28278 + Interview Questions in Maths in Class 12

1.	Let alpha,betaandgamma be the angles made by a line with the positive directions of the axes of reference in three dimensions. If theta is the acute angle given by costheta=(cos^(2)alpha+cos^(2)beta+cos^(2)gamma)/(sin^(2)alpha+sin^(2)beta+sin^(2)gamma), then theta equals.
Answer» `pi//6` `pi//3` `pi//2` `pi//4` ANSWER :B

Discussion

2.	The product of the perpendicular distances from any point of the hyperbola x^(2)/a^(2)-y^(2)/b^(2)=1 to its asymptotes is
Answer» `(a^(2)B^(2))/(a^(2)-b^(2))` `(a^(2)b^(2))/(a^(2)+b^(2))` `(a^(2)+b^(2))/(a^(2)b^(2))` `(a^(2)-b^(2))/(a^(2)b^(2))` ANSWER :B

Discussion

3.	If z= cos.(2pi)/(2n +1) +isin.(2pi)/(2n+1), n is a positive integer, then the equation whose roots are alpha = z+ z^(3)+ ….+ z^(2n-1)and beta = z^2 + z^4 + ….+ z^(2n). Is ________________.
Answer» ANSWER :`4X^2 + 4x + sec^2 (PI)/(2n+1)=0`.

Discussion

4.	Evaluate int _(0)^(infty) (tan^(-1)ax-tan^(-1)x)/(x)dx, where a is a parametar.
Answer» ANSWER :`=PI(SQRT(1-a^(2)-1))`

Discussion

5.	A room has 6 bulbs, each has an independent switch. Find the number of ways in which the room can be lighted ?
Answer» ANSWER :63

Discussion

6.	If alpha, beta, gamma are the roots of x^(3) + 2x^(2) - 4x - 3 = 0 then the equation whose roots are alpha//3, beta//3, gamma//3 is
Answer» `x^3 +6x^2 - 36x -81 =0` ` 9x^3 +6x^2 -4x -1=0` `9x^3 +6x^2 + 4x +1=0` ` x^3 - 6x^2 + 36 x+81 =0` ANSWER :B

Discussion

7.	Check whether the relation R defined in the set {1,2,3,4,5,6} as R={(a,b) : b=a+1} is reflexive, symmetric or transitive.
Answer» SOLUTION :R={(1,2),(2,3),(3,4),(4,5),(5,6),(6,7)} Since `!= 1+1,(1,1)!in R` `therefore`R is not reflexive` `We have (2,3) in R (therefore 3 = 2+1) but `(3,2) !in R (therefore 2 !in 3+1)` ` therefore ` R is not SYMMETRIC We have `(2,3) in R` and `(3,4) in R`but `(2,4) !in R (therefore 4 != 2+1)` ` therefore` R is not TRANSITIVE

Discussion

8.	The piont where the line 4x - 3y + 7 = 0 touches the circle x^(2) + y^(2) - 6x + 4y - 12 = 0 is
Answer» (1, 1) (1, -1) (-1, 1) (-1, -1) ANSWER :C

Discussion

9.	The points (-7, 4, -2), (-2, 1, 0) and (3, -2, 2) are
Answer» non-COLLINEAR non-coplanar non-collinear and non-coplanar collinear ANSWER :D

Discussion

10.	Evaluate: int 1/(1+ tan x) dx.
Answer» ANSWER :`\|cosx+sinx\|+c`

Discussion

11.	If there is an error of 0.05 cm in the measurement of the side as 2 cm of a cube, then relative errorin the volume is
Answer» 0.075 0.0075 7.5 0.75 Answer :A

Discussion

12.	A series of concentric ellipse E_1,E_2,E_3,…,E_n is constructed as follows: Ellipse E_n touches the extremities of the major axis of E_(n-1) and have its focii at the extremities of the minor axis of E_(n-1). If eccentricity of ellipse E_n is e_n, then the locus of (e_(n)^(2),e_(n-1)^(2)) is
Answer» a parabola an ellipse a hyperbola a RECTANGULAR hyperbola Answer :A::B::C

