28278 + Interview Questions in Maths in Class 12

1.	If x > 0 , y > 0 , z > 0 , xy+yz+zx < 1 and if tan^(-1)x+tan^(-1)y + tan^(-1)z=pi,then x+y+z equals to
Answer» 0 XYZ 3xyz `SQRT(xyz)` ANSWER :B

Discussion

2.	The vector equation of line passing through (2,-1,1) and parallel to the line barr=3hati-hatj+2hatk+lambda(2hati+7hatj-3hatk) is
Answer» `barr=2hati-hatj+hatk+lambda(3hati-hatj+2hatk)` `barr=3hati-hatj+2hatk+lambda(2hati-hatj+hatk)` `barr=2hati-hatj+hatk+lambda(2hati+7hatj-3hatk)` `barr=2hati-hatj+hatk+lambda(3hati-hatj+2hatk)` ANSWER :C

Discussion

3.	Find lambdaandmu if (2hati+6hatj+27hatk)xx(hati+lambdahatj+muhatk)=vec0.
Answer» ANSWER :`3,(27)/(2)`

Discussion

4.	Find theanglebetweentwo lineswhosedirection ratiosare "(i) 2,1,2 and4,8,1""""(ii) 5 ,-12 ,13 and -3,4,5" "(iii) 1 ,1,2 and" (sqrt(3)-1) ,(-sqrt(3)-1),4 """(iv)a,b,c and(b-c) ,(c-a),(a-b)"
Answer» Answer :`cos^(-1) ((2)/(3))(ii) cos^(-1) ((1)/(65)) (III) (pi)/(3) (iv)(pi)/(2) `

Discussion

5.	lim_(x to 2)((cos alpha)^(x) + (sin alpha)^(x)-1)/(x-2)=
Answer» `(COS^(2) ALPHA) ln cos alpha + (SIN^(2) alpha)ln sin alpha` 1 `ln((cos alpha)(sin alpha))` `ln((sin^(2) alpha) xx (cos^(2) alpha))` SOLUTION :`lim_(x to 2)((cos alpha)^(x) + (sin alpha)^(x) - sin^(2) alpha - cos^(2) alpha)/(x-2)` `lim_(x to 2) cos^(2) alpha ([cos^(x-2) alpha-1])/(x-2) + sin^(2)alpha ([sin^(x-2) alpha-1])/(x-2)` `cos^(2) alpha.ln cos alpha + sin^(2) alpha ln sin alpha`

Discussion

6.	Find the values of the following integrals (ii) int_(0)^(pi/2) sin^(4) x cos^(6) x dx
Answer» ANSWER :`(3PI)/(512)`

Discussion

7.	A person secures a job in a construction companyin which the probability that the workers go on strike is 0.65 and the probability that the construction job will be completed on time if there is no strike is 0.80. If the probability that the construction job will be completed on time even if there is a strike is 0.32, determine the probability that the constructed job will be completed on time.
Answer» ANSWER :0.488

Discussion

8.	A ray of light coming along the line (x - 1)/(1) = (y - 2)/(2) = (z - 3)/(3), strikes the plane mirror kept along the plane through points (2, 1, 1), (3, 0, 2) and(2 , -1, -2) . Then the equation of reflected ray is:
Answer» `(x - 3)/(1) = (y - 3)/(5) = (z - 2)/(-5)` `(x - 3)/(1) = (y - 3)/(5) = (z - 2)/(10)` `(x - 1)/(1) = (y - 2)/(5) = (z - 2)/(-5)` `(x - 3)/(1) = (y - 2)/(5) = (z - 2)/(10)` Solution :equation of plane `\|(x-2,y-1,z-1),(0,2,2),(1,1,1)\|=0` `2x+y-z-4=0` POINT on the line `(x-1)/(1)=(y-2)/(2)=(z-3)/(3)=R` Point on the line `(x-1)/(1)=(y-2)/(2)=(z-3)/(3)=r` is (1, 2, 3) Reflection of `(1, 2, 3)` in the plane `(x_(1)-1)/(2)=(y_(1)-2)/(1)=(z_(1)-3)/(-1)=(-2(2+2-3-4))/((2)^(2)+(1)^(2)+(-1)^(2))` `(x_(1)-1)/(2)=(y_(1)-2)/(1)=(z_(1)-3)/(-1)=(6)/(6)` `x_(1)=3` `y_(1)=3"(3, 3, 2)"` `z_(1)=2` Point of INTERSECTION of line and plane `2(1+r)+1(2+2r)-(3+3r)-4=0` `r=3` Point of intersection (4, 8, 12) Equation of line of reflection `(x-3)/(4-3)=(y-3)/(8-3)=(z-2)/(12-2),(-3)/(1)=(y-3)/(5)=(z-2)/(10)`

