28278 + Interview Questions in Maths in Class 12 Page 62 InterviewSolution

3051.	If for the matrix A=[(costheta, 2sintheta),(sintheta,costheta)],A^(-1)=A^(T)then number of possible value(s) of theta in [0, 2pi] is :
Answer» 2 3 1 4 Answer :B

Discussion

3052.	If three positive real numbers a, b, c are in A.P and abc = 4, then the minimum possible value of b is
Answer» `2^(3/2)` `2^(2/3)` `2^(1/3)` `2^(5/2)` ANSWER :B

Discussion

3053.	If a, b, c are positive integers such that a^2+ 2b^2-2ab = 169 and 2bc - c^2= 169 then a + b + c is:
Answer» ANSWER :`39`

Discussion

3054.	Find the probability of getting 5 exactly twice in 7 throws of a die.
Answer» ANSWER :`(7)/(12)((5)/(6))^(5)`

Discussion

3055.	Let z_(1) = 2 + 3i and z_(2) = 3 + 4i be two points on the complex plane. Then the set of complex numbers z satisfying abs(z - z_(1))^(2) + (z - z_(2))^(2) = (z_(1) - z_(2))^(2) represents
Answer» a straight line a point a circle a pair of straight lines Answer :C

Discussion

3056.	If y=(tan^(-1)x)^(2), show that (x^(2)+1)^(2)y_(2)+2x(x^(2)+1)y_(1)=2.
Answer» ANSWER :`(1+x^(2) ) y_(2) + 2X(1+x^(2) ) y_(1) =2`

Discussion

3057.	if y=sec(tan^(-1)x), then (dy)/dx is equal to
Answer» `X/(1+x^2)` `xsqrt(1+x^2)` `1/sqft(1+x^2)` `x/sqrt(1+x^2)` ANSWER :D

Discussion

3058.	If alpha, beta , gamma are the roots of x^(3) + 3px^(2) + 3px + r = 0then the equation whose roots are alpha - (1)/( beta gamma ) , beta - (1)/(gamma alpha), gamma - (1)/(alpha beta)is
Answer» `y^(3) - 29Y^(2) - 50Y + 625 = 0 ` `2y^(3) - 36y^(2) + 182y + 432 = 0 ` `r^(2) y^(3) + 3pr (r + 1) y^(2) + 3q (r + 1)^(2) y + (r + 1)^(3) = 0 ` `y^(3) - q^(2) y^(2) - 2qr^(2)y -r^(4) = 0 ` ANSWER :3

Discussion

3059.	(~~(~~p)^^q is equivalent to
Answer» <P>`~~p ^^ Q` `p^^q` `p^^ ~~q` `~~p ^^ ~~ q` ANSWER :B

Discussion

3060.	STATEMENT-1 : From point (4, 0) three different normals can be drawn to the parabola y^(2) =4x. and STATEMENT-2 : From any point, atmost three different normals can be drawn to a hyperbola.
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 :B

Discussion

3061.	(a) Find all rational values of x at which y=sqrt(x^(2)+x+3) is a rational number. (b) Prove that sqrt2 is an irrational number.
Answer» Answer :Prove that the RULE of contraies, putting `2=p^(2)/Q^(2)`, where p and q are positive integer without COMMON multiplier.s.

Discussion

3062.	Method of integration by parts : I_(1)=int sin^(-1)x dx and I_(2)= int sin^(-1) sqrt(1-x^(2))dx then.....
Answer» `I_(1)=I_(2)` `I_(2)=(pi)/(2I_(1))` `I_(1)+I_(2)=(pi)/(2x)` `I_(1)+I_(2)=(pi)/(2)` ANSWER :C

Discussion

3063.	The set of all real values of x for which f(x)=log_(e)sqrt((1+x)/(1-x))+log_(e)((1+sqrt(1-x^(2)))/x)+coth^(-1)x+log_(e)((1+sqrt(1+x^(2)))/x)+sinh^(-1)x is defined is
Answer» `PHI` (0, 1) (-1, 1) (0, 1] ANSWER :B

Discussion

3064.	A man is known to speak the truth on an average 3 out of 4 times. He throws a fair die and reports that it is a six. The probabilitythe itis actually a six is
Answer» `(3)/(5)` `(3)/(8)` `(3)/(4)` `(1)/(5)` ANSWER :B

