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This section includes 7 InterviewSolutions, each offering curated multiple-choice questions to sharpen your Current Affairs knowledge and support exam preparation. Choose a topic below to get started.
| 3. |
If p, p' be the lengths of perpendicular from (0, 0) on the lines: x sec theta+y "cosec"theta=2a and x cos theta+y sin theta=a cos 2theta respectively, then ((p)/(p')+(p')/(p))^(2) equals: |
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Answer» `4cos^(2)4theta` |
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| 4. |
Sum of the last 20 coefficients in the expansion of (1 + x)^(39), when expanded in ascending powers of x, is |
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Answer» `2^(19)` |
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| 5. |
Statement I f(x) = |x| sin x is differentiable at x = 0. Statement II If g(x) is not differentiable at x = a and h(x) is differentiable at x = a, then g(x).h(x) cannot be differentiable at x = a |
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Answer» STATEMENT I is correct, Statement II is ALSO correct, Statement II is the correct explanation of Statement I |
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| 6. |
Find the maximum volume of a cylinder, generated by rotating a rectangle of perimeter 48 cm about one of its sides. |
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| 7. |
If 1^(2)+2^(2)+3^(2)+…+2009^(2)=(2009)(4019)(335) and (1) (2009) +(2) (2008) +(3) (2007)+….+(2009) (1) =(2009) (335) (x), then x equals |
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Answer» 2011 |
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| 9. |
The equation of the directrix of the parabola whose vertex (3,2) and focus (2,-1) is |
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Answer» a,b,C |
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| 10. |
Given that A diamond B = 4A - B, what is the value of (3 diamond 2) diamond 3? |
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Answer» |
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| 11. |
The set solution satisfying inequality sintheta +sqrt3costhetage1, -pi |
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Answer» `THETAIN [PI/3,pi/2]` |
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| 12. |
If A, B, C, D are the sum of the square of the roots of 2x^(2) + x- 3=0, x^(2)-x+2= 0, 3x^(2) - 2x +1=0, x^(2)- x+1=0 then the ascending order of A, B, C, D is |
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Answer» `B LT D lt C lt A` |
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| 13. |
State with reason, "All natural numbers having at least one prime factor " is set or not ? |
| Answer» SOLUTION :It is a SET , as it is PROPERLY DEFINED. | |
| 14. |
If A and B are two independent events such that P(A)= (1)/(2), P(B)= (1)/(5), then P(A | (A cup B))= ……… |
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Answer» `(1)/(6)` |
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| 15. |
If the angle batween the line x=(y-1)/(2)=(z-3)/(lambda) and the plane x+2y+3z=4 is cos^(-1)(sqrt((5)/(14))), then lambda equals |
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Answer» `(2)/(3)` |
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| 16. |
Choose the correct answer int((10x^9+10^x log10)/(x^(10) + 10^x)) dx |
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Answer» `10^X-x^(10) +C` |
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| 17. |
If y=a cos (sin2x)+b sin(sin2x), then y^(n)+(2 tan 2x)y= |
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Answer» 0 |
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| 18. |
If cosalpha+cosbeta+cosgamma=0=sinalpha+sinbeta+singamma then sin(2alpha-beta-gamma)+sin(2beta-gamma-alpha)+sin(2gamma-alpha-beta)= |
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Answer» 0 |
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| 19. |
If the area bounded by circle x ^(2) + y^(2)=4, the parabola y = x ^(2) + x+1 and the curve y = [sin ^(2) ""(x)/(4) +cos ""(x)/(4)],(where [] denotes the greats integer function) and x-axis is (sqrt3 + (2pi)/(3) - (1)/(k)), then the numerical quantitity is should be : |
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| 20. |
If the mean deviation of the number a,a+d,a+2d,…….,a+200dfrom their mean is (2525)/(201)then |d|is equal to : |
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| 22. |
If int_(-1)^(4)f(x)dx=4andint_(2)^(4)[3-f(x)]dx=7" then "int_(-1)^(2)f(x)dx= |
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Answer» -2 |
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| 24. |
A point moves such that the area of the triangle formed by it with the points (1,5) and (3,-7) is 21 sq. units. Then locus of the point is |
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Answer» 6X + y - 32 = 0 |
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| 25. |
If the area bounded by the curves y=ax^(2) and x=ay^(2)(a gt 0) is 3 sq. units, then the value of 'a' is |
| Answer» Answer :B | |
| 26. |
Find an anti derivative (or integral) of the following functions by the method of inspection. (ax+b)^(2) |
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Answer» |
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| 27. |
(d)/(dx){e ^(x^(e))+ x ^(e^(x)) + e ^(x ^(x))}= |
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Answer» `E ^(X ^(e)) + x^(e^(x))+e^(x^(x))` |
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| 28. |
If the value of the nearest thousandth of cos theta is -0.892, which of the following could be true about theta ? |
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Answer» `0^@ le THETA lt 60^@` |
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| 30. |
A company has MR = 30 x + 15 x^(2) and MC = 64 -1 6x + (3)/(2)x^(2). Find out the profit function and the output x gt 0 when there is no profit if the fixed cost is zero. |
