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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.
| 1. |
For the two circles x^(2) + y^(2) =16 and x^(2) + y^(2) -2y =0 there is/are |
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Answer» ONE pair of common tangents |
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| 2. |
Evaluate the following definite integrals as limit of sums. int_(2)^(3)x^(2)dx |
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| 3. |
Let the sides of a triangle ABC are all integers with A as the origin. If (2, -1) and (3, 6) are points on the line AB and AC, respectively, (lines AB and AC may be extended to contain these points), and lengths of any two sides are primes that differ by 50. If a is least possible length of the third side and S is the least possible perimeter of the triangle then aS is equal to K^(2) where K = |
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| 4. |
Find the remainder when 3^(37) is divided with 80 ? |
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| 5. |
Compute the integrals (a)int_(1)^(sqrt(3)) (sqrt(1 + x^(2)))/(x^(2)) dx (b)int_(1)^(0^(2)) (dx)/(x sqrt(1 +I n x)) (c)int_(3)^(2) (3 sqrt((x - 2)^(2)))/(3 + 3 sqrt((x - 2)^(2)))dx |
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Answer» (B)`2 (sqrt(3)- 1)` (c)`8 + (3 sqrt(3))/(2) pi` |
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| 6. |
Consider the curve x^n+y^n=a^n(a gt 0). Tangent at any arbitrary point P(x_1,y_1)of the curve meets x-axis at A and y-axis at B(x_1y_1 ne 0), then : |
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Answer» OA+OB= CONSTANT `implies N=(1)/(2)`(O is origin) |
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| 8. |
Find the number of selections of six letters from the letters of the word 'K A R N A T A K A' |
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| 9. |
For what values of x the rate of increase of x^(3) - 2x^(2) + 3x + 8 is twice the rate of increase of x. |
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Answer» `(-(1)/(3), -3)` |
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| 10. |
One hundred students appeared for two examinations 60 passed in first, 50 passed the second and 30 passed both. The probability that a student selected at random has failed in both examinations is |
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Answer» `(1)/(5)` |
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| 11. |
If U_(n) = sin n theta*sec^(n)theta, V_(n) = cosntheta*sec^(n)theta for n= 0,1,2,… then V_(n) -V_(n-1)+U_(n-1)tantheta = |
| Answer» ANSWER :A | |
| 12. |
(i) Find the equation of the tangents to the circle x^(2)+y^(2)-4x+6y-12=0 which are parallel to x+y-8=0 (ii) Find the equations of the tangents to the circle x^(2)+y^(2)-5x+6y-12=0 which are paralel to x+2y-8=0 |
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Answer» (II) `x+2y+4+-5sqrt(5)=0` |
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| 13. |
Five point charges each of charge + q are placed on five vertices of a regular of side h as shown in the figure. Then |
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Answer» the forces on (-Q) at O due to charges +q at A and D are balanced. |
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| 14. |
If the petrol burnt in driving a motor boat varies as the cube of the velocity , then the speed (in km/hour) of the boat going against a water floe of C kms/hour so thatthe quantity of petro burnt is minimum is |
| Answer» Answer :B | |
| 15. |
If the line drawn from the point (-2, -1, -3) meets a plane at right angle at the point (1, -3, 3), then find the equation of the plane. |
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| 16. |
If alpha, beta are the roots of x^(2) + x + 1 = 0, then the equation whose roots are (1)/(alpha^(3)), (1)/(beta^(3))is |
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Answer» `2X^(2)+X+1=0` |
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| 18. |
Find the number of 4 - digited numbers that can be formed using the digits 2, 4, 5, 7 and 8. |
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| 19. |
Prove that the logarithmic function is strictly increasing on (0,oo) |
| Answer» Solution :WRITE f (X) = LOG x then `f(x)=1/xgt0` for all `x in(0,oo)thereforef` is STRICTLY increasing on `(0,oo)` | |
| 20. |
Let A(1, 2, 3), B(0, 0, 1) and C(-1, 1, 1) are the vertices of triangleABC. Q. The equation of altitude through B to side AC is |
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Answer» `r=K+t(7hat(i)-10hat(J)+2HAT(k))` |
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| 21. |
Find the angle between veca and vecb if |vecaxxvecb| = veca.vecb |
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Answer» Solution :`|vecaxxvecb|` = `veca.vecb` `implies |veca||vecb|SINTHETA` = `|veca||vecb|cos THETA` `implies sintheta` = `COSTHETA` `implies theta` = `pi/4` THEREFORE Angle between `veca` and `vecb` = `theta` = `pi/4` |
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| 23. |
Solve the following problem graphically. Maximize Z=3x+9y…………..1 subject to the constraints x+3yle60………….2 x+yge10…………..3 xley…………4 xge0,yge0…………..5 |
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| 25. |
Integrate the following : int(3/x^2+1/x^12)dx |
