14949 + Interview Questions in Maths in Class 11 Page 21 InterviewSolution

1001.	From the following data compose price index by applying weighted average of price relatives method using arithmetic means:
Answer» ANSWER :`193.18`

Discussion

1002.	If the slope of one of the lines represented by ax^(2) - 6xy + y^(2) = 0 is the square of the other, then the value of a is
Answer» `-27 or 8` `-3 or 2` `-64 or 27` `-4 or 3` ANSWER :A

Discussion

1003.	If a_(ij)=(2i-j)^(2),find A_(32).
Answer» ANSWER :`[(1,0),(9,4),(25,16)]`

Discussion

1004.	Statement -1 : For all n in N, x^( 2n+1) +y^(2n+1) is divisible by x+y Statement-2: If n in N, n^(3) + 2n is divisible by 6 Which of the above statement is true :
Answer» only 1 only 2 both 1 & 2 neither 1 nor 2 Answer :A

Discussion

1005.	Compute :lim_(xto0)(e^(3x)-1)/(x)
Answer» ANSWER :3

Discussion

1006.	"cosec" 10^(@) - sqrt(3)" sec" 10^(@) =
Answer» 4 2 0 `-4` ANSWER :A

Discussion

1007.	If sqrt(u/v)+sqrt(v/u)=6 , then (du)/(dv) =
Answer» `(17v-u)/(v-17u)` `(v-17u)/(17v-u)` `(17v+u)/(v-17u)` `(v+17u)/(17v-u)` ANSWER :B

Discussion

1008.	If the projection of a line of length d on the coordinate axes ared_(1),d_(2),d_(3) " respectively then, prove that" d^(2) = (d_(1)^(2)+d_(2)^(2)+d_(3)^(2))/2
Answer» ANSWER :`d^(2)`

Discussion

1009.	If A = (1,-1,0), B=(1,2,1), C=(2,3,0) andD=(0,1,t). Be four points. If the projection of bar(AB) " on " bar(CD)" is equal to that of " bar(CD) " on " bar(AB), then find t.
Answer» ANSWER :`pmsqrt2`

Discussion

1010.	If Pis a point on the altitude AD of the triangle ABC such that angleCBP =B//3, then AP is equal to
Answer» `2A "sin"(C)/(3)` `2b "sin"(C)/(3)` `2C"sin"(B)/(3)` `2c"sin"(C)/(3)` ANSWER :C

Discussion

1011.	Write theconverse of the contrapositive of p implies q .
Answer» <P> ANSWER :~p => ~Q

Discussion

1012.	Identify the Quantifiers in the following statements: There exists a real number x such that x^(2)+1=0.
Answer» ANSWER :EXISTENTIAL quanifier is USED

Discussion

1013.	Differentiate the following functions: 15. sqrt ( 3 x +2).
Answer» ANSWER :`(3)/( 2 SQRT(3 X +2) )`

Discussion

1014.	If xsqrt(1+y)+ysqrt(1+x)=0 then (dy)/(dx)=
Answer» `(X+1)/(x)` `1/(1+x)` `(-1)/((1+x)^2)` `x/(1+x)` ANSWER :C

Discussion

1015.	Equation of the line passing through (1, 2) and parallel to the line y=3x -1 is
Answer» `y+2 = X + 1` `y+2= 3( x+1)` `y-2 = 3( x-1)` `y-2 = x-1` ANSWER :C

Discussion

1016.	Statement-I: Periodof [x]where[.]representstheintegral partof x is 1, Statement-II: Periodof x-[x]where [.] representsthe integralpart xis 1. Statement-III : A realfunction f : A toB issuch thatf(a+x) = f(x ) AA a E RthenF iscalledperiodicfunction.Whichof theabovestate mentsis correct.
Answer» I and II only II and III only III and I only All ANSWER :2

Discussion

1017.	The weightsof a coffeein 70jars are shownin the following table . .Determine variance and standard deviation of the above distribution.
Answer» ANSWER :`1.16 : 1.08`

Discussion

1018.	If (1+x^2)^2(1+x)^n =a_0+a_1x+a_2x^2____ + x^(n+4) ____
Answer» 1 2 3 4 Answer :C

Discussion

1019.	If two pairs of straight lines with combinedequations xy + 4x - 3y - 12 = 0 and xy - 3x + 4y - 12 = 0 form a square. Then, the combined equation of its diagonals is
Answer» `X^(2)-2xy+y^(2)+x-y=0` `x^(2)+2xy+y^(2)+x+y=0` `x^(2)+y^(2)+x-y=0` `x^(2)-y^(2)+x+y=0` ANSWER :C