Discussion

9.	If y=(gof)(x)then dy/dx=______.
Answer» (DG)/dxdx/(DF) (dg)/(df)(df)/DX (df)/dxdx/(dg) (df)/(dg)(dg)/dx Answer :B

Discussion

10.	If y = (5x)^(3 cos 2x) find (dy)/(dx)
Answer» Answer :`(5x)^(3 cos 2X)[(3 cos 2x)/(X)-6 SIN 2x LOG 5x]`

Discussion

11.	If If A+B+C=pi then prove that "sin"A^(2)/2+"sin"^(2)B/2-"sin"^(2)C/2=1-2"cos"A/2"cos"B/2"sin"C/
Answer» ANSWER :RHS

Discussion

12.	Let f(t)=\|t-1\|-\|t\|+\|t+1\|, AA t in R. Find g(x) = max {f(t):x+1letlex+2}, AA x in R. Find g(x) and the area bounded by the curve y=g(x), the X-axis and the lines x=-3//2 and x=5.
Answer» Answer :`G(X)={(-x-1,x <=-5//2),(4+x,-5//2 -1//2):}` and area = `101/4` SQ units.

Discussion

13.	Find the principle value of the followingtan^(-1)(-sqrt3)
Answer» SOLUTION :`TAN(-pi/3)=-tan(pi/3)=-SQRT3 `and `-pi/3 in (-pi/2,pi/2)` `THEREFORE` The principal value of `tan^(-1)(-sqrt3)=-pi/3`

Discussion

14.	In a betting game in an exihibition two dice P and Q are being used. Dice P has four red faces and two white faces whereas dice Q has two red and four white faces. A fair coin is tossed once. If it shows head the game continues by throwing dice P .if it tail dice Q is thrown. If first n throws of the die all turn up red, then the proabability that P is being used is
Answer» `(1)/(2)` `(N)/(2^n +1)` `(2^n)/(2^n +1)` `(2)/(3)`. ANSWER :C

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15.	Evaluate the integral as limit of sum: int_(0)^(pi)sinxdx
Answer» ANSWER :2

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16.	The solution of the cosec^(2x)(dy)/(dx) - (1)/(y) = 0 is
Answer» `2Y^(2) = 2X - sin 2x + C` `2y^(2) = x - sin 2x` `2y^(2) = 2x + sin 2x + c` `2y^(2) = x + sin 2x + c` ANSWER :A

Discussion

17.	A rectangle ABCD is inscribed in a circle with a diameter lying along the line 3y=x+10. If A=(-6,7), B=(4,7) then the area of the rectangle is
Answer» 80 SQ. units 40 sq. units 160 sq. units 20 sq. units Answer :A

Discussion

18.	The value of lim _(xtopi) (sqrt(1+cos x)-1)/((pi-x)^(2))is-
Answer» `1/2` 0 `1/4` 1 Answer :C

Discussion

19.	Four cards are accidentally dropped from a pack of playing cards. What is the probability that they are one from each suit.
Answer» ANSWER :`(2197)/(20825)`

