28278 + Interview Questions in Maths in Class 12

1.	Let D be the domain of the real valued function f defined by f(x) = sqrt(25-x^2) . Then , write D .
Answer» SOLUTION :N/A

Discussion

2.	Let X{a,b,c} , Y = {1,2,3,4} Find Out which of the following relations are functions and which are not and why ? {(a,1),(a,2),(b,3),(b,4)}
Answer» SOLUTION :{(a,1),(a,2),(b,3),(b,4)} is not a FUNCTION as .a. has TWO IMAGES in Y.

Discussion

3.	Consider a set P consisting of 5 elements . A sub set .A. of P is chosen thereafter set .P. is reconstructed and finally another sub set .B. is chosen from P. The number of ways of choosing .A. and .B. such that (A cup B) ne P is :
Answer» <P> Solution :TOTAL no. of WAYS by which subsetsA and B can be formed `=4^5` Total no. of ways by which subsets A and B can be formed such that `A uu B = P ` is `3^5` `THEREFORE ` REQUIRED answer is `4^5- 3^5`

Discussion

4.	There are 5 cards numbered 1 to 5 , one number on one number on one card . Two cards are drawn at random without replacement . Let X denotes the sum of the numbers on two cards drawn . Find the mean and variance of X.
Answer» SOLUTION :Here, S={(1,2),(2,1),(1,3),(3,1),(2,3),(3,2),(1,4),(4,1),(1,5),(5,1),(2,4),(4,2),(2,5),(5,2),(3,4),(4,3),(3,5),(5,3),(5,4),(4,5)} `rArrn(S)=20` Let RANDOM variable variable be X which denotes the sum of the numbers on two cards DRAWN. X=3,4,5,6,7,8,9 At X=3,P(X)=`2/20=1/10` At X=4,P(X)`=2/10=1/10` At X =5,P(X)=`4/20=1/5` At X=6, P(X)=`4/20=1/5` At X=7,P(X)=`4/20=1/5` At X=8, P(X)=`2/20=1/10` At X=9,P(X)=`2/20=1/10` `THEREFORE` Mean,E(X)=`SigmaXP(X)=3/10+4/10+5/5+6/5+7/5+8/10+9/10` =`(3+4+10+12+14+8+9)/10=6` Also,`SigmaX^(2)P(X)=9/10+16/10+25/5+36/5+49/5+64/10+81/10` `=(9+16+50+72+98+64+81)/10=39` `therefore` Var(X)=`SigmaX^(2)P(X)-[SigmaXP(X)]^(2)` `=39-(6)^(2)=39-36=3`

Discussion

5.	Smaller area enclosed by the circle x^(2) + y^(2) = 4 and the line x + y = 2 is
Answer» `2 (PI - 2)` `pi - 2` `2PI - 1` `2 (pi + 2)` Answer :B

Discussion

6.	The locus of the vertices of the family of parabolas y = (a^(3)x^(2))/(3)+(a^(2)x)/(2)-2a is
Answer» ` XY = ( 35)/( 16) ` ` xy = ( 64)/( 105) ` ` xy =(105) /( 64) ` ` xy = ( 3)/(4) ` Answer :C

Discussion

7.	If omega is an imaginary cube root of unity and \|{:(x + omega^(2), omega , 1),(omega , omega^(2), 1 + x),(1, x + omega , omega^(2)):}\| = 0 , then one of the values of x is
Answer» 1 0 `-1` 2 Answer :B

Discussion

8.	If (x) {:{(x,x inQ),(0,x neQ):} and g(x)={:{(x,x in Q),(0,x inQ):}then (f-g) will be
Answer» ONE one ONTO one-one into MANY one onto many one into ANSWER :A

Discussion

9.	""^11C_0 + ""^11C_1 + ""^11C_2 + ……+ ""^11C_5 =
Answer» `2^7` `2^8` `2^9` `2^10` ANSWER :D

Discussion

10.	The vertices of DeltaABC are (2,0, 0), B(0, 1, 0), C(0, 0, 2). Its orthocentre is H and circumcentreis S. P is a point equidistant from A, B, C and the origin O. Q.The z-coordinate of H is :
Answer» 1 `1//2` `1//6` `1//3` ANSWER :D

Discussion

11.	Let X{a,b,c} , Y = {1,2,3,4} Find Out which of the following relations are functions and which are not and why ? {(a,a),(b,b),(c,c)}
Answer» SOLUTION : {(a,a),(B,b),(C,c)} is a FUNCTION from X to X.

