28278 + Interview Questions in Maths in Class 12

1.	IfF(x)=underset0overset(x)inte^(2t)cos5tdt, what is F'(x)?
Answer» Solution :F(X)=underset0overset(x)inte^(2T)COS(5t)dtifff(x)=E^(2x)cos(5X).`

Discussion

2.	Let the position vectors of vertices of a DeltaABC be OA=3i+j+2k, OB=i+2j+3k" and "OC=2i+3j+k. If length of altitude of DeltaABC from A is p, then 2p^(2)= ________
Answer» ANSWER :9

Discussion

3.	Find the remainder when 32^(32^(32)) is divided by 7.
Answer» SOLUTION :N/A

Discussion

4.	Let vec(a),vec(b) and vec( c ) be three vectors such that \|vec(a)\|=3,\|vec(b)\|=4,\|vec( c )\|=5 and each one the them being perpendicular to the sum of the other two, find \|vec(a)+vec(b)+vec( c )\|.
Answer» ANSWER :`5sqrt(2)`

Discussion

5.	Let p: Kiran passed the examination, q: Kiran is sad The symbolic from of a statement "It is not true that Kiran passed therefore he is said" is
Answer» <P>`(~prarr`Q) (p`RARR`q) ~(p`rarr`~q) ~(p`harr`q) Answer :B

Discussion

6.	Values of c of Rolle's theorem for f(x)=sin x-sin 2x on [0,pi]
Answer» Solution :We have,`F(x) = SINX - sin2x "in" [0,pi]` (i) SINCE , we know thatsinefunctionsare continuous functionshence `f(x)=sinx - sin2x` isa continuous function in `[0,pi]` (ii) `f(x) = cosx -COS2X. 2 = cos x - 2 cos 2X ` , which existin `(0,pi)` So, `f(x)`is differentiable in `(0,pi)`.Conditionsof mean value theoremare satisfied. Hence`3c in (0,pi)` such that,`f'(c) = (f(pi)-f (0))/(pi-0)` `rArr cos - 2 cos 2x = (sin pi - sin 2pi - sin 0 + sin 2.0)/(pi-0)` `rArr 2cos2c -cos c = (0)/( pi)` `rArr 2.(2cos^(2)c-1)-cosc= (0)` `rArr 4 cos^(2)-2-cosc=0` `rArr 4 cos^(2)c-cosc-2 = 0` `rArr cosc = (1+-sqrt(1+32))/(8) = (1+-sqrt(33))/(8)` `:. c= cos^(-1)((1+-sqrt(33))/(8))` Also, `cos^(-1) ((1+-sqrt(33))/(8))in (0,pi)` Hence, meanvalue therem has been verified.

Discussion

7.	Using integration find the area of the triangular region whose sides have the equations Y =2x + 1, y = 3x+1 andx=4.
Answer» ANSWER :`= 8` SQ. UNIT.

Discussion

8.	If A is square matrix such that A^(2)=A, then (I+A)^(3)-7A is equal to
Answer» A `I-A` `I ` 3A ANSWER :C

Discussion

9.	The quardritic equation in x such that the arithmetic meanof its roots is 5 and geometric mean of the roots is 4, is given by
Answer» `X^(2) + 20X + 16 = 0` `x^(2) - 10x + 16 = 0` `x^(2) + 10x + 16 = 0` `x^(2) - 10x - 16 = 0` Answer :B

Discussion

10.	Observe the following list {:("List-I","List-II"),(A. [vec(a)vec(b)vec(c )],1. \|vec(a)\|\|vec(b)\| cos (vec(a).vec(b))),(B.(vec(c ) xx vec(a)) xx vec(b), 2. (vec(a). vec(c )) vec(b) - (vec(a). vec(b)) vec(c)),(C. vec(a) xx (vec(b) xx vec(c )),3.vec(a).vec(b) xx vec(c )),(D. vec(a). vec(b), 4.\|vec(a)\| \|vec(b)\|),(,5.(vec(b) - vec(c )) vec(a) - (vec(a) . vec(b)) vec(c)):} Then the correct match for List-I from list II is
Answer» 1,2,3,4 3,5,2,1 3,2,5,1 2,3,4,1 Answer :B

