Saved Bookmarks
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. |
Which of the following statements is not a tautology? |
|
Answer» `(p^^q ^^R)RARR (~pvv ~q vv r)` |
|
| 2. |
Area of the shaded portion in the figure is equal to |
|
Answer» `int_d^cf(X)DX` |
|
| 3. |
The shortest distance between lines barr=(hati-hatj)+lambda(2hati+hatk)andbarr=(2hati-hatj)+mu(hati-hatj-hatk) is |
|
Answer» `(1)/(14)` |
|
| 4. |
Integration by partial fraction : int(dx)/(x(x^(n)+1))=.... |
|
Answer» `n"log"(X^(n))/(x^(n)+1)+C` |
|
| 5. |
Evaluate int (sin^(6) x + cos^(6)x )/(sin^(2) x cos^(2) x)dx |
|
Answer» |
|
| 6. |
Two friends A and B are 30 km apart and they start simultaneously on motorcycles to meet each other. The speed of A is 3 times that of B. The distance between them decreases at the rate of 2 km per minute. Ten minutes after they start, A's vehicle breaks down and A stops and waits for B to arrive. After how much time (in minutes) A started riding, does B meet A ? |
|
Answer» Solution :Speed of B = V km/hr Speed of A = 3 V km/hr Given 4 V =`2 XX 60` km/hr `rArr V = 30 ` km/hr Distance covered by then after 10 min ` = 2 xx 10 = 20` km so remaining distance = (30 - 20) km = 10 km Time taken by B to cover10 km = `(10)/(30//60)=20 ` min. TOTAL time = 20 + 10 = 30 min |
|
| 7. |
Let p be the proposition: Mathematics is interesting and let q be the proposition that Mathematics is difficult then the symbol p^^q means |
|
Answer» MATHEMATICS is INTERESTING IMPLIES that Mathematics is difficult |
|
| 8. |
What are the coordinates of the point P in the xy-plane that divides the line segment whose endpoints are A(-1, 4) and B(4, -6) into two segments such that the ratio of AP to PB is 2 to 3? |
|
Answer» `(1, 0)` |
|
| 9. |
If A=[{:(9, 7, 3), (5, -1, 4), (6, 8, 2):}]" find "A^(-1) and hence solve the system of equations: 9x+7y+3z=6, 5x-y+4z=1, 6x+8y+2z=4. |
|
Answer» |
|
| 10. |
If I = int(dx)/(1+sqrt(x^(2)+2x+2))=(5)/(8)Alog|x+1+sqrt(x^(2)+2x+2)|-(sqrt(x^(2)+2x+2)-1)/(x+1)+C then A is equal to. |
|
Answer» |
|
| 11. |
Let P be a set of all subset of set X. Prove that the functions defined by cup : P xx P to P, (A,B) to A cupB and cap : PxxP to P, (A,B) to A cap Bare binary on P. |
|
Answer» Solution :`:'` Union operation `CUP` relates every PAIR (A,B) of `P XX P` to unique element of `A cup B`. `:.` It is a binary operation. `:.` Intersection operation `cap` relates every pair (A,B) of `P xx P` to unique element of `A cap B` `:.` It is a binary operations. HENCE PROVED. |
|
| 12. |
Coefficient of x^3 in 1+(1+x) +(1 +x)^2 +…..+(1+x)^n is |
|
Answer» `""^nC_4` |
|
| 13. |
The term in (x + y)^50 which is greatest in absolute value if |x| = sqrt3 |y| is |
|
Answer» `T_17` |
|
| 14. |
The probabilities of outcomes of a random experiment are given below : Let = {2, 4, 6}, B = {1, 2, 3, 4} and C = {1, 2}. Then find P(A), P(B), P( C ), P(A nn B), P(B nn C) and P(C nn A). |
|
Answer» |
|
| 15. |
If vec(a),vec(b),vec( c ) are unit vectors such that vec(a)+vec(b)vec( c )=0, find the value of vec(a).vec(b)+vec(b).vec( c )+vec( c ).vec(a). |
|
Answer» |
|
| 16. |
Choose the correct answer: If A and B are any two events such that P(A) + P(B) - P(A and B) = P(A), then P(A/B)=? |
| Answer» Answer :B | |
| 17. |
A= {1,2,3,4} . A relation R is A is given by F = {(2,2),(3,3),(4,4),(1,2)}. Then R is relation. |
|
Answer» REFLEXIVE |
|
| 18. |
A toy company manufacutes two types of dolls, A and B. Each doll of type B takes twice as long to produce as one of type. A and the company would have time to make a maxium of 2000 prr day, if it produces only type.A the supply of plastic is sufficient to produce 1500 dolls per day (both A and B combined). Type B requires a fancy dress of which there are only 600 per day available. If the company makes profits of Rs.3 and Rs5 per doll respectively on dolls A and B, how many of each should be produced per day in order to mazimize the profit? Also, find the maximum profit. |
|
Answer» |
|
| 19. |
A man is known to speak the truth 4 out of 5 times. He throws a die and reports that it is a four. Find the probability that it is actually a four. |
|