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Answer» <P> |
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| 31. |
The radius and height of a cylinder are measured as 5 cm and 10 cm respectively and there is an error of 0.02 cm in the both measurements. The approximate error in the volume is |
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Answer» 4 `PI` CUBIC cm |
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| 32. |
Solution set of x^(2 log x) = 10 x^(2) is : |
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Answer» `{ 1 - sqrt(3) , 1 + sqrt(3) }` |
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| 33. |
If the area of the triangle with vertices (0,0),(1,0),(0,a) is 10 units, find the value of a. |
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Answer» Solution :Area of TRIANGLE with VERTICES (0,0),(1,0),(0,a) is 1/2*1*a=a/2 `THEREFORE` a/2=10 or, a=20 . |
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| 35. |
The remainder obtained when 1! + 2! + 3!+….+ 11! is divided by 12 is_______ |
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Answer» 1)6 |
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| 36. |
1/(x(x+1)(x+2)...(x+n))=A_(0)/x+A_(1)/(x+1)+A_(2)/(x+2)+...+A_(n)/(x+n), 0 le r le n rArr A_(r)= |
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Answer» `(-1)^(R)(r!)/((n-r)!)` |
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| 37. |
There are 4 copies (alike) each of 3 different books. Find the number of ways of arranging these 12 books in a shelf in single row. |
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| 38. |
Evaluate int(sin2x)/((a+bcosx)^(2))dx |
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| 39. |
Let L_1 and L_2 denote the lines r=hati+lambda(-hati+2hatj+2hatk).lambdainR. and r=mu(2hati-hatj+2hatk),muinR respectively. If L_3 is a line whichis perpendicular to both L_1 and L_2 and cuts both of them, then which of the following options describes (s)L_3 ? |
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Answer» `r=(2)/(9)(2hati-HATJ+2hatk)+t(2hati+2hatj-hatk),t in R` `L_i:r=hati+lambda(-hati+2hatj+2hatk),lambda in R and` `L_2:r=mu(2hati-hatj+2hatj+2hatk),mu in R` and since line `L_3` is perpendicular to both lines `L_1` and `L_2`. Then a vector along `L_3` will be, `|{:(hati,,hatj,,hatk),(-1,,2,,2),(2,,-1,,2):}|=hati(4+2)-hatj(-2-4)+hatk(1-4) =6hati+6hatj-3hatk=3(2hati+2hatj-hatk)`.........(i) Now, let a general POINT on line `L_1`. `P(1-lambda ,2lambda,2lambda)` and on line `L_2`. as `Q(2mu,-mu,2mu) ` and let P and Q are poitn of intersection of lines `L_1,L_3 and L_2,L_3`, so direction ratio's of `L_3`. `(2mu+lambda-1,-mu-2lambda,2mu-2lambda)` Now, `(2mu+lambda-1)/(2)=(-mu-2lambda)/(2)=(2mu-2lambda)/(-1)` [from Eqs. (i) and (ii)] `rArr lambda (1)/(9) and mu=(2)/(3)` So, `P((8)/(9),(2)/(9),(2)/(9)) and Q ((4)/(9),(2)/(9),(4)/(9))` Now, we can take EQUATION of line `L_3` as `r=a+t(2hati+2hatj-hatk)`, where a is position vector of any point on line`L_3` and possible vector of a are. `((8)/(9)hati+(2)/(9)hatj+(2)/(9)hatk)or ((4)/(9)hati+(2)/(9)hatj+(4)/(9)hatk)or ((2)/(3)hati+(1)/(3)hatk)` Hence, OPTIONS (a), (b) and (c) are correct. |
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| 40. |
Find the angle between two vectors vecaandvecb with magnitudes 1 and 2 respectively and when veca*vecb=1. |
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Answer» |
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| 41. |
The points representing root3(5+isqrt(3)) lie. |
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Answer» circle with centre at (0, 0) RADIUS `2sqrt(2)` |
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| 42. |
Using properties of determinants in Exercises prove that : {:[( alpha , alpha ^(2) ,beta +gamma ),( beta , beta ^(2) , gamma +alpha ),( gamma , gamma ^(2) ,alpha +beta ) ]:} =(beta -gamma ) (gamma -alpha ) (alpha -beta ) (alpha +beta +gamma ) |
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| 43. |
The order of the differential equation whose solution is given by y = (c_(1)+ c_(2)) cos (x + c_(3)) - c_(4) e^(x+c5) where c_(1), c_(2), c_(3), c_(4), c_(5)are arotrary constant - |
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Answer» 5 |
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| 44. |
Probability distribution of a discrete random variable X is given in the following table. 1) Find the probability of random variable X assuming negative values. 2) Find the value of P(0 le x le 3) |
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Answer» 0.40, 0.53 |
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| 45. |
By using the properties of definite integrals, evaluate the integrals int_(0)^(pi/2)(cos^(5)xdx)/(sin^(5)x+cos^(5)x) |
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Answer» |
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| 46. |
Distance between the two planes 2x-2y+z = 5 and 6x-6y+3z = 25 is .............. Units. |
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Answer» `20/9` |
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| 47. |
"Let"f(x)=Lim_(ntooo) ((x^(2)+4x+5+e^(x)+sgn(e^(-x)))^(n)-5)/(2(x^(2)+4x+5+e^(x)+sgn(e^(-x)))^(n)+9)then |
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Answer» f(x) is DISCONTINUOUS at x=0. `"So,"f(x)=(1)/(2)AAX in R`. |
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| 48. |
The set of solutions of the systemof equationsx+y=(2pi)/3 and cosx + cosy = 3/2 where x,y are real , is |
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Answer» `{(x,y): COS ((x-y)/2)=1/2}` |
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| 49. |
Find the second order derivatives of the functions sin (log x) |
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Answer» |
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| 50. |
underset(n rarroo)lim((sqrt(1)+2sqrt(2)+3sqrt(3)+...+nsqrt(n))/n^((5)/(2))) |
| Answer» ANSWER :D | |