28278 + Interview Questions in Maths in Class 12

1.	Let the number of elements of the sets A and B be p and q respectively. Then the number of the relations from the set A to the set B is
Answer» `2^(p+q)` `2^(PQ)` p+q pq Answer :B

Discussion

2.	If (a_(1)+ib_(1))(a_(2)+ib_(2))….(a_(n)+ib_(n))=A+iB, then (a_(1)^(2)+b_(1)^(2))(a_(2)^(2)+b_(2)^(2))…..(a_(n)^(2)+b_(n)^(2)) is equal to
Answer» 1 `A^(2)+B^(2)` `A+B` `1/(A^(2))+1/(B^(2))` ANSWER :B

Discussion

3.	(d)/(dx) (e^(sin^(-1)x + cos^(-1) x))= …….(\|x\| lt 1)
Answer» `(2)/(sqrt(1-X^(2)))` 0 `(1)/(sqrt(1-x^(2)))` `E^(sin^(-1) x + COS^(-1) x)` Answer :B

Discussion

4.	Find the area enclosed by the curve y=3x and y=6x-x^(2)
Answer» ANSWER :`(9)/(2)`

Discussion

5.	The points 2i + j + k, 6i - j + 2k, 14i - 5j + 4k are
Answer» COLLINEAR COPLANAR but not collinear noncoplanar none Answer :A

Discussion

6.	If a line makes angles alpha,beta,lambda,delta with the 4 diagonals of a cube then sin^(2) alpha + sin^(2)beta+sin^(2)lambda+sin^(2)delta
Answer» `(4)/(3)` `(8)/(3)` `(7)/(3)` `(5)/(3)` ANSWER :B

Discussion

7.	If A=[{:(1,3,3),(1,4,3),(1,3,4):}] , then verify that A adjA=\|A\|I. Also find A^(-1)
Answer» ANSWER :`A^(-1)=[{:(7,-3,-3),(-1,1,0),(-1,0,1):}]`

Discussion

8.	find all the points of discontinuity of the function f(x) defined by {:{(x+1, if x lt 1), (1 , if x =1), (x-1, if x gt1):}
Answer» Solution :The function f is defined at all points of the real line. Case I : Let x=c be any ARBITRARY point in the domain of f(x) ifc lt 1 , f(c)=c+1 , therefore `underset(x to c) lim f(x) = underset(x to c) lim (x+1) = c+1` Thus, f is continuous at all real numbers less than 1. Case II : If cgt 1 , then f(c) = c -1 , therefore `underset(x to c)lim f(x)= underset(x to c) lim (x -1) = c-1 = f(c)` Thus f is continuous at all point x gt 1 Case III. C =1 , the left hand LIMIT of f(x) at x =1 is ` underset(x to 1^(-)) lim f(x) = underset(x to 1^(-)) lim (x +1) = 1 + 1 = 2 ` The right hand limit of f at x =1 is ` underset(x to 1^(+)) lim f(x) = underset(x to 1^(+)) lim (x-1) = (1-1) =0` Since, the left and right hand limits of f at x =1 do not coincide, f is not continuous at x =1, Hence, x =1 is the only point of DISCONTINUITY of f. The graph of the function is as SHOWN.

Discussion

9.	A point P is taken at random on a straight line AB. The chance that the greater of the parts AP and PB is at least k times the smaller is
Answer» `2/(k+1)` `2/(k+2)` `2/(K^2+1)` `2/(K^2+2)` ANSWER :D

Discussion

10.	If omega = sqrt(z^(2) - 1) where omega is a cube root of unity and z = x +iy then (1)/(2)[Tan^(-1) ((y)/(x + 1)) + Tan^(-1) ((y)/(x-1))]
Answer» `(pi)/(2)` `(pi)/(6)` `(pi)/(3)` `(pi)/(4)` Answer :B

Discussion

11.	If for every ineger n , int_(n)^(n+1) f(x) dx=n^(2) then the value of int_(-2)^(4) f(x)dx=
Answer» 13 15 17 19 Answer :D

Discussion

12.	Show that one value of((1+sin""pi/8+i cos ""pi/8)/(1+sin"" pi/8-i cos"" pi/8))^(8/3)=-1
Answer»

Discussion

13.	Find all common tangents of the pairs of circles x^(2)+y^(2) =0 and x^(2) +y^(2) -16x -2y +49=0
Answer» ANSWER :`y-2 =0, y-3 =0 , x-1 =0,3x +4Y -5=0`