Discussion

11.	Find a point on the curve y = (x – 2)^(2) at which the tangent is parallel to the chord joining the points (2, 0) and (4, 4).
Answer» ANSWER :(3,1)

Discussion

12.	Let A, B, C be three sets. If AinBandBsubC then
Answer» `AsubC` `AcancelsubC` `AINC` `AcancelinC` ANSWER :B

Discussion

13.	Examin the following functions for continuity. f(x)= (1)/(x-5), x ne 5
Answer» ANSWER :CONTINUOUS FUNCTIONS.

Discussion

14.	The term independent of x in (2x^(1//2)-3x^(-1//3))^20
Answer» `""^20C_(7) 2^(8) 3^12` `""^20C_(8) 2^(7) 3^13` `""^(20)C_(8) C^(8) 3^12` `""^20C_(7)2^(7) 3^13` ANSWER :C

Discussion

15.	Two trains start from the same place. A person travel in a train whose speed is 50 km/h and it go to south direction. Another person travel in another train whose speed is 60 km/h and it go to west direction. After two hours, find the rate of distance between them.
Answer» ANSWER :`16sqrt(61)` km/h

Discussion

16.	If the two circles (x-1)^(2)+(y-3)^(2)=r^(2) and x^(2)+y^(2)-8x+2y+8=0 intersect in two distinct points, then
Answer» `rgt2` `2ltr LT 8` `rlt2` `r=2` ANSWER :B

Discussion

17.	If ((1-i)/(1+i))^(96)=a+ib, then (a,b) is
Answer» (1,1) (1,0) (0,1) (0,-1) ANSWER :B

Discussion

18.	The point of contact of the circle x^(2)+y^(2)+2x+2y+1=0 and x^(2)+y^(2)-2x+2y+1=0
Answer» (0,1) (0,-1) (1,0) (-1,0) ANSWER :B

Discussion

19.	If sqrt(1-x^(2)) + sqrt(1 -y^(2))= a(x-y), then prove that (dy)/(dx)= sqrt((1-y^(2))/(1-x^(2))). (Where \|x\| le 1, \|y\| le 1)
Answer» ANSWER :`(SQRT(1-y^(2)))/(sqrt(1-x^(2)))`

Discussion

20.	The value of a for which the points (9, 5), (1, 2), (a, 8) are collinear is equal to
Answer» 17 8 7 71 Answer :A

Discussion

21.	int((x^(2)-1)dx)/((x^(4)+3x^(2)+1)Tan^(-1)((x^(2)+1)/(x)))=
Answer» ANSWER :`L ntan^(-1)(X+(1)/(x))+C`

Discussion

22.	Which of the following undergoes partial hydrolysis?
Answer» `B_(2)H_(6)` `BCl_(3)` `SiF_(4)` `BF_(3)` Solution :Due to Back bonding.

Discussion

23.	Internal angle bisecotors of DeltaABC meets its circum circle at D, E and F where symbols have usual meaning. Q. The ratio of area of triangle ABC and triangle DEF is :
Answer» `GE1` `LE1` `GE 1//2` `le1//2` ANSWER :B

