28278 + Interview Questions in Maths in Class 12

1.	If 4 + (4 +d)/( 5) + (4 + 2d)/(5 ^(2)) ……….=1, then find d.
Answer» ANSWER :`- (64)/(5)`

Discussion

2.	Let X ={ ({:(a , b),(c,d):}) : a, b,c, d in R} Define f: X to Rby f(A) = det (A) , AA A in x . then , f is
Answer» ONE - one but not ONTO onto but not one - one one- one and onto NEITHER one - one nor onto ANSWER :B

Discussion

3.	int_(-2 pi)^(2pi) Sin^(5) x dx=
Answer» 0 `(3pi)/(16)` `(8)/(15)` `(27)/(16)` ANSWER :A

Discussion

4.	Prove that the locus of point of intersection of two perpendicular normals to the parabola y^(2) = 4ax is the parabola y^(2) = a(x-3a).
Answer» <P> Answer :HENCE the locus of `P( x_(1), y_(1) )` is `y^(2) =a(x-3a)`

Discussion

5.	One balanced coin is tossed. If two head comes up then two balanced dice are tossed and sum of the numbers obtained on it is noted. If tail is obtain then one card is selected from the card numbered 1 to 9 and its number is noted. Then ....... is the probability of event that noted number from card is 7 or 8.
Answer» `(15)/(72)` `(13)/(36)` `(19)/(72)` `(19)/(36)` ANSWER :C

Discussion

6.	Prove that the function f(x)=2x^2-3x+2 is continuous at at x=1.
Answer»

Discussion

7.	If A=sqrt(3) cot 20^(@) - 4 cos20^(@) and B= sin12^(@) sin48^(@) sin54^(@) be such that A + lambdaB=2, then the value of lambda^(3) +2000 is …………….
Answer» SOLUTION :2512

Discussion

8.	Prove the following: [[-a^2,ab,ac],[ab,-b^2,bc],[ac,bc,-c^2]]=4a^2b^2c^2
Answer» Solution :`[[-a^2,AB,ac],[ab,-b^2,bc],[ac,bc,-c^2]]` =`ABC[[-a,a,a],[b,-b,b],[c,c,-c]]`0,2A,a],[0,0,b],[2c,0,-c]]` (`C_1=C_1+C_2` `C_2=C_2+C_3`) =`abcxx2c[[2a,a],[0,b]]` `abcxx2c(2ab-0)` =`4a^2b^2c^2`

Discussion

9.	If bar(x)=(3,1,0),bar(y)=(2,2,3),bar(z)=(-1,2,1). If bar(x)_\|_(bar(y)+k bar(z)) then k = ……………
Answer» 8 4 `(1)/(8)` `(1)/(4)` ANSWER :A

Discussion

10.	Choose the correct answers If f (a + b - x) = f (x), then int_(a)^(b)xf(x) dx is equal to
Answer» `(a+B)/2int_(a)^(b)F(b-X)DX` `(a+b)/2int_(a)^(b)f(b+x)dx` `(b-a)/2int_(a)^(b)f(x)dx` `(a+b)/2int_(a)^(b)f(x)dx` ANSWER :D

Discussion

11.	Classify the following gas scalar and vector quantities : (i) Distance (ii) Displacement (iii) Force (iv) Velocity (v) Time (vi) Speed
Answer» Answer :SCALAR : (i), (III), (V), (vi), VECTOR : (II), (iv)

Discussion

12.	Find the area of the region bounded by the curves y= x^(2) and y= (2)/(1+x^(2))
Answer» ANSWER :`PI-(2)/(3)`

Discussion

13.	cos[cos^(-1)(-1/7)+sin^(-1)(-1/7)] is equal to
Answer» `-1/3` `0` `1/3` `4/9` ANSWER :B

Discussion

14.	A line segment AM=a moves in the XOY plane such that AM is parallel to the X-axis. If A moves along the circle x^(2)+y^(2)=a^(2), then the locus of M is
Answer» `X^(2)+y^(2)=4A^(2)` `x^(2)+y^(2)=2ax` `x^(2)+y^(2)=2ay` `x^(2)+y^(2)=2ax+2ay` ANSWER :B