Discussion

14.	Lt_(ntooo)[(1^(3))/(n^(4)+1^(4))+(2^(3))/(n^(4)+2^(4))+.........+(1)/(2n)]=
Answer» `1/4 LOG 4` `1/2 log 2` `1/4 log 2` `1/4 log 2` ANSWER :D

Discussion

15.	If f:R-{3/5} rarr Rbe defined by f(x) = (3x+2)/(5x-3) , then .........
Answer» `F^(-1)(x)=f(x)` `f^(-1)(x) =-f(x)` `"fof"(x) =-x` `f^(-1)(x) = 1/(19)f(x)` Solution :N/A

Discussion

16.	The vertices of triangleABC lie on a rectangular hyperbola such that the orhtocentre of the triangle is (2 3) and the asymptotes of the rectangular hyperbola are parallel to the coordinate axes. The two perpendicular tangents of the hyperbola intersect at the point (1, 1). Q. The equation of the asymptotes is
Answer» `xy-1=y-x` `xy+1=x+y` `xy-1=x-y` `xy+1=-x-y` ANSWER :B

Discussion

17.	Draw the graph of function y = \|2-\|x-2\|\|.
Answer»

Discussion

18.	Find the equation of plane passing through the line of intersectionof planes3x+4y-4=0 and x+7y+3z=0 and also through origin.
Answer» ANSWER :`5x+18y+6z=0

Discussion

19.	If int(f(x))/(1-x^(3))dx=log\|(x^(2)+x+1)/(x-1)\|+(A)/(sqrt(3))tan^(-1)(2x+1)/(sqrt(3))+C then A is equal to , where f(x) is a polynomial of second degree in x suh that f(0) = f(1)=3f(2)=3.(sqrt(3)=1.73)
Answer» ANSWER :`1.16`

Discussion

20.	Which of the following is concave down:
Answer» `y = -X^(2)` `y = x^(2)` `y = e^(x)` `y = x^(2) + 2X -3` Answer :A

Discussion

21.	underset(x rarr 0)(lim) (a^(x) - b^(x))/(c^(x) - d^(x)) is
Answer» `OO` 0 `LOG ((ab)/(CD))` `(log ((a)/(b)))/(log ((C )/(d)))` Answer :D

Discussion

22.	Find (dy)/(dx), if y+siny=cosx, " where "y ne (2n+1)pi
Answer» ANSWER :`(DY)/(DX)=(-SINX)/(1+cosy)`

Discussion

23.	Differentiate the following functions with respect to x: x^(2) + y^(2) = xy
Answer» ANSWER :`(y-2x)/(2y-x)`

Discussion

24.	The vertices of triangleABC lie on a rectangular hyperbola such that the orhtocentre of the triangle is (2 3) and the asymptotes of the rectangular hyperbola are parallel to the coordinate axes. The two perpendicular tangents of the hyperbola intersect at the point (1, 1). Q.The equation of the rectangular hyperbola is
Answer» `xy-5=y-x` `xy-1=x+y` `xy=x+y+1` `xy-11=-x-y` ANSWER :C

Discussion

25.	The vertices of triangleABC lie on a rectangular hyperbola such that the orhtocentre of the triangle is (2 3) and the asymptotes of the rectangular hyperbola are parallel to the coordinate axes. The two perpendicular tangents of the hyperbola intersect at the point (1, 1). Q. The number of real tangents that can be drawn from the point (1, 1) to the rectangular hyperbola is
Answer» `0` `2` `3` `4` ANSWER :B

Discussion

26.	If the number of aircraft, vehicles, and other conveyances was 572,000 in 1995, what was the approximate percentage increase from 1995 to 2000?
Answer» `37%` `32%` `27%` `20%` ANSWER :A

Discussion

27.	The polar of p with respect to a circle s=x^(2)+y^(2)+2gx+2fy+c=0 with centre C is
Answer» PARALLEL to the TANGENT at P Parallel to CP Perpendicular to CP Perpendicular to the tangent at P Answer :C

Discussion

28.	If x satisfies the equation x^(2)( int_(0)^(1) (dt)/(t^(2)+ 2t cos alpha+1))-x(int_(-3)^(3)(t^(2)+sin 2 t)/(t^(2)+1))-2=0 (0 lt alpha pi), then the valueof x, is
Answer» `+-2sqrt((SIN ALPHA)/(alpha))` `+-SQRT((sin alpha)/(alpha))` `+-4sqrt((sin alpha)/(alpha))` NONE of these ANSWER :A