Discussion

3065.	If u_(1) = ax + by + c, u_(2) = a'x + b'y + d, u_(3) = ax + by + c', u_(4) = a'x + b'y +d' then u_(1)= 0, u_(2) = 0, u_(3) = 0, u_(4) = 0 from a parallelogram. Then the diagonal.
Answer» BD can be GIVEN by `u_(2)u_(3) - u_(1)u_(4) = 0` BD can be given by `u_(1)u_(2) = u_(3)u_(4) = 0` AC can be given by `u_(1)u_(2) - u_(3)u_(4) = 0` AC can be given by `u_(2)u_(3) = u_(1)u_(4) = 0` ANSWER :A

Discussion

3066.	Solve (3x-4)/(2) ge (x+1)/(4) -1. Show the graph of the solutions on number line.
Answer» ANSWER :SOLUTION SET is [1, `OO`)

Discussion

3067.	Showthat thefunction f : R to R : f (x) = {[-1 \ if \ x \ is \ irrational ], [1 \ if \ x \ is \ rational ]} ismany-oneinto. Find(i) f ((1)/(2)) \ (ii)f (sqrt(2))\ (iii) f (pi) \ (iv)f (2 +sqrt(3))
Answer» ANSWER :`(i) 1 (II) -1 (III) -1 (IV) -1`

Discussion

3068.	Integrate the following functions 1/(sqrt(1+4x^2)
Answer» SOLUTION :`int1/sqrt(1+4x^2) DX = INT 1/sqrt(1+(2x)^2) dx` =`1/2log\|2x+sqrt(1+(2x)^2) dx` `1/2 log\|2x+sqrt(1+4x^2)\|+c`

Discussion

3069.	P(A' cup B') \| C = ………………
Answer» `1- P(A CAP B) \| C ` `1- P(A cup B') \| C ` `1- P(A cap B') \| C ` NONE of these Answer :A

Discussion

3070.	Equations of the line passing through (1,1,1) and perpendicular to the plane 2x+3y+z+5=0 are
Answer» `(x+1)/( 1) = (y-1)/(3) = (z-1)/(2)` `(x-1)/(3) = (y-1)/(3) = ( z-1)/(2)` `(x-1)/(2) = ( y-1)/(3) = (z-1)/(1)` `(x-1)/(3) = (y-1)/(1) + (z-1)/(1)` ANSWER :C

Discussion

3071.	Let a* b =1cm (a,b) for all values of a,b in N (i) Find (1216) (ii) Show that is commutative on N (iii) Find the identity element in N (iv) Find all invertible elements in N
Answer» Solution :(i) `1216 =1CM (12,16)=(4xx3xx4)=48` (ii)aB=1cm (a,b) =1cm (b,a)=ba (iii) let e be the identity element in N (iv) Let a in N be an ARBITRARY element Then `ab=1 rarr 1cm (a,b)=1 rarr a=b=1` `therefore` 1 is the only element in N which is ivertible

Discussion

3072.	The distance between the pair of parallel lines x^(2) + 4xy + 4y^(2) + 3x + 6y- 4 = 0 is
Answer» `(4sqrt3)/(3)` `2SQRT2` `4sqrt2` 4 Answer :D

Discussion

3073.	Statement-1 : The condition on a and b for which two distinct chords of the ellipse (x^(2))/(2a^(2))+(y^(2))/(2b^(2))=1 passing through (a,-b) are bisected by theine x+y=b "is" a^(2)+6ab-7b^(2) ge0. Because: Statement-2 equationof chord of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 whose mid point is (x_(1),y_(1)) is T=S_(1)
Answer» Statement 1 is TRUE, Statement -2 is True, Statement -2 is a correct exlpanation for Statement 1 Statement 1 is True, Statement -2 is True, Statement -2 is NOT a correct exlpanation for Statement 1 Statement-1 is True Statement-2 is FALSE Statement-1 is False, Statement-2 is True Answer :A

Discussion

3074.	The set of values of x which satisfy 5x+2 lt 3x +8 and (x+2)/(x-1) lt 4 is
Answer» `(2, 3)` `(-oo, 1) cup (2, 3)` `(-oo, 1)` `(1, 3)` Answer :B

Discussion

3075.	Um A contains 7 white and 3 black balls, um B contains 4 white and 6 black balls, um C contains 2 white and 8 black balls. One of these urns is chosen at random with probabilities 0.2, 0.6 and 0.2 respectively. From the chosen urn, two balls are drawn at random without replacement. Both the balls happen to be white. Find the probability that the balls drawn are from the urn C.
Answer» SOLUTION :`P(A)=0.2,P(B)=0.6andP(C )=0.2`. Let E be the event that 2 white BALLS are DRAWN. Then, `P(E//A)=(.^7C_2)/(.^10C_2),P(E//B)=(.^4C_2)/(.^10C_2),P(E//C)=(.^2C_2)/(.^10C_2)` `:.` required probability `=P(C//E)=(P(E//C).P(C))/(P(E//A).P(A)+P(E//B).P(B)+P(E//C).P(C))`.