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20.	If y=int((2x-1)/(x^(2)+1)) and f'(x)=sinx^(2), then (dy)/(dx) is :
Answer» `COSX^(2)F'(x)` `-cosx^(2)f'(x)` `(2(1+x-x^(2)))/((x^(2)+1)^(2))SIN((2x-1)/(x^(2)+1))^(2)` None of these. ANSWER :C

Discussion

21.	Find the vector and the cartesian equations of the line that passes through the points (3, - 2, – 5), (3, -2, 6).
Answer» ANSWER :`THEREFORE (x-3)/(0)=(y+2)/(0)=(z+5)/(11)`

Discussion

22.	If y =tan^(-1)(sinsqrt(x))+ "cosec"^(-1)(e^(2x+1)), " then " (dy)/(dx)=
Answer» ANSWER :`(-2)/(SQRT(E^(2(2x+1))-))`

Discussion

23.	If theinequation (sqrt(6+x-x^2 ))/( x+10)lesqrt((8-2x -x^2))/( 2x +9) then
Answer» `2 lex LE -1` `-2 le X le-1` `2 lex le , x=3` none Answer :B

Discussion

24.	int (1)/((2x +1)sqrt(x^(2) -x-))dx =
Answer» `- (1)/(sqrt(5)) tan^(-1) ((4X + 7)/(6x + 3)) +c` `- (1)/(sqrt(5)) sin^(-1) ((4x - 7)/(6x - 3)) +c` `- (1)/(sqrt(5)) cos^(-1) ((4x + 7)/(6x + 3)) + c` `- (1)/(sqrt(5)) sin^(-1) ((4x + 7)/(6x +3)) + c ` Answer :D

Discussion

25.	Prove that the following. [[1,1,1],[b+c,c+a,c+a],[b^2+c^2,c^2+a^2,a^2+b^2]]=(b-c)(c-a)(a-b)
Answer» SOLUTION :`[[1,1,1],[b+c,c+a,c+a],[b^2+c^2,c^2+a^2,a^2+b^2]]` `[[1,0,0],[b+c,a-b,b-c],[b^2+c^2,a^2-b^2,b^2-c^2]]` (REPLACING `C_2` and `C_3` by `C_3-C_1` and `C_3-C_2` RESPECTIVELY.) =`1XX[[a-b,b-c],[a^2-b^2,b^2-c^2]]` (a-b)(b-c)`[[1,1],[a+b,b+c]]` (a-b)(b-c)(b+c-a-b) (a-b)(b-c)(c-a)=R.H.S.

Discussion

26.	In a box there are 100 electric bulbs out of which 10 are defective. 5 bulbs are selected from it then ………..is the probability that bulb is defective.
Answer» `10^(-1)` `((1)/(2))^(5)` `((9)/(10))^(5)` `(9)/(10)` Answer :C

Discussion

27.	If the plane passing through (1,1,1),(1,-1,1) and (-1,3,-5) is also passing through (2,k,4) then , k = ..........
Answer» does not get Two VALUE exist All REAL numbers unique value exist Answer :C

Discussion

28.	Ifthe points(1,1, lambda) and (-3,0,1) are equidistant from the plane,3x + 4y-12z + 13 = 0, then lambda satisfiesthe equation
Answer» 0 1 2 3 Answer :B

Discussion

29.	Circle touching both the axes and radius 5 is
Answer» `X^(2)+y^(2)-10x-10y+25=0` `x^(2)+y^(2)-10x+10y+25=0` `x^(2)+y^(2)+10x-10y+25=0` all the above Answer :D

Discussion

30.	Find the coordinates of the point of intersection of tangent at the points where x+ 4y - 14 =0meets the circlex^(2) + y^(2) - 2x+ 3y -5=0
Answer» ANSWER :` ((109)/( 76) , (9)/(38))`

