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. |
The objective function `Z=4x_(1) +5x_(2)`, Subject to ` 2x_(1) +x_(2) ge 7,2x_(1)+3x_(2) le 15,x_(2)le 3, x_(1),x_(2)ge 0` has minimum value at the pointA. On x-axisB. On y-axisC. At the originD. On the line parallel to x-axis |
| Answer» Correct Answer - A | |
| 2. |
A box contains 6 pens , 2 of which are defective Two pens are taken randomy from the bax .If r,v. X., : Number of defective pens obtained , then standard deviation of x=A. `+- (4)/(3sqrt(5))`B. `(8)/(3)`C. `(16)/(45)`D. `(4)/(3sqrt(5))` |
| Answer» Correct Answer - D | |
| 3. |
The Solution of the differential equation `(dy)/(dx)=tan ((y)/(x))+(y)/(x)` isA. `cos ((y)/(x))=cx`B. `sin ((y)/(x))=cx`C. `cos((y)/(x))=cy`D. `sin ((y)/(x))=cy` |
| Answer» Correct Answer - B | |
| 4. |
A boy tosses faiir coin 3 times. If he gets Rs 2X for X heads, then his expected gain equals to Rs…..A. 1B. `(3)/(2)`C. 3D. 4 |
| Answer» Correct Answer - B | |
| 5. |
If `f(x)=log(sec^(2)x)^(cot2)` for `xne0` for x=0 is continuous at x=0, then K isA. `e^(-1) `B. `1`C. `e`D. `0` |
| Answer» Correct Answer - B | |
| 6. |
`int_(0) ^(3) [x] dx=`__________ where [x] is greatest integer functionA. 3B. 0C. 2D. 1 |
| Answer» Correct Answer - A | |
| 7. |
if `int (1)/(sqrt(9-16x^(2)))dx=alpha sin ^(-1) (beta x) +c.` then ` alpha +(1)/(beta )=`A. `1`B. `(7)/(12)`C. `(19)/(12)`D. `(9)/(12)` |
| Answer» Correct Answer - A | |
| 8. |
`f(x) = {{:(("tan"(pi)/(4)+x)^(1//x)",",x ne 0),(k",",x = 0):}` for what value of k, f(x) is continuous at x = 0 ?A. `e`B. `e^(-1)`C. `e^(2)`D. `e^(-2)` |
| Answer» Correct Answer - B | |
| 9. |
If `int(1)/((x^(2)+4)(x^(2)+9))dx=A" tan"^(-1)(x)/(2)+Btan^(-1)((x)/(3))+C`, then A-B=A. `1/6`B. `1/(30)`C. `-(1)/(30)`D. `-(1)/(6)` |
| Answer» Correct Answer - A | |
| 10. |
Which of the following statement pattern is a tautology?A. `p vv (qto p)`B. `~q to ~P`C. `(1 to p )vv (~p harr q)`D. `p ^^~p` |
| Answer» Correct Answer - C | |
| 11. |
`int _(0) ^(1) x tan ^(-1) x dx =`A. `(pi)/(4) +(1)/(2)`B. `(pi)/(4)-(1)/(2)`C. `(1)/(2)-(pi)/(4)`D. `-(pi)/(4)-(1)/(2)` |
| Answer» Correct Answer - B | |
| 12. |
If slopes of lines represented by `kx^(2)+5xy+y^(2)=0` differ by 1, then k=A. `2`B. `3`C. `6`D. `8` |
| Answer» Correct Answer - C | |
| 13. |
Let `square PQRS` be a quadrilateral. If M and N are the mid-points of the sides PQ and RS respectively, then PS+QR=A. `3 bar (MN)`B. `4 bar (MN)`C. `2bar(MN)`D. `2bar (NM)` |
| Answer» Correct Answer - C | |
| 14. |
if lines represented by equation `px^(2)-qy^(2)=0` are distinct, thenA. `pq gt 0`B. `pq lt 0`C. `pq =0`D. `p+q=0` |
| Answer» Correct Answer - A | |
| 15. |
The statement pattern `(~p ^^ q)` is logically equivalent toA. `(pvv q)vv ~P`B. `(p vv q)^^~P`C. `(p ^^q) to P`D. `(p vv q)to p` |
| Answer» Correct Answer - B | |
| 16. |
The inverse of the matrix `[(1,0,0),(3,3,0),(5,2,-1)]` isA. `-(1)/(3) [(-3,0,0),(3,1,0),(9,2,-3)]`B. `-(1)/(3)[(-3,0,0),(3,-1,0),(-9,-2,3)]`C. `-(1)/(3)[(3,0,0),(3,-1,0),(-9,-2,3)]`D. `-(1)/(3)[(-3,0,0),(-3,-1,0),(-9,-2,3)]` |
| Answer» Correct Answer - B | |
| 17. |
For a invertible matrix `A ` if ` A (adj A) =[(10,0),(0,10)]` then `|A|=`A. 100B. `-100`C. `10`D. `-10` |
| Answer» Correct Answer - C | |
| 18. |
If `alpha and beta` are roots of the equation `x^(2)+5|x|-6=0,` then the value of `|tan^(-1)alpha-tan^(-1)beta|` isA. `(pi)/(2)`B. `0`C. `pi`D. `(pi)/(4)` |
