28278 + Interview Questions in Maths in Class 12

1.	Solve the following equations : 2tan^(-1)(cosx)=tan^(-1)(2cosecx)
Answer» ANSWER :`x=N PI + (pi)/4, n epsilon Z`

Discussion

2.	Discuss the continuity of the function f given by f(x)= {(x",","if " x gt 0),(x^(2)",","if " x lt 0):}
Answer» ANSWER :F is continious FUNCTION

Discussion

3.	A point P moves inside a triangle formed by A(0,0),B(1,1/sqrt(3)),C(2,0) such that min {PA,PB,PC)=1, then the area bounded by the curve traced by P, is
Answer» `3sqrt(3)-(3pi)/(2)` `SQRT(3)+pi/2` `sqrt(3)-pi/2` `3sqrt(3)+(3pi)/(2)` ANSWER :C

Discussion

4.	Are the following sets relation ? A xx B from A to B.Determine the domain and range of each of the relations mentioned above.
Answer» SOLUTION :`A XX B` from A to B is a RELATION

Discussion

5.	Find the value of the following integral int_(0)^((pi)/(2)) sin^(9) x dx
Answer» ANSWER :`(128)/(315)`

Discussion

6.	The transformed equation of x^(4) + 2x^(3) - 12x^(2) + 2x - 1= 0by eliminating third term is
Answer» `x^(4) + 6X^(3) - 12x + 8 = 0 " or " x^(4) - 6x^(3) + 42X + 53 = 0 ` `x^(4) + 6x^(3) - 12x - 8 = 0 " or " x^(4) - 6x^(3) + 42x - 53 = 0 ` `x^(3) + x^(2) + 1 =0 " or " 27x^(3) - 27x^(2) + 23 = 0 ` `x^(3) - x^(2) + 1 =0 " or " 27x^(3) + 27x^(2) + 23 = 0 ` Answer :2

Discussion

7.	The mid point of the chord 4x-3y=5 of the hyperbola 2x^(2)-3y^(2)=12 is
Answer» ` (0,-(5)/(3)) ` `( 2,1) ` `((5)/(4) ,0 ) ` `((11)/( 4) ,2) ` ANSWER :B

Discussion

8.	If f(x) = sin theta. x + a and the equatio f(x) = f^(-1)(x) is satisfied by every real value of x, then
Answer» `THETA = (pi)/(2)` `theta = (3pi)/(2)` `a in R` `a = 1, theta = (pi)/(2)` Answer :B::C

Discussion

9.	Evaluate the following inegrals int cossecx log(cosecx - cotx)dx
Answer» ANSWER :`(1)/(2)(LOG(cosecx-cotx))^(2)+C`

Discussion

10.	If I=int_(0)^(pi//2)sin 2n x log cos x dx. Then l is same as
Answer» `int_(0)^(pi//3)cotcos 2nx dx` `int_(0)^(pi//2)cot SIN 2nx dx` `int_(0)^(pi//2)tancos 2nx dx` `(1)/(2N)int_(0)^(pi//2)tan sin 2n xdx` Answer :D

Discussion

11.	Find dy/dx if y^2 = a^(sqrt x)
Answer» Solution :`y^2 = a^(SQRT x) implies 2 In y = sqrt x CDOT In a implies 2/y dy/dx = (In a)/(2sqrt x) implies dy/dx =(y In a)/(4sqrt x) = (y^2 In a)/(4ysqrt x) ={(a^ sqrt x) In a}/(4ysqrt x)`

Discussion

12.	Evaluate the following integrals int[log(logx)+(1)/((logx)^(2))]dx
Answer» ANSWER :`x(LOG(LOGX)-(1)/(logx)]+C`

Discussion

13.	If x in (0, (pi)/(2)) " then " int sqrt([(sin x - sin^(3) x)/(1 + sin^(3) x) ])dx =
Answer» `(2)/(3) "COSH"^(-1) (sin" x")^((3)/(2) ) + c ` `(2)/(3) "SINH"^(-1) (sin" x")^((3)/(2)) + c ` `(2)/(3) "cosh"^(-1) (COS" x")^((3)/(2)) + c ` `(2)/(3) "sinh"^(-1) (cos" x")^((3)/(2)) + c ` Answer :B

Discussion

14.	Formthe polynomialwithrationalcoefficientswhoserootsare i- sqrt(5)
Answer» ANSWER :`x^4 -8x^2 +36=0`

Discussion

15.	The value of the expressionunderset(r=0)overset(n)Sigma overset(n)underset(p=0)Sigma""^(n)C_(r) ""^(r )C_(p)equals
Answer» `2^(n)-1` `3^(n)-1` `n+2^(-n)-1` `n-2^(n)-1` ANSWER :B