Discussion

15.	If the hyperbola xy = c^(2) touches the curve x^(2) + 2y^(2) + alpha xy = c^(2), then value of alpha is /are
Answer» `1- 2 SQRT2` `1 + 2 sqrt2` `1 PM 2 sqrt2` none of these Solution :N/A

Discussion

16.	A die is thrown 3 times. Find the probability of the event of getting sum of the numbers thrown as 15 when it is known that the first throw was a five.
Answer» ANSWER :`(1)/(12)`

Discussion

17.	If the vector veca=2hati+3hatj+6hatk and vecb are collinear and \|vecb\|=21," then "vecb is equal to
Answer» `PM (2hati+3hatj+6hatk)` `pm 3(2hati+3hatj+6hatk)` `(hati+hatj+hatk)` `pm 21 (2hati+3hatj+6hatk)` ANSWER :B

Discussion

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

Discussion

19.	The conic represented by 2x^(2) -12xy +23y^(2) -4x -28y -48 =0is
Answer» ANSWER :the GIVEN EQUATION REPRESENTS an ELLIPSE.

Discussion

20.	Four points are such that the line joining any two points is perpendicular to the line joining other two points. If three point out of these lie on a rectangular hyperbola, then the fourth point will lie on
Answer» the same HYPERBOLA the CONJUGATE hyperbola one of the directrix one of the asymptotes Solution :The POINT are such that one of the POINTS is the orthocenter of the triangle formed by other three points. When the vertices of a triangle LIE on a rectangular hyperbola, the orthocenter also lies on the same hyperbola.

Discussion

21.	Write the value of inte^(logcot^2x)dx
Answer» SOLUTION :`INTE^(Incot^2x)dx=intcot^2xdx=int(cosec^2x-1)dx=-cotx-x+c`

Discussion

22.	int (4x^(2) +x+1)/(x^(3) -1) dx=?
Answer» `log (x-1) -log (x^(3) -1) +C` `log (x^(3) -1) +log (x-1)+c` NONE of the above Answer :C

Discussion

23.	The modulus argument form of 1+iTantheta when theta epsilon (pi/2,pi) is
Answer» `SecthetaCIstheta` `-SecthetaCis(pi+theta)` `-SecthetaCis(theta-pi)` NONE of these Answer :C

Discussion

24.	int(cos2x-cos2alpha)/(cosx-cosalpha)dx
Answer» SOLUTION :`I=INT(cos2x-cos2alpha)/(cosx-cosalpha)DX` =`int((2cos^2x-1)-(2cos^2alpha-1))/(cosx-cosalpha)dx` =`2int(cosx+cosalpha)dx` =`2sinx+2xcosalpha+c`

Discussion

25.	If A and B are symmetric matrices , then ABA is :
Answer» symmetricmatrix skew - SYMMETRIC MATRIX SINGULAR matrix non - singular matrix ANSWER :A

Discussion

26.	A man can just push a box on 37^(@) concreate slope. When he keeps it at the point where the angle is 53^(@), he can just hold it from sliding black. If the coeffieceint of friction between the box and the concreate slope is mu find (1)/(mu). Assume that the man is applying same magnitude of force along the tangent to the curve only .
Answer» ANSWER :`7.00`

Discussion

27.	Evaluate int(2x - 5)/(3x^(2) + 4x + 5) dx.
Answer» ANSWER :`1/3log\|3x^(2)+4x+5\|-(19)/(3sqrt(11))tan^(-1)((3x+2)/(SQRT(11)))+c`

Discussion

28.	A vertical pole PO stands at the centre of a square ABCD. If AC subtends an angle 90° at the top P of the pole, then the angle subtended by a side of the square at Pis:
Answer» `30^(@)` `45^(@)` `60^(@)` NONE of these Answer :C

Discussion

29.	If vec(a) and vec(b) are two vectors such that \|vec(a)\| = \|vec(b)\| = sqrt(2) and vec(a).vec(b) = -1, then find the angle between them.
Answer» ANSWER :`THETA = (2PI)/(3)`