Discussion

3076.	If x ge 0, y ge 0, 2x+3y le 12, 3x+y le 12, then the minimum value of f=5x+7y is
Answer» 0 `204//7` 84 12 Answer :A

Discussion

3077.	The sloope of the line touching both the parabolas y^(2) =4x and x^(2) =32yis
Answer» `(1)/(2) ` ` ( 3)/(2) ` ` ( 1)/(8) ` ` ( 3)/(2) ` ANSWER :A

Discussion

3078.	Integration by partial fraction : int(4e^(x)+6e^(-x))/(9e^(x)-4e^(-x))dx=Ax+B log(9e^(x)-4e^(-x))+c then A+B=.
Answer» `(4)/(9)` `(4)/(36)` `(35)/(36)` `(9)/(4)` ANSWER :A

Discussion

3079.	Which month had the largest percentage of vegetable sales relative to total sales?
Answer» Jan Mar Jun Oct Answer :A

Discussion

3080.	If x in[(4n+1)(pi)/(2),(4n+3)(pi)/(2)] and n in N, then the value of int_(0)^(x)[cos t] dt, is
Answer» `(2n-1)(PI)/(2)-X` `(2n-1)(pi)/(pi)/(2)-x` `(2n+1)(pi)/(2)-x` `(2n+1)(pi)/(2)+x` Solution :The graph of f(x)=[cos x] is as shown in Fig.13. CLEARLY, it is a periodic function with period `2pi`. Now, `overset(x)UNDERSET(0)int [cos t]dt=overset((4n+1)pi//2)underset(0)int [cos t]dt+overset(x)underset((4n+1)pi//2)int[cos t]dt` `rArr overset(x)underset(0)int [cos t]dt=overset(2npi+pi//2)underset(0)int [cos t]x" dt"+overset(x)underset(2npi+pi//2)int [cos t]dt` `rArr overset(x)underset(0)int [cos t]dt=overset(2npi)underset(0)int [cos t]dt+overset(2npi+pi//2)underset(2npi)int [cos t]dt+overset(x)underset(2npi+pi//2)int [cos t]dt` `rArr overset(x)underset(0)int [cos t]dt=n overset(2npi)underset(0)int[cos t]dt+overset(pi//2)underset(0)int [cos t]dt+overset(x)underset(2npi+pi//2)int[cos t]dt` `rArr overset(x)underset(0)int [cos t]dt=n[overset(pi//2)underset(0)int 0 dt+overset(3PI//2)underset(pi//2)int (-1)dt+overset(2pi)underset(3pi//2)int 0 dt]+overset(pi//2)underset(0)int 0 dt+overset(x)underset(2npi+pi//2)int -1 dt` `rArr overset(x)underset(0)int [cos t]dt=n[-((3pi)/(2)-(pi)/(2))]-[x-(2n+(pi)/(2))]` `rArroverset(x)underset(0)int [cos t]dt=npi+(pi)/(2)-x=(2n+1)(pi)/(2)-x`

Discussion

3081.	Find value of sin^-1(cos((33pi)/5))
Answer»

Discussion

3082.	If P(A)=0.3, P("not" B)=0.4,P(AintB')=0.5 and A and B are independent events, find P(A and not B)
Answer» ANSWER :0.12

Discussion

3083.	Evaluate{:[( x,y , x+y),( y,x+y,x),( x+y,x,y)]:}
Answer» ANSWER :`-2(X^(3) +y^(3)) `

Discussion

3084.	Let N be the set of all natural number , Z be the set of all integers and sigma : N to Zbe difinedby{:sigma(n)={((n)/(2)",",if,n" is even"),(,,"then"),(-(n-1)/(2)",",if,n" is odd"):}
Answer» `SIGMA`is ONTO not ONE-one `sigma`is one -one but not one `SIGNA`is NEITHER one-one nor onto `sigma`is one -one and onto Answer :D

Discussion

3085.	Match the following
Answer» e,b,d,c b,a,c,d a,d,b,a d,c,a,c Answer :D

Discussion

3086.	Match the following
Answer» d,E,a,b b,C,a,e a,b,d,c c,d,b,e Answer :B

Discussion

3087.	Match the following
Answer» a,B,C,d a,d,c,b d,a,b,c a,c,d,b Answer :B

Discussion

3088.	Match the following
Answer» a,B,d,C c,d,a,b d,a,b,c a,c,d,b Answer :A

Discussion

3089.	A,B, and C are the unequal faces of a rectanglular tank. The tank contains a certain amount of water. When the tank is based on the face A, the height of the water is half the height of the tank. The dimensions of the side B are 3 ft. xx ft, and the dimensions of side C are 4 ft xx 5 ft, what is the measure of the hight of the water in the tank in feet?
Answer» 2 2.5 3 4 Answer :A