Discussion

24.	Match the following lists:
Answer» Solution :a. `I=int_(-2)^(2)(alphax^(3)+betax+gamma)dx` `alphax^(3)+betax` is an odd function `I=0+2int_(0)^(2)gamma dx=2xx2gamma=4gamma` b. `I=1/2 int_(0)^(1)2sin alpha x sin beta x dx` `=1/2int_(0)^(1)(cos(alpha-beta)x-cos(alpha+beta)x)dx` `=1/2[(sin(alpha-beta)x)/(alpha-beta)-(sin (alpha+beta)x)/(alpha+beta)]_(0)^(1)` `=1/2[(sin (alpha-beta))/(alpha-beta)-(sin (alpha+beta))/(alpha+beta)]`...........1 Also `2 alpha=tan alpha` and `2beta=tan beta` `:. 2 (alpha-beta)=tan alpha-tan beta ` and `2(alpha+beta)=tan alpha+tan beta` `2(alpha-beta)=(sin(alpha-beta))/(cos alpha cos beta)` and `2(alpha+beta)=(sin (alpha +beta))/(cos alpha cos beta)` substituting these values, we get C.`f(x+alpha)+f(x)=0` or `(x+2alpha)+f(x)+alpha)=0` or `f(x+2alpha)=f(x)` Thus, `f(x)` is periodic with periodic `2 alpha`. Hence `int_(beta)^(beta+2gamma alpha) f(x)dx=gamma int_(0)^(2alpha) f(x)dx` d. Let `I=int_(0)^(alpha)[SINX]dx, alpha epsilon[(2beta+1)pi,(2beta+2)pi],beta epsilon N`, ( wher [.] denotes the greatest INTEGER function) `=int_(0)^(2betapi) [sinx]dx+int_(2betapi)^((2beta+1)pi) [sinx]dx+int_((2beta+1)pi)^(alpha) [sinx] dx` `=betaint_(0)^(2PI) [sinx]dx+0+int_((2beta+1)pi)^(alpha) (-1)dx` `=-betapi+(2beta+1)pi-alpha` `=(beta+1)pi-alpha` Thus, `gamma int_(0)^(alpha) [sinx]dx` depends on `alpha beta` and `gamma`.

Discussion

25.	Match the following lists:
Answer» Solution :`lim_(nto oo) [(int_(0)^(2)(1+t/(n+1))^(n)dt)/(n+1)]=lim_(n to oo) [(1+t/(n+1))^(n-1)]_(0)^(2)` `=lim_(nto oo) (1+2/(n+1))^(n+1)-1` `=E^(2)-1` `f'(x)=f(x)impliesf(x)=Ce^(x)` and since `f(0)=1, 1=f(0)=C` Therefore `f(x)=e^(x)` and HENCE `g(x)=x^(2)-e^(x)`. THUS, `int_(0)^(1)f(x)g(x)DX=int_(0)^(1)(x^(2)e^(x)-e^(2x))dx` `=x^(2)e^(x)\|_(0)^(1)-2int_(0)^(1)xe^(x) dx=int_(0)^(1)(x^(2)e^(x)-e^(2x))dx` `=x^(2)e^(x)\|._(0)^(1)-2int_(0)^(1)xe^(x)dx-(e^(2x))/2\|_(0)^(1)` `=(e-0)-2xe^(x)\|._(0)^(1)+2e^(x)\|_(0)^(1)+2e^(x)\|_(0)^(1)-1/2(e^(2)-1)` `=(e-0)-2e+2e-2-1/2(e^(2)-1)` `=e-1/2e^(2)-3/2` `I=int_(0)^(1)e^(e^(x))(1+xe^(x))dx` Let `e^(x)=t` `:. int_(1)^(e)(1+tlogt)(dt)/t int_(1)^(e)e^(t)(1/t +logt)dt` `=[e^(t)logt]_(1)^(e)=e^(e)` d. `L=lim_(kto0)(int_(0)^(k)(1+sin2x)^(1/x)dx)/k` (form `0/0`) `=lim_(kto0) (1+sin2k)^(1/k)` `=e^(lim_(kto0)1/k(sin2k))=e^(2)`

Discussion

26.	Find the projection of the vector hati+3hatj+hatk on thevector 7hati-hatj+8hatk
Answer» ANSWER :`= ( 6)/( SQRT(114))`

