28278 + Interview Questions in Maths in Class 12

1.	What is x? (1) x = 4y = -4 xy = 8
Answer» ANSWER :E

Discussion

2.	Photons are incident from vacuum on a transparent material with a refractive index n for a given wavelength. Determine the momentum of the incident photon, if its wavelength in the material is equal to lambda.
Answer» `nh//lambda` `H//lambda` `h/(nlambda)` `h//lambda(n+1)` ANSWER :C

Discussion

3.	Find (dy)/(dx),x=sint,y=cos2t
Answer» SOLUTION :`(DY)/(DX)=-2sin2tdx/dt=costdy/dx(dy/dt)/(dy/dt)=(-2sin2t)/COST=(-4sintcost)/cost=-4sint`

Discussion

4.	lim_(n rarr oo)((1^(2) + 2^(2) ……. + n^(2))(n)^(1//n))/((n+1)(n+10)(n + 100)) =
Answer» 3 `(1)/(3)` `(2)/(3)` `OO` Answer :B

Discussion

5.	The shortest distance of (-5,4) to the circle x^(2)+y^(2)-6x+4y-12=0 is
Answer» 10 3 5 4 Answer :C

Discussion

6.	A die marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A be the event, 'the number is even,' and B be the event, 'the number is red'. Are A and B independent?
Answer» ANSWER :A and B are not INDEPENDENT

Discussion

7.	G is the centroid of DeltaABC. If AG = BC, then measure of /_BGC is
Answer» `bar(GP)` `2BAR(GP)` `3bar(GP)` `2bar(GA)` Answer :C

Discussion

8.	Let A be a 3xx3 matrix such that (A-2.2I_(3))(A-3.8 I_(3))=O_(3xx3) then trace of A+ 8.36A^(-1) is ________
Answer» ANSWER :`18.00`

Discussion

9.	Evaluate the following integrals intx sec^(-1)x dx
Answer» ANSWER :`(1)/(2)[X^(2)sec^(-1)x-sqrt(x^(2)-1)]+c`

Discussion

10.	The value of k for which the circle x^(2) + y^(2) -4x + 6y +3 =0will bisect the circumferece of the circle x^(2) +y^(2) +6x -4y +k=0is
Answer» `53` `-53` `47` `-47` ANSWER :A

Discussion

11.	Let veca=(cos theta)hati-(sin theta)hatj, vecb=(sin theta)hati+(cos theta)hatj,vecc=hatk and vecr=7hati+hatj+10hatk. IF vecr=x veca+y vecb+z vecc, then the value of (x^(2)+y^(2))/(z) is equal to
Answer» 3 5 50 7 Answer :B

Discussion

12.	Log_(e) ((1 + i)/(1- i))=
Answer» `(PI)/(2)` `-i"" (pi)/(2)` `i"" (pi)/(2)` `- (pi)/(2)` ANSWER :C

Discussion

13.	y=3x-2 is a straightline touching the parabola (-3)^(2)=12(x-2) if a line drawnperpendicular to this line at p on it touches the given parabola then the point p is
Answer» `(-1,-5)` `(-1,5)` `(-2,-8)` `(2,4)` ANSWER :A

Discussion

14.	Evaluate the following integrals. int(3x^(2))/(1+x^(6))dx
Answer» ANSWER :`TAN^(-1)(X^(3))+c`

Discussion

15.	Three cards are drawn successively without replacement from a pack of 52 well shuffled cards. What is the probability that the first two cards are kings and the third is an ace?
Answer» ANSWER :`(2)/(5525)`

Discussion

16.	Froma point P (alpha,beta) a pair of tangents PQ and PR are drawn to circle x^2+y^2-2x-2y-2=0 such that QR is chord of contact.Considering PQ and PR are adjacent sides a parallelogramPQRS is formed .Equation of chord of contact QRis x =0, S_1 and S_2be the circles circumscribing the triangle PQR and QRS. Equation of circle S_1=0 is
Answer» `x^2+y^2+4x-2y-2=0` `x^2+y^2-2x+2y-2=0` `x^2+y^2+2x-2y-2=0` NONE of these ANSWER :C