Discussion

13.	The mean of 5 observations is 3 and variance is 2. If three of the five observations are 1,3,5 the other two are
Answer» `2,6` ` 3,3` `1,5` `2.4` ANSWER :D

Discussion

14.	Find the particular solution of the following differential equaiton : (x+1)(dy)/(dx) = 2e^(-y) - 1, y = 0 when x = 0.
Answer» Answer :`y = LOG\|(2x + 1)/(X + 1)\|, x NE -1`

Discussion

15.	Statement I : The value of the integral int_(pi//6)^(pi//3)(dx)/(1+sqrt(tanx)) is equal to (pi)/(6) Statement II : int_(a)^(b)f(x)dx=int_(a)^(b)f(a+b-x)dx
Answer» Statement-1 is TRUE, Statement-2 is FALSE Statement-1 is false, Statement-2 is true Statement-2 is a CORRECT EXPLANATION forStatement-1 Statement-1 is true, Statement-2 is true, Statement-2 is not a correct explanation for Statement-1 Answer :B

Discussion

16.	Find the value of a it the area of the triangle formed by the liners x=0,y=0,3x+4y=a is 6 sq units.
Answer» SOLUTION :NA

Discussion

17.	Show that the points (3,-2,4)(1,1,1) and (-1,4,-1) are collinear.
Answer» Solution :Let A =(3,-2,4) B=(1,1,1) and C =(-1,4,-2) ` "D. rs of AB are" lt -2,3,-3 gt "D. rs of BC are" lt -2 ,3,-3 gt` As D .rs of AB are same as D .rs of BC it follows that A,B, C LIE on the same STRAIGHT line. So the points are collinear. (Proved)

Discussion

18.	The valueoftan(1^@ )+ tan(89 ^@ )is equalto
Answer» `(1)/( sin1^@ )` `(2)/( sin2^@)` `(2)/( sin1^@)` `(1)/( sin2^@)` ANSWER :B

Discussion

19.	If a,b and c are in G.P then (b - a)/(b - c) + (b + a)/(b + c)
Answer» `2SIN(3alpha+beta-gamma)` `2cos(3alpha+beta-gamma)` `COS(3alpha+beta-gamma)` `sin(3alpha+beta-gamma)` ANSWER :B

Discussion

20.	Let F_1(x_1, 0) and F_2(x_2, 0), for x_1 lt 0 and x_2 gt 0, be the foci of the ellipse x^2/9 +y^2/8 =1 Suppose a parabola having vertex at the origin and focus at F_2 intersects the ellipse at point M in the first quadrant and at point N in the fourth quadrant. The orthocentre of the triangle F_1MN is
Answer» `( -9/10,0)` ` (2/3,0)` ` (9/10,0)` `(2/3, SQRT6)` ANSWER :A

Discussion

21.	For a data consisting of 15 observations x_(i), i=1,2,3,…,15 the following results are obtained :sum_(i=1)^(15) x_(i)= 170, sum_(i=1)^(15) x_(i)^(2) = 2830. If one of the observation namely 20 was found wrong and was replaced by its correct value 30, then the corrected variance is
Answer» 80 78 76 75 Answer :B

Discussion

22.	Consider the unction f(x)=int_(0)^(x)(5ln(1+t^(2))-10t tan^(-1)t+16sint)dt f(x) is
Answer» negative for all `X in (0,1)` increasing for all `x in (0,1)` DECREASING for all `x in (0,1)` non-monotonic function for `x in (0,1)` Solution :`f(x)=int_(0)^(x)(5ln(1+t^(2))-10t tan^(-1)t+16sint)dt.` `rArr""f'(x)=5ln(1+x^(2))-10x tan^(-1)x+16 sinx` `rArr""f''(x)=2(8 cos x-5 tan^(-1)x)` `rArr""f''(x)=-2(8sinx+(5)/(1+x^(2)))lt0AAx in (0,1)` So, f''(x) is decreasing `AA x in (0,1)` `rArr""f''(x)gtf''(1)=2(8cos1-(5pi)/(4))` `""gt2(8COS.(pi)/(3)-(5pi)/(4))` `""=2(4-(5pi)/(4))gt0` So, f''(x) is increasing, for `x gt 0 , f'(x)gtf'(0)=0` So, f(x) is increasing, for `x gt0, f(x) gt f(0)=0` So, `int_(0)^(x)f(t)` is positive and increasing.