Discussion

27.	Match the following lists:
Answer» SOLUTION :a. `I_(1)=int_(pi//6)^(pi//3) sec^(2) thetaf(2sin THETA) d theta` Applying property `int_(a)^(b)f(a+b-x)dx=int_(a)^(b)f(x)dx` `I_(1)=int_(pi//6)^(pi//3)sec^(2)((pi)/2-theta)f(2sin2((pi)/2-theta))d theta` `=int_(pi//6)^(pi//3)cosec^(3) theta f(2sin 2 theta) d theta=I_(2)` b. `f(x+1)=f(x+3)` or `f(x)=f(x+2)` Thus, `f(x)` is periodic with period 2. Then `int_(a)^(a+b)f(x)dx` is independent of `a` for which `b` is multiple of 2. Thus, `b=2,4,6`........... c. Let `I=int_(1)^(4)(tan^(-1)[x^(2)])/(tan^(-1)[x^(2)]+tan^(-1)[25+x^(2)-10x])`.............1 Appling `int_(a)^(b)f(x)dx=int_(a)^(b)f(a+b-x)dx`, we get `I=int_(1)^(4)(tan[(5-x)^(2)])/(tan^(-1)[(5-x)^(2)]+tan^(-1)[x^(2)])dx`.............2 Adding equatiions 1 and 2 we get `2I=int_(1)^(4)dx` or `2I=3` or `I=3//2` d.Let` y=SQRT(x+sqrt(x+sqrt(x+)))..............=sqrt(x+y)` or `y^(2)-y-x=0` or `y=(1+-sqrt(1+4x))/(2.1)=(1+sqrt(1+4x))/2( :' YGT1)` `:.I=int_(0)^(2)(1+sqrt(1+4x))/2 dx` `=[x/2+((1+4x)^(3//2))/(3/2xx2xx4)]_(0)^(2)` `=[(1+27/12)=(0+1/12)]` `=1+26/12=19/6` `:. [I]=3` `[I]=3`

Discussion

28.	The value of the expression (1+cot7^(@))(1+cot9^(@))(1+cot11^(@))......(1+cot45^(@))(1-cot52^(@))(1-cot54^(@))......(1-cot88^(@)) is equal to
Answer» `2^(18)` `2^(19)` `2^(20)` `2^(21)` SOLUTION :Using`(1+costheta)(1-cot(45^(@)+THETA))=2` ` (1+cot45^(@))(2^(19))=(2^(19))=20^(20)`

Discussion

29.	If 3 fair dice are rolled, find the probability of getting sum 12.
Answer» ANSWER :`(25)/(216)`

Discussion

30.	The locus of the centre of a circle which touches externally the circle x^(2)+y^(2)-6x-6y+14=0 and also touches the y-axis is given by the equation.
Answer» `y^(2)-6x-10y-14=0` `y^(2)-6x+10y+14=0` `y^(2)+6x+10y+14=0` `y^(2)-6y-10x+14=0` ANSWER :D

Discussion

31.	A channel 27m wide falls at a right angle into another channel 64m wide. The greatest length of the log that can be floated along this system of channels is
Answer» 120 125 100 110 Answer :B

Discussion

32.	If \|vec(a)+vec(b)\|=60,\|vec(a)-vec(b)\|=40 and \|vec(b)\|=46 find \|vec(a)\|.
Answer» ANSWER :22

Discussion

33.	Thenormalat thepoint(2,-2)on thecurve3x^2-y^2 =8 is _____
Answer» `x+y =0` ` x+2y =-2` `x-3y=8` ` 3X +y=4` ANSWER :D

Discussion

34.	If (barb xx barc) xx (barb xx bara) = 3barc, then find [barb xx barc barc xx bara bara xx barb].
Answer» ANSWER :`= 9`

Discussion

35.	Which of the following is/are periodic?
Answer» f(x) = x - [x], where [x] DENOTES the greatest integral function f(x) = x (where x is a CONSTANT) `f(x) = 2tan.(1)/(2)(x-pi)` ANSWER :A::B::D

Discussion

36.	Integrate the functions 1/(x-x^(3))
Answer» ANSWER :`1/2logabs((X^(2))/(1-x^(2)))+C`

Discussion

37.	Evaluate the definite integrals int_(0)^(1)(2x+3)/(5x^(2)+1)dx
Answer» ANSWER :`3LOG2+(3PI)/8`

Discussion

38.	The solution of tany(dy)/(dx)=sin(x+y)+sin(x-y) is
Answer» `secy=2cosx+c` `secy=-2cosx+c` `tany=-2cosx+c` `SEC^(2)y=-2cosx+c` ANSWER :B