Discussion

3090.	Match the following
Answer» b,d,a,C c,b,E,d d,a,b,e e,c,d,a Answer :A

Discussion

3091.	Compute the following: [1 \ 2 \3]+ [2 \ 3 \ 4]
Answer» SOLUTION :`[[1,2,3]],[2,3,4]=[[2,3,4],[4,6,8],[6,9,12]]`

Discussion

3092.	a b = a^(2)+b^(2) + ab + 2on Z then 34 = ......
Answer» 39 40 25 41 Solution :N/A

Discussion

3093.	Find the equation of the tagent to the curve y^(2)-2x^(3)+8=0 at the point (2,1)
Answer»

Discussion

3094.	Match the following
Answer» a,B,d,E c,d,b,a b,a,e,c d,e,c,b Answer :C

Discussion

3095.	Match the following
Answer» a,B,c,d c,a,E,d b,a,c,d b,c,a,e Answer :D

Discussion

3096.	The solution of x dx + ydx = x^(2)y dy - xy^(2)dx is
Answer» `x^(2) - 1 = c(1+y^(3))` `x^(2) + 1 = c(1-y^(2))` `x^(2) - 1 = c(1+y^(2))` `x^(2) + 1 = c(1-y^(3))` ANSWER :C

Discussion

3097.	Show that when the curved surface of a is right circular cylinder inscribed in a sphere of radius R is maximum , then the height of the cylinder is sqrt(2R).
Answer» `sqrtR` `SQRT(10)R` `SQRT2 R` R Answer :C

Discussion

3098.	Between 5pm and 6pm, I looked at my watch mistaking the hour hand for the minute hand and the minute hand for the hour hand, I mistook the time to be 57 minutes earlier than the actual time. Find the number of minutes past 5 when I looked at my watch.
Answer» ANSWER :12 MIN

Discussion

3099.	int(x^(6)+7x^(5)+6x^(4)+5x^(3)+4x^(2)+3x+1)e^(x)dx=.......+c
Answer» `sum_(i=0)^(7)X^(i)E^(x)` `sum_(i=1)^(6)x^(i)e^(x)` `sum_(i=0)^(6)ie^(x)` `sum_(i=0)^(6)(XE)^(i)` ANSWER :B

Discussion

3100.	Let hat(alpha),hat(beta),hat(gamma) be three unit vectors such that hat(alpha)xx(hat(beta)xxhat(gamma)) =(1)/(2)(hat(beta)+hat(gamma))" where "hat(alpha)xx(hat(beta)xxhat(gamma))=(hat(alpha).hat(gamma))hat(beta)-(hat(alpha).hat(beta))hat(gamma). If hat(beta)" is not parallel to "hat(gamma)," then the angle between "hat(alpha)andhat(beta) is
Answer» `(5pi)/(6)` `(PI)/(6)` `(pi)/(3)` `(2pi)/(3)` Answer :D

Discussion

Explore topic-wise InterviewSolutions in .

If for the matrix A=[(costheta, 2sintheta),(sintheta,costheta)],A^(-1)=A^(T)then number of possible value(s) of theta in [0, 2pi] is :

If three positive real numbers a, b, c are in A.P and abc = 4, then the minimum possible value of b is

If a, b, c are positive integers such that a^2+ 2b^2-2ab = 169 and 2bc - c^2= 169 then a + b + c is:

Find the probability of getting 5 exactly twice in 7 throws of a die.

Let z_(1) = 2 + 3i and z_(2) = 3 + 4i be two points on the complex plane. Then the set of complex numbers z satisfying abs(z - z_(1))^(2) + (z - z_(2))^(2) = (z_(1) - z_(2))^(2) represents

If y=(tan^(-1)x)^(2), show that (x^(2)+1)^(2)y_(2)+2x(x^(2)+1)y_(1)=2.

if y=sec(tan^(-1)x), then (dy)/dx is equal to

If alpha, beta , gamma are the roots of x^(3) + 3px^(2) + 3px + r = 0then the equation whose roots are alpha - (1)/( beta gamma ) , beta - (1)/(gamma alpha), gamma - (1)/(alpha beta)is

(~~(~~p)^^q is equivalent to

STATEMENT-1 : From point (4, 0) three different normals can be drawn to the parabola y^(2) =4x. and STATEMENT-2 : From any point, atmost three different normals can be drawn to a hyperbola.