Discussion

17.	Froma point P (alpha,beta) a pair of tangents PQ and PR are drawn to circle x^2+y^2-2x-2y-2=0 such that QR is chord of contact.Considering PQ and PR are adjacent sides a parallelogramPQRS is formed .Equation of chord of contact QRis x =0, S_1 and S_2be the circles circumscribing the triangle PQR and QRS. Co-ordinate of point P(alpha,beta) is equal to
Answer» (3,2) (2,3) (-3,1) NONE of these ANSWER :C

Discussion

18.	The locus of the points of intersection of perpendicular normals of the parabola y^2=4ax is
Answer» `y^2-2ax+a^2=0` `y^2-ax+2a^2=0` `y^2-ax+2a^2=0` `y^2-ax+3a^2=0` ANSWER :D

Discussion

19.	Find the antiderivative (or integral) of the following functions by the method of inspection. e^(2x)
Answer» SOLUTION :`int e^(2x) DX = 1/2 e^(2x) +C`

Discussion

20.	If the area of the triangle with vertices (2,-6), (5,4) and (k,4) is 35 square units, find values of kusing determinants.
Answer» ANSWER :k=12 or -2

Discussion

21.	If f(x) = int_(0)^(x) t.e^(t) dt then f'(-1)=
Answer» E `1/e` `- 1/e` `-e` ANSWER :C

Discussion

22.	Findthe area of the region bounded by y= sinx, y = cosxand ordinatesx = 0, x = pi//2.
Answer» Solution :`UNDERSET(0)OVERSET(pi/2)INT\|sinx-cosx\|dx` `underset(0)overset(pi//4)int(cosx-sinx)dx + underset(pi//4)overset(pi//2)int(sinx-cosx) dx = 2(sqrt(2)-1)`

Discussion

23.	Find the number of divisors of the number 2^(10).5^(10).11^(11).13^(13)which of the form 4n+1(nge0)
Answer» ANSWER :924

Discussion

24.	Let Let 1/x_1,1/x_2...1/x_n(x _i ne0" for "i=1,2,...n) in A.P. Such that x_1=3 and x_21=20.If n is the least positiveinteger for which x_n gt 50" then" sum_(i=1)^n(1/x_i) is equal to:
Answer» `1//8` 3 `13//8` `13//4` ANSWER :D

Discussion

25.	If y= cos^(-1)x, Find (d^(2)y)/(dx^(2)) in terms of y alone
Answer» ANSWER :`-COT y.cosec^(2)y`

Discussion

26.	Find the range of x for which the following expansions are valid . (2-(3x)/(4))^(-15//4)
Answer» SOLUTION :N/A

Discussion

27.	If the lines (2x-5)/(k)= (y+2)/(-5) = (z)/(1) and (x)/(1) = (y)/(2) = (z)/(3) are perpendicular to each other, then value of k is....................
Answer» `-7` `14` `7` `26` ANSWER :B

Discussion

28.	If sum_(k=1)^n ɸ(k)=2_n/(n+1),then sum_(k=1)^10 1/(ɸ(k))isequal to
Answer» `11/20` 220 `55/18` 110 Answer :B

Discussion

29.	OP is a tower of height 20 m and AB is a pole of height 5 m. The angle of elevation of the top P of the tower from the top B of the pole is 45^(@). Both pole and tower stand on the same ground. The angle of elevation of the top P of the tower from the base A of the pole is
Answer» `"cos"^(-1) (3)/(5)` `"sin"^(-1) (3)/(5)` `"tan"^(-1) (3)/(4)` `"COT"^(-1) (3)/(4)` ANSWER :A

Discussion

30.	Equation of circle with centre (-1,2) and passing through the centroid of triangle formed by (3,1),(2,-1) and (1,3) is
Answer» `X^(2)+y^(2)-x+2y-5=0` `x^(2)+y^(2)+x-2y-5=0` `x^(2)+y^(2)-2x+4y-5=0` `x^(2)+y^(2)+2x-4y-5=0` ANSWER :D

