28278 + Interview Questions in Maths in Class 12

1.	The mean of a data set consisting of 20 observation is 40. If one observation 53 was wrongly recorded as 33, then the correctmean will be
Answer» 41 49 `40.5` `42.5` ANSWER :A

Discussion

2.	Evaluate Lt_(n to oo)[(1)/(1+n)+(1)/(2+n)+(1)/(3+n)+"...."+(1)/(10n)]
Answer» Solution :`underset(nrarr0)(LT)[(1)/(1+n)+(1)/(2+n)+(1)/(3+n)+"......"+(1)/(10N)] = underset(nrarroo)("Lt")underset(r=1)overset(9n)sum(1)/(r+n)` `=underset(nrarroo)(Lt)underset(r=1)overset(9n)sum(1)/(n) (1)/((r/n)+1) = underset(0)overset(9)int(dx)/(x+1)=[ln(x+1)]_(0)^(9)=ln10`

Discussion

3.	The perpendicular distance from the point (1,-1) to the line x + 5y-9=0 is equal to
Answer» `SQRT((2)/(13))` `sqrt((13)/(2))` `(13)/(2)` `(2)/(13)` ANSWER :B

Discussion

4.	from a bag containing 4 red and 2 black balls, two balls are drawn. the probability of getting two black balls is:
Answer» `1/2` `1/3` `1/6` `1/15` ANSWER :D

Discussion

5.	Find the remainder when 7^(103) is divided by 5.
Answer» SOLUTION :N/A

Discussion

6.	If three unequal real numbers are in G.P. then their reciprocals are in -
Answer» `A.M. LT G.M.` `A.M. le G.M.` `A.M. GE G.M.` `A.M. GT G.M.` ANSWER :B

Discussion

7.	Prove that :int_(0)^(pi) (x sin x)/(1+sinx) dx=pi((pi)/(2)-1)
Answer»

Discussion

8.	If S.P and R are the sum, product and sum of the reciprocals of n terms of an increasing G.P respectively and S^(n) = R^(n).P^(k), then k is equal to
Answer» 1 2 3 None of these Answer :B

Discussion

9.	If f(x)=x^(3) and g(x)=x^(3)-4x in -2lt x lt 2, then consider the statements : (a) f(x) and g(x) satisfy Mean Value Theorem (b) f(x) and g(x) both satisfy Rolle's theorem (c ) Only g(x) satisfies Rolle's theorem. OF THE STATEMENTS
Answer» (a) and (B) are CORRECT (a) alone is correct None is correct (a) and (C) are correct Answer :D

Discussion

10.	C_0^2+3.C_1^2+5. C_2^2+….+(2n+1) .C_n^2=
Answer» `(N-2)((2N)!)/((n!)^2)` `(n-1)((2n)!)/((n!)^2)` `(n+2)((2n)!)/((n!)^2)` `(n+1)((2n)!)/((n!)^2)` ANSWER :D

Discussion

11.	The negation of p rarr (~p.vee q) is
Answer» <P>p `^^` (~Q) p `^^` (~ q) p` ^^` q (~ p )` ^^` q ANSWER :A

Discussion

12.	Evaluate int_(0)^(1)e^(2-3x)dx as a limit of a sum.
Answer» ANSWER :`(1)/(3)(E^(3)-(1)/(e))`

Discussion

13.	For the curve x = e^(t) cos t, y = e^(t) sin t the tangent line is parallel to x-axis when t is equal to
Answer» `-(PI)/(4)` `(pi)/(4)` 0 `(pi)/(3)` ANSWER :A

Discussion

14.	If three six faces fair dice are thrown together, then the probability that the sum of the numbers appearing on the dice is (p le k le 14) is
Answer» `(k^(2)-21k+83)/(216)` `(k^(2)+21k+83)/(216)` `(21k-k^(2)-83)/(216)` `(21k-k^(2)+83)/(216)` Answer :C

Discussion

15.	If x, y, z are positive real numbers, then minimum value of (z)/(x+y)+(x)/(y+z)+(y)/(x+z) is
Answer» ANSWER :1.5

Discussion

16.	Let f(x) = [{:((2^(x)+2^(3-x) - 6)/(sqrt(2^(-x))-2^(1-x))",","if",x gt 2),((x^(2) - 4)/(x - sqrt(3x - 2))",","if",x lt 2):},then
Answer» `f(2) = 8 rArr f` is continuous at x = 2 `f(2) = 16 rArr f` is continuous at x = 2 `f(2^(-)) ne f(2^(+)) rArr f` is discontinuous f has a REMOVABLE DISCONTINUITY at x = 2 Answer :C

