14949 + Interview Questions in Maths in Class 11 Page 22 InterviewSolution

1051.	Find the number of terms in the following expansions. (1+6x+9x^(2) )^(23)
Answer» ANSWER :`=47`

Discussion

1052.	If bara,barb,barc are non-coplanar unit vectors such that baraxx(barbxxbarc)=(barbxxbarc)/(sqrt2) then (bara,barb)=
Answer» `(3PI)/4` `PI/4` `pi/2` `pi` ANSWER :A

Discussion

1053.	Find all the points of discontinuity of f defin ed by f(x)=\|x\|-\|x+1\|
Answer» ANSWER :there is no POINT of discontinouity

Discussion

1054.	If the joining A(1,3,4) and B is divided by the point (12,3,5) in the ratio 1:3 then B is …
Answer» (-8,12,20) (13,6,-13) (45,3,8) (-11,3,-8) ANSWER :C

Discussion

1055.	The perimeter of a triangleis equal to the diameter of the escribed circle then the triangles is
Answer» ISOSCELES RIGHT angled Equilateral Scalane ANSWER :B

Discussion

1056.	Using the simple aggregate method, calculate the price index number from the following data:
Answer» ANSWER :`164.5`

Discussion

1057.	Using the simple aggregate method, calculate the price index number from the following data:
Answer» ANSWER :`117.143`

Discussion

1058.	Using the simple aggregate method, calculate the price index number from the following data:
Answer» ANSWER :`120`

Discussion

1059.	The product of the perpendiculars from (f,-g) to the pair of st. linehxy+gxfy+c=0 is
Answer» `ABS(FG)` `abs((fg-c)/H)` `abs(fgh-c)` `abs((fgh-c)/h)` ANSWER :D

Discussion

1060.	Let POR be a triangle of area Delta with a = 2,b= (7)/(2) and c=(5)/(2) here a, b and c are the lengths of the sides of the triangle opposite to the angles at P, Q and R respectively. Then (2sinP-sin 2P)/(2sinP+sin2P) equals
Answer» `(3)/(4Delta)` `(45)/(4Delta)` `((3)/(4Delta))^(2)` `((45)/(4Delta))^(2)` ANSWER :C

Discussion

1061.	If acostheta+bsintheta=mandasintheta-bcostheta=n, then show that, a^(2)+b^(2)=m^(2)+n^(2).
Answer» ANSWER :`a^(2)+B^(2)`

Discussion

1062.	Let bara=a_(1)bari+a_(2)barj+a_(3)bark,barb=b_(1)bari+b_(2)barj+b_(3)barkbarc=c_(1)bari+c_(2)barj+c_(3)bark be three non-zero vectors such that barc be three non-zero vectors such that bara and barb. If theangle between bara and barb is pi//6 then abs({:(a_(1),a_(2),a_(3)),(b_(1),b_(2),b_(3)),(c_(1),c_(2),c_(3)):})^(2)=
Answer» 0 1 `1/4abs(BARA)^(2)ABS(barb)^(2)` `3/4abs(bara)^(2)abs(barb)^(2)` ANSWER :C

Discussion

1063.	If f(x) = int_(x)^(x^(2)) (t-1)dt, 1 le x le 2, find the greatest value of f(x).
Answer» ANSWER :4

Discussion

1064.	Evaluate the ""^12C_0 + ""^12C_1 + ""^12C_2 + ……..+""^12C_12
Answer» ANSWER :`2^12`

Discussion

1065.	(cos h x - sin h x)^(n) =
Answer» `cos H n X - sin h n x` `2 cos h n x` `2 sin h n x` `cos h n x + sin h n x` ANSWER :A

Discussion

1066.	Find co-ordinates of focii, equation of the directrix, length of the latus rectum, length of the major and mirror axis, the major and mirror axis, the eccentricity of each of following hyperbola. (1) (x^(2))/(100) - (y^(2))/(25) = 1 (2) x^(2) - y^(2) = 64 (3) 2x^(2) - 3y^(2) = 5 (4) 9y^(2) - 16x^(2) = 144 (5)(y^(2))/(25)-(x^(2))/(39)=1
Answer» ANSWER :`(##KPK_AIO_MAT_XI_C11_E01_046_S01##)`

Discussion

1067.	A is (-2, 0) and P is any point on the curve given by y^(2)=16x. If Q bisect AP, find the equation of the locus of Q.
Answer» ANSWER :`Q(ALPHA, BETA)" as "y^(2)=8x+8`

Discussion

1068.	Use p : I like this school , q : I like Mr. Sexena. Express each of the following statements in words .~(p ^^ q)
Answer» ANSWER :It is not TRUE that I LIKE this SCHOOL and I likeMr SAXENA .

