28278 + Interview Questions in Maths in Class 12

1.	If sin x _(1)+ sin x_(2) + sin x _(3) +…+ sin x _(n) is
Answer» N `PI` `n SIN "" (pi)/(n)` NONE of these Answer :C

Discussion

2.	State which of the following sets are finite sets or infinite. In case of finite set,
Answer» Solution :(i) A is not a NULL SET (ii) B is a null set (III) C is not a null set

Discussion

3.	Find the coordinates of the point where the line through (5, 1, 6) and (3, 4,1) crosses the YZ- plane.
Answer» <P> Answer :`P(0,(17)/(2),(-13)/(2))`

Discussion

4.	Let F_(1)andF_(2) be the points (0,-4)and(0,4). The locus of the point P such that \|PF_(1)\|+\|PF_(2)\|=6 is :
Answer» an ellipse the SEGMENT `[F_(1)F_(2)]` the st. line CONTAINING `F_(1)andF_(2)` None of these Answer :D

Discussion

5.	In tossing of a pair of dice, the probability of getting an odd number greater than 2 on each die is :
Answer» (1/3) (1/9) (1/6) (1/4) ANSWER :B

Discussion

6.	If int x^(3) e^(2) dx = e^(K)l + c then K , l =
Answer» ANSWER :4

Discussion

7.	If n is a positive integer, then(1+i)^n+(1-i)^n=
Answer» `2^((n//2)+1).COS(npi)/(3)` `2^((n//2)+1).cos(npi)/(4)` `2^((n//2)+1).cos(npi)/(5)` `2^((n//2)+1).cos(npi)/(6)` ANSWER :B

Discussion

8.	If A=(1)/(pi)[{:(sin^(-1)(pix),tan^(-1)((x)/(pi))),(sin^(-1)((x)/(pi)),cot^(-1)(pix)):}],B=(1)/(pi)[{:(-cos^(-1)(pix),tan^(-1)((x)/(pi))),(sin^(-1)((x)/(pi)),-tan^(-1)(pix)):}], then A-B is equal to ......
Answer» I 0 2I `(1)/(2)*I` ANSWER :D

Discussion

9.	The probability of getting a number between 1 and 100 which is divisible by one and itself only is……
Answer» `(1)/(4)` `(1)/(2)` `(3)/(4)` `(25)/(98)` Answer :D

Discussion

10.	Point P lie on 2xy=1. A triangle is contructed by P, S and S' (where S and S' are foci). The locus of ex-centre opposite S (S and P lie in first quandrant) is (x+py)^(2)=(sqrt(2)-1)^(2)(x-y)^(2)+q, then the value of p+q is
Answer» ANSWER :`(5)`

Discussion

11.	Let A = (a_(ij)_(3xx3) be a matrix with a_(ij ) in C. Let B be a matrix obtained by inerchanging two columns of A . Then det (A+B) is equal to
Answer» DET (A) +det (B) 0 2 det (A) det( A) - det(B) ANSWER :B

Discussion

12.	Atowersubtendsan anglealphaat apointAin the planeof itsbaseand the angleof depressionof thefootof thetowerata pointb fthustaboveA isbeta. Thenthe heightof thetower is
Answer» B TAN `alphacotbeta ` `bcotalphatan BETA ` `b cotalphacot beta ` `b tanalphatan beta ` ANSWER :A

Discussion

13.	Show that the area enclosed between y^(2)=4ax and y=mx is (8)/(3)(a^(2))/(m^(3)) sq units.
Answer» Answer :`=(8)/(3)(a^(2))/(m^(3))` SQ UNITS.

Discussion

14.	Is ** defined on the set {1,2,3,4,5} by a"*"b = L.C.M. of a and b a binary operation ?Justify your answer.
Answer» SOLUTION :N/A

Discussion

15.	Definite integration as the limit of a sum : lim_(ntooo)sum_(k=0)^(n)(n)/(n^(2)+k^(2))=..........
Answer» `PI/4` `pi/2` `pi` `0` ANSWER :C

Discussion

16.	Integrate the functions in exercise. (1)/(sqrt(x^(2)-2x+2))
Answer» ANSWER :`LOG\|(X+1)+SQRT(x^(2)+2x+2)\|+c`

Discussion

17.	if int((x^(2)-1)dx)/((x^(4)+3x^(2)+1)tan^(-1)""(x^(2)+1)/(x)) = log\|tan^(-1)f(x)\|+C then
Answer» `f(x) = x^(2) + 1` `f(x) = (x^(2) + 1)/(2X)` `f(x) = (1)/(2) (x^(2) + 1)` `f(x)= (x^(2) + 1)/(x)` Answer :D