| Answer» Correct Answer - A | |
| 19. |
If c denotes the contradication, then dual of the compound statement `~p ^^ (q vv c)` isA. `~P vv (q ^^t )`B. `~P^^(qvvt)`C. `p vv (~qvvt)`D. `~pvv(q^^ c)` |
| Answer» Correct Answer - A | |
| 20. |
The point on the curve ` y= sqrt(x-1)` where the tangent is perpendicular to the line `2x+y-5=0` isA. `(2,-1)`B. `(10,3)`C. `(2,1)`D. `(5,-2)` |
| Answer» Correct Answer - C | |
| 21. |
IF the inverse of the matrix `[(alpha , 14,-1),(2,3,1),(6,2,3)]` does not exist then the value of `alpha ` isA. 1B. `-1`C. `0`D. `-2` |
| Answer» Correct Answer - D | |
| 22. |
If the origin and the point `p(2,3,4),q(,1,2,3)R (x,y,z)` are coplanar thenA. `x-2y-z=0`B. `x+2y+z=0`C. `x-2y+z=0`D. `2x-2y+z=0` |
| Answer» Correct Answer - C | |
| 23. |
If `intsqrt((x-5)/(x-7))dx = A sqrt(x^(2) - 12 x + 35) + log|x-6 +sqrt(x^(2)-12x+35)| + C`, thenA. `-1`B. `(1)/(2)`C. `-(1)/(2)`D. `1` |
| Answer» Correct Answer - D | |
| 24. |
If `f(x ) = x "for" x le 0` `=0 "for " x gt 0` then f(x) at x=0 isA. continuous but not differentibleB. Not continuous but differentiableC. Contunuous and differentiableD. Not continuous and not differentiable |
| Answer» Correct Answer - A | |
| 25. |
If the distance of points `2 hati + 3 hatj +lamda hatk` from the plane ` barr .(3 hati + 2 hatj +6 hatk )=13 ` is 5 units then `lamda =`A. `6,-(17)/(3)`B. `6,(17)/(3)`C. `-6,-(17)/(3)`D. `-6,(17)/(3)` |
| Answer» Correct Answer - A | |
| 26. |
If the angle between the planes `bar r .(m hati -hatj+2hatk)+3=0 and bar r.(2hati -m hatj - hatk )-5=0 ` is `(pi)/(3)` , then m=A. 2B. `+-3`C. `3`D. `-2` |
| Answer» Correct Answer - C | |
| 27. |
Probability that a person will develop immunity after vaccination is 0.8 If 8 people are given the vaccine then probability that all develop immunity isA. `(0.2)^(8)`B. `(0.8)^(8)`C. `1`D. `""^(8)C_(6)(0.2)^(6)(0.8)^(2)` |
| Answer» Correct Answer - B | |
| 28. |
The value of ` cos ^(-1)""[cot ((pi)/(2))]+cos^(-1)""[sin ((2pi)/(3))]` isA. `(2pi)/(3)`B. `(pi)/(3)`C. `(pi)/(2)`D. `pi` |
| Answer» Correct Answer - A | |
| 29. |
The equation of the plane through (-1,1,2), whose normal makes equal acute angles with coordinate axes isA. `bar r .( hati +hatj +hatk )=2`B. `bar r .(hati +hatj +hatk)=6`C. `bar r .(3 hati -3hatj +3hatk)=2`D. `bar r .(hati -hatj +hatk)=3` |
| Answer» Correct Answer - A | |
| 30. |
If `int_(0)^(pi//2) log cos x dx =(pi)/(2)log ((1)/(2)),` then `int_(0)^(pi//2) log sec x dx =`A. `(pi)/(2)log ""((1)/(2))`B. `1-(pi)/(2)log ""((1)/(2))`C. `1+(pi)/(2) log ""((1)/(2))`D. `(pi)/(2) log 2` |
| Answer» Correct Answer - D | |
| 31. |
In `Delta ABC ` if `sin ^(2)A + sin ^(2) B = sin ^(2) B= sin ^(2)C and 1(AB)=10,` then the maximum value of the area of ` Delta ABC ` isA. 50B. `10sqrt(2)`C. `25`D. `25sqrt(2)` |
| Answer» Correct Answer - C | |
| 32. |
The equation of line equally inclined to co -ordinate axes and passing through (3,2,-5) isA. `(x+3)/(1)=(y-2)/(1)=(z+5)/(1)`B. `(x+3)/(-1)=(y-2)/(1)=(5+z)/(-1)`C. `(x+3)/(-1)=(y-2)/(1)=(z+5)/(-1)`D. `(x+3)/(-1)=(2-y)/(1) =(z+5)/(-1)` |
| Answer» Correct Answer - B | |
| 33. |
`A B C`is a triangle and `A=(235)dotB=(-1,3,2)a n dC=(lambda,5,mu)dot`If the median through `A`is equally inclined to theaxes, then find the value of `lambdaa n dmudot`A. `10,7`B. `9,10`C. `7,9`D. `7,10` |
| Answer» Correct Answer - D | |