28278 + Interview Questions in Maths in Class 12

1.	If the angle between the line·x=(y−1)/2=(z-3)/λ and the plane· x+ 2y+ 3z= 4 iscos-1(√(5/14)) then λ equals :
Answer» `2//5` `5//3` `2//3` `3//2` ANSWER :C

Discussion

2.	All the point (a, y) in the plane satisfying the equation x^(2)+2x sin (xy)+1=0 lie on -
Answer» a pair of STRAIGHT lines a family of hyperbolas a parabola an ellipse Solution :`X^(2)+2x sin (xy) +1=0` `2 sin (xy) = -(x+1/x)` `y=2npi//(PI)/(2), ninI` HENCE pair of straight lines.

Discussion

3.	Answer the followings true or false. (i) vecaand-veca are collinear.(ii)Two collinear vectors are always equal in magnitude. (iii)Two vectors having same magnitude are collinear. (iv)Two collinear vectors having the same magnitude are equal.
Answer» ANSWER :`20" m"//"SEC"^(2)` (ACCELERATION)

Discussion

4.	Let A = R - {3} and B = R - {1}. Consider the function f : A rarrB defined by , f(x) = ((x-2)/(x-3)) is f one - one and onto ?
Answer» SOLUTION :N/A

Discussion

5.	If x= sint, y= cos2t then prove that (dy)/(dx)= -4sint
Answer»

Discussion

6.	A load of mass M kg is suspended from a steel wire of length 2 m and radius 1.0 mm in Searle's apparatus experiment. The increase in length produced in the wire is 4.0 mm, Now the loads is fully immersed in a liquid of relative density 2. The relative density of the material of load is 8. The new value of increase in length of the steel wire is :
Answer» 3.0 mm 4.0 mm 5.0 mm zero Solution :NA

Discussion

7.	Let f(x) = sgn (x) and g (x) = x(x^(2)-5x+6). The function f(g(x)) is discontinuous at
Answer» Infinitely many points Exactly one point Exactly three points No point Solution :`becauseg(X)`is CONTINUOUS is R and f(x) is discontinuouse at x = 0. `THEREFORE f{g(x)}` is discontinuous at the points where g (x) =0 OR at x = 0,2,3.

Discussion

8.	Show that the function e^x/x^p is strictly increasing for x gt p gt 0.
Answer» Solution :Let `f(x) = e^x/x^p` Then ``f.(x) = (e^x CDOT x^p - e^x cdot px^p-1)/(x^2p)` The FUNCTION is increasing if f. `(x) GT 0` `RARR (e^x cdot x^p - e^x cdot px^p-1)/(x^2p)gt 0` `(e^x cdot x^(p-1) cdot (x-p) gt 0 rArr x gt p.

Discussion

9.	The sum of the roots of the equation x + 1 - 2 log_(2) (2^(x) + 3) + 2 log_(4) (10 - 2^(-x))= 0 "" is
Answer» `log_(2) 11` `log_(2) 12` `log_(2)13` `log_(2) 14` ANSWER :A

Discussion

10.	Matrices A and B will be inverse of each other only if-
Answer» AB = BA AB = BA = 0 AB = 0, BA = I AB = BA = I ANSWER :D

Discussion

11.	Integrate the following function : int(e^(x))/(sqrt(4-e^(2x)))dx
Answer» ANSWER :`SIN^(-1)((e^(x))/(2))+c`

Discussion

12.	The tangents at a point P onx^(2)//a^(2) -y^(2)//b^(2) =1cuts one of its directrices in Q. Then PQ subtends at the corresponding focus an angle of
Answer» `pi//3 ` `pi//6` ` pi//4` `pi//2` ANSWER :D

Discussion

13.	A die is rolled until a 6 is obtained. What is the probability that you end up in the third roll.
Answer» SOLUTION :Probability of GETTING a 6 in the 3rd ROLL `=5/6xx5/6xx1/6=25/216`

Discussion

14.	C_0^2 + C_1^2 + C_2^2 + ………+C_25^2 =
Answer» `""^49C_50` `""^49C_25` `""^50C_25` `""^39C_40` ANSWER :C

Discussion

15.	(a - b) . (b - c) xx (c - a) =
Answer» `(B XX C)` `2A. (b xx c)` `3A ( b xx c)` 0 Answer :D

Discussion

16.	Prove that the point of intersection of two perpendicular tangents tot he hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2)) = 1 lies on the circle x^(2) + y^(2) = a^(2) - b^(2)
Answer» ANSWER :`X^(2) + y^(2) = a^(2) - B^(2)`