Discussion

29.	A=cos 20^(@)cos 40^(@) cos60^(@)cos 80^(@), B=cos6^(@)cos42^(@)cos66^(@)cos78^(@) and C=cos 36^(@)cos72^(@)cos 108^(@)cos 144^(@) then
Answer» `AGTBGTC` `BgtCgtA` `CgtAgtB` `A=B=C` ANSWER :D

Discussion

30.	There are four machines and it is known that exactly two of them are faulty . Theyare tested one by one , in a random order till both the faulty machines are identified . Then , the probability that only two tests are needed is ,
Answer» `1/3` `1/6` `1/2` `1/4` ANSWER :A

Discussion

31.	The points (5, 2, 4), (6,-1, 2) and (8, -7, k) are collinear if k is equal to :
Answer» 2 `-1` 3 `-2` ANSWER :D

Discussion

32.	A triangle with vertices (4, 0), (-1, -1), (3, 5) is
Answer» ISOSCELES and RIGHT ANGLED isosceles but not right angled right angled but not isosceles neither right angled nor isosceles Answer :A

Discussion

33.	IF [x] is the greatest integer less than or equal to x and IxI is the modulus of x, then the system of three equations 2x+3\|y\|+5[z]=0,x+\|y\|-2[z]=4, z+\|y\|+[z]=1 has
Answer» a UNIQUE solution finitely MANY solutions infinitely many solutions no solution Answer :C

Discussion

34.	Find the adjoint of B=[[1,-1,2],[2,3,5],[-2,0,1]]
Answer» SOLUTION :ADJ B=[[3,1,11],[-12,5,-1],[6,2,5]]

Discussion

35.	Evaluate the following definite integrals : int_(1)^(2)(xdx)/((x+1)(x+2))
Answer» ANSWER :`LOG((32)/(27))`

Discussion

36.	10 beggars are sitting in a row. The number of ways in which a person having 4 one rupec coins (like), and 6 two rupee coins (like), can give away all coins to them so that each gets one coin and no two adjacent beggars will get one rupee coins. (Hint : By calling one rupee coin as A and two rupee coin as B, we have to arrange AAAABBBBBB so that no two A's are together)
Answer» ANSWER :`("^7P_4)/(4!)`

Discussion

37.	If in a Delta ABC, O and O' are the incentre and orthocentre respectively, then (O' A+O'B +O'C) is equal to
Answer» `2O' O` `O' O` `OO'` `2 OO'` SOLUTION :Here, `O'A =O'O+OA,` `O'B=O'O+OB and O'C =O'O +OC` `therefore O'A+O'B+O'C=3O'O+(OA+OB+OC)""…(i)` `because OA+OB+OC=O O' =-O'O` `therefore O'A+O'B+O'C =3O'O-O'O` [from EQ.(i)] `implies O'A+O'B+O'C=2O'O`

Discussion

38.	Can the inverse of the following matric be found ? [[1,2],[3,4]]
Answer» SOLUTION :`ABSA =4-6=-2 NE 0` `THEREFORE A^-1` EXISTS.

Discussion

39.	For given vectors veca=2hati-hatj+2hatkandvecb=-hati+hatj-hatk, find theunit vector in thedirection of the vector veca+vecb.
Answer» Answer :`(1)/(sqrt(2))HATI+(1)/(sqrt(2))HATK`

Discussion

40.	Find the angles which the vector vec(a)=hati-hatj+sqrt(2)hatk makes with the co-ordinate axes.
Answer» ANSWER :`(PI)/(3),(2PI)/(3),(pi)/(4)`

Discussion

41.	The value of hati.(hatj xx hatk)+hatj.(hati xx hatk)+hatk.(hati xx hatj) is ……..
Answer» 0 `-1` 1 3 Answer :C

Discussion

42.	If (f(x))^(n) = f(nx), find (f'(nx))/(f'(x)).
Answer» SOLUTION :F(NX) = `[f(X)]^nrArrf(nx)n=n[f(x)^(n-1)f(x)RARR(f(nx))/(f(x))=[f(x)]^(n-1)=f((n-1)x)`

Discussion

43.	Choose the correct answer The value of the integral int_(1/3)^(1)((x-x^(3))^(1/3))/(x^(4))dx is
Answer» 6 0 3 4 Answer :A