Answer» Solution :In a throw of die, let `E_1` = event of getting a FOUR `E_2` = event of getting not four and E = event that the man REPORTS that it is a four Thus,`P(E_1)=1/6 " and " P(E_2)=1-1/6=5/6` `P(E|E_1)` = probability that the man reports that four occurs, when four has actually occurred. = probability that the man speaks the truth `=4/5` `P(E|E_2)` = probability that the man reports that four occurs, when four has not actually occurred. = probability that the man does not SPEAK the truth `=(1-4/5)=1/5` Probability of getting a four, given that the man reports it to be a four `=P(E_1|E)` `=(P(E|E_1)P(E_1))/(P(E|E_1)P(E|E_2)P(E_2))` `=((4/5)(1/6))/((4/5)(1/6)+(1/5)(5/6))` `=4/(4+5)=4/9` |
|
| 22. |
int_(0)^(pi//2)(sinx)/(x)dx lies between |
|
Answer» 0 and 1 |
|
| 23. |
For natural numbers x and y, let (x,y) denote the god of x and y. How many pairs of natural numbers x and y with x s y satisfy equation xy = x + y + (x,y)? |
|
Answer» |
|
| 24. |
Sum of all the terms in the nth row of the triangle is |
|
Answer» `(1)/(2)N^(2)(n+1)` |
|
| 25. |
If the points (1, 1, p) and (-3, 0, 1) be equidistant from the plane vecr.(3hati+4hatj-12hatk)+13=0 then find the value of p. |
|
Answer» |
|
| 26. |
is(1)/(8)[((4g^2(x)-1)^(3//2))/(3)+9sqrt(4g^2(x)+1)]+C. Then g (x) = |
|
Answer» tanx |
|
| 27. |
If S_(n) denotes the sum of the products of the products of the first n natureal number taken two at a time then Sigma_(n=0)^(oo) (S_(n))/(n+1!) equals |
| Answer» Answer :b | |
| 28. |
If A=[{:(1,2),(4,1):}], find A^(2)+2A+7I. |
|
Answer» |
|
| 29. |
(i) Dissusse the continuity of the functionf(x)={(|x-a|", " xne a ),(""0 ", "x=a):} at x=a(ii)Discuss the continutiy of the functionf(x)={(|x-3|/(x-3)", " xne 3 ),(""0 ", "x=3):} at x=3 |
|
Answer» |
|
| 30. |
The transformed equation of a^(4) b^(3) x^(4) + a^(3) b^(2) x^(3) + a^(2) b^(2) x^(2) + bx + a = 0 into another with integral coefficients and unity for the coefficient of the first term is |
|
Answer» `x^(4) + ax^(3) + a^(2) bx^(2) + a^(2)bx + a^(5) b = 0` |
|
| 31. |
A crime is committed by one of two suspects, A and B. Initially, there is equal evidence against both of them. In further investigation at the crime scene, it is found that the guilty party had a blood type found in 20% of the population. If the suspect A does match this blood type , whereas the blood type of suspect B is unknown, then the probability that A is guilty party = |
|
Answer» `3//5` |
|
| 33. |
Findproducts : [[0,k],[1,0]][[a,b],[c,d]] |
|
Answer» SOLUTION :`[[0,k],[1,0]][[a,b],[C,d]]` `=[[0.a+k.c""0.b+k.d],[1.a+0.c" "1.b+0.d]]=[[KC,KD],[a,b]]` |
|
| 34. |
Solve the following differential equations. (dy)/(dx)=(x+2y+3)/(2x+3y+4) |
|
Answer» Where X = x-1 Y = y+2 |
|
| 35. |
If (1+x+2x^(2)+4x^(3))^(10)=a_(0)+a_(1)x+a_(2)x^(2)+….+a_(30)x^(30). Find the value of a_(1)+a_(3)+a_(5)+…+a_(29) |
|
Answer» |
|
| 36. |
Why was Franz feeling regretful and sad? |
|
Answer» for REACHING late |
|
| 37. |
Given : f(x){(x",",0lexlt1/2),(1/2",",x=1/2),(1-x",",1/2ltxle1):} and g(x)=(x-1/2)^(2),x in R. Then the area (in sq. units) of the region bounded by the curves, y=f(x) and y=g(x) between the lines, 2x=1 and 2x=sqrt(3), is : |
|
Answer» `(SQRT(3))/(4)-1/3` |
|
| 38. |
If lim_(x rarr 0)([(a-n)nx - tan x] sin nx)/(x^(2)) = 0, (n != 0) then the minimum possible positive value of a is |
| Answer» Answer :C | |
| 39. |
If A={2x/x in N and x lt 3},B ={x//x^(2)-4x+3=0 and x gt 1 } then A x B = |
|
Answer» {(4,3),(2,3)} |
|
| 40. |
If y= (a + bx)/(c + dx), where a, b, c, d are constants and lamda y_(1) y_(3)= mu y_(2)^(2) then the value of mu^(lamda^(2)) is ……… where y_(1), y_(2), y_(3) are respectively. First, second and third derivatives of y. |
|
Answer» 42 |
|
| 41. |
If (3+2isintheta)/(1-2isintheta) is purely imaginary, then theta = |
|
Answer» `pi/3` |
|
| 42. |
If the normal to the curve x^(2//3)+y^(2//3)=a^(2//3) makes an angle theta with the x -axis then the slope of the normal is ………. |
|
Answer» `- COT THETA` |
|
| 43. |
Evaluate the definite integrals int_(0)^(1)(dx)/(sqrt(1+x^(2))) |
|
Answer» |
|
| 44. |
Differentiate (x cos x)^(x)+(x sin x)^(1//x) with respect to x. |
|
Answer» |
|
| 45. |
Maximise Z=2x+3y subject to x+2yle6,x ge 4,yge0 is : |
|
Answer» 6 at (6, 0) |
|
| 46. |
Choose the correct answer The probability of obtaining an even prime number on each die, when a pair of dice is rolled is |
|
Answer» 0 |
|
| 48. |
Evaluate : int(dx)/(x^(2)(x^(4) + 1)^((3)/(4))) |
|
Answer» |
|