Discussion

39.	Solve 4xdy - y dx = x^(2) dy.
Answer» ANSWER :`c.y^(4)(x-4)`

Discussion

40.	In triangleABC,a(cosB+sinBcot((A)/(2)))=
Answer» `a+b+c` `c+a` `a+b` `b+c` ANSWER :D

Discussion

41.	Find the numerically greatest terms in the expansion of(3y + 7x)^10 whenx = 1/3, y = 1/2
Answer» ANSWER :`T_7 = 5/24.7^7`

Discussion

42.	Two cards are drawn simultaneously (or successively without replacement) from a well shuffled pack of 52 cards. Find the mean, variance and standard deviation of the number of kings.
Answer» ANSWER :`(34)/(221), (6800)/((221)^(2))` and 0.37

Discussion

43.	Find the approximate value of f(2.01), where f (x) = 4x^(2) + 5x + 2.
Answer» ANSWER :28.21

Discussion

44.	int_(-1)^(1)log ((2019 -x)/(2019+x)) dx =………
Answer» 0 LOG 2019 1 2. log( 2019 ) ANSWER :A

Discussion

45.	Findthe principalvalueofsin ^(-1)(-1/2)( in radiusand degrees .)
Answer» ANSWER :`- 30 ^@`

Discussion

46.	Solve the following linear programming problem graphically: Maximise Z=4x+y ………….1 subject to the constraints: x+yle50 ……………2 3x+yle90…………..3 xge0, yge0…………..4
Answer» ANSWER :(30,0)

Discussion

47.	Find the equation of plane passing through the point (-1,1,2) and parallel to the plane x + 2y + 3z - 5 = 0.
Answer» ANSWER :`x + 2Y + 3Z - 7 = 0`

Discussion

48.	A : If x=sin(alpha - beta ) sin (gamma - delta), y=sin(beta - gamma ) sin (alpha - delta) , z=sin(gamma - alpha ) sin ( beta - delta) " then " x+y+z=0 R :2 sin A sin B = cos(A-B)+cos(A+B)
Answer» A is TRUE , R is true and R is CORRECT explanation of A A is true , R is trueand R is not correct explanation of A A is true , R is FALSE A is false , R is true ANSWER :C

Discussion

49.	Evaluate: lim_(x to 0)(cotx)^(sin2x)
Answer» ANSWER :1

Discussion

50.	Prove that : Find the numerically greatest term in the binomial expansion of (1-5x)^(12) when x=(2)/(3).
Answer» SOLUTION :N/A

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

IfF(x)=underset0overset(x)inte^(2t)cos5tdt, what is F'(x)?

Let the position vectors of vertices of a DeltaABC be OA=3i+j+2k, OB=i+2j+3k" and "OC=2i+3j+k. If length of altitude of DeltaABC from A is p, then 2p^(2)= ________

Find the remainder when 32^(32^(32)) is divided by 7.

Let vec(a),vec(b) and vec( c ) be three vectors such that |vec(a)|=3,|vec(b)|=4,|vec( c )|=5 and each one the them being perpendicular to the sum of the other two, find |vec(a)+vec(b)+vec( c )|.

Let p: Kiran passed the examination, q: Kiran is sad The symbolic from of a statement "It is not true that Kiran passed therefore he is said" is

Values of c of Rolle's theorem for f(x)=sin x-sin 2x on [0,pi]

Using integration find the area of the triangular region whose sides have the equations Y =2x + 1, y = 3x+1 andx=4.

If A is square matrix such that A^(2)=A, then (I+A)^(3)-7A is equal to

The quardritic equation in x such that the arithmetic meanof its roots is 5 and geometric mean of the roots is 4, is given by

Find a point on the curve y = (x – 2)^(2) at which the tangent is parallel to the chord joining the points (2, 0) and (4, 4).

Let A, B, C be three sets. If AinBandBsubC then

Examin the following functions for continuity. f(x)= (1)/(x-5), x ne 5

The term independent of x in (2x^(1//2)-3x^(-1//3))^20

Two trains start from the same place. A person travel in a train whose speed is 50 km/h and it go to south direction. Another person travel in another train whose speed is 60 km/h and it go to west direction. After two hours, find the rate of distance between them.

