14949 + Interview Questions in Maths in Class 11 Page 194 InterviewSolution

9651.	If cosh(x)=(5)/(2) then cosh (2x) =
Answer» `(5sqrt(21))/(2)` `(23)/(5sqrt(21))` `(23)/(2)` `(7)/(2)` Answer :C

Discussion

9652.	If 3^(rd) and 10^(th) terms of an A.P. be 9 and 21 respectively. Then the sum of its first 12 terms is…….
Answer» 180 360 150 210 Answer :A

Discussion

9653.	cosecA + cot A=(2)/(3) rArr cos A=
Answer» `(5)/(13)` `(13)/(5)` `-(5)/(13)` `-(13)/(5)` ANSWER :C

Discussion

9654.	The points 2bar(a)+3bar(b)+bar(c), bar(a)+bar(b), 6bar(a)+11bar(b)+5bar(c) are
Answer» Collinear Coplanar but NON collinear non coplanar cannot be determined Answer :A

Discussion

9655.	Let f : (-1,1) rarr R such that f(cos 4 theta) = 2 /(2-sec^2 theta)for theta in (0,(pi)/(4)) cap (pi/2,pi/2) . Then the value (s) of f(1/3)is /are
Answer» `1-sqrt(3/2)` `1+sqrt(3/2)` `1-sqrt(2/3)` `1+sqrt(2/3)` ANSWER :A::B

Discussion

9656.	If Tan A = 1, TanB = 2, TanC = 3 then A + B + C =
Answer» `(npi)/(2),ninz` `npi,ninz` `(npi)/(4),ninz` `(2npi)/(3),N in Z` Answer :B

Discussion

9657.	P(n) : 2^(2^n) + 1 is a prime number . For n = ………., it is not true.
Answer» 1 2 0 5 Answer :D

Discussion

9658.	Consider the function y = f(x) satisfying the condition f(x+ 1/x)=x^(2)+ (1)/(x^(2))( != 0). Then the
Answer» domain of `f(X)` is R domain of f(x) is R-(-2, 2) RANGE of `f(x) ` is `[-2, oo)` range of `f(x)` is `[2, oo)` Answer :B::D

Discussion

9659.	Find the number of words formed containing 4 letters taken from the letters of the word 'INEFEECTIVE'.
Answer» ANSWER :PERMUTATION = 1422

Discussion

9660.	Givenpnepmq . Show that the solutions of cosPtheta+cosqtheta=0form two series each of which is in A.P . Find also the common difference of each A.P .
Answer» ANSWER :`(2PI)/((p-q))`

Discussion

9661.	f(x) is a polynomial funciton, f : R to R, such that f(2x) = f'(x) f^('')(x) Equation f(x) = x has
Answer» ONE-one and ONTO one-one and into MANY-one and onto many - one and into ANSWER :A

Discussion

9662.	An analysis of monthly wages paid to workers in two firms A and B belonging to the same industry gives the following results. {:(,"FirmA","Firm B"),("No.of wage earners",586,648),("Mean of monthly wages",Rs.5253,Rs.5253),("Variance of distribution of wages",100,121):}(i) Which firm A or B pays larger amount as monthly wages ?(ii) Which firmA or Bshows greater variability in individual wages .
Answer» ANSWER :(i) B, (II) B

Discussion

9663.	Let p: I will marry her, and let q: she is beautiful. Translate into symbolic form: If she is beautiful then I will not marry her.
Answer» <P> ANSWER :`Q=>~p`

Discussion

9664.	Find the sum up to the 17^(th) term of the series (1^3)/(1) + (1^3 + 2^3)/(1+3) + (1^3 + 2^3 + 3^3)/(1+3+5)+ ….
Answer» ANSWER :` S_(17) = 527`

Discussion

9665.	The smallest value of 'theta' satisfying the equation sqrt(3) (cot theta + tan theta)=4 is
Answer» `2 pi//3` `pi//3` `pi//6` `pi//12` ANSWER :C

