14949 + Interview Questions in Maths in Class 11 Page 90 InterviewSolution

4451.	Write the following sets in roster form : C= {x : x in N, x= 2n, n in N}
Answer» Answer :`C= {2, 4, 6, 8"………."}`

Discussion

4452.	Does empty set represents an event? If yes, name the tpye of event. If no, then give reason.
Answer» ANSWER :YES, Empty set REPRESENTS event. It is called Impossible event.

Discussion

4453.	sin h (cos h^(-1) x) =
Answer» `SQRT(X^(2) + 1)` `(1)/(sqrt(x^(2) + 1))` `sqrt(x^(2)-1)` `(1)/(sqrt(x^(2) - 1))` ANSWER :C

Discussion

4454.	If the pair of lines ax^2+2hxy+by^2=0,ax^2+2hxy+by^2+2gx+2fy+c=0 form a rhombus then prove that (a-b)fg+h(f^2-g^2)=0.
Answer» ANSWER :`(FG)/(H)`

Discussion

4455.	If cosec^(-1)(cosecx) and cosec(cosec^(-1)x) are equal funtions, then the maximum range of value of x is
Answer» `[-pi/2, -1] CUP [1, pi/2]` `[-pi/2, 0) cup[0, pi/2]` `(INFTY, -1] cup [1, infty)` `[-1, 0) cup [0, 1)` ANSWER :A

Discussion

4456.	cos^(2)(theta-45^(@))+cos^(2)(theta+15^(@)-cos^(2)(theta-15^(@))=
Answer» `1/2` `1/3` `1/sqrt2` `1/sqrt3` ANSWER :A

Discussion

4457.	Iftan x=(b)/(a) " then " sqrt((a+b)/(a-b))+sqrt((a-b)/(a+b))=
Answer» `(2 SINTHETA)/(SQRT(sin2theta))` `(2costheta)/(sqrt(cos2theta))` `(2costheta)/(sqrt(sin2theta))` `(2sintheta)/(sqrt(cos2theta))` ANSWER :B

Discussion

4458.	Two sides of a rhombus ABCD are parallel to the lines y=x+2 and y=7x+3. If the diagonals intersect at (1,2) and A is on the y-axis, find the possible coordinates of A.
Answer» ANSWER :(0,0) or (0,5/2)

Discussion

4459.	If the triangleABC whose vertices are A(-1,1,1), B(1,-1,1) and C(1,1,-1) is projected on XY plane and the area of the projected triangle is m then find (m(m+1))/(2)
Answer» ANSWER :3

Discussion

4460.	If "cosech"^(-1) ((sqrt(1-x^(2)))/(x))=ktanh^(-1)(x) then k =
Answer» 1)2 2)`(1)/(2)` 3)1 `4)-1` ANSWER :C

Discussion

4461.	Find the derivative of the following functions from first principle sin (x+1)
Answer» ANSWER :`cos(x+1)(because lim_(xto0)(SINX)/(x)=1)`

Discussion

4462.	Find the value of k so that 8k +4, 6k-2, and 2k + 7 will form an A.P.
Answer» ANSWER :(i) `7(1)/(2)`

Discussion

4463.	The sum of the coefficients in the expansion of(a+b)^n is 4096. Then ...... Is the biggest coefficient .
Answer» ANSWER :`((12),(6))`

Discussion

4464.	Use the graph to find the limits (if it exists).If the limit does not exist ,explain why? lim_(xrarr3) 1/(x-3)
Answer» ANSWER :LIMIT does not EXIST

Discussion

4465.	For 0 lt theta lt (pi)/(2) ,the, solution (s) of sum_(k = 1)^(6) cosec (theta + ((k - 1)pi)/(4)) cosec (0 + (k pi)/(4)) = 4 sqrt(2) is /are
Answer» `(PI)/(4)` `(pi)/(6)` `(pi)/(12)` `(5 pi)/(12)` ANSWER :C::D

Discussion

4466.	tan x+ tan(x+(pi)/(3))+ tan(x+(2pi)/(3))=3impliestan 3 x=
Answer» 3 2 1 0 Answer :C

Discussion

4467.	Graph the function. Show that f(x) continuous on (-infty,infty)
Answer» ANSWER :4

Discussion

4468.	A card
Answer» `17: 52` `52: 17` `9 : 4` `4:9` ANSWER :C

Discussion

4469.	If the unit vectors bara and barb " are inclined at an angle " 2theta " such that " abs(bara-barb)lt 1, then theta lies in the interval
Answer» `[0,PI/6)` `((5pi)/6,pi]` `[pi/6,pi/2]` `[pi/2,(5pi)/2]` Answer :A