Discussion

12.	Use the identity (1+x)^(m)(1+x)^(n)=(1+x)^(m+n) to prove Vandermonde's theorem, ""^(m)C_(r ) +""^(m)C_(r-1). ""^(n)C_( 1)+""^(m)C_(r -2) *""^(n)C_(2) +….+""^(n)C_(r )=""^((m+n))C_(r )
Answer» `""^((m+n)) C_r` `""^(MN) C_r` `""^((m+n)) C_(r+1)` `((m+n)) C_(r-1)` ANSWER :A

Discussion

13.	A,B,C are tossing a coin on the condition that the person who gets a head first wins the game. If A starts the game then the probability that B wins the game is
Answer» `(1)/(7)` `(2)/(7)` `(3)/(7)` `(4)/(7)` ANSWER :B

Discussion

14.	Find the general solution of (dy)/(dx) = sin^(-1)x
Answer» Answer :`y = X sin^(-1)x + sqrt(1 - x^(2)) + C`

Discussion

15.	The number of ways in which 4 letters can be put in 4 addressed envelopes so that I: atleast one letter goes into wrong envelope is 23. II : no letter goes into the envelope meant for it is 9. III : all the letters goes into the right addressed envelopes is24. Which of the above statements is true
Answer» only I is true only III is true both I and II are true II & III are true ANSWER :C

Discussion

16.	When do you say two lines in space are skew ? Do they intersect ?
Answer» SOLUTION :A PAIR of non-coplanar lines are CALLED SKEW lines. Skew lines do not INTERSECT.

Discussion

17.	The vertices of DeltaABC are (2,0, 0), B(0, 1, 0), C(0, 0, 2). Its orthocentre is H and circumcentreis S. P is a point equidistant from A, B, C and the origin O. Q.The y-coordinate of S is :
Answer» `5//6` `1//3` `1//6` `1//2` ANSWER :C

Discussion

18.	A line L_(1) with direction ratios -3,2,4 passes through the point A(7,6,2) and a line L_(2) with directions ratios 2,1,3 passes through the point B(5,3,4). A line L_(3) with direction ratios 2,-2,-1 intersects L_(1) and L_(3) at C and D, resectively. The lenth CD is equal to
Answer» 4 6 9 11 Solution :`L_(1) = (x-7)/-3= (y-6)/2 = (z-2)/4` and `L_(2) = (x-5)/2=(y-3)/1=(z-4)/3` `THEREFORE D(2mu+5,mu+3,3mu+4)` So, `(2-3lambda-2mu)/2=(3+2lambda-mu)/-2=(-2+4lambda-3mu)/-1` `therefore lambda=2, mu=1` So, C(1,10,10) and D(7,4,7) `RARR` CD=9.

Discussion

19.	The vertices of DeltaABC are (2,0, 0), B(0, 1, 0), C(0, 0, 2). Its orthocentre is H and circumcentreis S. P is a point equidistant from A, B, C and the origin O. Q.PA is equal to :
Answer» 1 `SQRT(2)` `sqrt((3)/(2))` `(3)/(2)` ANSWER :D

Discussion

20.	Ifc gt 0 and m and n are postive integers, which of the following is equivalent to c^(m/n)?
Answer» `c^m/c^N` `cm-n` `(rootmc)^n` `(rootmc)^m` ANSWER :D

Discussion

21.	On a multiple choice examination with three possible answers for each of the five questions, what is the probability that a candidate would get four or more correct answers just by guessing?
Answer» ANSWER :`(11)/(243)`