Discussion

1069.	If (2, 1, 3), ( 3, 1, 5) ana (1, 2, 4) are the mid points of the sides BC, CA AB of DeltaABC respectively, then the perimeter of the triangle is
Answer» `2sqrt(6)+sqrt(3)` `2(2sqrt(6)+sqrt(3))` `2(sqrt(6)+3)` `sqrt(6)+sqrt(3)` Answer :B

Discussion

1070.	If 3A=[(-1,2,2),(2,-1,2),(2,2,-1)] then
Answer» `A A^(T)=A^(T)A=I` `A A^(T)=A^(T)A=-I` `A A^(T)=A^(T)A=0` `A A^(T)=A^(T)A=A` ANSWER :A

Discussion

1071.	Bythe principleof mathematicalinduction , provethat forn le 1, 1^(2)+ 2^(2) + 3^(2) + …+ n^(2) >n^(3)/3
Answer» ANSWER :` > 1/3 ( K +1)^(3)`

Discussion

1072.	Use p : I like this school , q : I like Mr. Sexena. Express each of the following statements in words .~[(~p)^^ q]
Answer» ANSWER :It is not TRUE that I do not like this school and I like Mr. SAXENA.

Discussion

1073.	Answer the equation: int(3x+1)/(sqrt(2x^(2)+x+3))dx
Answer» Answer :`(3)/(2)SQRT(2X^(2)+x+3)+(1)/(4sqrt(2))log(4x+1)+sqrt((4x+1)^(2)+23)+c`

Discussion

1074.	For any two events A an B.
Answer» ANSWER :1

Discussion

1075.	We wish tto select 6 person from 8 but, if the person A is chosen, then B must be chosen. In how many ways can selections be made ?
Answer» ANSWER :22

Discussion

1076.	Find the mean deviation about the median for the following data: 3, 9, 5, 3, 12, 10, 18, 4, 7, 19, 21.
Answer» ANSWER :5.27

Discussion

1077.	X-axis is the intersection of two planes ____
Answer» XY and XZ YZ and ZX XY and YZ None of these Answer :A

Discussion

1078.	If tan alpha = 1/sqrt(x(x^(2)+x+1)), tan beta = sqrt(x)/sqrt(x^(2) +x+1) and tan gamma = sqrt(x^(-3) + x^(-2) + x^(-1)), then alpha + beta=
Answer» `GAMMA` `2gamma` `-gamma` `gamma//2` ANSWER :A

Discussion

1079.	If theta is angle between pair of lines x^(2)-5xy+py^(2)+3x-8y+2=0 then sin theta=
Answer» `(1)/(sqrt(50))` `(1)/(7)` `(1)/(5)` `(1)/(sqrt(10))` ANSWER :A

Discussion

1080.	Find the angle of rotation of the axes so that the equation sqrt(3) x - y + 1 = 0 may be reduced to the form Y = K
Answer» ANSWER :`(PI)/(3)`

Discussion

1081.	Find the derivative of the function (a-x)/(a +x)
Answer» ANSWER :`(-2A)/((a+x) ^(2))`

Discussion

1082.	Differentiate the following functions: 13. (3 x^7 + x^5 - 2x^4 + x-3)/( x^4)
Answer» Answer :`9x^(2) + 1 - (3)/(x^4) + (12)/( x^5)`

Discussion

1083.	Find the derivative of the function x.e^(x) sin x
Answer» ANSWER :`E ^(X) [ x COS x + x SIN + sin x]`

Discussion

1084.	Number of solution of equation cos x + cos y + cos z = - 3
Answer» One solution if `x, y, x in [0, PI]` One solution if `x, y Z in [0, 2 pi]` Two solution if `x, y, z in [0, 2 pi]` No solution if `x, y, z in [ 0, pi]` Answer :A::B::D

Discussion

1085.	Maximum value of (3sintheta+4costheta) is:
Answer» 5 `-5` 1 None of these Solution :N//A

Discussion

1086.	Findlimit of the following if it exists: lim_(xto0)(log(1+x^(3)))/(sin^(3)x)
Answer» ANSWER :1

Discussion

1087.	Find equation of lines which bisects the quadrents.
Answer» ANSWER :`XPM y=0`

Discussion

1088.	Differentiate the following functions: 11. 2x^((1)/(2)) + 6x^((1)/(3)) - 2x^((3)/(2))
Answer» ANSWER :`(1)/(X^(1//2) ) + (2)/( x^(2//3) ) - 3X^(1//2)`