Discussion

4470.	Show that the function f(x) = [x]^(2) - [x^(2)] is discontinuous at all integers except 1
Answer» ANSWER :1

Discussion

4471.	If an error of 0.02 cm is made while measuring the radius 10 cms of a sphere, then the error in the volume is
Answer» `8pi` CUBIC CM `80pi` cubic cm `0.06pi` cubic cm `16pi` cubic cm ANSWER :A

Discussion

4472.	One vertex of an equilateral triangle is (2,3) and the equation of one side is x-y+5=0. Then the equation to other sides are
Answer» `y-3=-(2pmsqrt3)(x-2)` `y-3=(2pmsqrt3)(x-2)` `y-3=(sqrt3pm)(x-2)` `y-3=(sqrtpm5)(x-2)` ANSWER :A

Discussion

4473.	Evaluate the following limits : Lim_( x to 1) x^(1/(x-1))
Answer» ANSWER :E

Discussion

4474.	Solve:sin 7 theta + sin 4 theta + sin theta = 0, 0 lt theta lt ( pi)/(2)
Answer» ANSWER :`(PI)/(4), (2pi)/(9), (4pi)/(9)`

Discussion

4475.	A function whose graph is symmetrical about the y-axis is given by:
Answer» `f(x)=sin[log(x+sqrt(x^(2)+1))]` `f(x)=(SEC^(4)x+cosec^(4)x)/(x^(3)+x^(4)cotx)` `f(x+y)=f(x)+f(y)AA x, y in R` `f(x)-x^(2)` ANSWER :D

Discussion

4476.	Evaluate the following limits in Exercises lim_(x to pi)(x-(22)/(7))
Answer» ANSWER :`PI-(22)/(7)`

Discussion

4477.	For a set of ungrouped values the following sums are found: ""n=15, sumx=480, sumx^(2)=15735. Find the standard deviation.
Answer» ANSWER :5

Discussion

4478.	It is given that f'(a) exists,thenlim_(xrarra)(xf(a) - af(x))/(x - a) is :
Answer» `F(a)-AF'(a)` `f'(a)` `-f'(a)` `f(a)+af'(a)` ANSWER :A

Discussion

4479.	Find the chance of throwing a total of 3 or 11 with two dice.
Answer» ANSWER :`=(1)/(9)`

Discussion

4480.	If f is periodic g is polynomial function and f(g(x)) is periodic and g(2)=3, g(4)=7 then g(6) is
Answer» 13 15 11 16 Answer :C

Discussion

4481.	If sin thetaand - cos thetaare the roots of the equation ax^2-bx-c=0 where a, b and c the side of a triangle ABC , then cos B is equal to :-
Answer» `1-(C )/(2A)` `1-(c )/(a)` `1+( c)/(2a)` `1+ (c )/(3A)` ANSWER :C

Discussion

4482.	Let O be a point inside Delta^("le") ABC such that lfloorOAB = lfloor OBC = lfloor OCA = theta " then " cos A + cos B + cosC=
Answer» `sin theta ` `cos theta` `COT theta ` `sec theta ` ANSWER :C

Discussion

4483.	Find the coordinates of the centroid of the triangle whose vertices are (x_(1),y_(1),z_(1)),(x_(2),y_(2),z_(2))and(x_(3),y_(3),z_(3)).
Answer» ANSWER :`((x_(1)+x_(2)+x_(3))/3,(y_(1)+y_(2)+y_(3))/3,(z_(1)+z_(2)+z_(3))/3)`

Discussion

4484.	Two sample sizes of 50 and 100 are given . The mean of these samples respectively are 56 and 50. Find the mean of the size 150 by combining the two samples.
Answer» ANSWER :`52`

Discussion

4485.	Fill in the blanks to make each of the following a true statement : The number of subsets of a set A having n elements is "………."
Answer» ANSWER :`=2^(N)`

Discussion

4486.	Find the acute angle between the lines y+2=0 and sqrt(3)x+y-1=0.
Answer» ANSWER :`60^(@)`

Discussion

4487.	The origin is shifted to (2,3) by the translation of axes. If a point P has changed as (4, 5), find the coordinates of P in the original system.
Answer» ANSWER :(6,8)