If the two circles (x-1)^(2)+(y-3)^(2)=r^(2) and x^(2)+y^(2)-8x+2y+8=0 intersect in two distinct points, then

If ((1-i)/(1+i))^(96)=a+ib, then (a,b) is

The point of contact of the circle x^(2)+y^(2)+2x+2y+1=0 and x^(2)+y^(2)-2x+2y+1=0

If sqrt(1-x^(2)) + sqrt(1 -y^(2))= a(x-y), then prove that (dy)/(dx)= sqrt((1-y^(2))/(1-x^(2))). (Where |x| le 1, |y| le 1)

The value of a for which the points (9, 5), (1, 2), (a, 8) are collinear is equal to

int((x^(2)-1)dx)/((x^(4)+3x^(2)+1)Tan^(-1)((x^(2)+1)/(x)))=

Which of the following undergoes partial hydrolysis?

Internal angle bisecotors of DeltaABC meets its circum circle at D, E and F where symbols have usual meaning. Q. The ratio of area of triangle ABC and triangle DEF is :

Match the following lists:

Match the following lists:

Find the projection of the vector hati+3hatj+hatk on thevector 7hati-hatj+8hatk

Match the following lists:

The value of the expression (1+cot7^(@))(1+cot9^(@))(1+cot11^(@))......(1+cot45^(@))(1-cot52^(@))(1-cot54^(@))......(1-cot88^(@)) is equal to

If 3 fair dice are rolled, find the probability of getting sum 12.

The locus of the centre of a circle which touches externally the circle x^(2)+y^(2)-6x-6y+14=0 and also touches the y-axis is given by the equation.

A channel 27m wide falls at a right angle into another channel 64m wide. The greatest length of the log that can be floated along this system of channels is

If |vec(a)+vec(b)|=60,|vec(a)-vec(b)|=40 and |vec(b)|=46 find |vec(a)|.

Thenormalat thepoint(2,-2)on thecurve3x^2-y^2 =8 is _____

If (barb xx barc) xx (barb xx bara) = 3barc, then find [barb xx barc barc xx bara bara xx barb].

Which of the following is/are periodic?

Integrate the functions 1/(x-x^(3))

Evaluate the definite integrals int_(0)^(1)(2x+3)/(5x^(2)+1)dx

The solution of tany(dy)/(dx)=sin(x+y)+sin(x-y) is

Solve 4xdy - y dx = x^(2) dy.

In triangleABC,a(cosB+sinBcot((A)/(2)))=

Find the numerically greatest terms in the expansion of(3y + 7x)^10 whenx = 1/3, y = 1/2

Two cards are drawn simultaneously (or successively without replacement)﻿ from a well shuffled pack of 52 cards. Find the mean, variance and standard deviation﻿ of the number of kings.

Find the approximate value of f(2.01), where f (x) = 4x^(2) + 5x + 2.

int_(-1)^(1)log ((2019 -x)/(2019+x)) dx =………

Findthe principalvalueofsin ^(-1)(-1/2)( in radiusand degrees .)

Solve the following linear programming problem graphically: Maximise Z=4x+y ………….1 subject to the constraints: x+yle50 ……………2 3x+yle90…………..3 xge0, yge0…………..4

Find the equation of plane passing through the point (-1,1,2) and parallel to the plane x + 2y + 3z - 5 = 0.

A : If x=sin(alpha - beta ) sin (gamma - delta), y=sin(beta - gamma ) sin (alpha - delta) , z=sin(gamma - alpha ) sin ( beta - delta) " then " x+y+z=0 R :2 sin A sin B = cos(A-B)+cos(A+B)

Evaluate: lim_(x to 0)(cotx)^(sin2x)

Prove that : Find the numerically greatest term in the binomial expansion of (1-5x)^(12) when x=(2)/(3).

Two cards are drawn simultaneously (or successively without replacement) from a well shuffled pack of 52 cards. Find the mean, variance and standard deviation of the number of kings.