Discussion

1089.	Let f(x)=a+b cos^(-1)x(b gt 0). If domain and range of f(x) are the same set then b-a is equal to
Answer» `1 - 2/pi` `1+2/pi` 2 `1- 1/pi` ANSWER :B

Discussion

1090.	The values of x between 0 and 2pi satsifying sinx sqrt(8cos^(2)x)=1 are in AP then common difference is
Answer» `(pi)/(4)` `(pi)/(8)` `(3PI)/(8)` `(5PI)/(8)` Answer :A

Discussion

1091.	Find lim_(xto0)f(x), where f(x)={{:((x)/(\|x\|)","xne0),(0","x=0):}
Answer» ANSWER :LIMIT does not EXIST at `X = 0`

Discussion

1092.	Value of (3 +cot 80^(@) cot 20^(@))/( cot 80^(@) cot 20 ^(@))
Answer» `COT 20^(@)` `TAN 50^(@)` `cot 50^(@)` `cot sqrt20` ANSWER :B

Discussion

1093.	If f(x) = {{:(ax^2 -b",", -1 lt x lt 1),((1)/(\|x\|)",", "elsewhere"):} is differentiable at x =1, then ............... .
Answer» `a= (1)/(2), B= (-3)/(2)` `a = (-1)/(2), b= (3)/(2)` ` a= - (1)/(2) , b= - (3)/(2)` `a = (1)/(2) , b= (3)/(2)` Answer :C

Discussion

1094.	The volume of a cube is increasing at the rate of 8cm^3//sec. How fast is the surface area increasing when the length of an edge is 12 cm ?
Answer» ANSWER :`8/3cm^(3)//SEC`

Discussion

1095.	A(2, 3), B(-1, 1) are two points if P is a point such that angleAPB=90^(@) then the locus of P is
Answer» `X^(2)+y^(2)-x-4y+1=0` `x^(2)+y^(2)+x+4y-1=0` `x^(2)+y^(2)-x+4y-1=0` `x^(2)+y^(2)+x-4y-1=0` ANSWER :1

Discussion

1096.	Assertion (A) : The matrix [(cosalpha,sinalpha),(-sinalpha,cosalpha)]is an orthogonal matrix. Reason (R) : If A is an orthogonal matrix then A A^(T)=A^(T)A=I
Answer» Both A and R are TRUE and R is the CORRECT EXPLANATION of A Both A and R are true R is not correct explanation of A A is true R is FALSE A is false R is true Answer :A

Discussion

1097.	If cos A = (5)/(13), Tan - (-15)/(8) and A and B are angles in the fourth quadrant and the second quadrant respectively then find sin (A + B) and cos (A + B). Also determine the quadrant to which the angle (A + B) relates.
Answer» Answer :`(171)/(221),(140)/(221)` FIRST QUADRANT

Discussion

1098.	Let bara,barb,barc be three vectors which satisfy baraxx(barbxxbarc)=(baraxxbarb)xxbarc if
Answer» `barbxx(baraxxbarc)=BAR0` `BARA.(BARBXXBARC)=0` `barcxxbara=baraxxbarb` `barcxxbarb=barbxxbara` ANSWER :A

Discussion

1099.	If sintheta=(-4)/(5)andtheta lies in third quadrant, then the value of cos""(theta)/(2) is
Answer» `(1)/SQRT(5)` `-(1)/(sqrt(10))` `-(1)/sqrt(5)` `(1)/(sqrt(10))` Answer :C

Discussion

1100.	If the plane 4 (x-1) +k ( y -2) + 8 ( z -5) =0 contains the line (x-1)/(2) = (y-2)/(4) = (z-5)/(3) then k is
Answer» 2 4 `-8` 8 Answer :C

Discussion

Explore topic-wise InterviewSolutions in .

Find the number of terms in the following expansions. (1+6x+9x^(2) )^(23)

If bara,barb,barc are non-coplanar unit vectors such that baraxx(barbxxbarc)=(barbxxbarc)/(sqrt2) then (bara,barb)=

Find all the points of discontinuity of f defin ed by f(x)=|x|-|x+1|

If the joining A(1,3,4) and B is divided by the point (12,3,5) in the ratio 1:3 then B is …

The perimeter of a triangleis equal to the diameter of the escribed circle then the triangles is

Using the simple aggregate method, calculate the price index number from the following data:

Using the simple aggregate method, calculate the price index number from the following data:

Using the simple aggregate method, calculate the price index number from the following data:

The product of the perpendiculars from (f,-g) to the pair of st. linehxy+gxfy+c=0 is

Let POR be a triangle of area Delta with a = 2,b= (7)/(2) and c=(5)/(2) here a, b and c are the lengths of the sides of the triangle opposite to the angles at P, Q and R respectively. Then (2sinP-sin 2P)/(2sinP+sin2P) equals

If acostheta+bsintheta=mandasintheta-bcostheta=n, then show that, a^(2)+b^(2)=m^(2)+n^(2).

