14949 + Interview Questions in Maths in Class 11 Page 96 InterviewSolution

4751.	A card is drawn from a well shuffled pack of 52 cards . Findthe probability of a spade
Answer» ANSWER :`(13)/(52),i.e,(1)/(4)`

Discussion

4752.	Find the coefficient of (1)/(x^(17)) in the expansion of (x^(4)-(1)/(x^(3)))^(15).
Answer» ANSWER :`-1365`

Discussion

4753.	If x=asec^(n)theta,y=btan^(n)theta then ((x)/(a))^(2//n)-((y)/(b))^(2//n)=
Answer» 0 -1 1 2 Answer :C

Discussion

4754.	Let f and g be two real functions given by f= {(0, 1), (2,), (3, -4), (4, 2), (5, 1)} and g= {(1,0), (2,2), (3,-1), (4,4),(5,3)}. Find Domain.
Answer» ANSWER :{2,3,4,5}

Discussion

4755.	If cos A+ cos B + cos C =0 then cos 3A+ cos 3B + cos 3X
Answer» `4 cos 3 A cos 3B cos 3C` `12 cos A cos B cos C` `8 cos A cos B cos C` `10 cos A cos B cos C` Answer :B

Discussion

4756.	Two unbiased dice are thrown . Find the probability that the totalnumbers on theis greater than 8 ,
Answer» ANSWER :`=(5)/(18)`

Discussion

4757.	The number of ways in which a team of eleven players can be selected from 22 players always including 2 of them and excluding 4of them is
Answer» `""^16C_11` `""^16C_5` `""^16C_9` `""^20C_9` ANSWER :A::C

Discussion

4758.	Two lines passing through the point (2,3) intersects each other at an angle of 60°. If slope of one line is 2, find equation of the other line.
Answer» ANSWER :`(sqrt3 + 2) X + (2 sqrt3 - 1) y = 8 sqrt3 + 1 " or " ( sqrt3 - 2) x + (1 + 2 sqrt3) y = - 1 + 8 sqrt3`

Discussion

4759.	Consider the following sentence: Every rectangle is a square.
Answer» ANSWER :STATEMENT

Discussion

4760.	Find the second derivative of the function (Find y" or (d ^(2) y)/(dx ^(2)) of the cos ^(3) x
Answer» ANSWER :` - 3/4 (COS X + 3 cos 3X)`

Discussion

4761.	There are 5 red and 5 black balls in first bag and 6 red and 4 black balls is second bag. One -one ball is drawn from each bag. Find the probability that: (i)both balls are of the same colour, (ii) one ball is red and other is black.
Answer» SOLUTION :N/a

Discussion

4762.	A class consists of 80 students 25 of them aregirls and 55 boys . If 10 are rich and remainingpoor and also 20 of them are intelligent,thenthe probability of selecting intelligent rich girls is ,
Answer» `(5)/(128)` `(25)/(128)` `(5)/(512)` `(5)/(64)` Answer :C

Discussion

4763.	Theminimum value of 5 cos x+3 cos ((pi)/(3) +x) +8 is
Answer» 1 `1//2` `-1` `15` ANSWER :1

Discussion

4764.	Let f: R to R be a positive increasing function with Lt_(x to oo)(f(3x))/(f(x))=1 then Lt_(x to oo)(f(2x))/(f(x))=
Answer» `(2)/(3)` `(3)/(2)` 3 1 Answer :D

Discussion

4765.	Find the distance between them.
Answer» SOLUTION :`37sqrt13/26`

Discussion

4766.	Ifx=sqrt((1- cos theta )/(1+ cos theta )), " then " (2 x)/(1-x^(2))=
Answer» `sintheta` `costheta` `TANTHETA` `COTTHETA` ANSWER :C

Discussion

4767.	Write down the converse of following statements: If you go to Agra, then you must visit Tajmahal.
Answer» ANSWER :If you must VISIT TAJMAHAL you GO to agra.

Discussion

4768.	Find a vector of magnitude and perpendicular to both the vectors vec(a)= 2vec(i)- 2vec(j) + vec(k) and vec(b)= 2vec(i) + 2vec(j) + 3vec(k)
Answer» ANSWER :`+- (2vec(i) + VEC(J)-2vec(K))`

Discussion

4769.	In a certain city, all telephone numbers have six digits How many telephone numbers are there with distinct digits?
Answer» SOLUTION :`^10p_6`

Discussion

4770.	If 2 Cos^(2)B - 1 = Tan^(2) A then Cos A Cos B =
Answer» `1/2` `PM (1)/(sqrt(2))` `(1)/(4)` `pm 1/4` ANSWER :B

Discussion

4771.	A(2, 3),B(1,5),C(-1, 2) are three points. If P is a point moves such that PA^(2)+PB^(2)=2PC^(2) then locus of P is lx+my+n=0. Then decreasing order of l,m,n
Answer» L, n, m l, m, n m, n, l n, l, m Answer :2