Discussion

22.	A line L_(1) with direction ratios -3,2,4 passes through the point A(7,6,2) and a line L_(2) with directions ratios 2,1,3 passes through the point B(5,3,4). A line L_(3) with direction ratios 2,-2,-1 intersects L_(1) and L_(3) at C and D, resectively. The volume of parallelopiped formed by vec(AB), vec(AC) and vec(AD) is equal to
Answer» 140 138 134 130 Solution :VOLUME `[bar(AB)bar(AC)bar(AD)]=\|{:(2,3,-2),(6,-4,-8),(0,2,-5):}\|`=138

Discussion

23.	Let A be a nonsingular square matrix of order 3xx3.Then \|adj A\| is equal to
Answer» \|A\| `\|A\|^(2) ` `\|A\|^(3) ` `3\|A\|` ANSWER :B

Discussion

24.	A line L_(1) with direction ratios -3,2,4 passes through the point A(7,6,2) and a line L_(2) with directions ratios 2,1,3 passes through the point B(5,3,4). A line L_(3) with direction ratios 2,-2,-1 intersects L_(1) and L_(3) at C and D, resectively.The equation of the plane parallel to line L_(1) and containing line L_(2) is equal to
Answer» `x+3y+4z=30` `x+2y+z=15` `2x-y+z=11` `2x+17y-7z=33` Solution :Equation of plant parallel to `L_(1)` and containing `L_(2)` is `a(x-5)+b(y-3)+c(z-4)=0` `a(x-5)+b(y-3)+c(z-4)=0` `THEREFORE 2a+b+3c=0` and `-3+2b+4c=0` `RARR a/-2=b/-17=c/7` So, required PLANE is `2x+17y-7z=33`.

Discussion

25.	Write the direction cosines of x-axis.
Answer» ANSWER :1,0,0or-1,0,0

Discussion

26.	int 9^(9^(9^(x))) dx is equal to
Answer» `(9^(9^(9^(x))))/(log 9)` `(9^(9^(x)))/((log 9)^(2))` `(9^(9^(9^(x))))/((log x)^2)` `(9^(9^(9^(x))))/((log 9)^3)` ANSWER :D

Discussion

27.	Find the values of the following integrals int_(0)^((pi)/(2)) sin^(8) x dx
Answer» ANSWER :`(35pi)/(256)`

Discussion

28.	The real part of (1)/(1+cos theta+i sin theta) is
Answer» `-(1)/(2)` `(1)/(2)` `SQRT2` `(1)/(sqrt2)` ANSWER :B

Discussion

29.	Find area of the triangle with vertices at the point given in each of the following: ( 2,7),( 1,1) ,( 10,8 )
Answer» ANSWER :`( 47)/(2) `

Discussion

30.	Find the distance between the point P (6,5, 9) and the plane determined by the points A (3, - 1, 2), B (5, 2, 4) and C (-1, - 1, 6).
Answer» ANSWER :`(3sqrt(34))/(17)`

Discussion

31.	The number of ways of selecting ' n ' things out of '3n ' things of which 'n ' are of one kind and alike and 'n ' are of second kind and alike and the rest unlike is :
Answer» `N2^(n-1)` `(n-1)2^(n-1)` `(n+1)2^(n-1)` `(n+2)2^(n-1)` ANSWER :D

Discussion

32.	Cosine of the angle between the lines whose vector equations are r=3i+2j-4k+lambda(i+2j+2k) and r=5i-2k+mu(3i+2j+6k),lambda,mu being parameters, is
Answer» `-1//3sqrt(29)` `3//7sqrt(29)` `23//29` `19//21` ANSWER :D

Discussion

33.	int sqrt(x^(2)-8x+7)dx=....
Answer» `(1)/(2)(x-4) sqrt(x^(2)-8x+7)+9log\|x-4+sqrt(x^(2)-8x+7)\|+c` `(1)/(2)(x+4) sqrt(x^(2)-8x+7)+9log\|x+4+sqrt(x^(2)-8x+7)\|+c` `(1)/(2)(x-4) sqrt(x^(2)-8x+7)-3sqrt(2) LOG x+4+sqrt(x^(2)-8x+7)\|+c` `(1)/(2)(x+4) sqrt(x^(2)-8x+7)+(9)/(2)log\|x-4+sqrt(x^(2)-8x+7)\|+c` Answer :D