Discussion

23.	Determine if A sub B or A cancel sub B where A=phi, B ={phi}
Answer» SOLUTION :Here `A sub B`, as PHI is the subset of every SET.

Discussion

24.	Three screws are drawn at random from a lot of 50 screws, 5 of which are defective. Find the probability of the event that all 3 screws are non-defective, assuming that the drawing is (a) with replacement (b) without replacement
Answer» ANSWER :`((9)/(10))^(3), (1419)/(1960)`

Discussion

25.	The points 2i + j - k, i + j + k, 2i + 2j + k, 2j + 5k are
Answer» COLLINEAR COPLANAR but not collinear noncoplanar none Answer :B

Discussion

26.	For simple pendulum, T = 2pi sqrt((l)/(g)) where T is the periodic time and l is the length of pendulum. If there is 4% error in the measure of periodic time then find the error percentage in the length of pendulum.
Answer» ANSWER :`8%`

Discussion

27.	To commute to his office, Mr. Brown can take either the A train or B train. Both train stations are the same distance from his apartment, and both stations claim that on average they run 10 minutes late from the scheduled arrival time . The standard deviation for the A train is 1 minute and for the B train is 5 minutes . Which of the following is a valid conclusion for Mr. Brown ?
Answer» If he REGULARLY takes the A TRAIN, he will arrive at approximately the same time EVERY day . if he takes the A train , he is less likely to arrive late If he takes the A train,he is more likely to be 15 minutes late than with the B train. If he takes theA train , he is more likely to arrive on time. Answer :A

Discussion

28.	Evaluate the following integrals int(dx)/((x+1)sqrt(2x^(2)+3x+1))
Answer» ANSWER :`2sqrt((2x+1)/(x+1))+C`

Discussion

29.	If zbarz=4 then the locus of z is
Answer» `X^(2) + y^(2) = 4` `x^(2)+ y^(2) =2 ` `x^(2) + y^(2) = 0` `x^(2) + y^(2) = 3` ANSWER :A

Discussion

30.	Statement 1 : If (a)/(a_(1)),(b)/(b_(1)),( c )/(c_(1)) are in A.P., then a_(1),b_(1),c_(1) are in G.P. because Statement 2 : If ax^(2)+bx+c=0 and a_(1)x^(2)+b_(1)x+c_(1)=0 have a common root and (a)/(a_(1)),(b)/(b_(1)),( c )/(c_(1)) are in A.P., then a_(1),b_(1),c_(1) are in G.P.
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 a correct explanation for Statement-1 Statement - 1 is True, Statement - 2 is FALSE Statement - 1 is False, Statement - 2 is True Answer :D

Discussion

31.	Distance of line y=\|(x+1,x,x),(x,x+2,x),(x,x,x+3)\| from the origin is
Answer» `6/11` `7/13` `6/(SQRT(122))` `7/(sqrt(122))` Answer :C

Discussion

32.	There are 4 pairs of hand gloves of 4 different colours. In how many ways can they be paired off so that a left hand glove and a right handed glove are not of same colour.
Answer» ANSWER :9

Discussion

33.	4 American and 1 Indian couple Total 5 couples seats around the circular table at random. If it is given that each American seat near by his wife then ......... is the probability of an event that Indian person can seat near by his wife.
Answer» `(1)/(2)` `(1)/(3)` `(2)/(5)` `(1)/(5)` Answer :C

Discussion

34.	If y+ sin y= cos x," find "(dy)/(dx).
Answer» ANSWER :`(-SIN X)/((1+cos y))`

Discussion

35.	E_(1), E_(2) are events of a sample space such that P(E_(1))=(1)/(4), P((E_(2))/(E_(1)))=(1)/(2), P((E_(1))/(E_(2)))=(1)/(4) then P((E_(1))/(E_(2)))+P((E_(1))/(barE_(2)))=
Answer» `1//4` `1//3` `1//2` `3//4` ANSWER :C

Discussion

36.	Find the angle of intersection of the curves y = 4-x^(2) and y=x^(2).
Answer» Answer :`ALPHA = TAN^(-1)((4sqrt(2))/(7))`.