Discussion

4772.	Write the relation R= {(x,x^3): x is a prime number less than 101) write in roster form.
Answer» ANSWER :R={(2,8),(,3,27),(,5,125),(7,343)}

Discussion

4773.	In DeltaABC, " if" (1)/(a+c)+(1)/(b+c)=(3)/(a+b+c)then show thatC=60^(@)
Answer» ` 60 ^(@) ` ` 30 ^(@) ` ` 90 ^(@)` ` 45 ^(@) ` ANSWER :A

Discussion

4774.	cos alpha * sin (beta - gamma ) + cos beta * sin ( gamma - alpha ) + cos gamma * sin ( alpha - beta )=
Answer» 0 1 -1 `4 COS ALPHA Cos beta Cos lambda` ANSWER :A

Discussion

4775.	Show that the function f (x) = I x I + I x -1 1 + I x - 2 I is continuous on R.
Answer» ANSWER :R

Discussion

4776.	If cos^(-1)(x)+cos^(-1)(y)+cos^(-1)(z)=pi(sec^(2)(u)+sec^(4)(v)+sec^(6)(w)), where u, v, w are least non-negative angles such that u lt v lt w, then the value of x^(2000)+y^(2002)+z^(2004)+(36pi)/(u+v+w) is
Answer» ANSWER :9

Discussion

4777.	Iftan^(2) A + tan^(2)B+tan^(2)C -tan B tan c-tan C tan A-tan A tan B=0 then DeltaABC is
Answer» Isosceles Equilateral Ritht ANGLED Right angled isosceles Answer :B

Discussion

4778.	Function f(x)=\|x\|-\|x-1\| is monotonically increasing when
Answer» `XLT0` `XGT1` `XLT1` `0LTXLT1` ANSWER :D

Discussion

4779.	Area of quadrilateral formed by two pair of lines x^(2)-y^(2)-3(x+y)=0 and x^(2)-y^(2)+3(x-y)=0 is
Answer» 9 18 `(9)/(2)` 36 Answer :C

Discussion

4780.	The volume of parallelopiped with edges bar(OA) = (lamda+ 2)bari +(lamda+2)(lamda+1)barj +bark, bar(OB) = (lamda+ 3)bari +(lamda+2)(lamda+3)barj +bark and bar(OC) = (lamda+ 4)bari +(lamda+3)(lamda+4)barj +bark is
Answer» 1 2 3 4 Answer :B

Discussion

4781.	cos2thetacos2phi+sin^(2)(theta-phi)-sin^(2)(theta+phi) is equal to
Answer» `SIN2(theta+phi)` `COS2(theta+phi)` `sin2(theta-phi)` `cos2(theta-phi)` ANSWER :B

Discussion

4782.	The position vector of A is pbari+barj. If A is rotated about O through an angle pi//6 in anticlockwise direction, it conincides with B whose position verctor is bari+qbarj. The value of p,q are
Answer» `SQRT3,3` `sqrt3,1/3` `sqrt3,sqrt3 or 1/sqrt3,1/sqrt3` `3,3 or 1/3,1/3` ANSWER :C

Discussion

4783.	Find the mean deviation about the mean.
Answer» ANSWER :6.32

Discussion

4784.	The maximum value ofcos^(4) x-sin^4xis
Answer» D,C,B,A A,C,B,D C,B,D,A B,A,D,C Answer :2

Discussion

4785.	A side of an equillateral triangle is 20cm long. A second equilateral triangle is inscribed in it by joining the mid-points of the sides of the first triangle. The progress is continued as shown in the accompanying diagram. Find the perimeter of the sixth inscribed equilateral triangle.
Answer» ANSWER :`(15)/(8)`

Discussion

4786.	z = (1+i)/(1-i)then z^4 = .......... .
Answer» ANSWER :1

Discussion

4787.	Let f(x)={:{(x^(2)-4x+3",",x lt 3,),(x-4,x ge 3,):} and g(x)={:{(x-3",",x lt 4),(x^(2)+2x+2,x ge 4):} . Then which of the following is/are true ?
Answer» `(f+G)(3.5)=0` `f(g(3))=3` `(fg)(2)=1` `(f-g)(4)=0` Answer :A::B::C

Discussion

4788.	Check whether the following sentences are statements. Give reasons for your answer. There is no rain without clouds.
Answer» ANSWER :TRUE.

