28278 + Interview Questions in Maths in Class 12

1.	Out of 3n consecutive natural numbers m, m+ 1, m + 2, .., m + 3n – 1, three are selected at random without replacement. Let p be the probability that sum of the three numbers is divisible by 3.If p=31/91, then n is equal to ____
Answer» ANSWER :5

Discussion

2.	int_(0)^(7) [x]dx=
Answer» 21 20 22 23 Answer :A

Discussion

3.	Differentiate the following w.r.t.x e^x/sinx
Answer» SOLUTION :`d/dx((e^X)/(SINX))=(SIN"x"xxe^x-e^"x"xxcosx)/(sin^2x)=(e^2[sinx-cosx])/(sin^2x)`

Discussion

4.	The points on the curve 9y^(2) = x^(3) , where the normal to the curve makes equal intercepts with the axes are
Answer» `(4, PM (8)/(3))` `(4,(-8)/(3))` `(4,pm(3)/(8))` `(pm 4,(3)/(8))` ANSWER :A

Discussion

5.	The set of value ofp for which the roots of the equation3x^(2)+2x+p(p-1)=0 are of opposite signs is
Answer» `(-OO, 0)` `(0, 1)` `(1, oo)` `(0, oo)` ANSWER :B

Discussion

6.	If C_(r) stands for ""^(n)C_(r) and sum_(r=1)^(n)(r*C_(r))/(C_(r-1))=210, then n equals:
Answer» 19 20 21 none of these Answer :B

Discussion

7.	(1-costheta+isintheta)^6=
Answer» `2^6sin^6(THETA)/(2)(icos3theta+sin3theta)` `2^6sin^6(theta)/(2)(sin3theta-icos3theta)` `2^6sin^6(theta)/(2)(cot3theta+isin3theta)` `2^6sin^6(theta)/(2)(-cot3theta+isin3theta)` ANSWER :B

Discussion

8.	A bag contains 50 tickets numbered 1, 2, 3, ... 50 of which five are drawn at random and arranged in ascending order of magnitude (x_(1) < x(2) < x_(3) < x_(4) < x_(5)). The probability that x_(3) cdot x_(4) = 85 is
Answer» `(.^(48)C_(3))/(.^(50)C_(5))` `(99)/(.^(50)C_(5))` `(99)/(5.^(49)C_(4))` `(33)/(.^(49)C_(4))` Solution :`{1,2,3,4} overset(5 17)(------){18,19,.....,50}` Required probability = `(.^(4)C_(2) xx .^(33)C_(1))/(.^(50)C_(5)) = 99/(5.^(49)C_(4))`.

Discussion

9.	Evaluate the integerals. int sqrt((5-x)/(x-2))dx on (2,5)
Answer» `sqrt(7x-x^(2)-10)-(3)/(2)Sin^(-1)((2x+7)/(3))+c` `sqrt(7x+x^(2)-10)-(3)/(2)Sin^(-1)((2x-7)/(3))+c` `sqrt(7x-x^(2)-10)+(3)/(2)Sin^(-1)((2x-7)/(3))+c` `sqrt(7x-x^(2)-10)+(3)/(2)Sin^(-1)((2x+7)/(3))+c` Answer :C

Discussion

10.	If 3 "tan^(-1)x+cot^(-1)x-=pi then x equal to
Answer» a.0 B.1 c.`-1` d.`1//2` ANSWER :B

Discussion

11.	The table above can be used to approximate the circumference of the head, in centimeters, during the first 5 years after birth. At 5 years of age, Jacob's head circuference was 81 cm. Based on the table, what was his approximate height,inn centimeters, at 1 years old?
Answer» `138` `145` `152` `157` ANSWER :A

Discussion

12.	The orthocentre of the triangle formed by three tangents to the parabola y^(2)=4ax lies on the
Answer» AXIS DIRECTRIX PARABOLA LATUS rectum Answer :B

Discussion

13.	The general solution of y^(2)dx+(x^(2)-xy+y^(2))dy=0 is
Answer» `TAN^(-1)((x)/(y)) + LOG y + c = 0` `2tan^(-1)((x)/(y)) + log x + c = 0` `log(y + sqrt(x^(2) + y^(2))) + log y + c = 0` `sin h^(-1)((x)/(y)) + log y + c = 0` ANSWER :A