Discussion

16.	Find the smallest natural number n which has last digit 6 & if this last is moved to the front of the number, the number becomes 4 times larger.
Answer» ANSWER :153846

Discussion

17.	The solution of defferential equation (dy)/(dx) + x/y. (x^2 + y^2 - 1)/(2(x^2 + y^2) + 1)= 0is
Answer» `x^2 + y^2 + 3 LOG (x^2 + y^2) = C ` `x^2 + 3xy - 3 log (x^2 + y^2 + 2) = c ` `x^2 + 2y^2 - 3 log (x^2 + y^2 + 2) = c ` `-x^2 - 2y^2 - 3 log (x^2 + y^2)= c ` ANSWER :C

Discussion

18.	A map is laid out in the standared (x,y) coordinate plane. How long in units is an airplane's path on the map as the airplane files along a striaght line from city A located at (20,14) to City B located at (5,10)?
Answer» `SQRT(1,201)` `sqrt(241)` `sqrt(209)` `7` Answer :B

Discussion

19.	Use product{:[( 1,-1,2),( 0,2,-3),( 3,-2,4) ]:} {:[( -2,0,1),(9,2,-3),(6,1,-2) ]:}to solve the system of equations x-y+2z=1 2y-3z=1 3x-2y+4z =2
Answer» ANSWER :X= 0, y= 5 and z=3

Discussion

20.	The remainder obtained when1!+2!+3!+…….+100 ! Is divided by 12 ,si
Answer» 7 6 8 9 Answer :D

Discussion

21.	If cos x+ cos y=asin x+siny=b then prove that tan(x+y)=(2ab)/(a^(2)-b^(2))
Answer» ANSWER :`(2AB)/(a^(2)-B^(2))`

Discussion

22.	Consider the curves y = x^(2) and y^(2) = 8x. (i) Find the points of intersection of the given two curves. (ii) Find the area of the region enclosed by the given two curves
Answer» ANSWER :(i) (0, 0) and (2,4) (II)`(8)/(3)`sq.unit

Discussion

23.	If veca, vecb, vecc are three non-coplanar vectors, then the vectors equation vecr=(1-p-q) veca+p vecb+q vecc represents a
Answer» STRAIGHT line Plane Plane PASSING through the origin Sphere Answer :B

Discussion

24.	The negative of the statement "All continuous functions are differentiable".
Answer» Some CONTINUOUS FUNCTIONS are not differentiable All continuous functions are not differentiable All continuous functions are differentiable Some continuous functions aredifferentiable Answer :A

Discussion

25.	Find the volume of the solid formed by revolving the region bounded by the ellipse(x^(2))/(a^(2))+(y^(2))/(b^(2))=1,a>b about the major x-axis,
Answer» ANSWER :`(4piab^(2))/(3)`

Discussion

26.	If veca makes equal angles with hati, hatj and hatk and has magnitude 3, prove that the angle between veca and each of hati, hatj and hatk is cos^(-)(1/sqrt3).
Answer» Solution :GIVEN `alpha = beta = GAMMA` therefore `cos^2alpha+cos^2beta+cos^2gamma = 1` `IMPLIES 3cos^2alpha = 1 implies COSALPHA = +-1/sqrt3` therefore `alpha = cos^(-1) (+-1/sqrt3) = beta = gamma`

Discussion

27.	Find (dy)/(dx) in the following: y= tan^(-1) ((3x-x^(3))/(1-3x^(2))), \|x\| < (1)/(sqrt3)
Answer» ANSWER :`(3)/(1 + X^(2))`

Discussion

28.	Find the number of selections of one or more things from the group of p identical things of one type, q identical things of another type, r identical things of the third type and n different things.
Answer» Solution :SINCE NUMBER of ways of selecting r things out of n identical things =1 for al `r LE n`. Number of ways of selecting zero or more things out of p identical things = p+1 Similarly, number of ways of selecting zero or more things out of q and r identical things is q+1 and r+1 RESPECTIVELY. Also, number of ways of selecting zero or more things out of n different things `=2xx2xx2xx..` n times `=2^(n)` Therefore, total number of ways of selecting zero or more things out of all given things `=(p+1)(q+1)(r+1)2^(n)` But number of ways of selecting one or more things out of given things `=(p+1)(q+1)(r+1)2^(n)-1`.