Discussion

34.	int_(pi//6)^(pi//3)(Sin^(3)x)/(Sin^(3)x+Cos^(3)x)dx=
Answer» `pi/16` `pi/12` `pi/2` `2PI` ANSWER :B

Discussion

35.	If the Arithmetic mean and Geometrical mean of three numbers are equal to x, then the each number is equal to
Answer» X 2x `SQRT(x)` `3sqrt(x)` ANSWER :A

Discussion

36.	Solve the following differential equations. (dy)/(dx)+(10x+8y-12)/(7x+5y-9)=0
Answer» ANSWER :`(x+y-1)^(2) (y+2x-3)^(2) = C`

Discussion

37.	Vector vec(a)=hati-hatj,vec(b)=hati+hatj+hatk. The vector vec( c ) is such that vec(a)xx vec( c )+vec(b)=0 and vec(a).vec( c )=4 then \|vec( c )\|^(2) = ……………
Answer» 8 `(19)/(2)` 9 `(17)/(2)` Answer :B

Discussion

38.	Integrate the functions e^(2x+3)
Answer» ANSWER :`1/2e^(2x+3)+C`

Discussion

39.	In Delta ABC, if (a-b) (s-c)= (b-c) (s-a) then r_1,r_2,r_3 are in
Answer» only I is true only II is true both I, II are true neither I nor II is true Answer :A

Discussion

40.	From first 100 natural numbers five are selected at random. Find the probability that all the five are not consecutive
Answer» Answer :`1 - (96)/(.^(100) C_(5))`

Discussion

41.	The shaded region shown in the figure is given by the inequations
Answer» `14x+5y GE 70, yle 14 and x-y ge 5` `14x+5y le 70, yle 14 and x-y ge 5` `14x+5y ge 70, y ge 14 and x-y ge 5` `14x+5y ge 70, y le 14 and x-y le 5` Answer :D

Discussion

42.	Integrate thefunction in Exercise. sqrt(sin 2x)cos 2x
Answer» Answer :`(1)/(3)(sin2x)^((3)/(2))+C`

Discussion

43.	Equation of a line and plane are respectively (x-1)/(2)=(y)/(3)=(z-3)/(2) and 4x-2y-z=1. Then
Answer» line is PARALLEL to the plane line is PERPENDICULAR to the plane line LIES in the plane none of these Answer :C

Discussion

44.	Verify property 1 forDelta ={:[( 2,-3,5),(6,0,4) ,( 1,5,-7) ]:}
Answer» ANSWER :`Delta_1 = -DELTA `

Discussion

45.	f (x) = lim _(x to oo) (x ^(2) + 2 (x+1)^(2n))/((x+1) ^(2n+1) + x^(2) +1),n in N and g (x) =tan ((1)/(2)sin ^(-1)((2f (x))/(1+f ^(2) (x)))), then lim_(x to -3) ((x ^(2) +4x +3))/(sin (x+3) g (x)) is equal to:
Answer» 1 2 4 Non-existent ANSWER :B

Discussion

46.	Let p and q be the following statements: p : X is a rectangle q : X is a square then which one of the following represents converse of p rarr q .
Answer» If XIS a RECTANGLE then X is a SQUARE. If Xis a rectangle then Xis not a square Xis a rectangle but Xis not a square Xis a square then Xis a rectangle ANSWER :D

