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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. |
int_(0)^(pi//2) ( sin x cos x )/( 1+ sin x ) dx is equal to |
| Answer» Answer :B | |
| 2. |
If A and B are two independent events such that P(B) =(2)/(7) , P(A cup B^(c)) = 0.8, then find P(A). |
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| 3. |
Transform the definite integral int_(0)^(2 pi) f(x) cos x dx by thesubstitution sin x = t |
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| 4. |
If I is the incentre of DeltaABCandP_(1),P_(2),P_(3) are respectively the radii of the circumcircles of the DeltaIBC,DeltaICAandDeltaIAB, then P_(1)P_(2)P_(3)= |
| Answer» Answer :C | |
| 5. |
If the curve ay+x^(2)=7 and x^(3)=y, cuts orthogonall at (1, 1), then the value of a is ………. |
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Answer» 1 |
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| 6. |
(1.4)/(0!) +(2.5)/(1!) + (3.6)/(2!)+...... = |
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Answer» 7e |
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| 7. |
If A=[{:(cosq,sinq),(-sinq,cosq):}], then show that A^(2)=[{:(cos(2q),sin(2q)),(-sin(2q),cos(2q)):}]. |
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| 8. |
If X~B(n,p) such that 4P(X=4)=P(X=2) and n=6. Find the distribution, mean and standard deviation of X. |
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Answer» (II) 2 (III) `SQRT(4/3)` |
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| 9. |
If A=cos^(2)""(3pi)/5 + cos^(2)""(4pi)/5 , B= cos^(2)""(pi)/8 + sin^(2)""(3pi)/8, C= " cosec " 10^(@) - sqrt(3) sec 10^(@)then |
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Answer» `A LT C lt B` |
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| 10. |
Let X denote the number of hours you study during randomly selected school day to probability that X can take the values of x, has the following form. P(X=x) = {{:(0.1, If x=0),(kx, if x=1 or 2),(k(5-x), if x =3 or 4),(0, " otherwise "):}find the value of k |
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| 11. |
(i) Find the area bounded by y = 3x +2, the x-axis and the ordinates x =-2 and x =1. (ii) Find the area bounded by y=x, the x-axis and the line x =-1 and x=2. |
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| 12. |
Determine all real solutions of the given equation where p is real number sqrt(x^(3) -p)+2sqrt(x^(2)-1)=x |
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Answer» <P> |
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| 13. |
Given f(x) is symmetrical about the line x=1, then find out the value of 'x' satisfying f(x-1)=f((x)/(x+1)) |
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| 14. |
Find the coefficient of variation of the data 6,8,10,12,14,16,18,20,22,24 |
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| 15. |
Show that the vectors 2hati-3hatj+4hatkand-4hati+6hatj-8hatk arecollinear. |
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| 17. |
Show that f: [-1, 1] to R, given by f (x) = (x)/((x +2)) is one-one. Find the inverse of the function f : [-1, 1] toRangle f. |
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| 18. |
At x=(5pi)/(6), f(x)=2 sin 3x + 3 cos (3x) is …………… |
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Answer» MAXIMUM |
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| 19. |
Total number of ways in which n^(2)number of identical balls can be put in 'n' numbered boxes {1.2.3. . . . n} such that i^(th) box contains atleasti number of balls |
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Answer» `""^(N^(2))C_(n - 1)` |
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| 20. |
The projection of the vector (-4,-2,4) on (2,1,1) is …………. |
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Answer» `(-2,1,1)` |
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| 21. |
Method of integration by parts : If u=inte^(ax)cos bx dx and v= int e^(ax) sin bx dx then (a^(2)+b^(2))(u^(2)+v^(2))=.... |
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Answer» `E^(2ax)` |
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| 22. |
Find the ara of the region bounded by : (i) the parabola y = x^(2) and the line y=x (ii) the parabola y ^(2) =x and line x+ y =2 (iii) the curve x ^(2) = 4y and the straight line x = 4y -2 (iv) the parabola y ^(2) = 4 ax and the chord y = mx (v) the parabola y ^(2) = 4 ax and its latus-rectum (vi) the parabola (I) y ^(2) = 8x (II) y ^(2) = 6xand the latus rectum. |
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| 23. |
If alpha, beta are roots of the equation x^(2)+bx+c=0 and alpha+h, beta+h are the roots of the equation x^(2)+qx+r=0 then h is equal to |
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Answer» -1 |
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| 24. |
If 1 , omega , omega^(2) are the cube roots of unity , then (x + y + z) (z + y omega +zomega^(2)) ( x + y omega^(2)+ z omega) = |
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Answer» `X^(3) + y^(3) + z^(3)` |
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| 25. |
Show that ""^(10)C_2+^(11)C_2+^(12)C_2+^(13)C_2+...+^(20)C_2=^(21)C_3-^(10)C_3. |
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| 26. |
The volume of spherical ballon being inflated changes at a constant rate. If initially its radius is 3 units and after 3 seconds it is 6 units. Find the radius of ballon after t seconds. |
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Answer» `3sqrt(63t+9)` |
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| 27. |