Discussion

9666.	(sin^(8)75^(@)-cos^(8)75^(@))=
Answer» 1 `(3sqrt(3))/(8)` `(3sqrt(3))/(16)` `(7sqrt(3))/(16)` Answer :B

Discussion

9667.	There are 5 red and 6 black balls in a bag. In how many ways 6 balls can be selected if there are at least 2 balls of each colour?
Answer» ANSWER :425

Discussion

9668.	Calcualte the mean deviation about the mean for the following frequency distribution:
Answer» ANSWER :3.84

Discussion

9669.	If x=tan^(-1)(1)+cos^(-1)(-1//2)+sin^(-1)(-1//2) and y=cos[1//2 cos^(-1)(1//8)] then
Answer» `x=2piy` `y=3pix` `x=piy` `y=pix` ANSWER :C

Discussion

9670.	IfA = {: [ ( 4,2) , ( -1, x) ]:}and such that (A -2I) ( A -3 I) = 0 , find the value of x . (b) Give yourownexamples of matrices satisfyingthe followingconditionsin eachcase : (i) A and B such thatABneBA (ii) A and Bsuch thatAB = 0 = BA,A ne 0 and B ne 0 (iii) A and Bsuch thatAB = 0 andBA ne 0
Answer» Answer :(a) X =1 , (b)(i)AB ` NE BA` (ii) `B ne 0` (iii)`BA ne 0`

Discussion

9671.	Calculate the least number of terms of the geometric progression 5 + 10 + 20 + ... whose sum would exceed 10,00,000.
Answer» ANSWER :18

Discussion

9672.	What universal set would you propose for each of the following : The set of rectangles.
Answer» ANSWER :The SET of all the QUADRILATERAL in the PLANE.

Discussion

9673.	If x_1 and x2 are two distinct roots of the equation a cos x + bsin x = c , then tan((x_(1)+x_(2))/2)is equal to
Answer» `a/B` `b/a` `c/a` `a/c` ANSWER :B

Discussion

9674.	If p denotes the distance of the straight line from origin and alpha denotes the angle made by the normal ray drawn from origin to the straight line with vec(OX) measured in anti clockwise sense. Find the equations of the straight lines with the following values of p and alpha p=4,alpha=90^(@)
Answer» ANSWER :`y=4`

Discussion

9675.	If p denotes the distance of the straight line from origin and alpha denotes the angle made by the normal ray drawn from origin to the straight line with vec(OX) measured in anti clockwise sense. Find the equations of the straight lines with the following values of p and alpha p=1,alpha=(7pi)/4
Answer» ANSWER :`x-y=sqrt(2)`

Discussion

9676.	If p denotes the distance of the straight line from origin and alpha denotes the angle made by the normal ray drawn from origin to the straight line with vec(OX) measured in anti clockwise sense. Find the equations of the straight lines with the following values of p and alpha p=2sqrt(2),alpha=(5pi)/4
Answer» ANSWER :`x+y+4=0`

Discussion

9677.	If p denotes the distance of the straight line from origin and alpha denotes the angle made by the normal ray drawn from origin to the straight line with vec(OX) measured in anti clockwise sense. Find the equations of the straight lines with the following values of p and alpha p=0,alpha=0
Answer» ANSWER :`x=0`

Discussion

9678.	If p denotes the distance of the straight line from origin and alpha denotes the angle made by the normal ray drawn from origin to the straight line with vec(OX) measured in anti clockwise sense. Find the equations of the straight lines with the following values of p and alpha p=6,alpha=150^(@)
Answer» ANSWER :`SQRT(3)x-y+12=0`

Discussion

9679.	If p denotes the distance of the straight line from origin and alpha denotes the angle made by the normal ray drawn from origin to the straight line with vec(OX) measured in anti clockwise sense. Find the equations of the straight lines with the following values of p and alpha p=5,alpha=60^(@)
Answer» ANSWER :`x+sqrt(3)y=10`

Discussion

9680.	What is the chance that a non leap year , selected at random , will contain 53 Sunday ?
Answer» ANSWER :`=(1)/(7)`.