Discussion

31.	If int_(0)^(x)2xf^(2)(t)dt=(int_(0)^(x)2f(x-t)dt)^(2) for f(1)=1 and f(x) is comtinuos function for xgto and {a_(n)} is a sequence such that a_(n+1)=a_(n)+sqrt(1+a_(n)^(2)) for a=0, if f(x) is an increasing function, then lim_(nto oo)(a_K)/(2^(n-1))= (where k=f(n^(sqrt2-1)))is
Answer» `PI//4` `4//pi` `pi` `pi//2` ANSWER :B

Discussion

32.	If the rangeof a discreter dateof n observation on is zero, then
Answer» allvaluesofdateare ZERO all values of DATA are EQUAL to STANDARD deviation all valueof dateareequal the extreme values ofdata aredifferent Answer :C

Discussion

33.	The sum of the coefficients in the binomial expansion of (1/x + 2x)^n is equal to 6561. The constant term in the expansionis
Answer» `""^8C_4` `16(""^8C_4)` `""^6C_4.2^4` `8(""^8C_4)` ANSWER :B

Discussion

34.	Solve graphically 5x + 6y lt 12
Answer» SOLUTION :

Discussion

35.	A game consists of tossing a coin 3 times and nothing its outcome. A boy wins if all tosses give the same outcomes and losses otherwise. Find the probability that the boy losses the game.
Answer» ANSWER :`(3)/(4)`

Discussion

36.	If from the point (alpha,alpha^2) two tangents drawn to any one branch of hyperbola x^2-4y^2=1, then :
Answer» `-(1)/(2) LT ALPHA lt (1)/(2)` `0 lt alpha lt (1)/(2)` `-1 lt alpha lt 1` None of these Answer :A

Discussion

37.	Ifx=a( theta+ sintheta)and y=a(1- costheta), prove that(dy)/(dx) = tan ""(theta//2)
Answer» ANSWER :`theta/2`

Discussion

38.	If a is a root of x^(2) - 3x-5=0 find the value of a^(4) - 2a^(3) - 7a^(2) -8a
Answer» ANSWER :5

Discussion

39.	ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 represents two parallel straight lines if
Answer» `SQRT((g^(2)-AC)/(h^(2)+a^(2)))` `2sqrt((g^(2)-ac)/(h^(2)+a^(2)))` `2sqrt((g^(2)-ac)/(a(a+b)))` `sqrt((g^(2)-ac)/(a(a+b)))` Answer :C

Discussion

40.	The points (5, -4, 2), (4, -3, 1), (7, -6, 4) and (8, -7, 5) are the vertices of a
Answer» SQUARE RECTANGLE RHOMBUS parallelogram Answer :D

Discussion

41.	Three dice are rolled simultaneously . The probability that the sum of the numbers on them is 6 is
Answer» `(1)/(36)` `(5)/(108)` `(26)/(51)` `(13)/(34)` ANSWER :B

Discussion

42.	There are 3 bags A , B and C. Bag A contains 2 white and 3 black balls, bag B contains 4 white and 2 black balls and Bag C contains 3 white and 2 black balls. If a ball is drawn at random from a randomly chosenbag, then the probability that the ball drawn is black, is
Answer» A `2/3` B`4/9` C`5/9` D`1/9` ANSWER :B

Discussion

43.	IF an error of 0.01 cm is made while measuring the radius 2 cm of a circle, then the relative error in the circumference is
Answer» A,B,C B,C,A C,A,B A,C,B Answer :C

Discussion

44.	intcos^2xdx
Answer» SOLUTION :`intcos^2xdx=int(1+cos2x)/2dx` =1/2(x+1/2 SIN2X)+C =1/2x+1/4sin2x+C

Discussion

45.	If 0 ltx ltpiand cosx + sinx = 1/2 , thentan xis
Answer» `((1- sqrt(7)))/(4)` `((4-sqrt(7)))/(3)` `-((4+sqrt(7)))/(3)` `((1+sqrt(7)))/(4)` Answer :C