Discussion

17.	Show that the direction cosines of a vector equally inclined to the axes OX, OY and OZ are (1)/(sqrt3). (1)/(sqrt3). (1)/(sqrt3).
Answer» Answer :`therefore L = m = N = (1)/(SQRT3)`

Discussion

18.	Lt_(ntooo){(n+1)/(n^(2)+1^(2))+(n+2)/(n^(2)+2^(2))+.......+1/(n)}
Answer» `pi/4 + 1/4 LOG 2` `pi/2 + 1/4 log 2` `pi/2 + 1/2 log 2` `pi/4 + 1/2 log 2` ANSWER :D

Discussion

19.	A coin and six faced die, both unbaised are thrown simultaneously . The probability of getting a head on the coin and an odd number on the die is
Answer» `1//2` `3//4` `1//4` `2//3` ANSWER :C

Discussion

20.	Derive the equation of a plane perpendicular to a given vector and passing through a given point in both vector and Cartesian form.
Answer» ANSWER :`A ( x-x_1) + B(y-y_1) + C ( z-z_1) = 0` is Cartesian form

Discussion

21.	Iff(x)=abs(x) and g(x)= [x] thenf@g(-1/2) is
Answer» 0 1 -2 -1 Answer :B

Discussion

22.	The number of ways in which 5 different coloured flowers be strung in the form of a garland is
Answer» 24 12 16 22 Answer :B

Discussion

23.	Given that a alpha^(2)+2b alpha +c!=0 and that the system of equations (a alpha =b)x+ay+bz=0, (b alpha+c)x+by+cz=0, (a alpha+b)y+(b alpha+c)z=0 has a non -trivial solution, then a,b,c lie in
Answer» ARITHMETIC progression GEOMETRIC progression Harmonic progression Arithmetic geometric progression Answer :B

Discussion

24.	If (x+c)/(1+x^2) where c is a constant , then when y is stationary , xy is equal to
Answer» `1//2` `3//4` `5//8` 1 Answer :A

Discussion

25.	Let X denote the number of hours you study during a randomly selected school day. The probability that X can take the values x, has the following form, where k is some unknown constant. P(X=x)={{:(0.1, "if "x =0),(kx, "if "x = 1or 2 ),(k(5-x), "if " x=3 or 4),(0,"otherwise"):} (a) Find the value of k. (b) What is the probability that you study at least two hours ? Exactly two hours? At most two hours?
Answer» ANSWER :(a) k=0.15, (B) 0.55

Discussion

26.	If 1, w, w^(2) are three cube roots of unity, then (1 - w+ w^(2)) (1 + w-w^(2)) is _______
Answer» 1)4 2)3 3)2 4)1 Answer :A

Discussion

27.	Find the second order derivatives of the functions given in Exercises 1 to 10. x. cos x
Answer» ANSWER :`-X COS x-2 SIN x`

Discussion

28.	When any two sides and one of the opposite acute angle are given, under certain additional conditions two triangles are possible. The case when two triangles are possible is called the ambiguous case. In fact when any two sides and the angle opposite to one of them are given either no triangle is posible or only one triangle is possible or two triangles are possible. In the ambiguous case, let a,b and angle A are given and c_(1), c_(2) are two values of the third side c. On the basis of above information, answer the following questions Two different triangles are possible when
Answer» `B SIN A LT a` `b sin A lt a and b GT a ` `b sin A lt a and b lt a ` `b sin A lt a and a =b` ANSWER :B

Discussion

29.	Integrate the functions (x^(3))/(sqrt(1-x^(8)))
Answer» ANSWER :`1/4sin^(-1)(X^(4))+C`

Discussion

30.	Find the particular solution of the differentialequation (dy)/(dx) = - 4xy^(2) given that y = 1, when x = 0.
Answer» ANSWER :`y = (1)/(2X^(2) + 1)`

Discussion

31.	If theta is the angle between the vectors overset(^)(i) + overset(^)(j) and overset(^)(j) + overset(^)(k), then theta=
Answer» `pi//2` `pi//3` `pi//4` `pi//6` ANSWER :B