Discussion

17.	Thesum ofthe coefficients inthe expansionof( 1 +x + x ^ 2 )^nis
Answer» 2 ` 2^N ` `3^n ` `4 ^ n ` Solution :Toobtain sum OFCO- efficientsofbinomialexpansion,substitute`X = 1 `intheexpansion `THEREFORE`sumofco -efficient`= (1+ 1+ 1) ^n ` `= 3^n `

Discussion

18.	Reflecting the point (2, –1) about y -axis,coordinate axes are rotated at 45^@angle in negative direction without shifting the origin. The new coordinates of the points are -
Answer» `( - (1)/(SQRT2) , - (3)/(sqrt2) )` `( (1)/(sqrt2) ,(1)/(sqrt2) )` `( - (3)/(sqrt2) , (1)/(sqrt2) )` NONE of these ANSWER :A

Discussion

19.	At what points in the interval [0, 2pi], does the function sin 2x attain its maximum value?
Answer» ANSWER :`At X= (PI)/(4) "and " (5PI)/(4)`

Discussion

20.	If the value of int_(-2)^(2) \| x cos pi x\| dx = k//pi then the value of k is
Answer» `4` `8` `12` NONE of these Answer :B

Discussion

21.	Let f(x)=(sqrt(sinx))/(1+root(3)(sinx)). If D is the domain of f, then D contains :
Answer» `(0,PI)` `(-2PI,-pi)` `(2pi,4pi)` `(4pi,6pi)` ANSWER :A

Discussion

22.	Find the critical points of each of the following functions : y=e^(x)sinx
Answer» ANSWER :MAX at `x=2npi+(3pi)/(4)` and Min at `x=2npi-(pi)/(4)`,where n = any integer

Discussion

23.	If sin(sin^(-1)((1)/(5))+cos^(-1)x)=1 then find the value of x.
Answer» ANSWER :`(1)/(5)`

Discussion

24.	Let f (x)= [{:(x ^(2alpha+1)ln x ,,, x gt0),(0 ,,, x =0):} If f (x) satisfies rolle's theorem in interval [0,1], thenalpha can be:
Answer» `-1/2` `-1/3` `-1/4` `-1` ANSWER :B::C

Discussion

25.	The valueof [veca xx vecp vecb xx vecq vecc xx vecr]+[veca xx vecq vecb xx vecr vecc xx vecp] +[veca xx vecr vecb xx vecp vecc xx vecq]equals to:
Answer» 0 `[veca vecb vecc]` `[VECP vecq vecr]` `2[veca vecb vecc]` Answer :A

Discussion

26.	A :cos^(3) x + cos^(3)(120^@ + x) + cos^(3)(120^(@) - x)=(3)/(4) cos 3 x R :cos theta + cos (120^(@) + theta ) cos (120^(@) - theta ) = 0 and cos thetacos(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

27.	Ifn is a positiveinteger, show that(1 + i)^(n)+ (1 - i)^(n) = 2 ^((n+2)/2) cos ((npi)/4).
Answer»

Discussion

28.	Which of the following is true :
Answer» `SIN '(pi)/(12)= (SQRT(3) - 1)/(2sqrt(2))` `cos'(pi)/(12) = (sqrt(3) + 1)/(2sqrt(2))` `tan 15^(@) = 2 - sqrt(3)` `sin'(pi)/(10) = (sqrt(5) - 1)/(4)` Answer :A

Discussion

29.	int_(0)^(2) (2x-2)/(2x-x^(2))dx=
Answer» 0 2 3 4 Answer :A

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30.	Prove that tan^(-1)1+tan^(-1)2+tan^(-1)3 =pi
Answer» ANSWER :`0.58`

Discussion

31.	If (1)/((ax+b)(cx+d))=(A)/(ax+b)+(B)/(cx+d) then (1)/((ax+b)^(2)(cx+d))=
Answer» `(A)/((ax-B)^(2))+(AB)/(ax-b)+(B^(2))/(cx+d)` `(A)/((ax+b)^(2))+(AB)/(ax-b)+(B^(2))/(cx+d)` `(A)/((ax+b)^(2))+(AB)/(ax+b)+(B^(2))/(cx+d)` `(A)/((ax-b)^(2))+(AB)/(ax+b)+(B^(2))/(cx-d)` ANSWER :C

Discussion

32.	C(13,5)=
Answer»

Discussion

33.	Range of the function f(x)= x^(2)-6x+5/x^(2)-5x+6 is
Answer» R `[F(-1-2sqrt3), f(-1+2sqrt3)]` `R-[f(-1-2sqrt3), f(-1+2 sqrt3)]` `R-{[f(-1-2sqrt3), f(-1+2sqrt3)]cup{1}}` Answer :C