If f(x) = int_(x)^(x^(2)) (t-1)dt, 1 le x le 2, find the greatest value of f(x).

Evaluate the ""^12C_0 + ""^12C_1 + ""^12C_2 + ……..+""^12C_12

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

A is (-2, 0) and P is any point on the curve given by y^(2)=16x. If Q bisect AP, find the equation of the locus of Q.

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

If (2, 1, 3), ( 3, 1, 5) ana (1, 2, 4) are the mid points of the sides BC, CA AB of DeltaABC respectively, then the perimeter of the triangle is

If 3A=[(-1,2,2),(2,-1,2),(2,2,-1)] then

Bythe principleof mathematicalinduction , provethat forn le 1, 1^(2)+ 2^(2) + 3^(2) + …+ n^(2) >n^(3)/3

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

Answer the equation: int(3x+1)/(sqrt(2x^(2)+x+3))dx

For any two events A an B.

We wish tto select 6 person from 8 but, if the person A is chosen, then B must be chosen. In how many ways can selections be made ?

Find the mean deviation about the median for the following data: 3, 9, 5, 3, 12, 10, 18, 4, 7, 19, 21.

X-axis is the intersection of two planes ____

If tan alpha = 1/sqrt(x(x^(2)+x+1)), tan beta = sqrt(x)/sqrt(x^(2) +x+1) and tan gamma = sqrt(x^(-3) + x^(-2) + x^(-1)), then alpha + beta=

If theta is angle between pair of lines x^(2)-5xy+py^(2)+3x-8y+2=0 then sin theta=

Find the angle of rotation of the axes so that the equation sqrt(3) x - y + 1 = 0 may be reduced to the form Y = K

Find the derivative of the function (a-x)/(a +x)

Differentiate the following functions: 13. (3 x^7 + x^5 - 2x^4 + x-3)/( x^4)

Find the derivative of the function x.e^(x) sin x

Number of solution of equation cos x + cos y + cos z = - 3

Maximum value of (3sintheta+4costheta) is:

Findlimit of the following if it exists: lim_(xto0)(log(1+x^(3)))/(sin^(3)x)

Find equation of lines which bisects the quadrents.

Differentiate the following functions: 11. 2x^((1)/(2)) + 6x^((1)/(3)) - 2x^((3)/(2))

Let f(x)=a+b cos^(-1)x(b gt 0). If domain and range of f(x) are the same set then b-a is equal to

The values of x between 0 and 2pi satsifying sinx sqrt(8cos^(2)x)=1 are in AP then common difference is

Find lim_(xto0)f(x), where f(x)={{:((x)/(|x|)","xne0),(0","x=0):}

Value of (3 +cot 80^(@) cot 20^(@))/( cot 80^(@) cot 20 ^(@))

If f(x) = {{:(ax^2 -b",", -1 lt x lt 1),((1)/(|x|)",", "elsewhere"):} is differentiable at x =1, then ............... .

The volume of a cube is increasing at the rate of 8cm^3//sec. How fast is the surface area increasing when the length of an edge is 12 cm ?

A(2, 3), B(-1, 1) are two points if P is a point such that angleAPB=90^(@) then the locus of P is

Assertion (A) : The matrix [(cosalpha,sinalpha),(-sinalpha,cosalpha)]is an orthogonal matrix. Reason (R) : If A is an orthogonal matrix then A A^(T)=A^(T)A=I

If cos A = (5)/(13), Tan - (-15)/(8) and A and B are angles in the fourth quadrant and the second quadrant respectively then find sin (A + B) and cos (A + B). Also determine the quadrant to which the angle (A + B) relates.

Let bara,barb,barc be three vectors which satisfy baraxx(barbxxbarc)=(baraxxbarb)xxbarc if

If sintheta=(-4)/(5)andtheta lies in third quadrant, then the value of cos""(theta)/(2) is

If the plane 4 (x-1) +k ( y -2) + 8 ( z -5) =0 contains the line (x-1)/(2) = (y-2)/(4) = (z-5)/(3) then k is