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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. |
If 4=5i is a root of the quadratic equation x^(2)+ax+b=0, then (a,b)= |
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Answer» `(8,41)` |
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| 2. |
Evaluate the following definite integrals : int_(0)^((pi)/(2)) e^(x)((1+sinx)/( 1+cosx))dx |
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| 3. |
If the systemof equations 2x+ay+6z=8, x+2y+z=5, 2x+ay+3z=4 has a unique solutionthen 'a' cannot be equal to : |
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Answer» 2 |
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| 4. |
Find the determinant of the matrix [(1^(2),2^(2),3^(2)),(2^(2),3^(2),4^(2)),(3^(2),4^(2),5^(2))] |
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| 5. |
If alpha and beta are roots of equation 3/4"sin"((theta)/9)=sin^(3)theta+3sin^(3)((theta)/3)+9sin^(3)((theta)/9)+1/(4sqrt(2)) for 0lt theta lt (pi)/2, then tanalpha+tanbeta is equal to |
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Answer» `2+SQRT(3)` `IMPLIES sin 3theta=1/(sqrt(2))="sin"(pi)/4` or `"sin"(3pi)/4` `implies theta=(pi)/12` or `(pi)/4` `:."tan"(pi)/12=2-sqrt(3)`or `"tan"(pi)/4=1` `:."tan"(pi)/12+"tan"(pi)/4=3-sqrt(3)` |
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| 6. |
Integrate the following functions x (logx)^2 |
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Answer» SOLUTION :`int X(logx)^2 DX` =`(logx)^2 x^2/2 -int 2 logx XX 1/x xx x^2/2 dx` =`x^2/2 (logx)^2 - int x logx dx` =`x^2/2 (logx)^2-[logx xx x^2/2-int 1/x x^2/2 dx]` =`x^2/2 (logx)^2-x^2/2 (logx) +1/2 x^2/2 +c` =`x^2/2 (logx)^2 - x^2/2 (logx)+x^4/4 +c` |
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| 7. |
If a.b = a.c, a xx b = a xx c then |
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Answer» a - B is PARALLEL to c |
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| 8. |
sec^(-1) x + cosec^(-1) x + cos^(-1) (x^(-1) ) + sin^(-1) ( x^(-1) ) = ….. (where |x| ge 1 , x in R ) |
| Answer» ANSWER :A | |
| 9. |
Find the number of ways of arranging 5 boys and 5 girls around a circle. |
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| 10. |
If x^(2)+y^(2)+2gx + 2fy-12 = 0 represents a circle with centre (2, 3), find g, f and its radius. |
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| 11. |
For any positive integer n let phi(n)denotes the number of positive divisors of n, and let phi(n)denote the number of elements from the set {1, 2,..... n} that are coprime to n. (For example, d(12) =6 and phi(12) = 4) Find the smallest positive integer n such that d(phi(n)) = 2017 |
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| 12. |
int_(4)^(10) ([x^(2)]dx)/([x^(2)-28 x + 196 ]+[x^(2)]), |
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Answer» `1/3` |
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| 13. |
Show that the relation R in the set A = {1,2,3,4,5} given by R = {(a,b) : |a-b| is even}, is an equivalence relation. Show that all the elements of {1,3,5} are related to each other and all the elements of {2,4} are related to each other. But no element of {1,3,5} is related to any element of {2,4}. |
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| 15. |
If 4 coins are tossed then the mean and variance of X where X is the number of head |
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Answer» 2,4 |
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| 19. |
If S_(n)=sum_(r=1)^(n)(n)/(n^(2)+rn+r^(2))andt_(n)=sum_(r=0)^(n=1)(n)/(n^(2)+rn+r^(2)). Prove that S_(n)lt(pi)/(3sqrt(3))ltt_(n)AAnin N. |
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| 20. |
In the following figure, find the locus of centroid of triangle PAB, where AP perpendicular to PB. |
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Answer» Solution :`:.`Slope of AP `=(2)/(t)` `rArr`Slope of BP `=-(t)/(2)` So, equation of line BP is `y-2t=-(t)/(2)(x-t^(2))`. Putting y = 0, we get POINT B as `(t^(2)+4,0)`. Now , let centroid of `Delta PAB` be (h,k). `:.""h=(t^(2)+t^(2)+4)/(3)andk=(2t)/(3)` Eliminating 't', we get `3h-4=2((3k)/(2))^(2)` `:.""3x-4=(9Y^(2))/(2)`, which is the required locus. |
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| 21. |
Find the area of the parabola y^(2) = 4ax bounded by its latus rectum. |
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| 22. |
Let f(x) ={{:( x+2, 0 le x lt 2),( 6-x, x ge 2):}, g(x)={{:( 1+ tan x, 0le x lt (pi) /(4)),( 3-cotx,(pi)/(4) le x lt pi ):} f(g(x)) is |
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Answer» discontinuous at `X=pi//4` |
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| 24. |
If I_(1)=int_(0)^(1)(1-(1-x^(3))^(sqrt(2)))^(sqrt(3)) x^(2)dx and I_(2)(1-(1-x^(3))^(sqrt(2)))^(sqrt(3)+1).x^(2)dx. Then ((I_(1))/(I_(2))-(sqrt(3)-1)/(2sqrt(2))+0.2)/10 is equal to _________ |
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Answer» `3l_(1)=int_(0)^(1)(1-t^(SQRT(2)))^(sqrt(3)) dt` and `3l_(2)=int_(0)^(1)(1-t^(sqrt(2)))^(sqrt(3)+1).1.dt` `=int_(0)^(1)(sqrt(3)+1)sqrt(2)(1-t^(sqrt(2)))^(sqrt(3))(1-t^(sqrt(2))-1)dt` (Using integration by parts) `3l_(2)=-(sqrt(3)+1)sqrt(2).3l_(2)+(sqrt(3)+1)sqrt(2).3l_(1)` So, `(l_(1))/(l_(2))-(sqrt(3)-1)/(2sqrt(2))+0.2=1+(sqrt(3)-1)/(sqrt(2))-(sqrt(3)-1)/(2sqrt(2))+0.2=1.2` |