Discussion

29.	The remainder of the polynomial f(x) when divided by x+1, x+2, x-2 are 6, 15, 3 the remainder of f(x) when divided by (x+1)(x+2)(x-2) is
Answer» `2X^(2)-3X+1` `3x^(2)-2x+1` `2x^(2)-x-3` `3x^(2)-2x+1` ANSWER :A

Discussion

30.	Prove thatint_(-a)^(a)f(x)dx={(2int_(0)^(a)f(x)dx ,"if f(x) is even function"),(0, "if f(x) is odd function"):} and hence evaluate int_(-(pi)/(2))^((pi)/(2))sin^(7)xdx
Answer» ANSWER :`int_(-(pi)/(2))^((pi)/(2))sin^(7)xdx =0`

Discussion

31.	If veca*vecb=\|vecaxxvecb\|, then angle between vector veca and vector vecb is :
Answer» pi/2 pi/6 pi/4 pi/3 Answer :C

Discussion

32.	Evaluation of definite integrals by subsitiution and properties of its : int_(-1)^(1)(dx)/((1+e^(x))(1+x^(2)))=...........
Answer» `(pi)/(2)` `(pi)/(4)` `(pi)/(8)` `(pi)/(16)` ANSWER :B

Discussion

33.	If \|vec(a)xx vec(b)\|=vec(a).vec(b) then find the angle between vec(a) and vec(b).
Answer» ANSWER :`(PI)/(4)`

Discussion

34.	If (a -a')^(2) + (b-b')^(2) + c-c')^(2) =p and (ab'-a'b)^(2)+ (bc'-b'c)^(2) + (ca'-c'a)^(2) =q, then the perpendicular distnce of the line ax + by + cz=1, a'x + b'y+c'z=1 from origin, is
Answer» <P>`SQRT ((p)/(Q))` `sqrt((q)/(p))` `(p)/(sqrtq)` `(q)/(SQRTP)` ANSWER :A

Discussion

35.	int(cos2x)/(cosx+sinx)dx
Answer» SOLUTION :`INT(COS2X)/(cosx+sinx)DX=int(cos^2x-sin^2x)/(cosx+sinx)dx` =`int(cosx-sinx)dx=sinx+cosx+C`

Discussion

36.	If A = [{:(1,1),(0,1):}] and I = [{:(1,0),(0,1):}], then for all n in N
Answer» `A ^(n) = NA` ` A ^(n) = nA + (n-1)L` `A ^(n) = (n -1) A -nl` `A ^(n)=nA - (n-1)l` Answer :D

Discussion

37.	The mean deviation about the median for the following data is
Answer» 13.57 14.29 15.18 17.23 Answer :B

Discussion

38.	A tower is standing in the centre of an elliptic field. If Adya observes that the angle of elevation of the top of the tower at an extremity of the major axis of the field is alpha, at its focus is beta and an extremity of the minor axis is gamma, then
Answer» `COT^(2) ALPHA = cot^(2) BETA - cot^(2) GAMMA` `cot^(2) beta = cot^(2) gamma - cot^(2) alpha` `cot^(2) gamma = cot^(2) alpha - cot^(2) beta` NONE of these Answer :C

Discussion

39.	If vec(a)=5hati-hatj+7hatk and vec(b)=hati-hatj+lambda hatk. If vec(a)+vec(b) and vec(a)-vec(b) are perpendicualr to each other then find the value of lambda.
Answer» ANSWER :`SQRT(75)`

Discussion

40.	The numberof real values of x that satisfies the equation x^(4)+4x^(3)+12x^(2)+7x-3=0 is
Answer» ANSWER :2

Discussion

41.	If P(overlineA) = 0.7, P(B) = 0.7 and P(B\|A) = 0.5, then P(AcupB )=
Answer» ANSWER :0.85

Discussion

42.	lim_(x rarr infty ) ( (6x^(2) - cos 3 x ) /(x^(2) + 5 ) - (5x^(3) + 3)/sqrt(x^(6) + 2) ) =
Answer» 11 0 -1 1 Answer :A

Discussion

43.	Consider all function f: {1,2,3,4} to {1,2,3,4} which are one-one, onto and satisfy the following property : If f (k) is odd then f (k+1) is even, K=1,2,3. The number of such function is :
Answer» 4 8 12 16 Answer :C

Discussion

44.	Find the domain and range of the following function: f(x)=sqrt(log_(1//2)log_(2)[x^(2)+4x+5]) where [.] denotes the greatest integer function
Answer» SOLUTION :NA