Discussion

32.	I : The angle between the asymptotes of the hyperbolax^(2) - 3y^(2) =3 "is" pi //3 II: The angle between the asymptotes of the hyperbolaxy =c^(2) "is" pi //2
Answer» only I is true only II is true both I and II are TURE neither I nor II true Answer :C

Discussion

33.	Find the equation of the circle which cuts the following circles orthogonally. x^2 + y^2 + 4x - 7 = 0.2x^2 + 2y^2 + 3x + 5y -9 =0, x^2 + y^2+ y = 0.
Answer» ANSWER :`x^2 + y^2 - 4X - 2Y - 1= 0`

Discussion

34.	A : If x+y+z=xyz " then " sum(3x-x^(3))/(1-3x^(2))=Pi(3x-x^(3))/(1-3x^(2)) . R : Iftan A + tan B + tan C= tan A tan B tan C " then " A+B+C=npi .
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

35.	Let z be a complex numbersatisfying z^(2) + 2zlambda + 1=0 , where lambdais a parameter whichcan take any realvalue. Forevery large value of lambda the roots are approximately.
Answer» `-2lambda, 1//lambda` `-lambda,-1//lambda` `-2lambda, -(1)/(2lambda)` none of these Solution :`z = - lambda PM sqrt(lambda^(2) -1)` Case I: When `-1 lt lambdalt 1`, we have `lambda^(2) lt 1 RARR lambda^(2) - 1 lt 0` `z = - lambda pmisqrt(1-lambda^(2))` `rArr y^(2) = 1 - x^(2) or x^(2) y + y^(2) = 1` Case II: `lambda gt 1 rArr lambda^(2) - 1 gt0` ` z=- lambda pmsqrt(lambda^(2) -1)` `or x = - lambda pm sqrt(lambda^(2) -1),y = 0` Roots are`(-lambda + sqrt(lambda^(2) -1,0),(-lambda - sqrt(lambda^(2))-1,0)`.One root lies inside the units circle and the other root lies outside the unit circle. Case III:When `lambda` is verylarge, then `z = - lambda- sqrt(lambda^(2) -1) ~~ - 2lambda` `z=- lambda+sqrt(lamda^(2) -1) =((-lambda + sqrt(lambda^(2) -1))(-lambda -sqrt(lambda^(2)-1)))/((-lambda - sqrt(lambda^(2) -1)))` `= (1)/(-lambda-sqrt(lambda^(2)-1)) =- (1)/(2lambda)`

Discussion

36.	What is the equation to the hyperbola if its latusrectum is 9/2 and eccentricity is 5/4.
Answer» ANSWER :1

Discussion

37.	The slope of the tangent to the curve y=x^(3)+x+54 which also passes through the originis
Answer» ANSWER :28

Discussion

38.	int (1)/(sqrt(5x-6-x^2))dx=
Answer» ANSWER :`SIN^(-1)(2x-5)+C`

Discussion

39.	n bitstrings aremadebyfillingthedigits0 or1 . Thenumberof stringin whichthereare exactlykzeroswithnotwo '0' s consecutive is
Answer» `""^((n-k))C_k` `""^((n-k+1))C_k` `""^((n-k-1))C_k` none Answer :B

Discussion

40.	Definite integration as the limit of a sum : lim_(ntooo)[(n!)/(n^(n))]^(1/n)=.........
Answer» E `(1)/(e)` `(PI)/(4)` `(4)/(pi)` Answer :B

Discussion

41.	int (x^3)/(sqrt(1+x))dx=
Answer» `SQRT(1+x^2)-(x)/(3)(1+x^2)^(3//2)+C` `xsqrt(1+x^2)+(2)/(3)(1+x^2)^(3//2)+c` `x^2sqrt(1+x^2)-(2)/(3)(1+x^2)^(3//2)+c` `x^2sqrt(1+x^2)-(1)/(3)(1+x^2)^(1//2)+c`. Answer :C

Discussion

42.	An urn contains 5 red and 2 black balls. Two balls are randomly drawn. Let X represent the number of black balls. What are the possible values of X?
Answer» ANSWER :X=0,1,2;

Discussion

43.	Let f (x) be a twice differentiable function defined on (-oo,oo) such that f (x) =f (2-x)and f '((1)/(2 )) =f' ((1)/(4))=0. Then int _(-1) ^(1) f'(1+ x ) x ^(2) e ^(x ^(2))dx is equal to :
Answer» 1 `PI` 2 0 Answer :D