Discussion

37.	A random variable X has the following probability distribution: (# #TRG_MAT_MCQ_XII_P2_C08_E02_004_Q01.png" width="80%"> Then, the value of P(0 lt X lt 4) is
Answer» `11/49` `15/49` `20/49` `40/49` ANSWER :B

Discussion

38.	The points on the line x + y = 4 lying at a unit distance from the line 4x+3y-10=0 are
Answer» (-7, 11), (3, 1) (7, -11), (3, -1) (-7, 11), (-3, 7) (7, -3), (21, -7) Answer :A

Discussion

39.	Let x_1,x_2 ,x_3 be the points where f(x)=\|1-\|x-4\|\|, x in R is not differentiable thenf(x_1)+f(x_2)+f(x_3) =
Answer» SOLUTION : Function is not DIFFERENTIABLE at x=3,4,5 So, f(3)+f(4)+f(5) 0+1+0=1

Discussion

40.	~(prarrq)rarr[(~p)vv(~q)] is
Answer» a TAUTOLOGY a contradiction neither a tautology nor contradicion cannot COME any statement. Answer :A

Discussion

41.	If f(x)=2x^(3)+3x^(2)-x+1 is divided with x+1 and x-1 and the respective remainders are 5 and -1 then find the remainder when f(x) is divided with x^(2)-1 ?
Answer» ANSWER :`:.` Remainder `=ax + B = -3X +2`

Discussion

42.	If omega=(-1+i sqrt(3))/(2) then (3+omega+3 omega^(2))^(4)=
Answer» 16 `-16` 16w `16w^(2)` ANSWER :A

Discussion

43.	If veca ne vec0, vecb ne vec0, vecc ne vec0, veca xx vecb =vec0 and vecb xx vecc=vec0," then "veca xx vecc is equal to
Answer» `VECB` `VECA` `VEC0` i+j+k Answer :C

Discussion

44.	Prove that the determinent \|{:(x,sintheta,costheta),(-sintheta,-x,1),(costheta,1,x):}\| is independent from value of theta
Answer» ANSWER :`-x^3`

Discussion

45.	Let A,B and C be three events such that P(A)=0.50, P(B)=0.40, P(A nn B)=0.20 P(C\| A nnB') =0.30 , P(C\|A' nn B)=0.25 and (A nn B)=0.20 then P(C\| A uu B) =_____
Answer» ANSWER :`0.18`

Discussion

46.	Let z_(1)be a fixedpoint on the circle of radius 1 centeredat the origin the Argandplaneand z_(1) nepm 1 .Consideran equilaternaltriangle inscribed in the circle with z_(1),z_(2),z_(3) as the vertices taken in the counter clockwise direction. Then z_(1)z_(2)z_(3) is equal to
Answer» `z_(1)^(2)` `z_(1)^(3)` `z_(1)^(4)` `z_(1)` ANSWER :B

Discussion

47.	x and y are a pair of correlated variables . Ten observations of their values (x_(p)y_(t)) have the following result : sum x = 55, sum y= 55, sum x^(2) = 385, sum xy = 350 . Predict the value of y when the value of x is 6
Answer» ANSWER :`5 . 79`

Discussion

48.	If vec(a)=hati+hatj+hatk,vec( c )=hatj-hatk are given vectors, then find a vector vec(b) satisfying the equations vec(a)xx vec(b)=vec( c ) and vec(a).vec(b)=3.
Answer» Answer :`VEC(b)=(5)/(3)HATI+(2)/(3)hatj+(2)/(3)HATK`