Discussion

9681.	What universal set(s) would you propose for each of the following : The set of isosceles triangles.
Answer» ANSWER :UNIVERSAL SET : The set of TRIANGLES in the PLANE.

Discussion

9682.	If C_(0),C_(1),C_(2)…….,C_(n) are the combinatorial coefficient in the expansion of (1+x)^n, n, ne N, then prove that following C_(1)+2C_(2)+3C_(3)+..+n.C_(n)=n.2^(n-1) C_(0)+2C_(1)+3C_(2)+......+(n+1)C_(n)=(n+2)C_(n)=(n+2)2^(n-1) C_(0),+3C_(1)+5C_(2)+.....+(2n+1)C_n =(n+1)2^n (C_0+C_1)(C_1+C_2)(C_2+C_3)......(C_(n-1)+C_n)=(C_0.C_1.C_2....C_(n-1)(n+1)^n)/(n!) 1.C_0^2+3.C_1^2+....+ (2n+1)C_n^2=((n+1)(2n)!)/(n! n!)
Answer»

Discussion

9683.	The value of cot(7pi)/16 + 2 cot(3pi)/8 + cot(15pi)/16 is:
Answer» 4 2 `-2` `-4` ANSWER :D

Discussion

9684.	6 le -3 (2x-4) lt 12
Answer» ANSWER :`(0,1]`

Discussion

9685.	Find the component statements of the following compound statements and check whether they are true or false: All integers are positive or negative.
Answer» ANSWER :All INTEGERS are POSITIVE; all integers are NEGATIVE (FALSE).

Discussion

9686.	Find the component statements of the following compound statements and check whether they are true or false: Number 3 is prime or it is odd.
Answer» Answer :Number 3 is PRIME; number 3 is odd (TRUE).

Discussion

9687.	Find the component statements of the following compound statements and check whether they are not or false: 100 is divisible by 3,11 and 5.
Answer» Answer :100 is DIVISIBLE by 3,100 is divisible by 11 and 100 is divisible by 5 (False).

Discussion

9688.	If A and B are subsets of the universal set cup, then show that, A sub A cup B
Answer» ANSWER :`A SUB A CUP B`

Discussion

9689.	Find the sum of the following series up to n terms: (i) 5+55+555+...... (ii) .6+.66.+.666+.............
Answer» Answer :`(50)/(81) (10^(n)-1) -(5N)/(9)`

Discussion

9690.	Find 6^(th) term of a G.P. sqrt3, (1)/(sqrt3), (1)/(3 sqrt3)……
Answer» ANSWER :`SQRT3 ((1)/(3))^(5)`

Discussion

9691.	If 1/6 sintheta, costheta and tantheta are in G.P. then the general solution for theta is-
Answer» `2npi+-pi/3` `2npi+-pi/6` `npi+-pi/3` none of these Solution :Since, `1/6sintheta,COSTHETA, tantheta` are in G.P. `RARR COS^(2)theta=1/6(sintheta.tantheta) rArr 6cos^(3)theta+cos^(2)theta-1=0` `therefore (2costheta-1)(3 cos^(2)theta+2costheta+1)=0` `rArr costheta=1/2` (other VALUES of `costheta` are imaginary) `rArr costheta=cospi/3 rArr theta=2npi+-pi/3, N in I`.