Discussion

30.	For each of the differential equations given inExercises 1 to 12, find the generalsolution : 1.(dy)/(dx) + 2y = sin x
Answer» ANSWER :`y = (1)/(5)(2 SIN x - cos x) + CE^(-2x)`

Discussion

31.	Evaluate intsqrt(e^(x)-4)dx
Answer» Answer :`2[sqrt(E^(X)-4)-2TAN^(-1)((1)/(2)sqrt(e^(x)-4))]+C`

Discussion

32.	Solve the following : [[2,2,x],[-1,x,4],[1,1,1]]=0
Answer» SOLUTION :`[[2,2,x],[-1,x,4],[1,1,1]]`=0 or, `[[0,2+2x,x+8],[0,x+1,5],[1,1,1]]`=0 (REPLACING `R_1` and `R_2` by `R_1+2R_2` and `R_2+R_3`) or, `1XX[[2+2x,x+8],[x+1,5]]`=0 or, `10+10x-x^2-8x-x-8=0` or, `x^2-2x+x-2=0` or, (x-2)(x+1)=0 `therefore` x=2,x=-1

Discussion

33.	Let M and m respectively denote the maximum and the minimum values of [f(theta)^2],where f(theta)=sqrt(a^2+cos^2theta+b^2sin^2theta)+sqrt(a^2 sin^2 theta+b^2 cos^2 theta). Then M-m=
Answer» `a^2+B^2` `(a-b)^2` `a^2 b^2` `(a+b)^2` ANSWER :B

Discussion

34.	A group of 10 items has mean 6. If the mean of 4 of these items is 7.5, then the mean of the remaining items is :
Answer» 6.5 5.5 4.5 `5.0` ANSWER :C

Discussion

35.	BaCO_(3)(s)+AcOHunderset(Delta)overset(Na_(2)C_(2)O_(4)"Solution")rarr? Comment on the product of this reaction.
Answer» `BaCO_(3)` remains UNAFFECTED. `BaC_(2)O_(4)` will be precipitated as white PRECIPITATE `BA(Oac)_(2)` will be precipitated as white precipitate Clear solution Solution :`rArr` PPT of `BaCO_(3)` and `BaC_(2)O_(4)` are soluble in `CH_(3)CO OH`.

Discussion

36.	Which of the following is incorrect regarding n^(th) roots of unity ?
Answer» There are `n` distinct roots The roots are in GP with COMMON RATIO `(2pi)/(n)` The ARGUMENT are in AP with common difference `(2pi)/(n)` PRODUCT of the roots `=0` Answer :D

Discussion

37.	Sand is pouring from a pipe at the rate of 12cm^(3)//sec. The falling sand forms a cone on the ground in such a way that the height of the cone is always one-sixth of the radius of the base. How fast is the height of the sand cone increasing when the height is 4 cm?
Answer» ANSWER :`(DH)/(DT)=1/(48pi)cm//s`

Discussion

38.	If the position vectors of the vertices A, B and C of DeltaABC are respectively vec(0),-20hat(i)+15hat(j)and36hat(i)+15hat(j), then find the position vector of the incentre of the triangle.
Answer» `HAT(i)+8hat(J)` `2HAT(i)+3HAT(j)` `4hat(i)+3hat(j)` `2hat(i)-5hat(j)` ANSWER :A

Discussion

39.	The substitution required to change equation (dy)/(dx) = (2x+3y+5)/(4x+6y+9) into variable separable is
Answer» `4X - 6y=z` `2X + 3y=z` `2x-3y = z` `y = v x` Answer :B

Discussion

40.	Show that the equations of common tangents to the circle x^(2)+y^(2)=2a^(2) and the parabola y^(2)=8ax "are" y=+-(x+2a).
Answer» ANSWER :`rArry=+-(x+2a)`

Discussion

41.	lim_(xto0)(sqrt(1+x^(2))-1)/(1-cosx)=
Answer» 1 `1/2` `1/4` `OO` ANSWER :A

Discussion

42.	For a random variable X given that P(X = k) = 2^(-k) find the mean and variance of X.
Answer» ANSWER :MEAN= 2, VARIANCE = 2