Discussion

47.	A doctor is to visit a patient. From past experience, it is known that the probabilities that he will come by train, bus, scooter or by car are repectively 3/10,1/5,1/10and2/5. The probabilities that he will be late are 1/4,1/3 and 1/12, if he comes by train,bus and scooter respectively, but if he comes by car, he will not be late. When he arrives, he is late. What is the probability that he has come by train ?
Answer» Solution :Let `E_1,E_2,E_3and E_4` be the events that the DOCTOR comes by train, bus, SCOOTER and car RESPECTIVELY. Then, `P(E_1)=3/10,P(E_2)=1/5,P(E_3)=1/10andP(E_4)=2/5`. Let E be the event that the doctor is late. Then, `P(E//E_1)` = probability that the doctor is late, given that he comes by train `=1/4`. `P(E//E-2)`= probability that the doctor is late, given thathe comes by bus `=1/3`. `P(E//E_3)`= probability that the doctor is late, given that the comes by scooter `=1/12`. `P(E//E_4)`= probability that the doctor is late, given that that he comes by car =0. Probability that he comes by train, given that he is late `P(E_1//E)` `(P(E_1).P(E//E_1))/(P(E_1).P(E//E_1)+P(E_2).P(E//E_2)+P(E_3).P(E//E_3)+P(E_4).P(E//E_4))`[by Bayes's theorem] `((3/10xx1/4))/((3/10xx1/4)+(1/5xx1/3)+(1/10xx1/12)+(2/5xx0))` `=(3/40xx120/18)=1/2` Hence, the required probability is `1/2`.

Discussion

48.	Define a binary operation on a set
Answer» ANSWER :`a"*" B, AA a,b in A`

Discussion

49.	Let A = [-1,1] . Then , discuss whether the following functions defined on A are one - one , onto or bijective. k(x) =x^2
Answer» SOLUTION :N/A

Discussion

50.	For the same loan, what is the loan balance after 3 years assuming no payments, and ul("quarterly") compounding? (Note : The exponent here is higher than you'd likely encounter on the GRE.)
Answer» ANSWER :`$18,132.82`

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Let D be the domain of the real valued function f defined by f(x) = sqrt(25-x^2) . Then , write D .

Let X{a,b,c} , Y = {1,2,3,4} Find Out which of the following relations are functions and which are not and why ? {(a,1),(a,2),(b,3),(b,4)}

Consider a set P consisting of 5 elements . A sub set .A. of P is chosen thereafter set .P. is reconstructed and finally another sub set .B. is chosen from P. The number of ways of choosing .A. and .B. such that (A cup B) ne P is :

There are 5 cards numbered 1 to 5 , one number on one number on one card . Two cards are drawn at random without replacement . Let X denotes the sum of the numbers on two cards drawn . Find the mean and variance of X.

Smaller area enclosed by the circle x^(2) + y^(2) = 4 and the line x + y = 2 is

The locus of the vertices of the family of parabolas y = (a^(3)x^(2))/(3)+(a^(2)x)/(2)-2a is

If omega is an imaginary cube root of unity and |{:(x + omega^(2), omega , 1),(omega , omega^(2), 1 + x),(1, x + omega , omega^(2)):}| = 0 , then one of the values of x is

If (x) {:{(x,x inQ),(0,x neQ):} and g(x)={:{(x,x in Q),(0,x inQ):}then (f-g) will be

""^11C_0 + ""^11C_1 + ""^11C_2 + ……+ ""^11C_5 =

The vertices of DeltaABC are (2,0, 0), B(0, 1, 0), C(0, 0, 2). Its orthocentre is H and circumcentreis S. P is a point equidistant from A, B, C and the origin O. Q.The z-coordinate of H is :

Let X{a,b,c} , Y = {1,2,3,4} Find Out which of the following relations are functions and which are not and why ? {(a,a),(b,b),(c,c)}

Use the identity (1+x)^(m)(1+x)^(n)=(1+x)^(m+n) to prove Vandermonde's theorem, ""^(m)C_(r ) +""^(m)C_(r-1). ""^(n)C_( 1)+""^(m)C_(r -2) *""^(n)C_(2) +….+""^(n)C_(r )=""^((m+n))C_(r )

A,B,C are tossing a coin on the condition that the person who gets a head first wins the game. If A starts the game then the probability that B wins the game is

Find the general solution of (dy)/(dx) = sin^(-1)x

The number of ways in which 4 letters can be put in 4 addressed envelopes so that I: atleast one letter goes into wrong envelope is 23. II : no letter goes into the envelope meant for it is 9. III : all the letters goes into the right addressed envelopes is24. Which of the above statements is true

When do you say two lines in space are skew ? Do they intersect ?