Discussion

18.	If \|a\|=2, \|b\|=3 and a, b are mutually perpendicular, then the area of the triangle whose vertices are 0, a+b, a-b is
Answer» 5 1 6 8 Solution :Let position vectors of the POITS A, B C are `0, a+b, a-b`respectively and `theta=90^@` `:.""` Area of triangle `=1/2\|(a+b)xx(a-b)\|` `=1/2\|(a+b)xx(a-b)\|` `=1/2\|2bxxa\|` `=\|b\|a\|sin theta=3xx2sin 90^@=6`

Discussion

19.	Show that the differential equation (x - y) (dy)/(dx)= x + 2y is homogeneous and solved it.
Answer» ANSWER :`log\|(x^(2) + XY + y^(2))\| = 2 sqart 3 tan^(-1)((x + 2y)/(SQRT3X)) + C`

Discussion

20.	\|A^(-1)\|ne\|A\|^(-1), where is non-singular matrix
Answer» ANSWER :FALSE

Discussion

21.	Triangle ABC is isosceles with AB = AC. If the radius of the cicum-circle of /_\ABC equals AB, find the measure of the angle A.
Answer» ANSWER :`120^(@)`

Discussion

22.	int ((1-sin x )/( 1- cos x )) e^(x) dx is equal to
Answer» ` - e^(X)tan""( x)/( 2) + C` `- e^(x) cot ""(x)/(2) +C` `- ( 1)/( 2) e^(x) tan""(x)/(2) +C` `- (1)/(2) e^(x) cot ""(x)/(2) +C` Answer :B

Discussion

23.	Find gof and fog, if (i) f (x) = \|x\| and g (x) = \|5x - 2\| (ii) f (x) = 8x ^(3) and g (x) = x ^(1/3).
Answer» Answer :(i) (gof) `(X) =\|5\|x\| -2\| , (FOG ) (x) =15 x -2\|` (ii) (gof)` (x)=2x, `(fog) `(x) = 8X`

Discussion

24.	Let S, S^(') are the focii and BB^(') be the minor axis of an ellipse. If angleBSS^(')=theta then its eccentricity is
Answer» `tan theta` `SIN theta` `cos theta` `COT theta` ANSWER :C

Discussion

25.	Verify mean value theorem for each of the functions: f(x)= sqrt(25-x^(2)), in x in [1, 5]
Answer» ANSWER :`sqrt15 in (1, 5)`

Discussion

26.	The point of intersection of the normals to the parabola y^(2) =4x at the ends of its latus rectum is
Answer» `(0,2)` ` ( 3,0 ) ` ` ( 0,3) ` `( 2,0 ) ` ANSWER :B

Discussion

27.	Integrate the following : int4x^3dx
Answer» SOLUTION :`int4x^3dx`=`4x^4/4+C`=`x^4+C`

Discussion

28.	If lim_(xtoa)(f(x))/(g(x))=linR and lim_(xtoa)g(x)=0 then
Answer» `lim_(xtoa)f(X)=l` `lim_(xtoa)f(x)=1` `lim_(xtoa)f(x)=0` `lim_(xtoa)f(x)=OO` Answer :C

Discussion

29.	The plane 2x-3y+6z-11=0 makes an angle sin^(-1)(alpha) with X-axis. The value of alpah is
Answer» `(SQRT(3))/(2)` `(sqrt(2))/(3)` `(2)/(7)` `(3)/(7)` ANSWER :C

Discussion

30.	Evaluate the determinants(i){:[( 3,-1,-2),( 0,0,-1),( 3,-5,0) ]:} "" (ii) {:[( 3,-4,5),( 1,1,-2),(2,3,1) ]:} (iii) {:[( 0,1,2),(-1,0,-3),(-2,3,0)]:}""(iv) {:[(2,-1,-2),(0,2,-1),(3,-5,0)]:}
Answer» Answer :` (i) -12, (II) 46, (iii) 0, (iv) 5`

Discussion

31.	In a bank, principal increases continuously at the rate of r% per yeat. Find the value of r if Rs 100 double itself in 10 years (log_(e) 2 = 0.6931)
Answer» 5 6.9 0.069 0.0069 Answer :B

Discussion

32.	Find the number of onto functions from a set containing A = {1, 2, 3, 4, 5) to another set B = {a, b, c, d) such that f(1) = a.
Answer» ANSWER :60