Discussion

46.	Let f (x) be a polynomial of degree three such that f(0) = 1, f(1) = 2 and 0 is a critical point of f(x) such that f(x) does not have a local extremum at 0. Them int(f(x))/(x^(2)+1) dx is equal to
Answer» `x-LOG(x^(2)+1)+TAN^(-1)x+C` `x+(1//2)log(x^(2)+1)-tan^(-1)x+C` `(1//2)x^(2)x(1//2)loga(x^(2)+1)-tan^(-1)x+C` `(1//2)(x^(2)-log(x^(2)+1))+tan^(-1)x+C` Answer :D

Discussion

47.	If ax + by = 1, cx^2 + dy^2 = 1 have only one solution, then a^2/c + b^2/d =1 and x= a/c, y=b/d
Answer» `a^2/C +b^2 /d = 1` `X = a/c` `x = c/a` `y = b/d` ANSWER :C

Discussion

48.	A : cos 40^(@) cos 80^(@) cos 160^(@) =-1//8 R :cos theta cos (120^(@) - theta ) cos (120^(@) + theta ) =(1)/(4) cos 3 theta
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 :A

Discussion

49.	(3x^(2) + 1)/(x^(2) -6x + 8) is equal to
Answer» `3 + (49)/(2(x -4))-(13)/(2(x -2))` `(49)/(2(x -4))-(13)/(2(x -2))` `(-49)/(2(x -4))+(13)/(2(x -2))` `(49)/(2(x -4))+(13)/(2(x -2))` ANSWER :A

Discussion

50.	Find the equation of the normal at theta=(pi)/(3) to the hyperbola 3x^(2)-4y^(2)=12.
Answer» ANSWER :`x+y=7`

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

What is x? (1) x = 4y = -4 xy = 8

Photons are incident from vacuum on a transparent material with a refractive index n for a given wavelength. Determine the momentum of the incident photon, if its wavelength in the material is equal to lambda.

Find (dy)/(dx),x=sint,y=cos2t

lim_(n rarr oo)((1^(2) + 2^(2) ……. + n^(2))(n)^(1//n))/((n+1)(n+10)(n + 100)) =

The shortest distance of (-5,4) to the circle x^(2)+y^(2)-6x+4y-12=0 is

A die marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A be the event,﻿ 'the number is even,' and B be the event, 'the number is red'. Are A and B﻿ independent?﻿

G is the centroid of DeltaABC. If AG = BC, then measure of /_BGC is

Let A be a 3xx3 matrix such that (A-2.2I_(3))(A-3.8 I_(3))=O_(3xx3) then trace of A+ 8.36A^(-1) is ________

Evaluate the following integrals intx sec^(-1)x dx

The value of k for which the circle x^(2) + y^(2) -4x + 6y +3 =0will bisect the circumferece of the circle x^(2) +y^(2) +6x -4y +k=0is

Let veca=(cos theta)hati-(sin theta)hatj, vecb=(sin theta)hati+(cos theta)hatj,vecc=hatk and vecr=7hati+hatj+10hatk. IF vecr=x veca+y vecb+z vecc, then the value of (x^(2)+y^(2))/(z) is equal to

Log_(e) ((1 + i)/(1- i))=

y=3x-2 is a straightline touching the parabola (-3)^(2)=12(x-2) if a line drawnperpendicular to this line at p on it touches the given parabola then the point p is

Evaluate the following integrals. int(3x^(2))/(1+x^(6))dx

Three cards are drawn successively without replacement from a pack of 52 well shuffled cards. What is the probability that the first two cards are kings and the third is an ace?

The locus of the points of intersection of perpendicular normals of the parabola y^2=4ax is

Find the antiderivative (or integral) of the following functions by the method of inspection. e^(2x)

If the area of the triangle with vertices (2,-6), (5,4) and (k,4) is 35 square units, find values of kusing determinants.

If f(x) = int_(0)^(x) t.e^(t) dt then f'(-1)=

Findthe area of the region bounded by y= sinx, y = cosxand ordinatesx = 0, x = pi//2.