Discussion

43.	If a and b are positive integers, and x = 2 cdot 3 cdot 7 cdot a and y = 2 cdot 2 cdot 8 cdot b, and the values of both x and y lie between 120 and 130 (not including the two), then a - b =
Answer» `-2` `-1` `0` `1` ANSWER :B

Discussion

44.	Express the following as trigonometric ratios of some acute angles.tan 235^@
Answer» SOLUTION :`TAN 235^@ = tan (180^@ + 45^@) = tan 45^@`

Discussion

45.	The solution of y-x((dy)/(dx)) = a(y^(2) + (dy)/(dx)) is
Answer» `(x+a)(y+a) = CY` `(x+a)(y-a) = cy` `(x+a)(y+(1)/(a)) = cy` `(x+a)(1-ay) = cy` ANSWER :D

Discussion

46.	Photo electric effect supports the quantum nature of light because:
Answer» there is a minimum frequency of light below which no photoelectrons are emitted. the maximum K.E. of photoelectrons depends only on the frequency of light and not on its intensity. even when the METAL SURFACE is FAINTLY illuminated by light of the approximate wavelength, the photoelectrons leave the surface immediately. ELECTRIC charge of photoelectrons is quantized. Answer :C

Discussion

47.	Statement: If sin A =sin B, cos A=cos B then A=2n pi +B Statement :II If A+B+C=90^(@) then sin 2A+sin 2B+sin 2C=sin A sin B sin C Which of the above statement is correct?
Answer» only I only II Both I and II Neither I nor II Answer :A

Discussion

48.	Let a = coefficient of x^(20) in (1+x+2x^(2)+3x^(3)+…+20x^(20))^(2)," then "(1)/(137) a=
Answer» ANSWER :10

Discussion

49.	If z = i(1+sqrt(3)),"then"z^(4)+2z^(3)+4z^(2) + 5 is equal to
Answer» 5 -5 `2 SQRT(3)i` `-2 sqrt(3)i` ANSWER :A

Discussion

50.	There are 10 examination papers for a course. i. Find out in how many ways these examination papers can be arranged. ii. Find out in how many ways these papers can be arranged so that two papers must be consecutive. iii. Find out in how many was these papers can be arranged so that two particular papers should not be consecutive.
Answer» <P> Answer :i. `""^(10)P_(10)=10!` II. `9!xx2!` iii. `8xx9!`

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

If 4 + (4 +d)/( 5) + (4 + 2d)/(5 ^(2)) ……….=1, then find d.

Let X ={ ({:(a , b),(c,d):}) : a, b,c, d in R} Define f: X to Rby f(A) = det (A) , AA A in x . then , f is

int_(-2 pi)^(2pi) Sin^(5) x dx=

Prove that the locus of point of intersection of two perpendicular normals to the parabola y^(2) = 4ax is the parabola y^(2) = a(x-3a).

Prove that the function f(x)=2x^2-3x+2 is continuous at at x=1.

If A=sqrt(3) cot 20^(@) - 4 cos20^(@) and B= sin12^(@) sin48^(@) sin54^(@) be such that A + lambdaB=2, then the value of lambda^(3) +2000 is …………….

Prove the following: [[-a^2,ab,ac],[ab,-b^2,bc],[ac,bc,-c^2]]=4a^2b^2c^2

If bar(x)=(3,1,0),bar(y)=(2,2,3),bar(z)=(-1,2,1). If bar(x)_|_(bar(y)+k bar(z)) then k = ……………

Choose the correct answers If f (a + b - x) = f (x), then int_(a)^(b)xf(x) dx is equal to

Classify the following gas scalar and vector quantities : (i) Distance (ii) Displacement (iii) Force (iv) Velocity (v) Time (vi) Speed

Find the area of the region bounded by the curves y= x^(2) and y= (2)/(1+x^(2))

cos[cos^(-1)(-1/7)+sin^(-1)(-1/7)] is equal to

A line segment AM=a moves in the XOY plane such that AM is parallel to the X-axis. If A moves along the circle x^(2)+y^(2)=a^(2), then the locus of M is

If the hyperbola xy = c^(2) touches the curve x^(2) + 2y^(2) + alpha xy = c^(2), then value of alpha is /are

A die is thrown 3 times. Find the probability of the event of getting sum of the numbers thrown as 15 when it is known that the first throw was a five.