Discussion

33.	Three numbers from an increasing G.P. If the middle term is doubled the new number are in A.P. The common ratio of G.P will be
Answer» `2 + SQRT(3)` `2 +- sqrt(3)` `3sqrt(2)` `3 + sqrt(2)` ANSWER :B

Discussion

34.	If f:[0,1]rarr [0,1]be difined by f(x) = {(x," if x is rational"),(1-x," if x is irrational"):}then fof(x) is ............
Answer» CONSTANT 1 + X x NONE of these SOLUTION :N/A

Discussion

35.	The probability distribution of a random variable X is given as under: Find k , and P (X lt 6) .
Answer» <P> ANSWER :`k=1/10;P(Xlt6)=0.81`

Discussion

36.	Let f(x) ={{:( x+2, 0 le x lt 2),( 6-x, x ge 2):}, g(x)={{:( 1+ tan x, 0le x lt (pi) /(4)),( 3-cotx,(pi)/(4) le x lt pi ):} the rangeof h(x) = g(x)) is
Answer» `(-OO,oo)` `(4,oo)` `(-oo,4]` NONEOF these Answer :C

Discussion

37.	Solve the inequalities (i) cos x le -1//2 (ii) sin x ge -1//2 (iii) tan gt-sqrt(3) (iv) sinx +sqrt(3cosx)gt0 (v)Prove that 0le(1+cos theta)/(2+sin theta)le 4/3 for all theta (vi)Solve theinequation sin^(4)(x)/(3)+cos^(4)(x)/(4)+cos^(4)(x)/(3)gt1/2
Answer» Answer :(i) `UNDERSET(n=1)bigcup[2npi+(2pi)/(3),2npi+(4pi)/(3)]` (ii)`underset(n=1)bigcup[2npi-(PI)/(6),2npi+(7pi)/(6)]` (iii) `underset(n=1)bigcup[NPI-(pi)/(3),npi+(pi)/(2)]` (iv)`underset(n=1)bigcup(6n-1)+(pi)/(3),2(3+1)(pi)/(3)` (vi)`R=3/2(npi)/(2)`

Discussion

38.	Let f(x) = (x^(2) + x + 1)/(x^(2) + 3 x + 3) x x in R . Let m be the mid-point ofthe range of f(x) , then 3m + 2 . 31 is equal to _______
Answer» ANSWER :`7 . 31`

Discussion

39.	For the curve y = 4x^(3) – 2x^(5) , find all the points at which the tangent passes through the origin.
Answer» ANSWER :. (0, 0), (1, 2), (–1, –2)

Discussion

40.	Two teams A and B play a tournament. The first one to win (n+1) games win the series. The probability that A wins a game is p and that B wins a game is q (no ties). Find the probability that A wins the series. Hence or otherwise prove that sum(r=0)(n)""^(n+1)C_(r)*(1)/(2^(n+r))=1.
Answer» ANSWER :`(((N-r)(N-r-1))/((N-1)(N-2)))`

Discussion

41.	Let f(x) = \|x\| "cos" (1)/(x) + 15x^(2), x ne 0, = k, x = 0, then f(x) is continuous at x = 0, if k is :
Answer» 15 -15 0 6 Answer :C

Discussion

42.	The smallest value of a for which both the roots of the equation x^(2) - 10 ax + 25 (a^(2) - a + 1) = 0""are real, distinct and have value at least 5 is _______
Answer» ANSWER :`2 . 00`

Discussion

43.	int (dx)/(x (log x - 2)(log x - 3))= I + c rArr I =
Answer» `(1)/(X) log \|(log x - 3)/(log x -2)\|` `log \|(log x - 3)/(log x -2)\|` `log \|(log x - 2)/(log x -3)\|` log \| (log x - 3 ) (log x - 2 )\| ANSWER :B

Discussion

44.	A vertical pole (more than 100 m high) consists of two protions, the lower being one third or the whole. If the upper portion subtends an angle tan ^(-1)((1)/(2)) at a point in a horizontal plance through the foot of the pole and distance 40 ft from it, then the height of the pole is
Answer» 100 gt 120 FT 150 ft None of these : Answer :B

Discussion

45.	Check the injectivity and surjectivity of the following function . f: RxxR - {0}rarr R , f(x,y) =x/(y)
Answer» SOLUTION :N/A