Find the number of divisors of the number 2^(10).5^(10).11^(11).13^(13)which of the form 4n+1(nge0)

Let Let 1/x_1,1/x_2...1/x_n(x _i ne0" for "i=1,2,...n) in A.P. Such that x_1=3 and x_21=20.If n is the least positiveinteger for which x_n gt 50" then" sum_(i=1)^n(1/x_i) is equal to:

If y= cos^(-1)x, Find (d^(2)y)/(dx^(2)) in terms of y alone

Find the range of x for which the following expansions are valid . (2-(3x)/(4))^(-15//4)

If the lines (2x-5)/(k)= (y+2)/(-5) = (z)/(1) and (x)/(1) = (y)/(2) = (z)/(3) are perpendicular to each other, then value of k is....................

If sum_(k=1)^n ɸ(k)=2_n/(n+1),then sum_(k=1)^10 1/(ɸ(k))isequal to

OP is a tower of height 20 m and AB is a pole of height 5 m. The angle of elevation of the top P of the tower from the top B of the pole is 45^(@). Both pole and tower stand on the same ground. The angle of elevation of the top P of the tower from the base A of the pole is

Equation of circle with centre (-1,2) and passing through the centroid of triangle formed by (3,1),(2,-1) and (1,3) is

If int_(0)^(x)2xf^(2)(t)dt=(int_(0)^(x)2f(x-t)dt)^(2) for f(1)=1 and f(x) is comtinuos function for xgto and {a_(n)} is a sequence such that a_(n+1)=a_(n)+sqrt(1+a_(n)^(2)) for a=0, if f(x) is an increasing function, then lim_(nto oo)(a_K)/(2^(n-1))= (where k=f(n^(sqrt2-1)))is

If the rangeof a discreter dateof n observation on is zero, then

The sum of the coefficients in the binomial expansion of (1/x + 2x)^n is equal to 6561. The constant term in the expansionis

Solve graphically 5x + 6y lt 12

A game consists of tossing a coin 3 times and nothing its outcome. A boy wins if all tosses give the same outcomes and losses otherwise. Find the probability that the boy losses the game.

If from the point (alpha,alpha^2) two tangents drawn to any one branch of hyperbola x^2-4y^2=1, then :

Ifx=a( theta+ sintheta)and y=a(1- costheta), prove that(dy)/(dx) = tan ""(theta//2)

If a is a root of x^(2) - 3x-5=0 find the value of a^(4) - 2a^(3) - 7a^(2) -8a

ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 represents two parallel straight lines if

The points (5, -4, 2), (4, -3, 1), (7, -6, 4) and (8, -7, 5) are the vertices of a

Three dice are rolled simultaneously . The probability that the sum of the numbers on them is 6 is

There are 3 bags A , B and C. Bag A contains 2 white and 3 black balls, bag B contains 4 white and 2 black balls and Bag C contains 3 white and 2 black balls. If a ball is drawn at random from a randomly chosenbag, then the probability that the ball drawn is black, is

IF an error of 0.01 cm is made while measuring the radius 2 cm of a circle, then the relative error in the circumference is

intcos^2xdx

If 0 ltx ltpiand cosx + sinx = 1/2 , thentan xis

Let f (x) be a polynomial of degree three such that f(0) = 1, f(1) = 2 and 0 is a critical point of f(x) such that f(x) does not have a local extremum at 0. Them int(f(x))/(x^(2)+1) dx is equal to

If ax + by = 1, cx^2 + dy^2 = 1 have only one solution, then a^2/c + b^2/d =1 and x= a/c, y=b/d

A : cos 40^(@) cos 80^(@) cos 160^(@) =-1//8 R :cos theta cos (120^(@) - theta ) cos (120^(@) + theta ) =(1)/(4) cos 3 theta

(3x^(2) + 1)/(x^(2) -6x + 8) is equal to

Find the equation of the normal at theta=(pi)/(3) to the hyperbola 3x^(2)-4y^(2)=12.

A die marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A be the event, 'the number is even,' and B be the event, 'the number is red'. Are A and B independent?