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 statement pattern `p^^(~p^^q)`isA. a tautolog yB. a contradictionC. equivalent to `p ^^ q`D. equivalent to `p vv q` |
| Answer» Correct Answer - B | |
| 2. |
The sum of the first 10 terms of the series `9+99+999 +….., ` isA. `(9)/(8)(9^(10)-1)`B. `(100)/(9)(10^(9)-1)`C. `10^(9)-1`D. `(100)/(9)(10^(10)-1)` |
| Answer» Correct Answer - B | |
| 3. |
If `int_(0)^(k)(dx)/(2+18x^(2))=(pi)/(24)`, then the value of k isA. 3B. 4C. `(1)/(3)`D. `(1)/(4)` |
| Answer» Correct Answer - C | |
| 4. |
The order of the differential equation of all parabolas , whose latus rectum is 4a and axis parallel to the x- axis isA. oneB. FourC. threeD. two |
| Answer» Correct Answer - D | |
| 5. |
In `DeltaABC`, with usual notations, if a,b,c are in AP then `acos^(2)((C)/(2))+cos^(2)((A)/(2))=`A. `(3a)/(2)`B. `(3c)/(2)`C. `(3b)/(2)`D. `(3abc)/(2)` |
| Answer» Correct Answer - C | |
| 6. |
The cartesian co - ordinates of the point on the parabola `y^(2)=- 16x` , whose parameter is `(1)/(2),` areA. `(-2, 4)`B. `(4,-1)`C. `(-1, -4)`D. `(-1, 4)` |
| Answer» Correct Answer - D | |
| 7. |
`int_(0)^(pi//4) x sec^(2)xdx`=A. `(pi)/(4)+logsqrt(2)`B. `(pi)/(4)-logsqrt(2)`C. `1+logsqrt(2)`D. `1-(1)/(2)log2` |
| Answer» Correct Answer - B | |
| 8. |
Evaluate : `int(1)/(sinx.cos^(2)x)dx`A. `secx+log|secx+tanx|+c`B. `secx.tanx+c`C. `secx+log|secx-tanx|+c`D. `secx+log|"cosec "x-cotx|+c` |
| Answer» Correct Answer - D | |
| 9. |
If `2sin(theta+(pi)/(3))=cos(theta-(pi)/(6))` then `tan theta`=A. `sqrt(3)`B. `(-1)/(sqrt(3))`C. `(1)/(sqrt(3))`D. `-sqrt(3)` |
| Answer» Correct Answer - D | |
| 10. |
IF ` tan ^(-1) 2x + tan ^(-1) 3x =(pi)/(4) , ` then x=A. `-1`B. `(1)/(3)`C. `(1)/(6)`D. `(1)/(2)` |
| Answer» Correct Answer - C | |
| 11. |
if `int(dx)/(sqrt(16-9x^(2)))=Asin^(-1)(Bx)+C`, then A+B=A. `(9)/(4)`B. `(19)/(4)`C. `(3)/(4)`D. `(13)/(12)` |
| Answer» Correct Answer - D | |
| 12. |
The equation of line passing through (3,-1,2) and perpendicular to the lines `vecr=(hati+hatj-hatk)+lamda(2hati-2hatj+hatk)` and `vecr=(2hati+hatj-3hatk) +mu(hati-2hatj+2hatk)` isA. `(x+3)/(2)=(y+1)/(3)=(z-2)/(2)`B. `(x-3)/(3)=(y+1)/(2)=(z-2)/(2)`C. `(x-3)/(2)=(y+1)/(3)=(z-2)/(2)`D. `(x-3)/(2)=(y+1)/(2)=(z-2)/(3)` |
| Answer» Correct Answer - C | |
| 13. |
If `f:R-{2}toR` is a function defined by `f(x)=(x^(2)-4)/(x-2)`, then its range isA. RB. R-{2}C. R-{4}D. `R-{-2,2}` |
| Answer» Correct Answer - C | |
| 14. |
IF ` y= ( tan ^(-1) x)^(2) " then " (x^(2) +1)^(2) (d^(2)y)/(dx^(2))+2x(x^(2)+1)(dy)/(dx)=`A. 4B. 2C. 1D. 0 |
| Answer» Correct Answer - B | |
| 15. |
The line ` 5x +y-1=0` coincides with one of the lines given by ` 5x^(2) +xy -kx - 2y+2=0` then the value of k isA. `-11`B. 31C. 11D. `-31` |
| Answer» Correct Answer - C | |
| 16. |
L and M are two points with position vectors `2vec(a)-vec(b)andvec(a)+2vec(b)`, respectively. The position vector of the pont N which divides the line segment LM in the ratio 2:1 externally isA. `3bar(b)`B. `4bar(b)`C. `5bar(b)`D. `3bar(a)+4bar(b)` |
| Answer» Correct Answer - C | |
| 17. |
IF `f(x) =x^(2) + alpha ` for ` x ge 0` ` = sqrt(x^(2) +1) + beta ` for ` x lt 0` is continuous at ` x=0 and f((1)/(2))=2,` then `alpha ^(2) + beta ^(2)` isA. 3B. `(8)/(25)`C. `(25)/(8)`D. `(1)/(3)` |
| Answer» Correct Answer - C | |
| 18. |
The point of intersection of lines represented by ` x^(2) -y ^(2) +x+3y -2=0` isA. `(1,0)`B. `(0,2)`C. `((-1)/(2),(3)/(2))`D. `((1)/(2),(1)/(2))` |
| Answer» Correct Answer - C | |
| 19. |
The maximum value of ` 2x +y ` subject to ` 3x +5y le 26 and 5x +3y le 30 , x ge 0, y ge 0` isA. 12B. 11.5C. 10D. 17.33 |
| Answer» Correct Answer - A | |
| 20. |
` cos1^@ . cos2^@ . cos3^@.........cos179^@` is equal to : |
| Answer» Correct Answer - A | |
| 21. |
The contrapositive of the statement: "If the weather is fine then my friends will come and we go for a picnic".A. The weather is fine but my friends will not come or we do not go for a picnic.B. If my friends do not come or we donot go for picnic then weather will not be fine.C. If the weather is not fine then my friends will not come or we do not go for a picnic.D. The weather is not fine but my friends will come and we go for a picnic. |
| Answer» Correct Answer - B | |
| 22. |
The minimum value of the function `f(x)=xlogx` isA. `(-1)/(e)`B. `-e`C. `(1)/(e)`D. e |
| Answer» Correct Answer - A | |
| 23. |
The sides of a rectangle are given by `x=pma` and `y=pmb`. The equation of the circle passing through the vertices of the rectangle isA. `x^(2)+y^(2)=a^(2)`B. `x^(2)+y^(2)=a^(2)+b^(2)`C. `x^(2)+y^(2)=a^(2)-b^(2)`D. `(x-(A)^(2)+(y-(B)^(2)=a^(2)+b^(2)` |
| Answer» Correct Answer - B | |
| 24. |
If the line y=4x-5 touches the curve `y^(2)=ax^(3)+b` at the point (2,3), then 7a+2b=0 |
| Answer» Correct Answer - A | |