Discussion

34.	Differntiate the following functions by proper substitution.cos^(-1)((1-t^2)/(1+t^2))
Answer» SOLUTION :`y=COS^(-1)((1-t^2)/(1+t^2))`[PUT`t=tantheta` `cos^(-1)FRAC(1-tan^2thet)(1+tan^2theta)` `=cos^(-1)cos2theta=2theta=2tan^(-1)t` `thereforedy/dx=2/(1+t^2)`

Discussion

35.	Let ABC be a given triangle. Points D and E are on sides AB and AC respectively and point F is on line segment DE. Let (AD)/(AB)=x, (AE)/(AC)=y, (DF)/(DE)=z. Let area of DeltaBDF=Delta_(1), Area of DeltaCEF=Delta_(2)and area of DeltaABC=Delta. Q. (Delta_(1))/(Delta) is equal to :
Answer» xyz `(1-X)y(1-Z)` `(1-x)yz` `x(1-y)z` ANSWER :C

Discussion

36.	Let ABC be a given triangle. Points D and E are on sides AB and AC respectively and point F is on line segment DE. Let (AD)/(AB)=x, (AE)/(AC)=y, (DF)/(DE)=z. Let area of DeltaBDF=Delta_(1), Area of DeltaCEF=Delta_(2)and area of DeltaABC=Delta. Q. (Delta_(2))/(Delta) is equal to :
Answer» `(1-X)y(1-Z)` `(1-x)(1-y)z` `x(1-y)(1-z)` `(1-x)YZ` ANSWER :C

Discussion

37.	Number of X is randomly selected from the set of odd numbers and Y is randomly selected from the set of even numbers of the set {1,2,3,4,5,6,7}. Let Z = X + Y, then What is P(Z=5) equal to?
Answer» <P>`1//2` `1//3` `1//4` `1//6` Solution :`n(S)=12` `n(E_(1))=12` `P(Z=5)=(n(E_(1)))/(n(S))=(2)/(12)=(1)/(6)`

Discussion

38.	Prove that, int sin n theta sec theta d theta =- ( 2 cos (n-1) theta)/(n -1) - int sin (n-2) theta sec theta d theta Hence or otherwise evaluate int _(0) ^(pi//2) ( cos 5 theta sin 3 theta)/(cos theta) d theta.
Answer» ANSWER :`- (181)/(105)`

Discussion

39.	If log_(7)12=a ,log_(12)24=b,then find value of log_(54)168 in terms of a and b.
Answer» ANSWER :`(ab+1)/(a(8-5b))`

Discussion

40.	If a lt b lt c lt d, then the eqution 3(x - a) (x - c) + 5 (x - b) (x - d) = 0 has
Answer» REAL and DISTINCT roots real and EQUAL roots purely IMAGINARY roots none of these Answer :A

Discussion

41.	Two A.M's A_(1) and A_(2), two G.M's G_(1) and G_(2) and two H.M's H_(1) and H_(2) are inserted between two numbers a and b. (i) Express A_(1) + A_(2) in terms of a and b. (ii) Express G_(1) G_(2) in terms of a and b. (iii) Express 1/H_(1) + 1/H_(2)1 in terms of a and b. (iv) Show that 1/H_(1) + 1/h_(2) = (A_(1) + A_(2))/(G_(1) G_(2))
Answer» ANSWER :(i) ` = a + B` (ii) `ab` (III) ` = (a + b)/(ab)` (IV) ` (A_(1) + A_(2))/(G_(1) G_(2))`(from (i) and (ii))

Discussion

42.	Fill int the blanks choosing correct answer from the bracket. InDelta ABC if b^2 + c^2 lt a^2 then _____ angle is obtuse.
Answer» A B C Answer :A

Discussion

43.	int(e^(x) (1+x))/(sin^(2) (x e^(x)))dx
Answer» ANSWER :`-COT (X E^(x)) +C`

Discussion

44.	consider the function f:R rarr R,f(x)=(x^(2)-6x+4)/(x^(2)+2x+4) Range of fX() is
Answer» `((-oo,-(2)/(3))] cup[2,0)` `[(-1)/(3),5]` `(-oo,2)cup[(7)/(3),oo)` `(20,oo)` SOLUTION :`f(X)=(x^(2)-6x+4)/(x^(2)+2x+4)=1-(8X)/(x^(2)+2x+4)` `f(x)-8((x^(2)+2x+4)-x(2x+2))/((x^(2)+2x+4)^(2)]` `f(X)=0 rarrx2 or -2` `f(2)=(4-12+4)/(4+4+4)=-4/12=-1/3` `f(2)=(4+12+4)/(4-4+4)=5` The graph of y =f(X) is as SHOWN