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| 25. |
Let p and q be any two propositions. statement -1 : ( p toq )harr q vv ~ p 1 is a tautology |
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Answer» Statement-1 is TRUE, Statement -2 is TURE, Statement -2 is a correct EXPLANATION for statement -4 |
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| 26. |
If A+B+C=180^@ thensin^(3) A cos (B-C) + sin^(3)B cos(C-A)+ sin^(3) C cos (A-B)= |
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Answer» `2 SIN A sin B cos C ` |
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| 27. |
Which of the following is a group ? |
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Answer» {1,2,4,8} under multiplication |
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| 28. |
{:(" " Lt),(n rarroo):} [(1)/(3n+1)+(1)/(3n+2)+.......+(1)/(4n)]= |
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Answer» `LOG (2/3)` |
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| 29. |
Find the values of the following integrals (ii) int_(0)^(pi/2) sin^(10)x dx |
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Answer» |
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| 30. |
int(1+2x+3x^(2)+4x^(3).....)dx=....+c(|x| lt 1) |
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Answer» `(1-x)^(-1)` |
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| 31. |
int(x^(6)-1)/(x^(2)+1)dx=....+c |
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Answer» `(x^(5))/(5)-(x^(3))/(3)+x-2tan^(-1)x` |
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| 32. |
Three cards are drawn successively, without replacement from a pack of 52 well shuffled cards. What is the probability that first two cards are kings and the third card is an ace? |
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| 33. |
abs(A xx B) = 6. If (-1,y), (1,x),(0,y) are in A xx B. Write other elements in A xx B , where x ne y. |
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Answer» Solution :Let `abs(A XX B)` = 6and (-1,y) (1,x) (0,y) `in A xx B` `rArr -1, 1,0 in A and x,y in B` As `abs(A xx B)` = 6 and 3` xx` 2 = 6 We have A = { -1,1,0} and {x,y} Thus other element of `A xx B`are (-1,x), (1,y) (0,x) |
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| 35. |
A bag contains 19 Tickets numbered 1to 19. A ticket is drawn first and later another ticket is drawn without replacement. The probability that both tickets show even number is |
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Answer» `1//19` |
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| 36. |
~[(~p)^^q] is logically equivalent to : |
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| 37. |
int sin x*cos x*cosx2x *cos 4x*cos 8x* cos 16x dx=....+c |
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Answer» `(sin 16X)/(1024)` |
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| 38. |
3 statements are given below each of which is either True of false. Indicate the correct order sequence I (log_(3) 169) (log_(13) 243)=10""II cos (cos pi)=cos (cos 0^(@)) III cos x + 1/(cos x)=3/2 |
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Answer» <P>TFF |
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| 39. |
int(sin2x)/(sqrt(1-sin^(4)x))dx= |
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Answer» `SIN^(-1)(2sinx)+C` |
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| 40. |
bar(a)=(1,2,-3),bar(b)=(2,1,-1). The vector bar(mu) is such that bar(a)xx bar(mu)=bar(a)xx bar(b)and bar(a).bar(mu)=0then |bar(mu)| = ……….. |
| Answer» Answer :D | |
| 41. |
A ray of light coming along the line 3x+4y-5=0 gets reflectedfrom the line ax+by-1=0 and goes along the line 5x-12y-10=0, then : |
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Answer» `a=(64)/(115), b=(112)/(15)` |
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| 42. |
By using the properties of definite integrals, evaluate the integrals int_((-pi)/2)^(pi/2)sin^(2)xdx |
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| 43. |
Evaluate the following determinants: [[1^2,2^2,3^2],[2^2,3^2,4^2],[3^2,4^2,5^2]] |
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Answer» SOLUTION :`[[1^2,2^2,3^2],[2^2,3^2,4^2],[3^2,4^2,5^2]]=[[1,4,9],[4,9,16],[9,16,25]]` = `1[[9,16],[16,25]]-4[[4,16],[9,25]]+9[[4,9],[9,16]]` =225-256-4(100-144)+9(64-81) -31+176-153=-184+176 =-8 |
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| 44. |
If the function f:A to B is one-one onto and g:B to A , is the inverse of f, then fog =? |
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Answer» f |
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| 46. |
Distancebetweenthe twoplanes2x + 3y +4z -4=0and 4x + 6 y+ 8z= 12is ……. |
| Answer» Answer :D | |
| 47. |
If two tangents are drawn from a point on x^(2)+y^(2)=16 to the circle x^(2)+y^(2)=8 then the angle between the tangents is |
| Answer» Answer :A | |
| 48. |
inte^(x loga)*e^(x)dx=....+c |
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Answer» `a^(x)*E^(x)` |
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| 49. |
Find the mean deviation of the set of number 3,10,9,4,7,9,14 from Mean and Median and show that mean deviation from Mean is greater than that from Median |
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