Discussion

44.	6 boys and 6 girls are randomly divided into two equal groups. Find the probability that each group contains same number of boys and girls.
Answer» ANSWER :`(100)/(231)`

Discussion

45.	Solve the following differential equation:(x+tan y)dy = sin 2y dx
Answer» SOLUTION :N/A

Discussion

46.	Which of thefollowing are not dependent on the intensity of the incident radiation in a photoelectric experiment ?
Answer» Amount of photoelectric current Stopping POTENTIAL to reduce the photoelectriccurrent to zero Work FUNCTION of the MAXIMUM kinetic energyof photoelectrons Solution :Intensity INCREASES no. of photon coming on plates therefore it wouldn't change stopping potential work function maximum K.E.

Discussion

47.	If 2a + 3b + 6c + 0 (a,b,c in R) then the quadractic equation ax^(2) + bx + c =0 has
Answer» at LEAST ONE ROOT in [0,1] at least one root in [2,3] at least one root NONE of these Answer :A

Discussion

48.	Statement 1: In a triangle ABC , If base BC is fixed and perimeter of the triangle is constant, then vertex A moves on an Ellipse. Statement 2: If the sum of distances of a point P from two fixed points is constant then locus of P is a real ellipse
Answer» Both the STATEMENT are TRUE and statement 2 is the correct explanation of statement 1 Both the statement are True but Statement 2 is Not the correct explanation of Statement 1 Statement 1 is True and Statement 2 is false Statement 1 is false and statement 2 is true. Answer :C

Discussion

49.	If a plane cuts intercepts -6,3,4 on the co-ordinate axes, then the length of the perpendicular form the origin to the plane is
Answer» `(1)/(sqrt(61))` `(13)/(sqrt(61))` `(12)/(sqrt(29))` `(5)/(sqrt(41))` Answer :C

Discussion

50.	Consider a binary opertion on the set {1,2,3,4,5} given by the following multiplication table (Table 1.2) (i) Compute (2 3) 4 and 2 (34) (ii) Is commutative ? (iii) Compute (2 3) (4 **5).
Answer» ANSWER :(i) ` (2 3) 4=1 and 2 (3 4) =1 ` (II) Yes (iii) 1

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Let the number of elements of the sets A and B be p and q respectively. Then the number of the relations from the set A to the set B is

If (a_(1)+ib_(1))(a_(2)+ib_(2))….(a_(n)+ib_(n))=A+iB, then (a_(1)^(2)+b_(1)^(2))(a_(2)^(2)+b_(2)^(2))…..(a_(n)^(2)+b_(n)^(2)) is equal to

(d)/(dx) (e^(sin^(-1)x + cos^(-1) x))= …….(|x| lt 1)

Find the area enclosed by the curve y=3x and y=6x-x^(2)

The points 2i + j + k, 6i - j + 2k, 14i - 5j + 4k are

If a line makes angles alpha,beta,lambda,delta with the 4 diagonals of a cube then sin^(2) alpha + sin^(2)beta+sin^(2)lambda+sin^(2)delta

If A=[{:(1,3,3),(1,4,3),(1,3,4):}] , then verify that A adjA=|A|I. Also find A^(-1)

find all the points of discontinuity of the function f(x) defined by {:{(x+1, if x lt 1), (1 , if x =1), (x-1, if x gt1):}

A point P is taken at random on a straight line AB. The chance that the greater of the parts AP and PB is at least k times the smaller is

If omega = sqrt(z^(2) - 1) where omega is a cube root of unity and z = x +iy then (1)/(2)[Tan^(-1) ((y)/(x + 1)) + Tan^(-1) ((y)/(x-1))]

If for every ineger n , int_(n)^(n+1) f(x) dx=n^(2) then the value of int_(-2)^(4) f(x)dx=

Show that one value of((1+sin""pi/8+i cos ""pi/8)/(1+sin"" pi/8-i cos"" pi/8))^(8/3)=-1

Find all common tangents of the pairs of circles x^(2)+y^(2) =0 and x^(2) +y^(2) -16x -2y +49=0

Lt_(ntooo)[(1^(3))/(n^(4)+1^(4))+(2^(3))/(n^(4)+2^(4))+.........+(1)/(2n)]=

If f:R-{3/5} rarr Rbe defined by f(x) = (3x+2)/(5x-3) , then .........

Draw the graph of function y = |2-|x-2||.