Discussion

45.	The straight line x + y + 1 = 0 bisects an angle between the pair of lines of which one is 2x + 3y - 4 = 0. Then, the equation of the other line is
Answer» 3X - 2y + 5 =0 3x - 2y - 9 = 0 3x + 2y + 9 = 0 x-y-1=0 Answer :C

Discussion

46.	Evaluate int_(0)^(100)[tan^(-1)x] dx where [ ]denotes the GIF
Answer» ANSWER :`100-tan 1`

Discussion

47.	The lim_(xrarr0) x^(8)[(1)/(x^(3))] (where [x]is the greatest integer function) is
Answer» a non-zero REAL NUMBER a rational number an integer zero Answer :B,C,D

Discussion

48.	The maximum and minimum values of p^(2)+q^(2)-14q-6q+57 if p^(2)+4q^(2)=24q-AA p, q in R , are l_(1) and l_(2) resepectively then,
Answer» `(l_(1))/(l_(2))=(10)/(3)` `l_(1)l_(2)=30` `l_(1)-l_(E)=14` `l_(1)+l_(2)=104` Answer :A::D

Discussion

49.	If (3, -4) and (-6,5) are the extremities of the diagonal of a parallelogram and (-2, 1) is its third vertex, then the fourth vertex is
Answer» (-1,2) (-1, -2) (2,1) (-1,0) Answer :D

Discussion

50.	If int(x^(2)+37)/(x^(4)-3x^(2)-28)dx=a log((x-sqrt7)/(x+sqrt7))+b tan^(-1)((x)/(2))+c, then (a, b)-=
Answer» `((2)/(SQRT7),(2)/(3))` `((sqrt7)/(2),(3)/(2))` `((sqrt7)/(2),(-3)/(2))` `((2)/(sqrt7),(-3)/(2))` ANSWER :D

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Solve the following equations : 2tan^(-1)(cosx)=tan^(-1)(2cosecx)

Discuss the continuity of the function f given by f(x)= {(x",","if " x gt 0),(x^(2)",","if " x lt 0):}

A point P moves inside a triangle formed by A(0,0),B(1,1/sqrt(3)),C(2,0) such that min {PA,PB,PC)=1, then the area bounded by the curve traced by P, is

Are the following sets relation ? A xx B from A to B.Determine the domain and range of each of the relations mentioned above.

Find the value of the following integral int_(0)^((pi)/(2)) sin^(9) x dx

The transformed equation of x^(4) + 2x^(3) - 12x^(2) + 2x - 1= 0by eliminating third term is

The mid point of the chord 4x-3y=5 of the hyperbola 2x^(2)-3y^(2)=12 is

If f(x) = sin theta. x + a and the equatio f(x) = f^(-1)(x) is satisfied by every real value of x, then

Evaluate the following inegrals int cossecx log(cosecx - cotx)dx

If I=int_(0)^(pi//2)sin 2n x log cos x dx. Then l is same as

Find dy/dx if y^2 = a^(sqrt x)

Evaluate the following integrals int[log(logx)+(1)/((logx)^(2))]dx

If x in (0, (pi)/(2)) " then " int sqrt([(sin x - sin^(3) x)/(1 + sin^(3) x) ])dx =

Formthe polynomialwithrationalcoefficientswhoserootsare i- sqrt(5)

The value of the expressionunderset(r=0)overset(n)Sigma overset(n)underset(p=0)Sigma""^(n)C_(r) ""^(r )C_(p)equals

Find the smallest natural number n which has last digit 6 & if this last is moved to the front of the number, the number becomes 4 times larger.

The solution of defferential equation (dy)/(dx) + x/y. (x^2 + y^2 - 1)/(2(x^2 + y^2) + 1)= 0is

A map is laid out in the standared (x,y) coordinate plane. How long in units is an airplane's path on the map as the airplane files along a striaght line from city A located at (20,14) to City B located at (5,10)?

Use product{:[( 1,-1,2),( 0,2,-3),( 3,-2,4) ]:} {:[( -2,0,1),(9,2,-3),(6,1,-2) ]:}to solve the system of equations x-y+2z=1 2y-3z=1 3x-2y+4z =2

The remainder obtained when1!+2!+3!+…….+100 ! Is divided by 12 ,si

If cos x+ cos y=asin x+siny=b then prove that tan(x+y)=(2ab)/(a^(2)-b^(2))

Consider the curves y = x^(2) and y^(2) = 8x. (i) Find the points of intersection of the given two curves. (ii) Find the area of the region enclosed by the given two curves

If veca, vecb, vecc are three non-coplanar vectors, then the vectors equation vecr=(1-p-q) veca+p vecb+q vecc represents a

The negative of the statement "All continuous functions are differentiable".