Discussion

4488.	Find the derivativ of the function from first principles : sqrt (ax+b), x gt - (b)/(a)
Answer» ANSWER :`=a`

Discussion

4489.	n(U)=600,n(A)=460,n(B)=390 and n(AnnB)=325 then n(AuuB)'
Answer» 75 525 70 155 Answer :A

Discussion

4490.	Write contrapositive and converse of the following statements: If a^(2)=b^(2) then a=+-b (a,b epsilonR)
Answer» ANSWER :Contrapostive: If `a!=+-B` then `a^(@)!=b^(2)` CONVERSE: If `a=+-b` then `a^(2)=b^(2)` `(a,b INR)`

Discussion

4491.	Write the sample space in each of the following : A coin is tossed and then a die is rolled only in casehead is shown on the coin.
Answer» Answer :{H1, H2, H3, H4, H5, H6, T}

Discussion

4492.	If2x_y=5then the maximum valueof x^(2)+3xy+y^(2) is
Answer» `(125)/(4)` `(4)/(125)` `(625)/(4)` `(4)/(625)` ANSWER :A

Discussion

4493.	Hensof a certainbreedlay eggs5 days5daysa weakoneanaverage.Apoulatrykeeperwith5 hensof thisbreedexpectsto getat least4 eggsper day, then,in a seasonof 100days , hiswishwillbefulfilledon….. [ Given: ((5)/(7))^(5) =0.1859]
Answer» 55 days 56 days 57 days noneof these ANSWER :B

Discussion

4494.	(1+Cot78^(@)) (1+Cot57^(@))
Answer» 0 1 2 `(1)/(2)` ANSWER :C

Discussion

4495.	The slope of a line which passes through the origin the mid-point of the line segment joining the points (0,-4) and (8,0) is
Answer» `(1)/(2)` `-(1)/(2)` `1` `2` ANSWER :B

Discussion

4496.	The value of tan^(-1)(m/n)-tan^(-1)((m-n)/(m+n)) is
Answer» `(PI)/2` `(pi)/3` `(pi)/4` `(3pi)/4` ANSWER :C

Discussion

4497.	Find distance PQ between the points P ( a cos alpha, a sin alpha) and Q ( a cos beta, a sin beta).
Answer» Answer :`2a SIN ((ALPHA - beta)/(2)) unit`

Discussion

4498.	The statement (3 sin ^(4) x - 2 cos ^(6) x + y - 2 in ^(6) x + 3 cos ^(4) x) ^(2) = 9 is ture for
Answer» `x = (5 PI)/(13) and y = 2` `x = (7 pi)/( 16) and y = - 4 ` `x = (pi)/(7) and y = 1 ` `x = (pi)/(5) and y = - 1` Answer :A::B

Discussion

4499.	If y=128 sin ^(3) x cos ^(4) x ,then find (d^(2)y)/dx^(2)
Answer» ANSWER :`128 SIN x cos ^(2) x (12 sin ^(4) x-31 sin ^(2) x .cos^(2) x +6 cos ^(4)x)`

Discussion

4500.	A card is drawn at random from pack of 52 playing cards. Find the probability of getting (i) a face card (ii) red card.
Answer» Answer :(i) `(3)/(13)` (ii) `(1)/(2)`

Discussion

Explore topic-wise InterviewSolutions in .

Write the following sets in roster form : C= {x : x in N, x= 2n, n in N}

Does empty set represents an event? If yes, name the tpye of event. If no, then give reason.

sin h (cos h^(-1) x) =

If the pair of lines ax^2+2hxy+by^2=0,ax^2+2hxy+by^2+2gx+2fy+c=0 form a rhombus then prove that (a-b)fg+h(f^2-g^2)=0.

If cosec^(-1)(cosecx) and cosec(cosec^(-1)x) are equal funtions, then the maximum range of value of x is

cos^(2)(theta-45^(@))+cos^(2)(theta+15^(@)-cos^(2)(theta-15^(@))=

Iftan x=(b)/(a) " then " sqrt((a+b)/(a-b))+sqrt((a-b)/(a+b))=

Two sides of a rhombus ABCD are parallel to the lines y=x+2 and y=7x+3. If the diagonals intersect at (1,2) and A is on the y-axis, find the possible coordinates of A.

If the triangleABC whose vertices are A(-1,1,1), B(1,-1,1) and C(1,1,-1) is projected on XY plane and the area of the projected triangle is m then find (m(m+1))/(2)

If "cosech"^(-1) ((sqrt(1-x^(2)))/(x))=ktanh^(-1)(x) then k =

Find the derivative of the following functions from first principle sin (x+1)

Find the value of k so that 8k +4, 6k-2, and 2k + 7 will form an A.P.