Discussion

4789.	If the coefficients of x^2 and x^3 in the expansion of (3 + ax)^(9) be same, then the value of a is
Answer» (a) `(3)/(7)` (B) `(7)/(3)` (C) `(7)/(9)` (d) `(9)/(7)` Answer :D

Discussion

4790.	If y =sqrt((1-sin2x)/(1+sin2x)) then ((dy)/(dx))_(x = 0) =
Answer» `1/2` 1 `-2` 2 Answer :C

Discussion

4791.	Consider three planes 2x + py + 6z = 8,x + 2y + qz = 5 and x + y + 3z =4 Three planes do not have any common point of intersection if
Answer» `p 2, Q NE 3` `p ne 2,q ne 3` `p ne 2,q = 3` `p = 2,q =3` ANSWER :C

Discussion

4792.	If the matrix A=[(1,2,3,0),(2,4,3,2),(3,2,1,3),(6,8,7,alpha)] is of rank 3, then alpha=
Answer» `-5` 5 4 1 Answer :B

Discussion

4793.	(sin3alpha)/(cos2alpha)lt0 if alpha lies in
Answer» `((13pi)/48,(14pi)/48)` `((14pi)/48,(18pi)/48)` `((18pi)/48,(23pi)/48)` `(0,(PI)/2)` ANSWER :A

Discussion

4794.	construct truthtable forp ^^ (q vv r)
Answer» ANSWER :`(##SCH_OPM_ISC_MAT_XI_C27_E04_025_A01##)`

Discussion

4795.	Obtain equation of circle inx^(2) + y^(2) - x + y = 0
Answer» ANSWER :CENTRE `((1)/(2),-(1)/(2))`, RADIUS `(1)/(SQRT(2))`

Discussion

4796.	Let f:[0,4pi] to [0, pi] be defined by f(x)=cos^(-1)(cosx). The number of points x in [0,4pi] satisfying the equation f(x)=(10-x)/10 is
Answer» ANSWER :3

Discussion

4797.	Find the domain and range of f(x)=(x+2)/(\|x+2\|).
Answer» ANSWER :`{-1,1}`

Discussion

4798.	A straight line which makes equal intercepts on positive X and Y axes and which is at a distance unit from the origin intersects the striaght line y=2x+3+sqrt2 " at " (x_0,y_0). " Then " (2x_0+y_0) =
Answer» `3+sqrt2` `sqrt2-1` 1 0 Answer :A

Discussion

4799.	A(3,2,0), B(5,3,2), C(-9,6,-3) are vertices of a triangle. bar(AD), the bisector of lfloorBAC meets bar(BC) att D. Find the coordinates of D.
Answer» ANSWER :`(38/16,57/16,17/16)`

Discussion

4800.	Use p : I like this school , q : I like Mr. Sexena. Express each of the following statements in words . p^^q
Answer» ANSWER :I LIKE this SCHOOL and I like MR. SAXENA

Discussion

Explore topic-wise InterviewSolutions in .

A card is drawn from a well shuffled pack of 52 cards . Findthe probability of a spade

Find the coefficient of (1)/(x^(17)) in the expansion of (x^(4)-(1)/(x^(3)))^(15).

If x=asec^(n)theta,y=btan^(n)theta then ((x)/(a))^(2//n)-((y)/(b))^(2//n)=

Let f and g be two real functions given by f= {(0, 1), (2,), (3, -4), (4, 2), (5, 1)} and g= {(1,0), (2,2), (3,-1), (4,4),(5,3)}. Find Domain.

If cos A+ cos B + cos C =0 then cos 3A+ cos 3B + cos 3X

Two unbiased dice are thrown . Find the probability that the totalnumbers on theis greater than 8 ,

The number of ways in which a team of eleven players can be selected from 22 players always including 2 of them and excluding 4of them is

Two lines passing through the point (2,3) intersects each other at an angle of 60°. If slope of one line is 2, find equation of the other line.

Consider the following sentence: Every rectangle is a square.

Find the second derivative of the function (Find y" or (d ^(2) y)/(dx ^(2)) of the cos ^(3) x

There are 5 red and 5 black balls in first bag and 6 red and 4 black balls is second bag. One -one ball is drawn from each bag. Find the probability that: (i)both balls are of the same colour, (ii) one ball is red and other is black.

A class consists of 80 students 25 of them aregirls and 55 boys . If 10 are rich and remainingpoor and also 20 of them are intelligent,thenthe probability of selecting intelligent rich girls is ,

Theminimum value of 5 cos x+3 cos ((pi)/(3) +x) +8 is

Let f: R to R be a positive increasing function with Lt_(x to oo)(f(3x))/(f(x))=1 then Lt_(x to oo)(f(2x))/(f(x))=

Find the distance between them.