Discussion

45.	The vector equation of the plane containing the line vec r (-2 hat i - 3 hat+ 4 hatk) + lambda (3 hat i - 2 hat j - hat k) and the point hat i + 2 hatj + 3 hat kis ..........
Answer» `vec R . (vec i + 3 HAT k) = 10 ` `VECR . (hat i - 3 hat k)= 10` `vec r . (3 hat i + hat k) = 10` None of these Answer :A

Discussion

46.	If alpha, beta, gamma are the roots of x^(3) + 2x + 5 = 0 thent the equation whose rootsbeta gamma + (1)/(alpha), gamma alpha + (1)/(beta), alpha beta + (1)/(gamma)is
Answer» `5X^(3) + 8x- 64 =0 ` `5x^(3) - 8x^(2) + 64 = 0 ` `5x^(2) - 8x^(2) - 64 = 0 ` `5x^(2) + 8x^(2) - 64= 0 ` Answer :3

Discussion

47.	The points (2,1, -1), (1,1,1), (2,2,1), (0,2,5) are
Answer» coplanar collinear noncoplanar none Answer :A

Discussion

48.	Find the equation of the circle which cuts each of the following circles orthogonally. x^2+y^2+2x+17y+4=0 x^2+y^2+7x+6y+11=0 x^2+y^2-x+22y+3=0
Answer» ANSWER :`x^2+y^2-6x-4y-44=0`

Discussion

49.	Prove that the infinitesimals alpha=x and beta=x cos (1//x) (as x to 0) are not comparable, ie, their ratio has no limit.
Answer» ANSWER :(a) 100x is an INFINITESIMAL of the same order as X; (b) `x^(2)` is an infinitesimal of an order higher than x; (c) 6 sin x is an infinitesimal of the same order as x; (d) `sin^(3)`x is an infinitesimal of an order higher than x. (e) `ROOT3(TAN^(2)x)`

Discussion

50.	I : The degree of the differential equation of ((d^(3)y)/(dx^(3))) + 4((d^(3)y)/(dx^(2))) = x^(2) log ((d^(2)y)/(dx^(2))) is 2 II : The number of arbitrary constant in the general number of a differential equation is equal to the degree of the differential equation. Which of the above statement is correct.
Answer» only I only II Both I and II Neither I nor II Answer :D

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

If the angle between the line·x=(y−1)/2=(z-3)/λ and the plane· x+ 2y+ 3z= 4 iscos-1(√(5/14)) then λ equals :

All the point (a, y) in the plane satisfying the equation x^(2)+2x sin (xy)+1=0 lie on -

Answer the followings true or false. (i) vecaand-veca are collinear.(ii)Two collinear vectors are always equal in magnitude. (iii)Two vectors having same magnitude are collinear. (iv)Two collinear vectors having the same magnitude are equal.

Let A = R - {3} and B = R - {1}. Consider the function f : A rarrB defined by , f(x) = ((x-2)/(x-3)) is f one - one and onto ?

If x= sint, y= cos2t then prove that (dy)/(dx)= -4sint

Let f(x) = sgn (x) and g (x) = x(x^(2)-5x+6). The function f(g(x)) is discontinuous at

Show that the function e^x/x^p is strictly increasing for x gt p gt 0.

The sum of the roots of the equation x + 1 - 2 log_(2) (2^(x) + 3) + 2 log_(4) (10 - 2^(-x))= 0 "" is

Matrices A and B will be inverse of each other only if-

Integrate the following function : int(e^(x))/(sqrt(4-e^(2x)))dx

The tangents at a point P onx^(2)//a^(2) -y^(2)//b^(2) =1cuts one of its directrices in Q. Then PQ subtends at the corresponding focus an angle of

A die is rolled until a 6 is obtained. What is the probability that you end up in the third roll.

C_0^2 + C_1^2 + C_2^2 + ………+C_25^2 =

(a - b) . (b - c) xx (c - a) =

Prove that the point of intersection of two perpendicular tangents tot he hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2)) = 1 lies on the circle x^(2) + y^(2) = a^(2) - b^(2)

Thesum ofthe coefficients inthe expansionof( 1 +x + x ^ 2 )^nis

Reflecting the point (2, –1) about y -axis,coordinate axes are rotated at 45^@angle in negative direction without shifting the origin. The new coordinates of the points are -

At what points in the interval [0, 2pi], does the function sin 2x attain its maximum value?