Find the volume of the solid formed by revolving the region bounded by the ellipse(x^(2))/(a^(2))+(y^(2))/(b^(2))=1,a>b about the major x-axis,

If veca makes equal angles with hati, hatj and hatk and has magnitude 3, prove that the angle between veca and each of hati, hatj and hatk is cos^(-)(1/sqrt3).

Find (dy)/(dx) in the following: y= tan^(-1) ((3x-x^(3))/(1-3x^(2))), |x| < (1)/(sqrt3)

Find the number of selections of one or more things from the group of p identical things of one type, q identical things of another type, r identical things of the third type and n different things.

The remainder of the polynomial f(x) when divided by x+1, x+2, x-2 are 6, 15, 3 the remainder of f(x) when divided by (x+1)(x+2)(x-2) is

Prove thatint_(-a)^(a)f(x)dx={(2int_(0)^(a)f(x)dx ,"if f(x) is even function"),(0, "if f(x) is odd function"):} and hence evaluate int_(-(pi)/(2))^((pi)/(2))sin^(7)xdx

If veca*vecb=|vecaxxvecb|, then angle between vector veca and vector vecb is :

Evaluation of definite integrals by subsitiution and properties of its : int_(-1)^(1)(dx)/((1+e^(x))(1+x^(2)))=...........

If |vec(a)xx vec(b)|=vec(a).vec(b) then find the angle between vec(a) and vec(b).

If (a -a')^(2) + (b-b')^(2) + c-c')^(2) =p and (ab'-a'b)^(2)+ (bc'-b'c)^(2) + (ca'-c'a)^(2) =q, then the perpendicular distnce of the line ax + by + cz=1, a'x + b'y+c'z=1 from origin, is

int(cos2x)/(cosx+sinx)dx

If A = [{:(1,1),(0,1):}] and I = [{:(1,0),(0,1):}], then for all n in N

The mean deviation about the median for the following data is

A tower is standing in the centre of an elliptic field. If Adya observes that the angle of elevation of the top of the tower at an extremity of the major axis of the field is alpha, at its focus is beta and an extremity of the minor axis is gamma, then

If vec(a)=5hati-hatj+7hatk and vec(b)=hati-hatj+lambda hatk. If vec(a)+vec(b) and vec(a)-vec(b) are perpendicualr to each other then find the value of lambda.

The numberof real values of x that satisfies the equation x^(4)+4x^(3)+12x^(2)+7x-3=0 is

If P(overlineA) = 0.7, P(B) = 0.7 and P(B|A) = 0.5, then P(AcupB )=

lim_(x rarr infty ) ( (6x^(2) - cos 3 x ) /(x^(2) + 5 ) - (5x^(3) + 3)/sqrt(x^(6) + 2) ) =

Consider all function f: {1,2,3,4} to {1,2,3,4} which are one-one, onto and satisfy the following property : If f (k) is odd then f (k+1) is even, K=1,2,3. The number of such function is :

Find the domain and range of the following function: f(x)=sqrt(log_(1//2)log_(2)[x^(2)+4x+5]) where [.] denotes the greatest integer function

The straight line x + y + 1 = 0 bisects an angle between the pair of lines of which one is 2x + 3y - 4 = 0. Then, the equation of the other line is

Evaluate int_(0)^(100)[tan^(-1)x] dx where [ ]denotes the GIF

The lim_(xrarr0) x^(8)[(1)/(x^(3))] (where [x]is the greatest integer function) is

The maximum and minimum values of p^(2)+q^(2)-14q-6q+57 if p^(2)+4q^(2)=24q-AA p, q in R , are l_(1) and l_(2) resepectively then,

If (3, -4) and (-6,5) are the extremities of﻿ the diagonal of a parallelogram and (-2, 1)﻿ is its third vertex, then the fourth vertex is﻿

If int(x^(2)+37)/(x^(4)-3x^(2)-28)dx=a log((x-sqrt7)/(x+sqrt7))+b tan^(-1)((x)/(2))+c, then (a, b)-=

If (3, -4) and (-6,5) are the extremities of the diagonal of a parallelogram and (-2, 1) is its third vertex, then the fourth vertex is