Discussion

9692.	Let f(x)+f(y)=f (x sqrt(1-y^(2))+ y sqrt(1-x^(2))) [f(x) is not identically zero]. Then
Answer» `f(4x^(3)-3x) + 3F(x)=0` `f(4x^(3)-3x)=3f(x)` `f(2X sqrt(1-x^(2)))+2F(x)=0` `f(2x sqrt(1-x^(2)))=2f(x)` ANSWER :A::D

Discussion

9693.	Find theta,0ltthetalt90^(@), if (i) sintheta=0.7071(ii)cos theta= 0.9604 (iii) tantheta=34.37(iv) cottheta= 3.018
Answer» ANSWER :(i)`45^(@)` (ii)`16^(@)` 11' (III)`88^(@)` 20' (iv)`18^(@)` 20'

Discussion

9694.	Is the function f , defined by f(x)={{:(x^(2),"if "xle1),(x,"if "xgt1):} continuous on R ?
Answer» ANSWER :CONTINOUS at 1 discontinous at 2

Discussion

9695.	A card is drawn from a pack of cards . Findthe probability that it is a black card
Answer» ANSWER :`=(1)/(2)`.

Discussion

9696.	Find the sum to n terms of the sequence, 8, 88, 888, 8888… .
Answer» ANSWER :`80/81(10^(N)-1)-8/9n`

Discussion

9697.	If tan^(-1)x+tan^(-1)y+tan^(-1)z=(pi)/2 then
Answer» `xy+yz+zx=1` `X^(2)+y^(2)+Z^(2)+2xyz=1` `x+y+z=xyz` `sumx+sumyz=1+xyz` ANSWER :A

Discussion

9698.	Find the equation of line joining the origin to the point of intersection of 4x+3y=8 and x+y=1.
Answer» ANSWER : `4x+5y=0`

Discussion

9699.	Determine the two middle terms in the expansion of(x^2 +a^2)^5
Answer» ANSWER :`10x^6 a^4` and `10x^4 a^6`

Discussion

9700.	If the extremities of a diagonal of a square are (1,2,3) and (2,-3,5), then its side is of length
Answer» `SQRT2` 15 `sqrt15` 3 Answer :C

Discussion

Explore topic-wise InterviewSolutions in .

If cosh(x)=(5)/(2) then cosh (2x) =

If 3^(rd) and 10^(th) terms of an A.P. be 9 and 21 respectively. Then the sum of its first 12 terms is…….

cosecA + cot A=(2)/(3) rArr cos A=

The points 2bar(a)+3bar(b)+bar(c), bar(a)+bar(b), 6bar(a)+11bar(b)+5bar(c) are

Let f : (-1,1) rarr R such that f(cos 4 theta) = 2 /(2-sec^2 theta)for theta in (0,(pi)/(4)) cap (pi/2,pi/2) . Then the value (s) of f(1/3)is /are

If Tan A = 1, TanB = 2, TanC = 3 then A + B + C =

P(n) : 2^(2^n) + 1 is a prime number . For n = ………., it is not true.

Consider the function y = f(x) satisfying the condition f(x+ 1/x)=x^(2)+ (1)/(x^(2))( != 0). Then the

Find the number of words formed containing 4 letters taken from the letters of the word 'INEFEECTIVE'.

Givenpnepmq . Show that the solutions of cosPtheta+cosqtheta=0form two series each of which is in A.P . Find also the common difference of each A.P .

f(x) is a polynomial funciton, f : R to R, such that f(2x) = f'(x) f^('')(x) Equation f(x) = x has

Let p: I will marry her, and let q: she is beautiful. Translate into symbolic form: If she is beautiful then I will not marry her.

Find the sum up to the 17^(th) term of the series (1^3)/(1) + (1^3 + 2^3)/(1+3) + (1^3 + 2^3 + 3^3)/(1+3+5)+ ….

The smallest value of 'theta' satisfying the equation sqrt(3) (cot theta + tan theta)=4 is

(sin^(8)75^(@)-cos^(8)75^(@))=

There are 5 red and 6 black balls in a bag. In how many ways 6 balls can be selected if there are at least 2 balls of each colour?

