 11. |
Solve for `x` `(i) |x+1|=4x+3` `(ii) |x+1|=|x+3|` `(iii) 7|x-2|-|x-7|=5` `(iv) ||x-1|-2|=6x+8` `(v) |2x^(2)-3x+1|=|x^(2)+x-3|` |
| Answer» Correct Answer - `(i) -(2)/(3)` `(ii) -2` `(iii) (1)/(3),(13)/(4)` `(iv) -(9)/(7)` `(v) 2,(1+-sqrt(7))/(3)` | |
| 12. |
Find the range of `lambda` for which equation `x^3+x^2-x-1-lambda=0` has `3` real solution. |
| Answer» Correct Answer - `((-32)/(27),0)` | |
| 13. |
Find the number of positive integral value of `x` satisfying the inequality `((3^(x)-5^(x))(x-2))/((x^(2)+5x+2))ge0` |
| Answer» Correct Answer - `2` | |
| 14. |
If `1lt(x-1)/(x+2)lt7` then find the range of `(i) x` `(ii) x^(2)` `(iii) (1)/(x)` |
| Answer» Correct Answer - `(i) (-oo,-(5)/(2))` `(ii) ((25)/(4),oo)` `(iii) -(2)/(5),0)` | |
| 15. |
`(1)/(sin3alpha)[sin^(3)alpha+sin^(3)((2pi)/(3)+alpha)+sin^(3)((4pi)/(3)+alpha)]` is equal toA. `(4)/(3)`B. `(3)/(4)`C. `(-3)/(4)`D. `(-4)/(3)` |
| Answer» Correct Answer - C | |
| 16. |
In a `DeltaPQR`. if `3 sinP +4 cosQ=6` and `4sinQ+3cosP=1`, then the angle `R` is equal to:A. `(5pi)/(6)`B. `(pi)/(6)`C. `(pi)/(4)`D. `(3pi)/(4)` |
| Answer» Correct Answer - B | |
| 17. |
Let `P={theta:sintheta-costheta=sqrt2cos theta}and Q={theta:sintheta+costheta=sqrt2sintheta}` be two ses. Then,A. `PsubeQ` and `Q-Pneocancel`B. `QcancelsubeP`C. `PcancelsubeQ`D. `P=Q` |
| Answer» Correct Answer - D | |
| 18. |
If `A=(x : x=4n+1,nle5,n in N}` and `B={3n : n le 8, n in N}`, then find `(A-(A-B))`. |
| Answer» Correct Answer - `{9,21}` | |
| 19. |
If `aN = {ax|x in N}` and `bN nn cN = dN`, where `b,c epsilon N`, then |
| Answer» Correct Answer - `d=bc` | |
| 20. |
Solve the following equations (where `[*]` dentoes greatest integer function and `{*}` represent fractional part function) `(i) 2[x]+3[x]=4x-1` `(ii) 4[x]=x+{x}` `(iii) [x]+2{-x}=3x` |
| Answer» Correct Answer - `(i) x in phi ``(ii) {0}` `(iii) {0,2//5,-1//5}` | |
| 21. |
The maximum value of the expression `(1)/(sin^(2)theta+3sinthetacostheta+5cos^(2)theta)` is |
| Answer» Correct Answer - `2` | |
| 22. |
Which of the following sets in an finite/infinite set ? `(i)` Set of divisors of `24` `(ii)` Set of all real number which lie between `1` and `2` `(iii)` Set of all humman beings living in India. `(iv)` Set of all three digit natural numbers |
| Answer» Correct Answer - `(i)` Finite `(ii)` Infinite `(iii)` Finite `(iv)` Finite | |
| 23. |
Which of the following is the empty/non-empty set `(i) {x:x"is a real number and"x^(2)-1=0}` `{x : x"is a real number and" x^(2)+1=0}` `(iii) {x : x "is a real number and" x^(2)-9=0}` `(iv) {x : x"is a real number and " x^(2)=x+2}` |
| Answer» Correct Answer - `(i)` non empty `(ii)` empty `(iii)` non-empty `(iv)` non-empty | |
| 24. |
Write the set `A={x : x "is a positive prime" lt 10}` in the tabular form |
| Answer» Correct Answer - `{2,3,5,7}` | |
| 25. |
Which of the following collections is not a set ? `(i)` The collection of natural numbers between `2` and `20` `(ii)` The collection of numbers which satisfy the equation `x^(2)-5x+6=0` `(iii)` The collection of prime numbers between `1` and `100`. `(iv)` The collection of all intelligent women in Jalandhar. |
| Answer» Correct Answer - `(iv)` | |
| 26. |
Solve for `x` (where `[*]` denotes greatest integer function and `{*}` represent fractional part function) `(i) [2x]=1` `(ii) {x}^(2)+[x]=2` `(iii) 6{x}^(2)-5{x}+1=0` `(iv) 6{x}^(2)-5{x}-1=0` |