Discussion

14.	Find the values of k so that the function f is continuous at the indicated point in Exercises 26 to 29. f(x)={{:((k cos x)/(pi -2x)," if "x ne (pi)/(2)),(3," if "x= (pi)/(2)):}" at "x=(pi)/(2).
Answer» ANSWER :`k=6`

Discussion

15.	Assertion (A) : The area bounded by one of the arcs of y=cos ax and X-axis is 2/a s.units.Reason ( R ): The area bounded by y=f(x)gt0 and y = 0 between x = a and x = b is underset(a)overset(b)int ydx The correct answer is
Answer» Both (A) and ( R ) are TRUE and R is the CORRECT EXPLANATION of A Both (A) and ( R ) are true and R is not the correct explanation of A (A) is true, ( R ) is false (A) false ( R ) is true Answer :A

Discussion

16.	Find the values of k so that the function f is continuous at the indicated point in Exercises 26 to 29. f(x)={{:(kx+1," if "x le 5),(3x-5," if "x gt 5):}" at "x= 5.
Answer» ANSWER :`K=(9)/(5)`

Discussion

17.	int(1+x)/(1+3sqrt(x))dx is equal to
Answer» `(3)/(5)X^(5//3)+x-(3)/(4)x^(4//3)+x+C` `(3)/(5)x^(5//3)-(3)/(4)x^(4//3)+C` `(3)/(5)x^(5//3)-(3)/(4)x^(4//3)+C` NONE of these Answer :a

Discussion

18.	Find the values of k so that the function f is continuous at the indicated point in Exercises 26 to 29. f(x)={{:(kx^(2)," if "x le2),(3," if "x gt 2):}" at "x= 2.
Answer» ANSWER :`K=(3)/(4)`

Discussion

19.	Using integration , find the area bounded between the curvey = x^(2) and y=- \|x\| + 2
Answer» Answer :` 2(1)/(3)` SQ units

Discussion

20.	If 1^circ=alpha radians, then the approximate value of cos(60^circ1')
Answer» `1/2+(alpharoot()3)/120` `1/2-alpha/120` `1/2-(alpharoot()3)/120` `1/2+alpha/120` ANSWER :C

Discussion

21.	Find the value of x and y from the equation. [{:(3x+7,5),(y+1,2-3x):}]=[{:(-2,5),(1,11):}]
Answer» ANSWER :`x=-3,y=0`

Discussion

22.	Find the values of k so that the function f is continuous at the indicated point in Exercises 26 to 29. f(x)={{:(kx+1," if "x le pi),(cos x," if "x gt pi):}" at "x= pi.
Answer» ANSWER :`K=(-2)/(PI)`.

Discussion

23.	Find all the points of discontinuity of f defined by f(x) = \|x\| - \|x+1\|
Answer» ANSWER :`AA X in R`

Discussion

24.	A spherical balloon subtends an angle 2 alpha at a man's eye and the elevation of its centre is beta. If theta is the elevation of the hightest point of the balloon at A then tan theta is equal to
Answer» `(SIN alpha + COS BETA)/(sin beta)` `(sin alpha + sin beta)/(cos beta)` `(sin alpha + cos beta)/(sin alpha)` `(sin alpha + sin beta)/(cos alpha)` ANSWER :B

Discussion

25.	Evaluateint (dx)/(5+ 4 cos x ).
Answer» ANSWER :`(1)/(3) TAN^(-1) ((1)/(3) tan THETA)+ C `

Discussion

26.	The probability distribution of a random variable X is given below. Find mean and variance of X.
Answer» ANSWER :`11//3, 14//9`

Discussion

27.	Differentiate (lnx)/x^2
Answer» Solution :`y=lnx/x^2` `(DY)/(dx)=(d/(dx)(lnx)cdotx^2-lnxcdotd/(dx)(x^2))/((x^2)^2)` `=(1/xcdotx^2-lnxcdot2x)/x^4=(x-2xcdotlnx)/x^4` `(1-2lnx)/(x^3)=(lne-lnx^2)/(x^3)=(LN(e/x^2)/x^3`

Discussion

28.	Integrate the following : int(x+3)(2-x)dx
Answer» SOLUTION :`INT(x+3)(2-x)DX` =`int(2x+6-x^2-3x)dx` =`int(-x^2-x+6)dx` `-1/3x^3-1/2x^2+6x+C`

Discussion

29.	If the mean of a Poisson distribution is 1/2 , then the ratio of P(X = 3) to P(X = 2)is
Answer» `1:2` `1:4` `1:6` `1:8` ANSWER :C