Calcualte the mean deviation about the mean for the following frequency distribution:

If x=tan^(-1)(1)+cos^(-1)(-1//2)+sin^(-1)(-1//2) and y=cos[1//2 cos^(-1)(1//8)] then

IfA = {: [ ( 4,2) , ( -1, x) ]:}and such that (A -2I) ( A -3 I) = 0 , find the value of x . (b) Give yourownexamples of matrices satisfyingthe followingconditionsin eachcase : (i) A and B such thatABneBA (ii) A and Bsuch thatAB = 0 = BA,A ne 0 and B ne 0 (iii) A and Bsuch thatAB = 0 andBA ne 0

Calculate the least number of terms of the geometric progression 5 + 10 + 20 + ... whose sum would exceed 10,00,000.

What universal set would you propose for each of the following : The set of rectangles.

If x_1 and x2 are two distinct roots of the equation a cos x + bsin x = c , then tan((x_(1)+x_(2))/2)is equal to

If p denotes the distance of the straight line from origin and alpha denotes the angle made by the normal ray drawn from origin to the straight line with vec(OX) measured in anti clockwise sense. Find the equations of the straight lines with the following values of p and alpha p=4,alpha=90^(@)

If p denotes the distance of the straight line from origin and alpha denotes the angle made by the normal ray drawn from origin to the straight line with vec(OX) measured in anti clockwise sense. Find the equations of the straight lines with the following values of p and alpha p=1,alpha=(7pi)/4

If p denotes the distance of the straight line from origin and alpha denotes the angle made by the normal ray drawn from origin to the straight line with vec(OX) measured in anti clockwise sense. Find the equations of the straight lines with the following values of p and alpha p=0,alpha=0

If p denotes the distance of the straight line from origin and alpha denotes the angle made by the normal ray drawn from origin to the straight line with vec(OX) measured in anti clockwise sense. Find the equations of the straight lines with the following values of p and alpha p=6,alpha=150^(@)

If p denotes the distance of the straight line from origin and alpha denotes the angle made by the normal ray drawn from origin to the straight line with vec(OX) measured in anti clockwise sense. Find the equations of the straight lines with the following values of p and alpha p=5,alpha=60^(@)

What is the chance that a non leap year , selected at random , will contain 53 Sunday ?

What universal set(s) would you propose for each of the following : The set of isosceles triangles.

The value of cot(7pi)/16 + 2 cot(3pi)/8 + cot(15pi)/16 is:

6 le -3 (2x-4) lt 12

Find the component statements of the following compound statements and check whether they are true or false: All integers are positive or negative.

Find the component statements of the following compound statements and check whether they are true or false: Number 3 is prime or it is odd.

Find the component statements of the following compound statements and check whether they are not or false: 100 is divisible by 3,11 and 5.

If A and B are subsets of the universal set cup, then show that, A sub A cup B

Find the sum of the following series up to n terms: (i) 5+55+555+...... (ii) .6+.66.+.666+.............

Find 6^(th) term of a G.P. sqrt3, (1)/(sqrt3), (1)/(3 sqrt3)……

If 1/6 sintheta, costheta and tantheta are in G.P. then the general solution for theta is-

Let f(x)+f(y)=f (x sqrt(1-y^(2))+ y sqrt(1-x^(2))) [f(x) is not identically zero]. Then

Find theta,0ltthetalt90^(@), if (i) sintheta=0.7071(ii)cos theta= 0.9604 (iii) tantheta=34.37(iv) cottheta= 3.018

Is the function f , defined by f(x)={{:(x^(2),"if "xle1),(x,"if "xgt1):} continuous on R ?

A card is drawn from a pack of cards . Findthe probability that it is a black card

Find the sum to n terms of the sequence, 8, 88, 888, 8888… .

If tan^(-1)x+tan^(-1)y+tan^(-1)z=(pi)/2 then

Find the equation of line joining the origin to the point of intersection of 4x+3y=8 and x+y=1.

Determine the two middle terms in the expansion of(x^2 +a^2)^5

If the extremities of a diagonal of a square are (1,2,3) and (2,-3,5), then its side is of length