| Answer» Correct Answer - `(i) x in[(1)/(2),1)` `(ii) 2` `(iii) x in uuu_(n in I){n+(1)/(3),n+(1)/(2)}` `(iv) x in [1,2)` | |
| 27. |
The number of values of `theta` in the interval `(-pi/2,pi/2)` such that `theta != npi/5` for `ninN` and `tan theta = cot 5theta` as well as `sin2theta = cos 4theta` is |
| Answer» Correct Answer - `3` | |
| 28. |
If `f(x)={x}+{x+[(x)/(1+x^(2))]}+{x+[(x)/(1+2x^(2))]}+{x+[(x)/(1+3x^(2))]}.......+{x+[(x)/(1+99x^(2))]}`, then values of `[f(sqrt(3))]` is where `[*]` denotes greatest integer function and `{*}` represent fractional part function)A. `5050`B. `4950`C. `17`D. `73` |
| Answer» Correct Answer - D | |
| 29. |
If n (A) =3 ,n(3)=6 and `A sube B` .Then the number of elements in `A cup B` is equal to |
| Answer» Correct Answer - `6` | |
| 30. |
Find Power set of the set `A={phi,{phi}}`. |
| Answer» Correct Answer - `P(A)={phi,{phi},{{phi}},{phi,{phi}}}={phi,{phi},{{phi}},A}` | |
| 31. |
If `A={x : -3 lt x lt 3, x in Z}` then find the number of subsets of `A` . |
| Answer» Correct Answer - `32` | |
| 32. |
A class has `175` students. The following data shows the number of students obtaining one or more subjects : Mathematics `100`, Physics `70`, Chemistry `40`, Mathematics and Physics `30`, Mathematics and Chemistry `28`, Physics and Chemistry `23`, Mathematics & Physics & Chemistry `18`. How many students have offered Mathematics alone ? |
| Answer» Correct Answer - `60` | |
| 33. |
In a class of 55 students, the number of students studying different subjects are 23 in Mathematics, 24 in Physics, 19 in Chemistry, 12 in Mathematics and Physics, 9 in Mathematics and Chemistry, 7 in Physics and Chemistry and 4 in all the three subjects. Find the number of students who have taken exactly one subject.A. `15`B. `30`C. `22`D. `27` |
| Answer» Correct Answer - C | |
| 34. |
In a survery, it was found that `21` persons liked product `A`, `26` liked product `B` and `29` liked product `C`. If `14` persons liked products `A` and `B`, `12` liked products `C` and `A`, `13` persons liked products `B` and `C` and `8` liked all the three products then `(i)` Find the number of persons who liked the product `C` only `(ii)` The number of persons who like the products `A` and `B` but not `C` |
| Answer» Correct Answer - `(i) 12 (ii) 6` | |
| 35. |
Number of positive integral solution of the equation `|x^(2)-3x-3| gt |x^(2)+7x-13|` is/areA. `0`B. `1`C. `2D. `3` |
| Answer» Correct Answer - A | |
| 36. |
The number of integral values of a for which the equation `cos2x+a sin x=2a-7` possessess a solution.A. `0`B. `1`C. `3`D. `5` |
| Answer» Correct Answer - D | |
| 37. |
If `A={2,3,4,8,10}`, `B={3,4,5,10,12}`, `C={4,5,6,12,14}` then find `(AnnB)uu(AnnC)`. |
| Answer» Correct Answer - `{3,4,10}` | |
| 38. |
Solve the following equations `(i) sgn({[x]})=0` `(ii) sgn(x^(2)-2x-8)=-1` `(iii)sgn((x^(2)-5x+4)/({x}))=-1` |
| Answer» Correct Answer - `(i) x in R` `(ii) x in (-2,4)` `(iii) (1,2)uu(2,3)uu(3,4)` | |
| 39. |
The smallest integral value of a such that `|x+a-3|+|x-2a|=|2x-a-3|` is true `AA x in R` isA. `0`B. `1`C. `2D. `3` |
| Answer» Correct Answer - B | |
| 40. |
The expression `(tanA)/(1-cotA)+(cotA)/(1-tanA)` can be written as :A. `sinA+cosA+1`B. `secAcosecA+1`C. `tanA+cotA`D. `secA+cosecA` |