Discussion

46.	Evaluate the integrals in exercise. overset(1) underset(-x) int (dx)/(x^(2)+2x+5)
Answer» ANSWER :`(PI)/(8)`

Discussion

47.	Out of the following …………. Is the unit vector in the direction of (3hati+4hatj-5hatk)+2(2hati+hatj).
Answer» `(7)/(sqrt(110))HATI+(6)/(sqrt(110))HATJ-(5)/(sqrt(110))HATK` `-(7)/(sqrt(110))hati-(6)/(sqrt(110))hatj-(5)/(sqrt(110))hatk` `(7)/(sqrt(110))hati-(6)/(sqrt(110))hatj-(5)/(sqrt(110))hatk` `(5)/(sqrt(110))hati+(6)/(sqrt(110))hatj-(5)/(sqrt(110))hatk` Answer :A

Discussion

48.	Using integration ,find the area of the region{(x,y) : y^(2) le 4x, 4x^(2) +4y^(2)le 9 }
Answer» ANSWER :` ((9)/(4) sin ^(-1)""( 2SQRT2)/(3)+ (SQRT2)/(6))) ` sq. UNIT

Discussion

49.	int (1 + 4x + 6x^(2) + 4x^(3) + x^(4))dx
Answer» 4 + 12 X + `12x^(2) + 4x^(3) + C ` `((1 + x)^(5))/(5) + C ` `((1 + x)^(6))/(5) + C ` `((1 + x)^(3))/(3)` + C Answer :B

Discussion

50.	If the algebraic sum of the distances from the points (2,0), (0, 2) and (1, 1) to a variable line be zero then the line passes through the fixed point.
Answer» (0,0) (1, 1) (-1, 1) (2,1) ANSWER :B

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

If sin x _(1)+ sin x_(2) + sin x _(3) +…+ sin x _(n) is

State which of the following sets are finite sets or infinite. In case of finite set,

Find the coordinates of the point where the line through (5, 1, 6) and (3, 4,1) crosses the YZ- plane.

Let F_(1)andF_(2) be the points (0,-4)and(0,4). The locus of the point P such that |PF_(1)|+|PF_(2)|=6 is :

In tossing of a pair of dice, the probability of getting an odd number greater than 2 on each die is :

If int x^(3) e^(2) dx = e^(K)l + c then K , l =

If n is a positive integer, then(1+i)^n+(1-i)^n=

If A=(1)/(pi)[{:(sin^(-1)(pix),tan^(-1)((x)/(pi))),(sin^(-1)((x)/(pi)),cot^(-1)(pix)):}],B=(1)/(pi)[{:(-cos^(-1)(pix),tan^(-1)((x)/(pi))),(sin^(-1)((x)/(pi)),-tan^(-1)(pix)):}], then A-B is equal to ......

The probability of getting a number between 1 and 100 which is divisible by one and itself only is……

Point P lie on 2xy=1. A triangle is contructed by P, S and S' (where S and S' are foci). The locus of ex-centre opposite S (S and P lie in first quandrant) is (x+py)^(2)=(sqrt(2)-1)^(2)(x-y)^(2)+q, then the value of p+q is

Let A = (a_(ij)_(3xx3) be a matrix with a_(ij ) in C. Let B be a matrix obtained by inerchanging two columns of A . Then det (A+B) is equal to

Atowersubtendsan anglealphaat apointAin the planeof itsbaseand the angleof depressionof thefootof thetowerata pointb fthustaboveA isbeta. Thenthe heightof thetower is

Show that the area enclosed between y^(2)=4ax and y=mx is (8)/(3)(a^(2))/(m^(3)) sq units.

Is ** defined on the set {1,2,3,4,5} by a"*"b = L.C.M. of a and b a binary operation ?Justify your answer.

Definite integration as the limit of a sum : lim_(ntooo)sum_(k=0)^(n)(n)/(n^(2)+k^(2))=..........

Integrate the functions in exercise. (1)/(sqrt(x^(2)-2x+2))

if int((x^(2)-1)dx)/((x^(4)+3x^(2)+1)tan^(-1)""(x^(2)+1)/(x)) = log|tan^(-1)f(x)|+C then

If |a|=2, |b|=3 and a, b are mutually perpendicular, then the area of the triangle whose vertices are 0, a+b, a-b is

Show that the differential equation (x - y) (dy)/(dx)= x + 2y is homogeneous and solved it.

|A^(-1)|ne|A|^(-1), where is non-singular matrix

Triangle ABC is isosceles with AB = AC. If the radius of the cicum-circle of /_\ABC equals AB, find the measure of the angle A.

int ((1-sin x )/( 1- cos x )) e^(x) dx is equal to

Find gof and fog, if (i) f (x) = |x| and g (x) = |5x - 2| (ii) f (x) = 8x ^(3) and g (x) = x ^(1/3).

