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)ge7,2x_(1)+3x_(2)le15,x_(2)le3,x_(1),x_(2)ge0` 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. |
The area of the reggion bounded by the lines `y=2x+1,y=3x+1" and "x=4` isA. 16 sq. unitsB. `(121)/(3)` sq. unitsC. `(121)/(6)` sq. unitsD. 8 sq. units |
| Answer» Correct Answer - D | |
| 3. |
If the volume of spherical ball is increasing at the rate of `4pi" cc/s"`, then the rate of change of its surface area when the volume is 288 `pi` cc isA. `(4pi)/(3)" cm"^(2)//"sec".`B. `(2pi)/(3)" cm"^(2)//"sec."`C. `4pi" cm"^(2)//"sec."`D. `2pi" cm"^(2)//"sec."` |
| Answer» Correct Answer - A | |
| 4. |
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 | |
| 5. |
For a invertible matrix `A ` if ` A (adj A) =[(10,0),(0,10)]` then `|A|=`A. 100B. `-100`C. 10D. `-10` |
| Answer» Correct Answer - C | |
| 6. |
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 | |
| 7. |
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 | |
| 8. |
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. `3bar(MN)`B. `4bar(MN)`C. `2bar(MN)`D. `2bar(NM)` |
| Answer» Correct Answer - C | |
| 9. |
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 ).(3hati-3hatj+3hatk)=2`D. `bar( r ).(hati-hatj+hatk)=3` |
| Answer» Correct Answer - A | |
| 10. |
If `f(x) = x` for `x le 0 = 0 ` for `x gt 0`, then `f(x)` at `x = 0` isA. continuous but not differentibaleB. not continuous but differentibaleC. continuous and differentiableD. not continuous and not differentiable |
| Answer» Correct Answer - A | |
| 11. |
If c denotes the contradication, then dual of the compound statement `~p ^^ (q vv c)` isA. `~p vv(q ^^ t)`B. `~p ^^(q vv t)`C. `p vv(~p vv t)`D. `~p vv(q ^^ c)` |
| Answer» Correct Answer - A | |
| 12. |
The maximum value of `f(x)=(logx)/(x)(x ne 0, x ne1)` isA. eB. `(1)/(e)`C. `e^(2)`D. `(1)/(e^(2))` |
| Answer» Correct Answer - B | |
| 13. |
All parabolas whose axis is the Y-axis.A. `x(d^(2)y)/(dx^(2))-(dy)/(dx)=0`B. `x(d^(2)y)/(dx^(2))+(dy)/(dx)=0`C. `(d^(2)y)/(dx^(2))-y=0`D. `(d^(2)y)/(dx^(2))-(dy)/(dx)=0` |
| Answer» Correct Answer - A | |
| 14. |
`int_(0)^(3)[x]dx=…,` where [x] is greatest integer function.A. 3B. 0C. 2D. 1 |
| Answer» Correct Answer - A | |
| 15. |
`int_(0)^(1)xtan^(-1)xdx=`A. `(pi)/(4)+(1)/(2)`B. `(pi)/(4)-(1)/(2)`C. `(1)/(2)-(pi)/(4)`D. `(-pi)/(4)-(1)/(2)` |
| Answer» Correct Answer - B | |
| 16. |
O(0,0), A(1,2), B(3,4) are the vertices of `DeltaOAB`. The joint equation of the altitude and median drawn from O isA. `x^(2)+7xy-y^(2)=0`B. `x^(2)+7xy+y^(2)=0`C. `3x^(2)-xy-2y^(2)=0`D. `3x^(2)+xy-2y^(2)=0` |
| Answer» Correct Answer - D | |
| 17. |
`int(sec^(8)x)/("cosec x")dx=`A. `(sec^(8)x)/(8)+c`B. `(sec^(7)x)/(7)+c`C. `(sec^(6)+x)/(6)+c`D. `(sec^(9)x)/(9)+c` |
| Answer» Correct Answer - B | |
| 18. |
If `int_(0)^(pi//2) log(cosx) 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)log2` |
| Answer» Correct Answer - D | |
| 19. |
if `int (1)/(sqrt(9-16x^(2)))dx=alpha sin ^(-1) (beta x) +c.` then ` alpha +(1)/(beta )=`A. 1B. `(7)/(12)`C. `(19)/(12)`D. `(9)/(12)` |
| Answer» Correct Answer - A | |
| 20. |
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 | |
| 21. |
If `alpha and beta` are the roots of the equation `x^(2)+5|x|-6=0`, then the value of the `|tan^(-1)alpha-tan^(-1)beta|` isA. `(pi)/(2)`B. 0C. `pi`D. `(pi)/(4)` |
| Answer» Correct Answer - A | |
| 22. |
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 | |
| 23. |
If `x=a(t-(1)/(t)),y=a(t+(1)/(t))`, where t be the parameter, then `(dy)/(dx)=?`A. `(y)/(x)`B. `(-x)/(y)`C. `(x)/(y)`D. `(-y)/(x)` |
| Answer» Correct Answer - C | |
| 24. |
The particular solution of the differential equation x dy+2y dx=0, then x=2, y=1 isA. xy = 4B. `x^(2)y=4`C. `xy^(2)=4`D. `x^(2)y^(2=4` |
| Answer» Correct Answer - B | |
| 25. |
`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, 7B. 9, 10C. 7, 9D. 7, 10 |
| Answer» Correct Answer - D | |