| Answer» Correct Answer - B | |
| 41. |
If `X""=""{4^n-3n-1"":""n in N}""a n d""Y""=""{9(n-1)"": n in N}`, where N is the set of natural numbers, then `XuuY`is equal to(1) N(2) Y - X(3) X(4) YA. `X`B. `Y`C. `N`D. `Y-X` |
| Answer» Correct Answer - B | |
| 42. |
Let `f_K(x)""=1/k(s in^k x+cos^k x)`where `x in R`and `kgeq1`. Then `f_4(x)-f_6(x)`equals(1) `1/6`(2) `1/3`(3) `1/4`(4) `1/(12)`A. `(1)/(4)`B. `(1)/(12)`C. `(1)/(6)`D. `(1)/(3)` |
| Answer» Correct Answer - B | |
| 43. |
Let `A_(1)`, `A_(2)` and `A_(3)` be subsets of a set `X`. Which one of the following is correct ?A. `A_(1)uuA_(2)uuA_(3)` is the smallest subset of `X` containing elements of each of `A_(1)`, `A_(2)` and `A_(3)`B. `A_(1)uuA_(2)uuA_(3)` is the smallest subset of `X` containing elements either `A_(1)` or `A_(2)uuA_(3)` but not bothC. The smallest subset of `X` containing `A_(1)uuA_(2)` and `A_(3)` equals the smallest subset of `X` containing both `A_(1)` and `A_(2)uuA_(3)` only if `A_(2)=A_(3)`D. None of these |
| Answer» Correct Answer - A | |
| 44. |
Consider the following statements : `1.` If `A={(x,y) in [RxxR : x^(3)+y^(3)=1]}` and `B={(x,y) in [R: (x-y)=1]}`, then `AnnB` contains exactly one elements. `2.` If `A={(x,y) in [RxxR : x^(3)+y^(3)=1]}` and `B={(x,y) in [R: (x+y)=1]}`, then `AnnB` contains exactly two elements. which of the above statements is/are correct ?A. `1` onlyB. `2` onlyC. Both `1` and `2`D. Neither `1` nor `2` |
| Answer» Correct Answer - C | |
| 45. |
Let `A={x : x in R,-1 lt x lt 1}`, `B={x : x in R, x le0 or x ge 2}` and `AuuB=R-D`, then find set `D` |
| Answer» Correct Answer - `{:({x:1 le x lt 2}),((3){x : 1 le x le 2}),((4){x : 1 ltx lt2}):}` | |
| 46. |
The solution of `sqrt(5-2sinx) ge 6 sinx-1` isA. `[pi(12n-7)//6,pi(12n+7)//6] (n in Z)`B. `[pi(12n-7)//6,pi(12n+1)//6] (n in Z)`C. `[pi(2n-7)//6,pi(2n+1)//6] (n in Z)`D. `[pi(12n-7)//3,pi(12n+1)//3] (n in Z)` |
| Answer» Correct Answer - B | |
| 47. |
Find the number of solution of the following equation both `|sin x|=|x/10|` |
| Answer» Correct Answer - `(i) 11` `(ii) 6` | |
| 48. |
Solve the following inequations `(i) (sinx-2)(2sinx-1) lt 0` `(ii) (2cosx-1)(cosx) le 0` `(iii) sinx+sqrt(3)cosx ge 1` `(iv) cos^(2)x+sinx le 2` `(v) tan^(2)x gt 3` |
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Answer» Correct Answer - `(i) x in uuu_(n in I)((pi)/(6)+2npi,(5pi)/(6)+2npi)` `(ii)x in uu_(n in I)[(-pi)/(2)+2npi,(-pi)/(3)+2npi]uu[(pi)/(3)+2npi,(pi)/(2)=2npi]` `(iii)x in uu_(n in I)[-(pi)/(6)+2npi,2npi+(pi)/(2)]` `(iv) x in R` `(v)x in uuu_(n in I)(-(pi)/(2)+2npi,-(pi)/(3)+2npi)uu((pi)/(3)+2npi,(pi)/(2)+2npi)` |
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| 49. |
Solve the following inequalities `(i) log_(5)(3x-1) lt 1` `(ii) (log_(.5)x)^(2)+log_(.5)x-2 le 0` `(iii) log_(3)(x+1)+log_(3)(x+7) ge 3` `(iv)log_(1//2)log_(3)(x^(2)+5)+1 le 0` |
| Answer» Correct Answer - `(i) ((1)/(3),2)` `(ii)[(1)/(2),4]` `(iii)[2,oo)` `(iv)(-oo,-2]uu[2,oo)` | |
| 50. |
Solve the following inequalities `(i) |log_(3)x|-log_(3)x-3 lt 0` `(ii)(x-1)/(log_(3)(9-3^(x))-3) le 1` `(iii)log_((x-1)/(x-5))(x-2) gt 0` `(iv) log_(x)(x^(3)-x^(2)-2x) lt 3` |
| Answer» Correct Answer - `(i) ((1)/(3^(3//2)),oo)` `(ii) [log_(3)9//10,2)` `(iii) (5,oo)` `(iv) (2,oo)` | |