Find the approximate change in volume of a cube of side x meters caused by an increase in the side by 3%. |
| Answer» SOLUTION :`v=x^3/_\v=3X^2/_\x=3x^2xx(3x)/100=9/100x^3=0.09x^3m^3` | |
| 28. |
The sum of the coefficients of all even degree terms is x in the expansion of (x + sqrt(x^(3) - 1))^(6) + (x - sqrt(x^(2) - 1))^(6), (x gt 1) is equal to |
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Answer» 29 `(a + b)^(N) + (a - b)^(n) =` `2[.^(n)C_(0) a^(n) + .^(n)C_(2) a^(n - 2) b^(2) + .^(n)C_(4) a^(n - 1) b^(4)` + …… 1 Given expansion is `(x + SQRT(x^(3) - 1))^(6) + (x - sqrt(x^(3) - 1))^(6)` `= 2[.^(6)C_(0) x^(6) + .^(6)C_(2) x^(4) (sqrt(x^(2) - 1))^(2)` `{ :' (a + b)^(n) + (a - b)^(n)` `= 2 [.^(n)C_(0) a^(n) + .^(n)C_(2) a^(n - 2) b^(2) + .^(n)C_(4)a^(n - 4) b^(4) + ...]}` The SUM of the terms with EVEN power of x. ` 2[.^C_0x^6+.^C_2(-x^4)+.^6C_4x^8+.^6C_4x^2+.^6C_6(-1-3x^6)]`. ` =2[.^6C_0x^6-.^6C_2x^4+.^6C_4x^8 +.^6C_4x^2-1 -3x^6]` Now, the required sum of the coefficient of even powers of x in `(x+sqrt(x^3-1))^6+(x-sqrt(x^3-1))^6` ` =2[.^6C_0-.^6C_2+.^6C_4+.^6C_4-1-3]` ` =2[1-15+15+15-1-13]=2(15-3]=2(15-3)=24` |
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| 29. |
Applying Newton.s method , find the an accuracy up to 0.01 the positiveroots of the following equations : (a) x^(3) +50 x - 60 = 0 (b) x^(3) +x - 32 = 0 |
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| 30. |
There are two routes joining city A to a city B and three routes joining B to another city C . In how many ways can a person perform a journey from A to C ? |
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Answer» Solution :There are TWO routes JOINING a city A to a city B and three routes joining B to another city C. `:.`By the fundamental principle of counting, the TOTAL number of JOURNEY in which person can perform from A to C is `2xx3=6.` |
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| 31. |
cos alpha sin (beta - gamma) + cos beta sin (gamma - alpha ) + cos gamma sin (alpha - beta )is equla to |
| Answer» Answer :A | |
| 32. |
If 2(y - a) is the H.M between y - x and y - z, then x - a, y -a, z - a are in |
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Answer» A.P |
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| 33. |
A binary sequenceis anarrayof'0's and1's. Thenumberofn-digitbinarysequenceswhichcontainevennumberof 0 s is : |
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Answer» `2^(N-1)` |
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| 34. |
If .^(9)P_(5)+5*.^(9)P_(4), then n+r equals |
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Answer» 13 |
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| 35. |
A(cos theta, sin theta), B (sin theta,- cos theta) are two points then centroid of triangle formed by A,B andorigin lies on a circle whose centre and radius are |
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Answer» `(1,1),SQRT(2//3)` |
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| 36. |
Twenty identical rupee coins are distributed among 5 children at random. Find the probability that the total number of coins received by first two children is exactly 15 coins. |
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| 37. |
int(dx)/((-1)sqrt(1+x^2))= |
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Answer» `(1)/(SQRT(2))log|(1)/(1-x)-(1)/(2)+sqrt((1)/(1-x)^2-(1)/(1-x)+(1)/(2))|+c` |
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| 38. |
If x = sin (2 Tan^(-1) 2) and y = sin((1)/(2) Tan^(-1).(4)/(3)), then |
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Answer» `X gt y` |
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| 39. |
Integration of some particular functions : int(2x)/(sqrt(x^(2)-2x+7))dx=....+c |
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Answer» `2 SQRT(X^(2)-2x+7)+2log|x-1+sqrt(x^(2)-2x+7)|` |
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| 40. |
intx^7Inxdx |
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Answer» Solution :`intx^7Inxdx` [CHOOSEN In X as FIRST FUNCTION and `x^7` as 2nd function.] =`1nx.x^8/8-int1/x.x^8/8dx` =`1/8x^8 1nx-1/8intx^7dx` =`1/8x^8 1nx-1/64x^8+C` |
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| 41. |
Show that the differential equation x cos ((y)/(x))(dy)/(dx) = y cos ((y)/(x)) + x ishomogeneous and solve it. |
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| 42. |
Find two numbers whose sum is 24 and whose product is as large as possible. |
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| 43. |
Solvex^4 +x^3- 16x^2 -4x + 48=0giventhat the productof twoof the rootsis 6. |
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| 44. |
Statement-1: The maximum value of |sqrt(x^(4)-3x^(2)-6x+13)-sqrt(x^(4)-x^(2)+1)|" is"sqrt10,AAx inR. Statement-2: If |PA - PB| = k(constant), then locus of P is a hyperbola provided KltAB. |
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Answer» Statement - 1 is True, Statement - 2 is True, Statement-2 is a correct EXPLANATION for Statement-1 |
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| 45. |
I= int ( x^2 + 3) /( sqrt ( 2x -5)^(3) )dx. |
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| 46. |
Prove that : int_(pi//4)^(3pi//4) (1)/(1+cos x) dx = 2 |
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| 48. |
Find the area of the smaller region bounded by the ellipse x^(2)/9 + y^(2)/4 = 1 and the line x/3 + y/2 = 1. |
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| 49. |
Which part of the digestive system Produces basis solution, enzymes and insulim :- |
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Answer» Liver |
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