Ifx=sqrt((1- cos theta )/(1+ cos theta )), " then " (2 x)/(1-x^(2))=

Write down the converse of following statements: If you go to Agra, then you must visit Tajmahal.

Find a vector of magnitude and perpendicular to both the vectors vec(a)= 2vec(i)- 2vec(j) + vec(k) and vec(b)= 2vec(i) + 2vec(j) + 3vec(k)

In a certain city, all telephone numbers have six digits How many telephone numbers are there with distinct digits?

If 2 Cos^(2)B - 1 = Tan^(2) A then Cos A Cos B =

A(2, 3),B(1,5),C(-1, 2) are three points. If P is a point moves such that PA^(2)+PB^(2)=2PC^(2) then locus of P is lx+my+n=0. Then decreasing order of l,m,n

Write the relation R= {(x,x^3): x is a prime number less than 101) write in roster form.

In DeltaABC, " if" (1)/(a+c)+(1)/(b+c)=(3)/(a+b+c)then show thatC=60^(@)

cos alpha * sin (beta - gamma ) + cos beta * sin ( gamma - alpha ) + cos gamma * sin ( alpha - beta )=

Show that the function f (x) = I x I + I x -1 1 + I x - 2 I is continuous on R.

If cos^(-1)(x)+cos^(-1)(y)+cos^(-1)(z)=pi(sec^(2)(u)+sec^(4)(v)+sec^(6)(w)), where u, v, w are least non-negative angles such that u lt v lt w, then the value of x^(2000)+y^(2002)+z^(2004)+(36pi)/(u+v+w) is

Iftan^(2) A + tan^(2)B+tan^(2)C -tan B tan c-tan C tan A-tan A tan B=0 then DeltaABC is

Function f(x)=|x|-|x-1| is monotonically increasing when

Area of quadrilateral formed by two pair of lines x^(2)-y^(2)-3(x+y)=0 and x^(2)-y^(2)+3(x-y)=0 is

The volume of parallelopiped with edges bar(OA) = (lamda+ 2)bari +(lamda+2)(lamda+1)barj +bark, bar(OB) = (lamda+ 3)bari +(lamda+2)(lamda+3)barj +bark and bar(OC) = (lamda+ 4)bari +(lamda+3)(lamda+4)barj +bark is

cos2thetacos2phi+sin^(2)(theta-phi)-sin^(2)(theta+phi) is equal to

The position vector of A is pbari+barj. If A is rotated about O through an angle pi//6 in anticlockwise direction, it conincides with B whose position verctor is bari+qbarj. The value of p,q are

Find the mean deviation about the mean.

The maximum value ofcos^(4) x-sin^4xis

A side of an equillateral triangle is 20cm long. A second equilateral triangle is inscribed in it by joining the mid-points of the sides of the first triangle. The progress is continued as shown in the accompanying diagram. Find the perimeter of the sixth inscribed equilateral triangle.

z = (1+i)/(1-i)then z^4 = .......... .

Let f(x)={:{(x^(2)-4x+3",",x lt 3,),(x-4,x ge 3,):} and g(x)={:{(x-3",",x lt 4),(x^(2)+2x+2,x ge 4):} . Then which of the following is/are true ?

Check whether the following sentences are statements. Give reasons for your answer. There is no rain without clouds.

If the coefficients of x^2 and x^3 in the expansion of (3 + ax)^(9) be same, then the value of a is

If y =sqrt((1-sin2x)/(1+sin2x)) then ((dy)/(dx))_(x = 0) =

Consider three planes 2x + py + 6z = 8,x + 2y + qz = 5 and x + y + 3z =4 Three planes do not have any common point of intersection if

If the matrix A=[(1,2,3,0),(2,4,3,2),(3,2,1,3),(6,8,7,alpha)] is of rank 3, then alpha=

(sin3alpha)/(cos2alpha)lt0 if alpha lies in

construct truthtable forp ^^ (q vv r)

Obtain equation of circle inx^(2) + y^(2) - x + y = 0

Let f:[0,4pi] to [0, pi] be defined by f(x)=cos^(-1)(cosx). The number of points x in [0,4pi] satisfying the equation f(x)=(10-x)/10 is

Find the domain and range of f(x)=(x+2)/(|x+2|).

A straight line which makes equal intercepts on positive X and Y axes and which is at a distance unit from the origin intersects the striaght line y=2x+3+sqrt2 " at " (x_0,y_0). " Then " (2x_0+y_0) =

A(3,2,0), B(5,3,2), C(-9,6,-3) are vertices of a triangle. bar(AD), the bisector of lfloorBAC meets bar(BC) att D. Find the coordinates of D.

Use p : I like this school , q : I like Mr. Sexena. Express each of the following statements in words . p^^q