Discussion

30.	For the circle x^(2)+y^(2)-2x+2y+1=0, the points (-6,1),(2,3),(14/15,-11/15) are
Answer» collinear lie on a diameter pair WISE conjuate none Answer :C

Discussion

31.	Prove that \|{:(yz-x^2,zx-y^2,xz-z^2),(zx-y^2,xy-z^2,yz-x^2),(xy-z^2,yz-x^2,zx-y^2):}\|=\|{:(r^2,U^2,U^2),(U^2,r^2,U^2),(U^2,U^2,r^2):}\| where r^2+y^2+z^2 and U^2=xy+yz+zx (Hint : Use \|adjA\|=\|A\|^2\|
Answer» ANSWER :`\|{:(r^2,U^2,U^2),(U^2,r^2,U^2),(U^2,U^2,r^2):}\|`

Discussion

32.	Let H be the orthocenter of triangle ABC, then angle subtended by side BC at the centre of incircle of DeltaCHB is :
Answer» `(A)/(2)+(PI)/(2)` `(B+C)/(2)+(pi)/(2)` `(B-C)/(2)+(pi)/(2)` `(B+C)/(2)+(pi)/(4)` ANSWER :B

Discussion

33.	If y=mx+c be a tangent to hyperbola (x^(2))/(lambda^(2))-(y^(2))/((lambda^(3)+lambda^(2)+lambda)^(2))=1, then least value of 16m^(2) equals to :
Answer» 0 1 4 9 Answer :D

Discussion

34.	Let S = {a,b,c} and T ={1,2,3}. Find F ^(-1) of the following F from S to T, if exists. (i) F = {(a,3), (b,2), (c,1)} (ii) F = {(a,2), (b,1), (c,1)}
Answer» Answer :`(i) F ^(-1) = {3,a) , (2,b) ,(1,c) } ,(II) F ^(-1) ` does not EXIST

Discussion

35.	Let A = { a,b,c }, absB = {1,2} Is there any relation which is both a relation from A to B and B to A ? How many ?
Answer» SOLUTION :`PHI` is the only RELATION which is from A to B and from B to A .

Discussion

36.	Differentiate a^(x) w.r.t x, where a is a positive constant
Answer» ANSWER :`a^(X) LOG a`

Discussion

37.	Differentiate the following w.r.t. x : e^(cos x)
Answer» ANSWER :`= -(SIN X)E^(COS x)`.

Discussion

38.	If f(x) be an even function. Then f'(x)
Answer» is an EVEN function is an ODD function may be even or odd none of these Answer :B

Discussion

39.	Let f(x)=lim_(nrarro)(cos sqrt((x)/(n)))^(n), g(x)=lim_(nrarroo)(1-x+xrootn(e ))^(n) Now consider the function y=h(x)," where " g(x)=tan^(-1)(g^(-1)(f^(-1)(x))) lim_(xrarr0)(ln(f(x)))/(ln(g(x)))
Answer» `1//2` `-1//2` 0 1 Answer :B

Discussion

40.	Choose the correct answer. int dx/(e^x+e^-x) =
Answer» `tan^-1(e^x)+C` `tan^-1(e^-x)+c` `LOG(e^x-e^-x)+c` `log(e^x+e^-x)+c` ANSWER :A

Discussion

41.	Find the number of numbers that are greater than 4000 which can be formed using the digits 0,2,4,6,8 without repetition.
Answer» ANSWER :168

Discussion

42.	On N^() = N-{1}, define a relation as follows: a,b in N, aRb if thereexists m in N^(), such that m\|a and m\|b, Then
Answer» R is reflexive and SYMMETRIC only R is symmetric and TRANSITIVE only R is anti-symmetric R is an equivalence relation ANSWER :A

Discussion

43.	if A = [[cos theta, sin theta],[-sin theta, cos theta]] where theta = (2pi)/(7) then sum_(r=1)^(6) A^(r) =
Answer» `[[1,0],[0,1]]` `[[3,0],[0,3]]` `[[-1,0],[0,-1]]` NONE of these Solution :`A + A^(2) + A^(3) + A^(4) + A^(5) + A^(6)` `=[[COS THETA + cos 2 theta + cos 3 theta + cos 4 theta + cos 5 theta + cos 6 theta""sin theta + sin 2 theta+ sin 3theta+ sin 4 theta + 5 sin theta + sin 6 theta],[-[sin theta + sin 2 theta + sin theta + sin 4 theta+ sin 5 theta+ sin 6theta]"" cos theta + cos 2 theta + cos 3 theta + cos 4 theta + cos 5 theta + cos 6 theta]]` `=[[-1,0],[0,-1]]`