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Answer» Solution :`int(3/X^2+1/x^12)dx` =`3intx^-2dx`+`intx^-12dx` =`3X^(-1)/-1`+`x^(-11)/-11`+C `-3/x-1/11xx1/x^(11)+C` |
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| 26. |
Let ** be the binaryoperation defined on Q. Find which of the following binary operations are commutative. a**b=(a-ab)^2, AA a,b in Q |
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| 27. |
If alpha, betaare the roots of the quadratic equation x^(2)+px +q=0, then the values of alpha^(3) +beta^(3) and alpha^(4) +alpha^(2)beta^(2)+beta^(4) are |
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Answer» <P>`3PQ-p^(3) and p^(4) -3P^(2)q +3q^(2)` |
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| 28. |
Let ** be the binaryoperation defined on Q. Find which of the following binary operations are commutative. a**b=a+ab, AA a,b in Q |
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| 29. |
Let ** be the binaryoperation defined on Q. Find which of the following binary operations are commutative. a**b=a-b, AA a,b in Q |
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| 30. |
Find the area of the region in the first quadrant enclosed by the x-aixs, the line y = x, and the circle x^(2) + y^(2) = 32. |
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| 31. |
Let ** be the binaryoperation defined on Q. Find which of the following binary operations are commutative. a**b=a^2+b^2, AA a,b in Q |
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| 32. |
Areaof theregionboundedby thecurve y= cosxbetweenx=0 andx=piis ……. |
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Answer» 2 |
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| 33. |
Evaluate the following definite integrals int_1^2 (1/x - 1/(2x^2)) e^(2x) dx |
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Answer» SOLUTION :`int_1^2(1/x -1/(2X^2)) e^(2x) DX` =`int_1^2 1/x e^(2x) dx - int_1^2 1/(2x^2) e^(2x) dx` `[1/x (e^(2x))/2]_1^2 - int_1^2 -1/x^2 e^(2x)/2 dx - int_1^2 1/(2x^2) e^(2x) dx` =`1/2 [e^4/2 -e^2/1] = (e^4-2e^2)/4 = (e^2(e^2-2))/4` |
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| 34. |
IFO isattheoriginOAis alongthe x- axisand ( -40 ,9) isa pointonOBthen thevalueof sinangleAOBis |
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Answer» `(13)/(40)` |
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| 35. |
|{:(sinx,cosx),(sinx,sinx):}|=|{:(cosx,cosx),(cosx,sinx):}|,x in(0,pi/2) then x=………. |
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Answer» `pi/3` |
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| 36. |
If a and b are rationalshow thatthe equation x^2-2ax+(a^2-b^2-6ab-9)=0 are rational. |
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| 37. |
int(x^(3))/(x+1)dx=.....+C |
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Answer» `X+(x^(2))/(2)+(x^(3))/(3)-log|1-x|` |
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| 38. |
For any vecotr vec(a), The value of hati xx(vec(a)xx hati)+j xx(vec(a)xx vec(j))+hatk xx(vec(a)xx hatk) is …………. |
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Answer» `2vec(a)` |
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| 39. |
A tangent to the hyperbola (x^(2))/( 4) -(y^(2))/( 2) =1meets x-axis at P and y-axis at Q . Lines PR and QR are drawn such that OPRQ is a rectangle (where O is the origin ) then R lies on |
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Answer» ` (4)/( X^(2)) +(2)/(y^(2))` |
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| 41. |
If y= log sqrt((1+x cos x)/(1- x cos x))," find "(dy)/(dx) in simplified form. |
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| 42. |
State which of the following are positive ?sin 302^@ |
| Answer» Solution :`SIN 302^@` is -ve as SING is -ve in 4TH quadrant. | |
| 43. |
Prove that int _(0) ^(pi//2) (x sin x cos x )/((a ^(2) cos ^(2) x + b^(2) sin ^(2) x ))dx = (pi)/(4ab^(2) (a+b)) |
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| 44. |
Let veca,vecbandveccbe three vectors such that |veca|=3,|vecb|=4,|vecc|=5andeach one of them being perpendicular to the sum of theother two , find |veca+vecb+vecc|. |
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| 45. |
Integration by partial fraction : int(5x^(4)+4x^(5))/((x^(5)+x+1)^(2))dx=f(x)+c then f(x)=..... |
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Answer» `(1)/(x^(5)+x+1)` |
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| 46. |
Find the area enclosed between the parabola y^(2) = 4ax and the line y = mx. |
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| 47. |
If (i) A=[{:(cosalpha,sinalpha),(-sinalpha,cosalpha):}] then verify that A'A=I. (ii)A=[{:(sinalpha,cosalpha),(-cosalpha,sinalpha):}]then verify that A'A=I. |
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Answer» (II)`=[{:(1,0),(0,1):}]=I` |
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| 48. |
If 4 fair dice are rolled, find the probability that the greatest number on the dice is 4. |
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| 49. |
Equation of a line passing through the point with position vector 2hati-3hatj+4hatk and in the direction of the vector 3hati+4hatj-5hatk is |
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Answer» `4x+3y=17,5y-4z=1` |
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