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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 (dy)/(dx) when x and y are connected by the relation given: sin (xy) + (x)/(y) = x^(2)-y |
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| 2. |
Which one of the following is wrong? |
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Answer» The elements on the MAIN DIAGONAL of a SYMMETRIC matrix are all zero |
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| 3. |
If the 9^(th) term of A.P. is zero, then the ratio of 29^(th) term to 19^(th) term is |
| Answer» ANSWER :C | |
| 6. |
Let S = {a,b,c} and T = {1,2,3} . Find F^(-1) of the following functions F from S to T , if it exists . F = {(a,2),(b,1),(c,1)} |
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| 7. |
If x^(2) + x + 1 =0 , then the value of(x + (1)/(x))^(2) + (x^(2) + (1)/(x^(2)))^(2) + … + (x^(27) + (1)/(x^(27)))^(2) is |
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Answer» 27 |
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| 9. |
How many 6 digited numbers that can be formed using 1, 2, 3, 4, 5, 6 which are divisible by 3 when repetition is allowed. |
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| 10. |
The maximum area of triangle formed by a tangent line to the curve x^(2//3)+y^(2//3) =1 and the coordinates axes is |
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Answer» 1/4 SQ . Units |
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| 11. |
Determine if A sub B or A cancel sub B where A={x:x "is an odd integer"},B ={ x :x "is real and not an even integer "} |
| Answer» SOLUTION :` A SUB B` | |
| 12. |
Two pairs of straight lines with combined equations xy + 4x - 3y - 12 = 0 and xy - 3y + 4y- 12 = 0 form a square . Then the combined equation of its diagonals is |
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Answer» `x^(2) - 2X y + y^(2) + x - y = 0` |
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| 13. |
Let n!, the factorial of a positive integer n, be defined as the product of the integers 1,2, …n. In other words, n! =1 xx 2xx……xxn. What is the number of zeros at the end of the integer 10^(2)! + 11^(2)! + 12^(2)! + --- + 99^(2)!? |
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| 14. |
A and B are two independent events. The probability that both A and B occur, is 1//6 and the probability that neither of them occur, is 1//3. Then the probability of occurance of A is |
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Answer» `(1)/(2)` |
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| 15. |
e^(2((1)/(3)+(1)/(3)*(1)/(3^(3))+(1)/(5)*(1)/(3^(5))+….))= |
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Answer» 2 |
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| 17. |
If y=(4)/(x)-(32)/(x^(3)),x=2, deltax=0.2, thendelta y ~~... |
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Answer» `0.01` |
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| 18. |
If g(x) is continuous function in [0, oo) satisfying g(1) = 1. If int_(0)^(x) 2x . g^(2)(t)dt = (int_(0)^(x) 2g(x - t)dt)^(2), find g(x). |
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| 20. |
It is currently raining cats and dogs in the ratio of 5:6. If there are 18 fewer cats than dogs, how many dogs are raining? |
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| 21. |
If y = tan^(-1)((sqrt(1 + a^(2)x^(2))-1)/(ax)) , then (1+a^(2)x^(2))y^(n) + 2a^(2)xy is equal to |
| Answer» Answer :D | |
| 22. |
If sin alpha, cos alpha are the roots of the equation ax^(2) + bx + c = 0, (a ne 0) , then |
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Answer» `a^(2) - b^(2) +2ac = 0` |
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| 23. |
Find the value ofaif 2x^(2) + ay^(2) -3x + 2y -1 =0represents a circle and also find its radius |
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| 25. |
The value of Sigma_(r=1)^(n)(-1)^(r+1)(""^(n)C_(r))/(r+1)) is equal to |
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Answer» `-(1)/(N+1)` |
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| 26. |
y=e^(asin^(-1x))rArr(1-x^(2))y_(n+2)-(2n+1)xy_(n+1) is equal to |
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Answer» `-(N^(2) + a^(2))y_(n)` |
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| 28. |
If vec(a) and vec(b) are the vectors determined by two adjacent sides of a regular hexagonn ABCDEF. What are the vectors determined by the other sides taken in order ? |
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| 29. |
Solve the following problem graphically Minimise and Maximise z=3x+9y Subject to the constraints: x+3y le 60, x+y ge 10, x le y x ge 0, y ge 0 |
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| 30. |
Let |overset(to)(x) | = |overset(to)(y)| = |overset(to)(x) + overset(to)(y) | = 1 and if measure of the angle between overset(to)(x) and overset(to)(y) is alpha, then sin alpha= ...... |
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Answer» `- (1)/( 2)` |
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| 31. |
Find the centre of gravity of the semicircle x^(2) + y^(2) = a^(2) situated above the x-axis. |
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| 32. |
Examine if Rolle's theorem is applicable to any of the following functions. f(x)= [x], x in [5,9] |
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| 33. |
Find the equation of the circle passing through (2,3) and concentric with the circle x^(2) +y^(2) + 8x + 12y + 15= 0 |
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| 34. |
Evaluate the following integrals (viii) int_(0)^(pi//4)(1)/(2+sin^(2)x) dx |
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| 35. |
Find (dy)/(dx)of y =4^x |
| Answer» SOLUTION :`d/dx(4^x)=4^xlog4` | |
| 36. |
Examine if Rolle's theorem is applicable to any of the following functions. f(x)= [x], x in [-2, 2] |
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| 38. |
Examine if Rolle's theorem is applicable to any of the following functions. Can you say some thing about the converse of Rolle's theorem from these example? f(x) = x^(2)-1 " for "x in [1, 2]. |
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| 39. |
Which of the following is correct relations a symmetrical distribution is |
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Answer» `A.M. - M_(o) = 3(A.M. - M_(d))` |
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| 40. |
Find the Cartesian coordinates of the center of gravity of the are of the cardioid rho = a (1 + cos varphi) " between " varphi = 0 and varphi = pi. |
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| 41. |
In a bag there are six balls of unknown colours. Three balls are drawn at random and found to be all black. Find the probability that the bag contains exactly 3 black balls. |
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| 43. |
The normal at the point (1, 1) on the curve 2y+x^(2)=3 is ………… |
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Answer» `x+y=0` |
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| 44. |
If z=sqrt(2)- isqrt(2) si rotated through an angle 45^(@) in the anti-clockwise direction about the origin, then the co-ordianates of its new position are |
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Answer» `(2,0)` |
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| 45. |
Ify= (sinx+cosx)+(sin4x+cos4x)^(2), then : |
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Answer» `y gt 0 AA X in R` |
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| 47. |
Find the area of the region bounded by the parabola y = x^(2) and y = |x|. |
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| 48. |
Evalute the following integrals int (x sin^(-1) x)/(sqrt(1 -x^(2))dx |
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| 49. |
If (sum_(n)^(n=1) (n^(2)+3n+3)(n+1)!)/((n+2)!)=8, then n is equal to : |
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Answer» `impliesunderset(n=-1)overset(n)(Sigma)((n+2)^(2)-(n+1)(n+1)! = 8 (n+2)!` `impliesunderset(n=-1)overset(n)(Sigma)((n+2).(n+2)!-(n+1)(n+1)!)=8(n+2)!` `implies(n+2).(n+2) ! = 8 (n+2)!` `implies n+2=8impliesn=6` |
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