The vertices of DeltaABC are (2,0, 0), B(0, 1, 0), C(0, 0, 2). Its orthocentre is H and circumcentreis S. P is a point equidistant from A, B, C and the origin O. Q.The y-coordinate of S is :

A line L_(1) with direction ratios -3,2,4 passes through the point A(7,6,2) and a line L_(2) with directions ratios 2,1,3 passes through the point B(5,3,4). A line L_(3) with direction ratios 2,-2,-1 intersects L_(1) and L_(3) at C and D, resectively. The lenth CD is equal to

The vertices of DeltaABC are (2,0, 0), B(0, 1, 0), C(0, 0, 2). Its orthocentre is H and circumcentreis S. P is a point equidistant from A, B, C and the origin O. Q.PA is equal to :

Ifc gt 0 and m and n are postive integers, which of the following is equivalent to c^(m/n)?

On a multiple choice examination with three possible answers for each of the﻿ five questions, what is the probability that a candidate would get four or more﻿ correct answers just by guessing?

Let A be a nonsingular square matrix of order 3xx3.Then |adj A| is equal to

Write the direction cosines of x-axis.

int 9^(9^(9^(x))) dx is equal to

Find the values of the following integrals int_(0)^((pi)/(2)) sin^(8) x dx

The real part of (1)/(1+cos theta+i sin theta) is

Find area of the triangle with vertices at the point given in each of the following: ( 2,7),( 1,1) ,( 10,8 )

Find the distance between the point P (6,5, 9) and the plane determined by the points A (3, - 1, 2), B (5, 2, 4) and C (-1, - 1, 6).

The number of ways of selecting ' n ' things out of '3n ' things of which 'n ' are of one kind and alike and 'n ' are of second kind and alike and the rest unlike is :

Cosine of the angle between the lines whose vector equations are r=3i+2j-4k+lambda(i+2j+2k) and r=5i-2k+mu(3i+2j+6k),lambda,mu being parameters, is

int sqrt(x^(2)-8x+7)dx=....

int_(pi//6)^(pi//3)(Sin^(3)x)/(Sin^(3)x+Cos^(3)x)dx=

If the Arithmetic mean and Geometrical mean of three numbers are equal to x, then the each number is equal to

Solve the following differential equations. (dy)/(dx)+(10x+8y-12)/(7x+5y-9)=0

Vector vec(a)=hati-hatj,vec(b)=hati+hatj+hatk. The vector vec( c ) is such that vec(a)xx vec( c )+vec(b)=0 and vec(a).vec( c )=4 then |vec( c )|^(2) = ……………

Integrate the functions e^(2x+3)

In Delta ABC, if (a-b) (s-c)= (b-c) (s-a) then r_1,r_2,r_3 are in

From first 100 natural numbers five are selected at random. Find the probability that all the five are not consecutive

The shaded region shown in the figure is given by the inequations

Integrate thefunction in Exercise. sqrt(sin 2x)cos 2x

Equation of a line and plane are respectively (x-1)/(2)=(y)/(3)=(z-3)/(2) and 4x-2y-z=1. Then

Verify property 1 forDelta ={:[( 2,-3,5),(6,0,4) ,( 1,5,-7) ]:}

f (x) = lim _(x to oo) (x ^(2) + 2 (x+1)^(2n))/((x+1) ^(2n+1) + x^(2) +1),n in N and g (x) =tan ((1)/(2)sin ^(-1)((2f (x))/(1+f ^(2) (x)))), then lim_(x to -3) ((x ^(2) +4x +3))/(sin (x+3) g (x)) is equal to:

Let p and q be the following statements: p : X is a rectangle q : X is a square then which one of the following represents converse of p rarr q .

Define a binary operation on a set

Let A = [-1,1] . Then , discuss whether the following functions defined on A are one - one , onto or bijective. k(x) =x^2

For the same loan, what is the loan balance after 3 years assuming no payments, and ul("quarterly") compounding? (Note : The exponent here is higher than you'd likely encounter on the GRE.)

On a multiple choice examination with three possible answers for each of the five questions, what is the probability that a candidate would get four or more correct answers just by guessing?