Discussion

44.	Evaluate the following definite integrals : int_(0)^(1)(dx)/(2x-3)
Answer» ANSWER :`-(1)/(2)LOG3`

Discussion

45.	Solve the following problem graphically : Minimise and Maximise Z = 3x + 9y "…(1)" subject to the constraints : x+3y le 60"…(2)" x+y ge 10 "…(3)" x le y"…(4)" x ge 0, y ge 0"…(5)"
Answer» Answer :The maximum value of Z on the feasible REGION occurs at the 2 CORNER POINTS C(15, 15) and D(0, 20) and it is 180 in each case.

Discussion

46.	Write down negations of Money is necessary for happiness.
Answer» SOLUTION :MONEY is not NECESSARY for HAPPINESS.

Discussion

47.	Evaluate the following integrals int x^(2)e^(-3x) dx
Answer» Answer :`-(e^(-3x))/(27)(9X^(2)+6x+2)+C`

Discussion

48.	Method of integration by parts : If intf(x)dx=phi(x) then intx^(5)f(x^(3))dx=..........
Answer» `(1)/(3)[x^(3)phi(x^(3))-intx^(2)phi(x^(3))dx]\+C` `(1)/(3)[x^(3)phi(x^(3))-3intx^(3)phi(x^(2))dx]+c` `(1)/(3)[x^(2)phi(x^(3))-3intx^(2)phi(x^(3))dx]+c` `(1)/(3)[x^(3)phi(x^(3))-3intx^(3)phi(x^(3))dx\]+c` Answer :C

Discussion

49.	Write the general solution of the differential equations : dy/dx=2/s^2
Answer» SOLUTION :`dy/dx=2/x^2rArr8y=2intx^-2dx=2((x^-1)/-1)+crArry=^(-2)/x=C` is the requaired SOLUATION

Discussion

50.	Compute [(p,q),(q,p)]+[(p,q),(-q,p)].
Answer» ANSWER :`[(2p,2q),(0,2p)]`

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Out of 3n consecutive natural numbers m, m+ 1, m + 2, .., m + 3n – 1, three are selected at random without replacement. Let p be the probability that sum of the three numbers is divisible by 3.If p=31/91, then n is equal to ____

int_(0)^(7) [x]dx=

Differentiate the following w.r.t.x e^x/sinx

The points on the curve 9y^(2) = x^(3) , where the normal to the curve makes equal intercepts with the axes are

The set of value ofp for which the roots of the equation3x^(2)+2x+p(p-1)=0 are of opposite signs is

If C_(r) stands for ""^(n)C_(r) and sum_(r=1)^(n)(r*C_(r))/(C_(r-1))=210, then n equals:

(1-costheta+isintheta)^6=

A bag contains 50 tickets numbered 1, 2, 3, ... 50 of which five are drawn at random and arranged in ascending order of magnitude (x_(1) < x(2) < x_(3) < x_(4) < x_(5)). The probability that x_(3) cdot x_(4) = 85 is

Evaluate the integerals. int sqrt((5-x)/(x-2))dx on (2,5)

If 3 "tan^(-1)x+cot^(-1)x-=pi then x equal to

The table above can be used to approximate the circumference of the head, in centimeters, during the first 5 years after birth. At 5 years of age, Jacob's head circuference was 81 cm. Based on the table, what was his approximate height,inn centimeters, at 1 years old?

The orthocentre of the triangle formed by three tangents to the parabola y^(2)=4ax lies on the

The general solution of y^(2)dx+(x^(2)-xy+y^(2))dy=0 is

Find the values of k so that the function f is continuous at the indicated point in Exercises 26 to 29. f(x)={{:((k cos x)/(pi -2x)," if "x ne (pi)/(2)),(3," if "x= (pi)/(2)):}" at "x=(pi)/(2).

Assertion (A) : The area bounded by one of the arcs of y=cos ax and X-axis is 2/a s.units.Reason ( R ): The area bounded by y=f(x)gt0 and y = 0 between x = a and x = b is underset(a)overset(b)int ydx The correct answer is

Find the values of k so that the function f is continuous at the indicated point in Exercises 26 to 29. f(x)={{:(kx+1," if "x le 5),(3x-5," if "x gt 5):}" at "x= 5.

int(1+x)/(1+3sqrt(x))dx is equal to

Find the values of k so that the function f is continuous at the indicated point in Exercises 26 to 29. f(x)={{:(kx^(2)," if "x le2),(3," if "x gt 2):}" at "x= 2.