Discussion

31.	Events A and B are such that P(A) =(1)/(2), P(B) =(7)/(12) and "P(not A or not B)"=(1)/(4). State whether A and B are independent ?
Answer» ANSWER :A and B are MOT INDEPENDENT

Discussion

32.	Integrate the following functions with respect to x. (cosecx)/(cosecx-cotx)
Answer» ANSWER :`-cotx-cosecx+c`

Discussion

33.	If I_(m,n) - int (x^(m) (logx)^(n)dx then I_(m,n) - (x^(m+1))/((m + 1)) (logx)^(n) =
Answer» `(N)/(m + 1) .I_(m,n-1) ` `(m)/(n + 1) .I_(m,n-1) ` `-(n)/(m + 1) .I_(m,n-1) ` `(n)/(m + 1) .I_(m-1 , n - 1 ) ` ANSWER :C

Discussion

34.	Relation " parallel" in the set of all straight lines in a plane is :
Answer» only REFLEXIVE only symmetric only TRANSITIVE EQUIVALENCE RELATION Answer :D

Discussion

35.	If there are m students in a class, then find the probability that (i) all the students have different birthdays in a non leap year (ii) All the students have same birthday in a non leap year
Answer» <P> ANSWER :`(i) (.^(365)P_(m))(365^(m))` `(II) (365)/(365^(m))`

Discussion

36.	int_(0)^((pi)/(2))(4sqrt(cot x))/(4sqrt(tan x) + 4sqrt(cot x)) dx
Answer» ANSWER :`(PI)/(4)`

Discussion

37.	If int _(0) ^(pi) ((x )/( 1 + sin x ))^(2) dx = lamda then show that int _(0) ^(x) ( 2x ^(2) cos ^(2) (x//2))/( (1+ sin x )^(2))dx = lamda + 2pi-pi^(2).
Answer» Answer :HENCE `1 = LAMDA -2PI + pi^(2)`

Discussion

38.	Let A, B and C be three sub-sets of a universal set U. if A DeltaC = B DeltaC,then
Answer» A=B `A CAP B sube C` `A cup B sube C` `A cap B sube C'` the complement of C. ANSWER :A

Discussion

39.	Number of ways in which three distinct numbers can be selected between 1 and 20 both inclusive, whose sum is even is______.
Answer» Solution :All even +2 ODD 1 even `""^(10)C_(3)+""^(10)C_(2)XX""^(10)C_(1)` `(10xx9xx8)/(6)+(10xx9)/(2)xx10` `120+450+570`

Discussion

40.	If n is a positive integer, then 2.4^(2n+1)+3^(3n+1) is divisible by :
Answer» 2 7 11 27 Answer :C

Discussion

41.	Integrate the functions x^(2)e^(X)
Answer» ANSWER :`E^(X)(x^(2)-2x+2)+C`

Discussion

42.	For the equation \|x^(2)\|+\|x\|-6=0,the roots are
Answer» ONE and only one REAL number Real with SUM one Real with sum zero Real with PRODUCT zero Answer :C

Discussion

43.	Through a point a plane is drawn at right angles to OP, to meet the axes in A, B, C. If OP = r, the centroid of the triangle ABC is :
Answer» `((f)/(3r), (g)/(3r), (h)/(3r))` `((r^(2))/(3r ^(2)), (r ^(2))/(3g ^(2)), (r ^(2))/(3H^(2)))` `(r ^(2))/(3f), (r ^(2))/(3g), (r ^(2))/(3h))` None of these ANSWER :C

Discussion

44.	Find the 6th term in the expansion of (x^2+a^4/y^2)^10.
Answer» Solution :6TH term i.e. (5+1)TH term in the expansion of `(x^2+a^4/y^2)^10` is `"^10C_5(x^2)^10-5(a^4/y^2)^5` `= 10!/5!5!x^10(a^20/y^10) ` ` = 10.9.8.7.6/5.4.3.2.1(x^10a^20)/y^10= 252x^10a^20/y^10`