(a) Find all rational values of x at which y=sqrt(x^(2)+x+3) is a rational number. (b) Prove that sqrt2 is an irrational number.

Method of integration by parts : I_(1)=int sin^(-1)x dx and I_(2)= int sin^(-1) sqrt(1-x^(2))dx then.....

The set of all real values of x for which f(x)=log_(e)sqrt((1+x)/(1-x))+log_(e)((1+sqrt(1-x^(2)))/x)+coth^(-1)x+log_(e)((1+sqrt(1+x^(2)))/x)+sinh^(-1)x is defined is

A man is known to speak the truth on an average 3 out of 4 times. He throws a fair die and reports that it is a six. The probabilitythe itis actually a six is

If u_(1) = ax + by + c, u_(2) = a'x + b'y + d, u_(3) = ax + by + c', u_(4) = a'x + b'y +d' then u_(1)= 0, u_(2) = 0, u_(3) = 0, u_(4) = 0 from a parallelogram. Then the diagonal.

Solve (3x-4)/(2) ge (x+1)/(4) -1. Show the graph of the solutions on number line.

Showthat thefunction f : R to R : f (x) = {[-1 \ if \ x \ is \ irrational ], [1 \ if \ x \ is \ rational ]} ismany-oneinto. Find(i) f ((1)/(2)) \ (ii)f (sqrt(2))\ (iii) f (pi) \ (iv)f (2 +sqrt(3))

Integrate the following functions 1/(sqrt(1+4x^2)

P(A' cup B') | C = ………………

Equations of the line passing through (1,1,1) and perpendicular to the plane 2x+3y+z+5=0 are

Let a* b =1cm (a,b) for all values of a,b in N (i) Find (12*16) (ii) Show that* is commutative on N (iii) Find the identity element in N (iv) Find all invertible elements in N

The distance between the pair of parallel﻿ lines x^(2) + 4xy + 4y^(2) + 3x + 6y- 4 = 0 is

The set of values of x which satisfy 5x+2 lt 3x +8 and (x+2)/(x-1) lt 4 is

If x ge 0, y ge 0, 2x+3y le 12, 3x+y le 12, then the minimum value of f=5x+7y is

The sloope of the line touching both the parabolas y^(2) =4x and x^(2) =32yis

Integration by partial fraction : int(4e^(x)+6e^(-x))/(9e^(x)-4e^(-x))dx=Ax+B log(9e^(x)-4e^(-x))+c then A+B=.

Which month had the largest percentage of vegetable sales relative to total sales?

If x in[(4n+1)(pi)/(2),(4n+3)(pi)/(2)] and n in N, then the value of int_(0)^(x)[cos t] dt, is

Find value of sin^-1(cos((33pi)/5))

If P(A)=0.3, P("not" B)=0.4,P(AintB')=0.5 and A and B are independent events, find P(A and not B)

Evaluate{:[( x,y , x+y),( y,x+y,x),( x+y,x,y)]:}

Let N be the set of all natural number , Z be the set of all integers and sigma : N to Zbe difinedby{:sigma(n)={((n)/(2)",",if,n" is even"),(,,"then"),(-(n-1)/(2)",",if,n" is odd"):}

Match the following

Match the following

Match the following

Match the following

Match the following

Compute the following: [1 \ 2 \3]+ [2 \ 3 \ 4]

a **b = a^(2)+b^(2) + ab + 2on Z then 3**4 = ......

Find the equation of the tagent to the curve y^(2)-2x^(3)+8=0 at the point (2,1)

Match the following

Match the following

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

Show that when the curved surface of a is right circular cylinder inscribed in a sphere of radius R is maximum , then the height of the cylinder is sqrt(2R).

Between 5pm and 6pm, I looked at my watch mistaking the hour hand for the minute hand and the minute hand for the hour hand, I mistook the time to be 57 minutes earlier than the actual time. Find the number of minutes past 5 when I looked at my watch.

int(x^(6)+7x^(5)+6x^(4)+5x^(3)+4x^(2)+3x+1)e^(x)dx=.......+c

((p)^^q is equivalent to

Let a* b =1cm (a,b) for all values of a,b in N (i) Find (1216) (ii) Show that is commutative on N (iii) Find the identity element in N (iv) Find all invertible elements in N

The distance between the pair of parallel lines x^(2) + 4xy + 4y^(2) + 3x + 6y- 4 = 0 is

a b = a^(2)+b^(2) + ab + 2on Z then 34 = ......