Discussion

44.	The positive root of x^(2)-78.8=0 after first approximation by Newton Raphson method assuming initial approximation to the root is 14, is
Answer» 9.821 9.814 9.715 9.915 Solution :Here, `x_(0)=14, f(x)=x^(2)-78.8` `and f'(x)=2x` `THEREFORE x_(1)=x_(0)-(f(x_(0)))/(f'(x_(0)))` `=14-((14)^(2)-(78.8))/(2xx14)=9.814`

Discussion

45.	If f(x)=\|{:(0,x-a,x-b),(x+a,0,x-c),(x+b,x+c,0):}\|, then "............"
Answer» F(a)=0 f(B)=0 f(0)=0 f(1)=0 Answer :C

Discussion

46.	Statement-1 : fog = gof rArr f^(-1) = g or g^(-1) = f. and Statement-2 : fog != gof.
Answer» STATEMENT-1 is True, Statement-2 is True, Statement-2 is a CORRECT EXPLANATION for Statement-1. Statement-1 is True, Statement-2 is True, Statement-2 is NOT acorrect explanation for Statement-1. Statement -1 is FALSE, Statement -2 is False Statement -1 is False, Statement -2 is True Answer :B

Discussion

47.	overset((pi)/(2))underset(0)int sqrt(1-sin(2x))dx=.....
Answer» `2sqrt(2)` `2(SQRT(2)+1)` 2 `2(sqrt(2)-1)` ANSWER :D

Discussion

48.	The mean age of a combined group of men and women is 30 years. If the means of the age of men and women are respectively 32 and 27, then the percentage of women in the group is
Answer» 30 40 50 60 Answer :B

Discussion

49.	By using the properties of definite integrals, evaluate the integrals int_(0)^(a)(sqrtx)/(sqrtx+sqrt(a-x))dx
Answer»

Discussion

50.	Verify that the function y = e^(-3x) is a solution of the differential equation (d^(2)y)/(dx^(2)) + (dy)/(dx) - 6y = 0
Answer» `(DY)/(DX ) - 3y =0` ` (d^2 y)/( dx^2) +(dy )/(dx) -6y =0` `(d^2 y)/(dx^2)-9Y =0` `(dy )/(dx)-9y =0` ANSWER :C

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

The mean of a data set consisting of 20 observation is 40. If one observation 53 was wrongly recorded as 33, then the correctmean will be

Evaluate Lt_(n to oo)[(1)/(1+n)+(1)/(2+n)+(1)/(3+n)+"...."+(1)/(10n)]

The perpendicular distance from the point﻿ (1,-1) to the line x + 5y-9=0 is equal to

from a bag containing 4 red and 2 black balls, two balls are drawn. the probability of getting two black balls is:

Find the remainder when 7^(103) is divided by 5.

If three unequal real numbers are in G.P. then their reciprocals are in -

Prove that :int_(0)^(pi) (x sin x)/(1+sinx) dx=pi((pi)/(2)-1)

If S.P and R are the sum, product and sum of the reciprocals of n terms of an increasing G.P respectively and S^(n) = R^(n).P^(k), then k is equal to

If f(x)=x^(3) and g(x)=x^(3)-4x in -2lt x lt 2, then consider the statements : (a) f(x) and g(x) satisfy Mean Value Theorem (b) f(x) and g(x) both satisfy Rolle's theorem (c ) Only g(x) satisfies Rolle's theorem. OF THE STATEMENTS

C_0^2+3.C_1^2+5. C_2^2+….+(2n+1) .C_n^2=

The negation of p rarr (~p.vee q) is

Evaluate int_(0)^(1)e^(2-3x)dx as a limit of a sum.

For the curve x = e^(t) cos t, y = e^(t) sin t the tangent line is parallel to x-axis when t is equal to

If three six faces fair dice are thrown together, then the probability that the sum of the numbers appearing on the dice is (p le k le 14) is

If x, y, z are positive real numbers, then minimum value of (z)/(x+y)+(x)/(y+z)+(y)/(x+z) is

Let f(x) = [{:((2^(x)+2^(3-x) - 6)/(sqrt(2^(-x))-2^(1-x))",","if",x gt 2),((x^(2) - 4)/(x - sqrt(3x - 2))",","if",x lt 2):},then

Show that the direction cosines of a vector equally inclined to the axes OX, OY and OZ are (1)/(sqrt3). (1)/(sqrt3). (1)/(sqrt3).