Discussion

49.	The matrix A=[{:(0,-5,8),(5,0,12),(-8,-12,0):}]is a .....
Answer» DIAGONAL matrix SYMMETRIC matrix skew symmetric matrix Scalar matrix Answer :C

Discussion

50.	Find the real values of a for which the point (-2a, a+ 1) lies in the smaller region bounded by the circle x^(2) + y^(2) =4 and the parabola y^(2) = 4x.
Answer» ANSWER :`RARR a in (-1, -5+2sqrt(6) )`

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Let alpha,betaandgamma be the angles made by a line with the positive directions of the axes of reference in three dimensions. If theta is the acute angle given by costheta=(cos^(2)alpha+cos^(2)beta+cos^(2)gamma)/(sin^(2)alpha+sin^(2)beta+sin^(2)gamma), then theta equals.

The product of the perpendicular distances from any point of the hyperbola x^(2)/a^(2)-y^(2)/b^(2)=1 to its asymptotes is

If z= cos.(2pi)/(2n +1) +isin.(2pi)/(2n+1), n is a positive integer, then the equation whose roots are alpha = z+ z^(3)+ ….+ z^(2n-1)and beta = z^2 + z^4 + ….+ z^(2n). Is ________________.

Evaluate int _(0)^(infty) (tan^(-1)ax-tan^(-1)x)/(x)dx, where a is a parametar.

A room has 6 bulbs, each has an independent switch. Find the number of ways in which the room can be lighted ?

If alpha, beta, gamma are the roots of x^(3) + 2x^(2) - 4x - 3 = 0 then the equation whose roots are alpha//3, beta//3, gamma//3 is

Check whether the relation R defined in the set {1,2,3,4,5,6} as R={(a,b) : b=a+1} is reflexive, symmetric or transitive.

The piont where the line 4x - 3y + 7 = 0 touches the circle x^(2) + y^(2) - 6x + 4y - 12 = 0 is

The points (-7, 4, -2), (-2, 1, 0) and (3, -2, 2) are

Evaluate: int 1/(1+ tan x) dx.

If there is an error of 0.05 cm in the measurement of the side as 2 cm of a cube, then relative errorin the volume is

A series of concentric ellipse E_1,E_2,E_3,…,E_n is constructed as follows: Ellipse E_n touches the extremities of the major axis of E_(n-1) and have its focii at the extremities of the minor axis of E_(n-1). If eccentricity of ellipse E_n is e_n, then the locus of (e_(n)^(2),e_(n-1)^(2)) is

The mean of 5 observations is 3 and variance is 2. If three of the five observations are 1,3,5 the other two are

Find the particular solution of the following differential equaiton : (x+1)(dy)/(dx) = 2e^(-y) - 1, y = 0 when x = 0.

Statement I : The value of the integral int_(pi//6)^(pi//3)(dx)/(1+sqrt(tanx)) is equal to (pi)/(6) Statement II : int_(a)^(b)f(x)dx=int_(a)^(b)f(a+b-x)dx

Find the value of a it the area of the triangle formed by the liners x=0,y=0,3x+4y=a is 6 sq units.

Show that the points (3,-2,4)(1,1,1) and (-1,4,-1) are collinear.

The valueoftan(1^@ )+ tan(89 ^@ )is equalto

If a,b and c are in G.P then (b - a)/(b - c) + (b + a)/(b + c)

For a data consisting of 15 observations x_(i), i=1,2,3,…,15 the following results are obtained :sum_(i=1)^(15) x_(i)= 170, sum_(i=1)^(15) x_(i)^(2) = 2830. If one of the observation namely 20 was found wrong and was replaced by its correct value 30, then the corrected variance is

Consider the unction f(x)=int_(0)^(x)(5ln(1+t^(2))-10t tan^(-1)t+16sint)dt f(x) is

Determine if A sub B or A cancel sub B where A=phi, B ={phi}

Three screws are drawn at random from a lot of 50 screws, 5 of which are defective. Find the probability of the event that all 3 screws are non-defective, assuming that the drawing is (a) with replacement (b) without replacement

The points 2i + j - k, i + j + k, 2i + 2j + k, 2j + 5k are

For simple pendulum, T = 2pi sqrt((l)/(g)) where T is the periodic time and l is the length of pendulum. If there is 4% error in the measure of periodic time then find the error percentage in the length of pendulum.