If the vector veca=2hati+3hatj+6hatk and vecb are collinear and |vecb|=21," then "vecb is equal to

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

The conic represented by 2x^(2) -12xy +23y^(2) -4x -28y -48 =0is

Four points are such that the line joining any two points is perpendicular to the line joining other two points. If three point out of these lie on a rectangular hyperbola, then the fourth point will lie on

Write the value of inte^(logcot^2x)dx

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

The modulus argument form of 1+iTantheta when theta epsilon (pi/2,pi) is

int(cos2x-cos2alpha)/(cosx-cosalpha)dx

If A and B are symmetric matrices , then ABA is :

Evaluate int(2x - 5)/(3x^(2) + 4x + 5) dx.

A vertical pole PO stands at the centre of a square ABCD. If AC subtends an angle 90° at the top P of the pole, then the angle subtended by a side of the square at Pis:

If vec(a) and vec(b) are two vectors such that |vec(a)| = |vec(b)| = sqrt(2) and vec(a).vec(b) = -1, then find the angle between them.

For each of the differential equations given inExercises 1 to 12, find the generalsolution : 1.(dy)/(dx) + 2y = sin x

Evaluate intsqrt(e^(x)-4)dx

Solve the following : [[2,2,x],[-1,x,4],[1,1,1]]=0

Let M and m respectively denote the maximum and the minimum values of [f(theta)^2],where f(theta)=sqrt(a^2+cos^2theta+b^2sin^2theta)+sqrt(a^2 sin^2 theta+b^2 cos^2 theta). Then M-m=

A group of 10 items has mean 6. If the mean of 4 of these items is 7.5, then the mean of the remaining items is :

BaCO_(3)(s)+AcOHunderset(Delta)overset(Na_(2)C_(2)O_(4)"Solution")rarr? Comment on the product of this reaction.

Which of the following is incorrect regarding n^(th) roots of unity ?

Sand is pouring from a pipe at the rate of 12cm^(3)//sec. The falling sand forms a cone on the ground in such a way that the height of the cone is always one-sixth of the radius of the base. How fast is the height of the sand cone increasing when the height is 4 cm?

If the position vectors of the vertices A, B and C of DeltaABC are respectively vec(0),-20hat(i)+15hat(j)and36hat(i)+15hat(j), then find the position vector of the incentre of the triangle.

The substitution required to change equation (dy)/(dx) = (2x+3y+5)/(4x+6y+9) into variable separable is

Show that the equations of common tangents to the circle x^(2)+y^(2)=2a^(2) and the parabola y^(2)=8ax "are" y=+-(x+2a).

lim_(xto0)(sqrt(1+x^(2))-1)/(1-cosx)=

For a random variable X given that P(X = k) = 2^(-k) find the mean and variance of X.

If a and b are positive integers, and x = 2 cdot 3 cdot 7 cdot a and y = 2 cdot 2 cdot 8 cdot b, and the values of both x and y lie between 120 and 130 (not including the two), then a - b =

Express the following as trigonometric ratios of some acute angles.tan 235^@

The solution of y-x((dy)/(dx)) = a(y^(2) + (dy)/(dx)) is

Photo electric effect supports the quantum nature of light because:

Statement: If sin A =sin B, cos A=cos B then A=2n pi +B Statement :II If A+B+C=90^(@) then sin 2A+sin 2B+sin 2C=sin A sin B sin C Which of the above statement is correct?

Let a = coefficient of x^(20) in (1+x+2x^(2)+3x^(3)+…+20x^(20))^(2)," then "(1)/(137) a=

If z = i(1+sqrt(3)),"then"z^(4)+2z^(3)+4z^(2) + 5 is equal to