Using integration , find the area bounded between the curvey = x^(2) and y=- |x| + 2

If 1^circ=alpha radians, then the approximate value of cos(60^circ1')

Find the value of x and y from the equation. [{:(3x+7,5),(y+1,2-3x):}]=[{:(-2,5),(1,11):}]

Find the values of k so that the function f is continuous at the indicated point in Exercises 26 to 29. f(x)={{:(kx+1," if "x le pi),(cos x," if "x gt pi):}" at "x= pi.

Find all the points of discontinuity of f defined by f(x) = |x| - |x+1|

A spherical balloon subtends an angle 2 alpha at a man's eye and the elevation of its centre is beta. If theta is the elevation of the hightest point of the balloon at A then tan theta is equal to

Evaluateint (dx)/(5+ 4 cos x ).

The probability distribution of a random variable X is given below. Find mean and variance of X.

Differentiate (lnx)/x^2

Integrate the following : int(x+3)(2-x)dx

If the mean of a Poisson distribution is 1/2 , then the ratio of P(X = 3) to P(X = 2)is

For the circle x^(2)+y^(2)-2x+2y+1=0, the points (-6,1),(2,3),(14/15,-11/15) are

Prove that |{:(yz-x^2,zx-y^2,xz-z^2),(zx-y^2,xy-z^2,yz-x^2),(xy-z^2,yz-x^2,zx-y^2):}|=|{:(r^2,U^2,U^2),(U^2,r^2,U^2),(U^2,U^2,r^2):}| where r^2+y^2+z^2 and U^2=xy+yz+zx (Hint : Use |adjA|=|A|^2|

Let H be the orthocenter of triangle ABC, then angle subtended by side BC at the centre of incircle of DeltaCHB is :

If y=mx+c be a tangent to hyperbola (x^(2))/(lambda^(2))-(y^(2))/((lambda^(3)+lambda^(2)+lambda)^(2))=1, then least value of 16m^(2) equals to :

Let S = {a,b,c} and T ={1,2,3}. Find F ^(-1) of the following F from S to T, if exists. (i) F = {(a,3), (b,2), (c,1)} (ii) F = {(a,2), (b,1), (c,1)}

Let A = { a,b,c }, absB = {1,2} Is there any relation which is both a relation from A to B and B to A ? How many ?

Differentiate a^(x) w.r.t x, where a is a positive constant

Differentiate the following w.r.t. x : e^(cos x)

If f(x) be an even function. Then f'(x)

Let f(x)=lim_(nrarro)(cos sqrt((x)/(n)))^(n), g(x)=lim_(nrarroo)(1-x+xrootn(e ))^(n) Now consider the function y=h(x)," where " g(x)=tan^(-1)(g^(-1)(f^(-1)(x))) lim_(xrarr0)(ln(f(x)))/(ln(g(x)))

Choose the correct answer. int dx/(e^x+e^-x) =

Find the number of numbers that are greater than 4000 which can be formed using the digits 0,2,4,6,8 without repetition.

On N^(*) = N-{1}, define a relation as follows: a,b in N, aRb if thereexists m in N^(*), such that m|a and m|b, Then

if A = [[cos theta, sin theta],[-sin theta, cos theta]] where theta = (2pi)/(7) then sum_(r=1)^(6) A^(r) =

Evaluate the following definite integrals : int_(0)^(1)(dx)/(2x-3)

Solve the following problem graphically : Minimise and Maximise Z = 3x + 9y "…(1)" subject to the constraints : x+3y le 60"…(2)" x+y ge 10 "…(3)" x le y"…(4)" x ge 0, y ge 0"…(5)"

Write down negations of Money is necessary for happiness.

Evaluate the following integrals int x^(2)e^(-3x) dx

Method of integration by parts : If intf(x)dx=phi(x) then intx^(5)f(x^(3))dx=..........

Write the general solution of the differential equations : dy/dx=2/s^2

Compute [(p,q),(q,p)]+[(p,q),(-q,p)].

On N^() = N-{1}, define a relation as follows: a,b in N, aRb if thereexists m in N^(), such that m|a and m|b, Then