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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. |
Find the union of each of the following pairs of sets : A = {x : x is a natural number and multiple of 3} B = {x : x is a natural number less than 6} |
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Answer» `A cup B= {1, 2, 3, 4, 5, 6, 9, 12, 15, 18,……,……}`={x : x = 1, 2, 4, 5 or MULTIPLE of `3, x in N` } |
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| 3. |
Let f(x) = x + 1/(2x + 1/(2x + 1/(2x + ....oo))) " then " sqrt((f(50) f^'(50))/(2)) = |
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| 4. |
Find the equation of the circle passing through the points (2,3) and (-1,-1) and whose centre is on the line x-3y-11=0. |
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| 6. |
For x, y, z, t in R, sin^(-1)x+cos^(-1)y+sec^(-1)z ge t^(2)-sqrt(2pi)t+3pi The value of cos^(-1)(min{x,y,z}) is |
| Answer» ANSWER :D | |
| 7. |
A has 3 shares in a lottery containing 3 prizes and 9 blanks , B hastwo shares in lottery containing 2 prizes and 6 blanks , Copare their chances of success . |
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| 8. |
Ifa_0 = x, a_( n+1) = f(a_n) , " where"n = 0,1,2……… then answer the following questions If f(x) = (1)/( 1-x)then which of the following is not true? |
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Answer» `a_(N) = (1)/(1-X)` if `n= 3k+1` |
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| 9. |
Find the sum of the series 1^(2)+3^(2)+5^(2)+...to n terms |
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| 10. |
Find a point on the X-axis, which is equidistant from the points (7,6) and (-3,4). |
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Answer» <P> |
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| 11. |
Statement-I : The point A(3,1,6) is the miror image of the point B(1,3,4) in the plane x-y+z=5. Statement-II : The plane x-y+z=5 bisects the line segment joining A(3,1,6) and B(1,3,4) |
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Answer» STATEMENT 1 is false, statement 2 is true. |
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| 12. |
If A + B + C = 90^(@) and if none of A,B,C is an odd multipl of 90^(@) then P.T. TanA Tan B + Tan B Tan C + Tan C Tan A = 1 and hence S.T. |
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| 13. |
A= {1, 2, 3, 4, 5}, B= {1, 3, 5, 6}, C= {1, 2, 3}, then find the following sets. B- C |
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| 14. |
When the axes are rotated through an angle 60^(0)the point Q is changed as (-7,2). Find Q. |
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Answer» (ii) 0 = 1 |
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| 15. |
The transformed equation of 3x^(2) + 3y^(2) + 2xy =2 when the coordinate axes are rotated through an angle of 45^(@)is |
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Answer» `x^(2) + 2y^(2) = 1` |
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| 17. |
If sin^(2) x gt sqrt(2) sin^(2) x = ( 2 - sqrt(2)) cos ^(2) xthen |
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Answer» `x in ( n PI + (pi)/( 6) , n pi + (pi)/( 4)), n in Z` |
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| 19. |
If x,y,z,t are real numbers such that x^(2) + y^(2) =9,z^(2) + t^(2)=4 and xt-yz=6, then the greatest value of xz is: |
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Answer» 1 |
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| 20. |
Find the coefficient of x^4 in the expansion of (1+x)^n(1-x)^n |
| Answer» SOLUTION :`C_0C_4-C_1C_3+C_2C_2-C_3C_1+C_4C_0=C_2` | |
| 21. |
Let y= (x + (1)/(x))^(2)Find the rate of change of y with respect to x when x=2. |
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| 22. |
If for DeltaABC, cotA cotB cotC gt0then the triangle is |
| Answer» Answer :B | |
| 23. |
If the position vectors of A, B, C, D are 3bar(i)+2bar(j)+bar(k), 4bar(i)+5bar(j)+5bar(k), 4bar(i)+2bar(j)-2bar(k), 6bar(i)+5bar(j)-bar(k) respectively then the position vector of the point of intersection of lines AB and CD is |
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Answer» `2bar(i)+BAR(J)-3BAR(K)` |
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| 26. |
Write the following sets in the set-builder form : (3, 6, 9, 12} |
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| 28. |
If the median Ad of Delta^("le") ABC makes an angle lfloorADC=45^(@) then |cotB-cotC|= |
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Answer» 1 |
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| 29. |
Consider the expansion of (3x^2-1/(2x^3))^10 Find the (r+1)^(th) term in the expansion |
| Answer» SOLUTION :`(-1)^R"^10C_r,(3x^2)^(10-r)(1/(2x^3))^r` | |
| 30. |
Obtain the equation of he circle circum circle of the triangle with verticies (-2,3), (5, 2) and (6, -1). |
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| 31. |
If x_(1), x_(2), x_(3) and y_(1),y_(2), y_(3) are in arithmetic progression with the same common difference then the points (x_(1),y_(1)) (x_(2),y_(2)) (x_(3), y_(3)) are: |
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Answer» VERTICES of an equilateral TRIANGLE |
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| 32. |
(sin ^(3) theta - cos^(3) theta)/(sin theta - cos theta) - (cos theta)/(sqrt(1 + cot^(2)theta))-2 tan theta cot theta = - 1 , if |
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Answer» `THETA in (0 (pi)/2)` |
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| 33. |
Consider the points A(1,-1,1), B(5,-5,4), C(5,0,8) and D(1,4,5) Find AB,BC,CD and DA |
| Answer» SOLUTION :`sqrt41, sqrt41, sqrt41, sqrt41` | |
| 35. |
Let h(x)=f(x)-a(f(x))^(2)+a(f(x))^(3) for all real xh(x) increases as f(x) increases for all x if |
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Answer» `a in(0.3)` |
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| 36. |
Find the orthocentre of the triangle formed by (0,0), (2,-1) (-1,3) whose circumcentre is (5/2,5/2). |
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| 37. |
If det (A_(3xx3))=6, then det (Adj 2A) = |
| Answer» Answer :B | |
| 38. |
Show that the set of all points such that the difference of their distances from (4,0) and (-4,0) is alwaysequal to 2 represent a hyperbola. Find its equation. |
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| 39. |
If the sides of a triangle are in A.P and greatest angle exceeds the least angle of the triangle by 90^(@). Then ratio of the sides . |
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Answer» `3 : 4 : 5` |
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| 40. |
In triangle ABC, if r_(1)=3, r_(2)=10, r_(3)=15 then R= |
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Answer» 5 |
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| 41. |
If a = 18, b=24, c= 30and if l = r_2- r_1 , m = r_3 - r_2, n= r_3 - r_1thendescendingorder of l, m, n is |
| Answer» ANSWER :A | |
| 42. |
Make correct statements by filling in the symbols ⊂ or ⊄ in the blank spaces : {x : x is a circle in the plane} . . .{x : x is a circle in the same plane with radius 1 unit} |
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| 43. |
Given P(A)= (3)/(5) and P(B) = (1)/(5) . Find P(A or B), ifA & B are mutually exclusive events. |
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| 44. |
Solve: 2x^(2)+2x-3=0, giving your answer correct to one decimal place. |
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| 45. |
The perpendicular from the origin to a line meets it at the point (-2,9), find the equation of the line. |
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| 46. |
Find the approximate value of log (2.01) give that log 2 = 0.6934 |
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| 47. |
The distance of point A(-2,3,1)from the line PQ through P( 3,5,2), which make equal angles with the axes is |
| Answer» Answer :B | |
| 49. |
If barr is any vector then barr = |
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Answer» `(barr.BARA^(1))bara+(barr.BARB^(1))barb+(barr.BARC^(1))barc` |
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