The sum of the coefficients in the expansion of(a+b)^n is 4096. Then ...... Is the biggest coefficient .

Use the graph to find the limits (if it exists).If the limit does not exist ,explain why? lim_(xrarr3) 1/(x-3)

For 0 lt theta lt (pi)/(2) ,the, solution (s) of sum_(k = 1)^(6) cosec (theta + ((k - 1)pi)/(4)) cosec (0 + (k pi)/(4)) = 4 sqrt(2) is /are

tan x+ tan(x+(pi)/(3))+ tan(x+(2pi)/(3))=3impliestan 3 x=

Graph the function. Show that f(x) continuous on (-infty,infty)

A card

If the unit vectors bara and barb " are inclined at an angle " 2theta " such that " abs(bara-barb)lt 1, then theta lies in the interval

Show that the function f(x) = [x]^(2) - [x^(2)] is discontinuous at all integers except 1

If an error of 0.02 cm is made while measuring the radius 10 cms of a sphere, then the error in the volume is

One vertex of an equilateral triangle is (2,3) and the equation of one side is x-y+5=0. Then the equation to other sides are

Evaluate the following limits : Lim_( x to 1) x^(1/(x-1))

Solve:sin 7 theta + sin 4 theta + sin theta = 0, 0 lt theta lt ( pi)/(2)

A function whose graph is symmetrical about the y-axis is given by:

Evaluate the following limits in Exercises lim_(x to pi)(x-(22)/(7))

For a set of ungrouped values the following sums are found: ""n=15, sumx=480, sumx^(2)=15735. Find the standard deviation.

It is given that f'(a) exists,thenlim_(xrarra)(xf(a) - af(x))/(x - a) is :

Find the chance of throwing a total of 3 or 11 with two dice.

If f is periodic g is polynomial function and f(g(x)) is periodic and g(2)=3, g(4)=7 then g(6) is

If sin thetaand - cos thetaare the roots of the equation ax^2-bx-c=0 where a, b and c the side of a triangle ABC , then cos B is equal to :-

Let O be a point inside Delta^("le") ABC such that lfloorOAB = lfloor OBC = lfloor OCA = theta " then " cos A + cos B + cosC=

Find the coordinates of the centroid of the triangle whose vertices are (x_(1),y_(1),z_(1)),(x_(2),y_(2),z_(2))and(x_(3),y_(3),z_(3)).

Two sample sizes of 50 and 100 are given . The mean of these samples respectively are 56 and 50. Find the mean of the size 150 by combining the two samples.

Fill in the blanks to make each of the following a true statement : The number of subsets of a set A having n elements is "………."

Find the acute angle between the lines y+2=0 and sqrt(3)x+y-1=0.

The origin is shifted to (2,3) by the translation of axes. If a point P has changed as (4, 5), find the coordinates of P in the original system.

Find the derivativ of the function from first principles : sqrt (ax+b), x gt - (b)/(a)

n(U)=600,n(A)=460,n(B)=390 and n(AnnB)=325 then n(AuuB)'

Write contrapositive and converse of the following statements: If a^(2)=b^(2) then a=+-b (a,b epsilonR)

Write the sample space in each of the following : A coin is tossed and then a die is rolled only in casehead is shown on the coin.

If2x_y=5then the maximum valueof x^(2)+3xy+y^(2) is

Hensof a certainbreedlay eggs5 days5daysa weakoneanaverage.Apoulatrykeeperwith5 hensof thisbreedexpectsto getat least4 eggsper day, then,in a seasonof 100days , hiswishwillbefulfilledon….. [ Given: ((5)/(7))^(5) =0.1859]

(1+Cot78^(@)) (1+Cot57^(@))

The slope of a line which passes through the origin the mid-point of the line segment joining the points (0,-4) and (8,0) is

The value of tan^(-1)(m/n)-tan^(-1)((m-n)/(m+n)) is

Find distance PQ between the points P ( a cos alpha, a sin alpha) and Q ( a cos beta, a sin beta).

The statement (3 sin ^(4) x - 2 cos ^(6) x + y - 2 in ^(6) x + 3 cos ^(4) x) ^(2) = 9 is ture for

If y=128 sin ^(3) x cos ^(4) x ,then find (d^(2)y)/dx^(2)

A card is drawn at random from pack of 52 playing cards. Find the probability of getting (i) a face card (ii) red card.