Find the equation of plane passing through the line of intersectionof planes3x+4y-4=0 and x+7y+3z=0 and also through origin.

If int(f(x))/(1-x^(3))dx=log|(x^(2)+x+1)/(x-1)|+(A)/(sqrt(3))tan^(-1)(2x+1)/(sqrt(3))+C then A is equal to , where f(x) is a polynomial of second degree in x suh that f(0) = f(1)=3f(2)=3.(sqrt(3)=1.73)

Which of the following is concave down:

underset(x rarr 0)(lim) (a^(x) - b^(x))/(c^(x) - d^(x)) is

Find (dy)/(dx), if y+siny=cosx, " where "y ne (2n+1)pi

Differentiate the following functions with respect to x: x^(2) + y^(2) = xy

If the number of aircraft, vehicles, and other conveyances was 572,000 in 1995, what was the approximate percentage increase from 1995 to 2000?

The polar of p with respect to a circle s=x^(2)+y^(2)+2gx+2fy+c=0 with centre C is

If x satisfies the equation x^(2)( int_(0)^(1) (dt)/(t^(2)+ 2t cos alpha+1))-x(int_(-3)^(3)(t^(2)+sin 2 t)/(t^(2)+1))-2=0 (0 lt alpha pi), then the valueof x, is

A=cos 20^(@)cos 40^(@) cos60^(@)cos 80^(@), B=cos6^(@)cos42^(@)cos66^(@)cos78^(@) and C=cos 36^(@)cos72^(@)cos 108^(@)cos 144^(@) then

There are four machines and it is known that exactly two of them are faulty . Theyare tested one by one , in a random order till both the faulty machines are identified . Then , the probability that only two tests are needed is ,

The points (5, 2, 4), (6,-1, 2) and (8, -7, k) are collinear if k is equal to :

A triangle with vertices (4, 0), (-1, -1), (3, 5)﻿ is﻿

IF [x] is the greatest integer less than or equal to x and IxI is the modulus of x, then the system of three equations 2x+3|y|+5[z]=0,x+|y|-2[z]=4, z+|y|+[z]=1 has

Find the adjoint of B=[[1,-1,2],[2,3,5],[-2,0,1]]

Evaluate the following definite integrals : int_(1)^(2)(xdx)/((x+1)(x+2))

If in a Delta ABC, O and O' are the incentre and orthocentre respectively, then (O' A+O'B +O'C) is equal to

Can the inverse of the following matric be found ? [[1,2],[3,4]]

For given vectors veca=2hati-hatj+2hatkandvecb=-hati+hatj-hatk, find theunit vector in thedirection of the vector veca+vecb.

Find the angles which the vector vec(a)=hati-hatj+sqrt(2)hatk makes with the co-ordinate axes.

The value of hati.(hatj xx hatk)+hatj.(hati xx hatk)+hatk.(hati xx hatj) is ……..

If (f(x))^(n) = f(nx), find (f'(nx))/(f'(x)).

Choose the correct answer The value of the integral int_(1/3)^(1)((x-x^(3))^(1/3))/(x^(4))dx is

6 boys and 6 girls are randomly divided into two equal groups. Find the probability that each group contains same number of boys and girls.

Solve the following differential equation:(x+tan y)dy = sin 2y dx

Which of thefollowing are not dependent on the intensity of the incident radiation in a photoelectric experiment ?

If 2a + 3b + 6c + 0 (a,b,c in R) then the quadractic equation ax^(2) + bx + c =0 has

Statement 1: In a triangle ABC , If base BC is fixed and perimeter of the triangle is constant, then vertex A moves on an Ellipse. Statement 2: If the sum of distances of a point P from two fixed points is constant then locus of P is a real ellipse

If a plane cuts intercepts -6,3,4 on the co-ordinate axes, then the length of the perpendicular form the origin to the plane is

Consider a binary opertion ** on the set {1,2,3,4,5} given by the following multiplication table (Table 1.2) (i) Compute (2 **3) **4 and 2 ** (3**4) (ii) Is ** commutative ? (iii) Compute (2 **3) ** (4 **5).

A triangle with vertices (4, 0), (-1, -1), (3, 5) is

Consider a binary opertion on the set {1,2,3,4,5} given by the following multiplication table (Table 1.2) (i) Compute (2 3) 4 and 2 (34) (ii) Is commutative ? (iii) Compute (2 3) (4 **5).