Lt_(ntooo){(n+1)/(n^(2)+1^(2))+(n+2)/(n^(2)+2^(2))+.......+1/(n)}

A coin and six faced die, both unbaised are thrown simultaneously . The probability of getting a head on the coin and an odd number on the die is

Derive the equation of a plane perpendicular to a given vector and passing through a given point in both vector and Cartesian form.

Iff(x)=abs(x) and g(x)= [x] thenf@g(-1/2) is

The number of ways in which 5 different coloured flowers be strung in the form of a garland is

Given that a alpha^(2)+2b alpha +c!=0 and that the system of equations (a alpha =b)x+ay+bz=0, (b alpha+c)x+by+cz=0, (a alpha+b)y+(b alpha+c)z=0 has a non -trivial solution, then a,b,c lie in

If (x+c)/(1+x^2) where c is a constant , then when y is stationary , xy is equal to

If 1, w, w^(2) are three cube roots of unity, then (1 - w+ w^(2)) (1 + w-w^(2)) is _______

Find the second order derivatives of the functions given in Exercises 1 to 10. x. cos x

Integrate the functions (x^(3))/(sqrt(1-x^(8)))

Find the particular solution of the differentialequation (dy)/(dx) = - 4xy^(2) given that y = 1, when x = 0.

If theta is the angle between the vectors overset(^)(i) + overset(^)(j) and overset(^)(j) + overset(^)(k), then theta=

I : The angle between the asymptotes of the hyperbolax^(2) - 3y^(2) =3 "is" pi //3 II: The angle between the asymptotes of the hyperbolaxy =c^(2) "is" pi //2

Find the equation of the circle which cuts the following circles orthogonally. x^2 + y^2 + 4x - 7 = 0.2x^2 + 2y^2 + 3x + 5y -9 =0, x^2 + y^2+ y = 0.

A : If x+y+z=xyz " then " sum(3x-x^(3))/(1-3x^(2))=Pi(3x-x^(3))/(1-3x^(2)) . R : Iftan A + tan B + tan C= tan A tan B tan C " then " A+B+C=npi .

Let z be a complex numbersatisfying z^(2) + 2zlambda + 1=0 , where lambdais a parameter whichcan take any realvalue. Forevery large value of lambda the roots are approximately.

What is the equation to the hyperbola if its latusrectum is 9/2 and eccentricity is 5/4.

The slope of the tangent to the curve y=x^(3)+x+54 which also passes through the originis

int (1)/(sqrt(5x-6-x^2))dx=

n bitstrings aremadebyfillingthedigits0 or1 . Thenumberof stringin whichthereare exactlykzeroswithnotwo '0' s consecutive is

Definite integration as the limit of a sum : lim_(ntooo)[(n!)/(n^(n))]^(1/n)=.........

int (x^3)/(sqrt(1+x))dx=

An urn contains 5 red and 2 black balls. Two balls are randomly drawn. Let X﻿ represent the number of black balls. What are the possible values of X?

Let f (x) be a twice differentiable function defined on (-oo,oo) such that f (x) =f (2-x)and f '((1)/(2 )) =f' ((1)/(4))=0. Then int _(-1) ^(1) f'(1+ x ) x ^(2) e ^(x ^(2))dx is equal to :

The positive root of x^(2)-78.8=0 after first approximation by Newton Raphson method assuming initial approximation to the root is 14, is

If f(x)=|{:(0,x-a,x-b),(x+a,0,x-c),(x+b,x+c,0):}|, then "............"

Statement-1 : fog = gof rArr f^(-1) = g or g^(-1) = f. and Statement-2 : fog != gof.

overset((pi)/(2))underset(0)int sqrt(1-sin(2x))dx=.....

The mean age of a combined group of men and women is 30 years. If the means of the age of men and women are respectively 32 and 27, then the percentage of women in the group is

By using the properties of definite integrals, evaluate the integrals int_(0)^(a)(sqrtx)/(sqrtx+sqrt(a-x))dx

Verify that the function y = e^(-3x) is a solution of the differential equation (d^(2)y)/(dx^(2)) + (dy)/(dx) - 6y = 0

The perpendicular distance from the point (1,-1) to the line x + 5y-9=0 is equal to

An urn contains 5 red and 2 black balls. Two balls are randomly drawn. Let X represent the number of black balls. What are the possible values of X?