Discussion

45.	Find the values of p so that the lines(1-x)/(3)=(7y-14)/(2p)=(z-3)/(2) and (7-7x)/(3p)=(y-5)/(1)=(6-z)/(5) are at right angles.
Answer» <P> ANSWER :`THEREFORE P=(70)/(11)`

Discussion

46.	Evaluation of definite integrals by subsitiution and properties of its : int_(0)^(pi/2)(x-[sinx])dx=..........
Answer» `(PI^(2))/(8)` `(pi^(2))/(8)-1` `(pi^(2))/(8)-2` None of these ANSWER :A

Discussion

47.	{:("Column-I","Column-II"),("(A) If for some real x, then equation", "(P) "2),(""x+(1)/(x)=2cos theta" holds",),("then " cos theta" is equal to","(Q) "1),("(B) If "sin theta"cosec"theta=2",", "(Q) "1),("then "sin^(2008)theta+"cosec"^(2008)theta" is equal to", "(R) "0),("(C) Maximum value of "sin^(4)theta+cos^(4)theta" is",),("(D) Least value of "2 sin^(2)theta+3cos^(2)theta" is","(S) "-1):}
Answer» ANSWER :A::B::C::D

Discussion

48.	Fill in the blanks in each of the following, using the answers given against each of them : The distance between the lines 3x - 1 = 0 and x + 3 = 0 is _____ units.
Answer» 4 2 `8/3` `10/3` ANSWER :D

Discussion

49.	Find two numbers whose product is 100 and whose sum is minimum.
Answer» ANSWER :Hence the sum of TWO NUMBERS is MINIMUM when the numbers are 10 and 10.

Discussion

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

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

If x > 0 , y > 0 , z > 0 , xy+yz+zx < 1 and if tan^(-1)x+tan^(-1)y + tan^(-1)z=pi,then x+y+z equals to

The vector equation of line passing through (2,-1,1) and parallel to the line barr=3hati-hatj+2hatk+lambda(2hati+7hatj-3hatk) is

Find lambdaandmu if (2hati+6hatj+27hatk)xx(hati+lambdahatj+muhatk)=vec0.

Find theanglebetweentwo lineswhosedirection ratiosare "(i) 2,1,2 and4,8,1""""(ii) 5 ,-12 ,13 and -3,4,5" "(iii) 1 ,1,2 and" (sqrt(3)-1) ,(-sqrt(3)-1),4 """(iv)a,b,c and(b-c) ,(c-a),(a-b)"

lim_(x to 2)((cos alpha)^(x) + (sin alpha)^(x)-1)/(x-2)=

Find the values of the following integrals (ii) int_(0)^(pi/2) sin^(4) x cos^(6) x dx

A ray of light coming along the line (x - 1)/(1) = (y - 2)/(2) = (z - 3)/(3), strikes the plane mirror kept along the plane through points (2, 1, 1), (3, 0, 2) and(2 , -1, -2) . Then the equation of reflected ray is:

If y=(gof)(x)then dy/dx=______.

If y = (5x)^(3 cos 2x) find (dy)/(dx)

If If A+B+C=pi then prove that "sin"A^(2)/2+"sin"^(2)B/2-"sin"^(2)C/2=1-2"cos"A/2"cos"B/2"sin"C/

Let f(t)=|t-1|-|t|+|t+1|, AA t in R. Find g(x) = max {f(t):x+1letlex+2}, AA x in R. Find g(x) and the area bounded by the curve y=g(x), the X-axis and the lines x=-3//2 and x=5.

Find the principle value of the followingtan^(-1)(-sqrt3)

Evaluate the integral as limit of sum: int_(0)^(pi)sinxdx

The solution of the cosec^(2x)(dy)/(dx) - (1)/(y) = 0 is

A rectangle ABCD is inscribed in a circle with a diameter lying along the line 3y=x+10. If A=(-6,7), B=(4,7) then the area of the rectangle is

The value of lim _(xtopi) (sqrt(1+cos x)-1)/((pi-x)^(2))is-

Four cards are accidentally dropped from a pack of playing cards. What is the probability that they are one from each suit.