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

If zbarz=4 then the locus of z is

Statement 1 : If (a)/(a_(1)),(b)/(b_(1)),( c )/(c_(1)) are in A.P., then a_(1),b_(1),c_(1) are in G.P. because Statement 2 : If ax^(2)+bx+c=0 and a_(1)x^(2)+b_(1)x+c_(1)=0 have a common root and (a)/(a_(1)),(b)/(b_(1)),( c )/(c_(1)) are in A.P., then a_(1),b_(1),c_(1) are in G.P.

Distance of line y=|(x+1,x,x),(x,x+2,x),(x,x,x+3)| from the origin is

There are 4 pairs of hand gloves of 4 different colours. In how many ways can they be paired off so that a left hand glove and a right handed glove are not of same colour.

4 American and 1 Indian couple Total 5 couples seats around the circular table at random. If it is given that each American seat near by his wife then ......... is the probability of an event that Indian person can seat near by his wife.

If y+ sin y= cos x," find "(dy)/(dx).

E_(1), E_(2) are events of a sample space such that P(E_(1))=(1)/(4), P((E_(2))/(E_(1)))=(1)/(2), P((E_(1))/(E_(2)))=(1)/(4) then P((E_(1))/(E_(2)))+P((E_(1))/(barE_(2)))=

Find the angle of intersection of the curves y = 4-x^(2) and y=x^(2).

A random variable X has the following probability distribution: (# #TRG_MAT_MCQ_XII_P2_C08_E02_004_Q01.png" width="80%"> Then, the value of P(0 lt X lt 4) is

The points on the line x + y = 4 lying at a﻿ unit distance from the line 4x+3y-10=0﻿ are﻿

Let x_1,x_2 ,x_3 be the points where f(x)=|1-|x-4||, x in R is not differentiable thenf(x_1)+f(x_2)+f(x_3) =

~(prarrq)rarr[(~p)vv(~q)] is

If f(x)=2x^(3)+3x^(2)-x+1 is divided with x+1 and x-1 and the respective remainders are 5 and -1 then find the remainder when f(x) is divided with x^(2)-1 ?

If omega=(-1+i sqrt(3))/(2) then (3+omega+3 omega^(2))^(4)=

If veca ne vec0, vecb ne vec0, vecc ne vec0, veca xx vecb =vec0 and vecb xx vecc=vec0," then "veca xx vecc is equal to

Prove that the determinent |{:(x,sintheta,costheta),(-sintheta,-x,1),(costheta,1,x):}| is independent from value of theta

Let A,B and C be three events such that P(A)=0.50, P(B)=0.40, P(A nn B)=0.20 P(C| A nnB') =0.30 , P(C|A' nn B)=0.25 and (A nn B)=0.20 then P(C| A uu B) =_____

Let z_(1)be a fixedpoint on the circle of radius 1 centeredat the origin the Argandplaneand z_(1) nepm 1 .Consideran equilaternaltriangle inscribed in the circle with z_(1),z_(2),z_(3) as the vertices taken in the counter clockwise direction. Then z_(1)z_(2)z_(3) is equal to

x and y are a pair of correlated variables . Ten observations of their values (x_(p)y_(t)) have the following result : sum x = 55, sum y= 55, sum x^(2) = 385, sum xy = 350 . Predict the value of y when the value of x is 6

If vec(a)=hati+hatj+hatk,vec( c )=hatj-hatk are given vectors, then find a vector vec(b) satisfying the equations vec(a)xx vec(b)=vec( c ) and vec(a).vec(b)=3.

The matrix A=[{:(0,-5,8),(5,0,12),(-8,-12,0):}]is a .....

Find the real values of a for which the point (-2a, a+ 1) lies in the smaller region bounded by the circle x^(2) + y^(2) =4 and the parabola y^(2) = 4x.

The points on the line x + y = 4 lying at a unit distance from the line 4x+3y-10=0 are