If the value of int_(-2)^(2) | x cos pi x| dx = k//pi then the value of k is

Let f(x)=(sqrt(sinx))/(1+root(3)(sinx)). If D is the domain of f, then D contains :

Find the critical points of each of the following functions : y=e^(x)sinx

If sin(sin^(-1)((1)/(5))+cos^(-1)x)=1 then find the value of x.

Let f (x)= [{:(x ^(2alpha+1)ln x ,,, x gt0),(0 ,,, x =0):} If f (x) satisfies rolle's theorem in interval [0,1], thenalpha can be:

The valueof [veca xx vecp vecb xx vecq vecc xx vecr]+[veca xx vecq vecb xx vecr vecc xx vecp] +[veca xx vecr vecb xx vecp vecc xx vecq]equals to:

A :cos^(3) x + cos^(3)(120^@ + x) + cos^(3)(120^(@) - x)=(3)/(4) cos 3 x R :cos theta + cos (120^(@) + theta ) cos (120^(@) - theta ) = 0 and cos thetacos(120^(@) + theta ) cos (120^(@) - theta ) = (1)/(4) cos 3 theta

Ifn is a positiveinteger, show that(1 + i)^(n)+ (1 - i)^(n) = 2 ^((n+2)/2) cos ((npi)/4).

Which of the following is true :

int_(0)^(2) (2x-2)/(2x-x^(2))dx=

Prove that tan^(-1)1+tan^(-1)2+tan^(-1)3 =pi

If (1)/((ax+b)(cx+d))=(A)/(ax+b)+(B)/(cx+d) then (1)/((ax+b)^(2)(cx+d))=

C(13,5)=

Range of the function f(x)= x^(2)-6x+5/x^(2)-5x+6 is

Differntiate the following functions by proper substitution.cos^(-1)((1-t^2)/(1+t^2))

Let ABC be a given triangle. Points D and E are on sides AB and AC respectively and point F is on line segment DE. Let (AD)/(AB)=x, (AE)/(AC)=y, (DF)/(DE)=z. Let area of DeltaBDF=Delta_(1), Area of DeltaCEF=Delta_(2)and area of DeltaABC=Delta. Q. (Delta_(1))/(Delta) is equal to :

Let ABC be a given triangle. Points D and E are on sides AB and AC respectively and point F is on line segment DE. Let (AD)/(AB)=x, (AE)/(AC)=y, (DF)/(DE)=z. Let area of DeltaBDF=Delta_(1), Area of DeltaCEF=Delta_(2)and area of DeltaABC=Delta. Q. (Delta_(2))/(Delta) is equal to :

Number of X is randomly selected from the set of odd numbers and Y is randomly selected from the set of even numbers of the set {1,2,3,4,5,6,7}. Let Z = X + Y, then What is P(Z=5) equal to?

Prove that, int sin n theta sec theta d theta =- ( 2 cos (n-1) theta)/(n -1) - int sin (n-2) theta sec theta d theta Hence or otherwise evaluate int _(0) ^(pi//2) ( cos 5 theta sin 3 theta)/(cos theta) d theta.

If log_(7)12=a ,log_(12)24=b,then find value of log_(54)168 in terms of a and b.

If a lt b lt c lt d, then the eqution 3(x - a) (x - c) + 5 (x - b) (x - d) = 0 has

Fill int the blanks choosing correct answer from the bracket. InDelta ABC if b^2 + c^2 lt a^2 then _____ angle is obtuse.

int(e^(x) (1+x))/(sin^(2) (x e^(x)))dx

consider the function f:R rarr R,f(x)=(x^(2)-6x+4)/(x^(2)+2x+4) Range of fX() is

The vector equation of the plane containing the line vec r (-2 hat i - 3 hat+ 4 hatk) + lambda (3 hat i - 2 hat j - hat k) and the point hat i + 2 hatj + 3 hat kis ..........

If alpha, beta, gamma are the roots of x^(3) + 2x + 5 = 0 thent the equation whose rootsbeta gamma + (1)/(alpha), gamma alpha + (1)/(beta), alpha beta + (1)/(gamma)is

The points (2,1, -1), (1,1,1), (2,2,1), (0,2,5) are

Find the equation of the circle which cuts each of the following circles orthogonally. x^2+y^2+2x+17y+4=0 x^2+y^2+7x+6y+11=0 x^2+y^2-x+22y+3=0

Prove that the infinitesimals alpha=x and beta=x cos (1//x) (as x to 0) are not comparable, ie, their ratio has no limit.