Let S, S^(') are the focii and BB^(') be the minor axis of an ellipse. If angleBSS^(')=theta then its eccentricity is

Verify mean value theorem for each of the functions: f(x)= sqrt(25-x^(2)), in x in [1, 5]

The point of intersection of the normals to the parabola y^(2) =4x at the ends of its latus rectum is

Integrate the following : int4x^3dx

If lim_(xtoa)(f(x))/(g(x))=linR and lim_(xtoa)g(x)=0 then

The plane 2x-3y+6z-11=0 makes an angle sin^(-1)(alpha) with X-axis. The value of alpah is

Evaluate the determinants(i){:[( 3,-1,-2),( 0,0,-1),( 3,-5,0) ]:} "" (ii) {:[( 3,-4,5),( 1,1,-2),(2,3,1) ]:} (iii) {:[( 0,1,2),(-1,0,-3),(-2,3,0)]:}""(iv) {:[(2,-1,-2),(0,2,-1),(3,-5,0)]:}

In a bank, principal increases continuously at the rate of r% per yeat. Find the value of r if Rs 100 double itself in 10 years (log_(e) 2 = 0.6931)

Find the number of onto functions from a set containing A = {1, 2, 3, 4, 5) to another set B = {a, b, c, d) such that f(1) = a.

Three numbers from an increasing G.P. If the middle term is doubled the new number are in A.P. The common ratio of G.P will be

If f:[0,1]rarr [0,1]be difined by f(x) = {(x," if x is rational"),(1-x," if x is irrational"):}then fof(x) is ............

The probability distribution of a random variable X is given as under: Find k , and P (X lt 6) .

Let f(x) ={{:( x+2, 0 le x lt 2),( 6-x, x ge 2):}, g(x)={{:( 1+ tan x, 0le x lt (pi) /(4)),( 3-cotx,(pi)/(4) le x lt pi ):} the rangeof h(x) = g(x)) is

Solve the inequalities (i) cos x le -1//2 (ii) sin x ge -1//2 (iii) tan gt-sqrt(3) (iv) sinx +sqrt(3cosx)gt0 (v)Prove that 0le(1+cos theta)/(2+sin theta)le 4/3 for all theta (vi)Solve theinequation sin^(4)(x)/(3)+cos^(4)(x)/(4)+cos^(4)(x)/(3)gt1/2

Let f(x) = (x^(2) + x + 1)/(x^(2) + 3 x + 3) x x in R . Let m be the mid-point ofthe range of f(x) , then 3m + 2 . 31 is equal to _______

For the curve y = 4x^(3) – 2x^(5) , find all the points at which the tangent passes through the origin.

Two teams A and B play a tournament. The first one to win (n+1) games win the series. The probability that A wins a game is p and that B wins a game is q (no ties). Find the probability that A wins the series. Hence or otherwise prove that sum(r=0)(n)""^(n+1)C_(r)*(1)/(2^(n+r))=1.

Let f(x) = |x| "cos" (1)/(x) + 15x^(2), x ne 0, = k, x = 0, then f(x) is continuous at x = 0, if k is :

The smallest value of a for which both the roots of the equation x^(2) - 10 ax + 25 (a^(2) - a + 1) = 0""are real, distinct and have value at least 5 is _______

int (dx)/(x (log x - 2)(log x - 3))= I + c rArr I =

A vertical pole (more than 100 m high) consists of two protions, the lower being one third or the whole. If the upper portion subtends an angle tan ^(-1)((1)/(2)) at a point in a horizontal plance through the foot of the pole and distance 40 ft from it, then the height of the pole is

Check the injectivity and surjectivity of the following function . f: RxxR - {0}rarr R , f(x,y) =x/(y)

Evaluate the integrals in exercise. overset(1) underset(-x) int (dx)/(x^(2)+2x+5)

Out of the following …………. Is the unit vector in the direction of (3hati+4hatj-5hatk)+2(2hati+hatj).

Using integration ,find the area of the region{(x,y) : y^(2) le 4x, 4x^(2) +4y^(2)le 9 }

int (1 + 4x + 6x^(2) + 4x^(3) + x^(4))dx

If the algebraic sum of the distances from﻿ the points (2,0), (0, 2) and (1, 1) to a variable line be zero then the line passes﻿ through the fixed point.﻿

If the algebraic sum of the distances from the points (2,0), (0, 2) and (1, 1) to a variable line be zero then the line passes through the fixed point.