If y=int((2x-1)/(x^(2)+1)) and f'(x)=sinx^(2), then (dy)/(dx) is :

Find the vector and the cartesian equations of the line that passes through the points (3, - 2, – 5), (3, -2, 6).

If y =tan^(-1)(sinsqrt(x))+ "cosec"^(-1)(e^(2x+1)), " then " (dy)/(dx)=

If theinequation (sqrt(6+x-x^2 ))/( x+10)lesqrt((8-2x -x^2))/( 2x +9) then

int (1)/((2x +1)sqrt(x^(2) -x-))dx =

Prove that the following. [[1,1,1],[b+c,c+a,c+a],[b^2+c^2,c^2+a^2,a^2+b^2]]=(b-c)(c-a)(a-b)

In a box there are 100 electric bulbs out of which 10 are defective. 5 bulbs are selected from it then ………..is the probability that bulb is defective.

If the plane passing through (1,1,1),(1,-1,1) and (-1,3,-5) is also passing through (2,k,4) then , k = ..........

Ifthe points(1,1, lambda) and (-3,0,1) are equidistant from the plane,3x + 4y-12z + 13 = 0, then lambda satisfiesthe equation

Circle touching both the axes and radius 5 is

Find the coordinates of the point of intersection of tangent at the points where x+ 4y - 14 =0meets the circlex^(2) + y^(2) - 2x+ 3y -5=0

Events A and B are such that P(A) =(1)/(2), P(B) =(7)/(12) and "P(not A or not﻿ B)"=(1)/(4). State whether A and B are independent ?

Integrate the following functions with respect to x. (cosecx)/(cosecx-cotx)

If I_(m,n) - int (x^(m) (logx)^(n)dx then I_(m,n) - (x^(m+1))/((m + 1)) (logx)^(n) =

Relation " parallel" in the set of all straight lines in a plane is :

If there are m students in a class, then find the probability that (i) all the students have different birthdays in a non leap year (ii) All the students have same birthday in a non leap year

int_(0)^((pi)/(2))(4sqrt(cot x))/(4sqrt(tan x) + 4sqrt(cot x)) dx

If int _(0) ^(pi) ((x )/( 1 + sin x ))^(2) dx = lamda then show that int _(0) ^(x) ( 2x ^(2) cos ^(2) (x//2))/( (1+ sin x )^(2))dx = lamda + 2pi-pi^(2).

Let A, B and C be three sub-sets of a universal set U. if A DeltaC = B DeltaC,then

Number of ways in which three distinct numbers can be selected between 1 and 20 both inclusive, whose sum is even is______.

If n is a positive integer, then 2.4^(2n+1)+3^(3n+1) is divisible by :

Integrate the functions x^(2)e^(X)

For the equation |x^(2)|+|x|-6=0,the roots are

Through a point a plane is drawn at right angles to OP, to meet the axes in A, B, C. If OP = r, the centroid of the triangle ABC is :

Find the 6th term in the expansion of (x^2+a^4/y^2)^10.

Find the values of p so that the lines(1-x)/(3)=(7y-14)/(2p)=(z-3)/(2) and (7-7x)/(3p)=(y-5)/(1)=(6-z)/(5) are at right angles.

Evaluation of definite integrals by subsitiution and properties of its : int_(0)^(pi/2)(x-[sinx])dx=..........

Fill in the blanks in each of the following, using the answers given against each of them : The distance between the lines 3x - 1 = 0 and x + 3 = 0 is _____ units.

Find two numbers whose product is 100 and whose sum is minimum.

Evaluate the following integrals int(logx)/(x^(2))dx

Events A and B are such that P(A) =(1)/(2), P(B) =(7)/(12) and "P(not A or not B)"=(1)/(4). State whether A and B are independent ?