Discussion

1020.	If vec(a) is a non zero vector and vec(a).vec(b)= vec(a).vec(c ), vec(a) xx vec(b)= vec(a) xx vec(c ), then
Answer» `VEC(a)//vec(B)` `vec(b)= vec(C )` `vec(b) NE vec( c)` `vec(a) ne vec(b) and vec(a) = vec(c )` ANSWER :B

Discussion

1021.	Find the distance between each of pair of point: (-4,-2,0) and (3,3,5)
Answer» ANSWER :`25sqrt21` so UNITS

Discussion

1022.	Find anle between planes bar(r ).(2bar(i)-bar(j) + 2 bar(k)) = 3, bar(r ).(3bar(i)+6bar(j) + bar(k)) = 4
Answer» ANSWER :`COS^(-1)(2/(3sqrt46))`

Discussion

1023.	A spring was hung from hook in the ceiling. . A number of different weight were attached to the spring to make it stretch, and the total of the spring was measured each time shown in the following table. {:("Weight(kg)",2,4,5,8),("Length (cm)",3,4,4.5,6):} (i) Draw a graph showing the results . (ii) Find the equation relating the length of the spring to the weight on it . (iii) What is the actual length of the spring . (iv) If the spring has to stretch to 9 cm long , how much weight should be added ? (v) How long will the spring be when 6 kilograms of weight on it ?
Answer» Answer :(i) `(X-2)/(4-2)`,(ii) x - 2Y + 4 = 0 (iii) 2cm 5 cm .

Discussion

1024.	Maximum value of (x+5)^(4)(13-x)^(5)is
Answer» `7^(4)11^(5)` `6^(4)14^(5)` `8^(4)10^(5)` `7^(5)10^(5)` Answer :C

Discussion

1025.	Examine whether the following statements are true or false : phi sub {x, y, z}
Answer» ANSWER :1

Discussion

1026.	A light is at the top of 64m high. A ball is dropped from the same height from a point 20 m away from the light. Assuming that the ball falls according to the law s=5t^(2), how fast is the shadowof the ball moving along the ground 2 second later?
Answer» ANSWER :`-64` m/sec

Discussion

1027.	The maximum value of f(x)=tan^(-1)(((sqrt(12)-2)x^(2))/(x^(4)+2x^(2)+3)) is
Answer» `18^(@)` `36^(@)` `22.5^(@)` `15^(@)` ANSWER :D

Discussion

1028.	Represent the complex number sqrt3+i in the polar form.
Answer» ANSWER :`2[cos((pi)/6) + ISIN((pi)/6)]`

Discussion

1029.	Let f(x)=a_(5)x^(5)+a_(4)x^(4)+a_(3)x^(3)+a_(2)x^(2)+a_(1)x, wherea_(i) s are real and f(x) =0 has a positive root alpha_(0) . Then
Answer» f(X)=0 has a ROOT `alpha_(1)` such that `0ltalpha_(1)ltalpha_(0)` f(x) =0 has at least two real roots f(x) = 0 has at least ONE real root None of these Answer :A::B::C::D

Discussion

1030.	Centriod of triangle formed by lines 8x^(2)-14xy+5y^(2)=0, x-2y+3=0 is
Answer» (2,2) (-2,3) `((2)/(3),(1)/(3))` `((8)/(3),(8)/(3))` ANSWER :A

Discussion

1031.	If tantheta=(a)/(b), then bcos2theta+asin2theta is equal to
Answer» a B `(a)/(b)` NONE of these Answer :B

Discussion

1032.	Find the angle between the planes x+2y+2z-5=0 and 3x+3y+2z-8=0.
Answer» ANSWER :`COS^(-1)((13)/(3sqrt(22)))`

Discussion

1033.	Equation of a bisector of the angle between the line y-b=(2m)/(1-m^2)(x-a) and y-b=(2m')/(1-m^2)(x-a) is
Answer» (y-b)(m+m ')+(x-a)(1-mm ')=0 (y-b)(m-m ')+(x-a)(1-mm ')=0 (y-b)(m+m ')-(y-b)(1-mm ')=0 (y-b)(m+m ')+(y-b)(1-mm ')=0 Answer :(y-b)(1-mm')-(x-a)(m+m')=0

Discussion

1034.	If \|cos theta (sin theta + sqrt( sin ^(2) theta + sin ^(2) alpha ) )\| le kthen the value of k is
Answer» `SQRT (1 + COS ^(2) alpha )` `sqrt (1 + SIN ^(2) alpha )` `sqrt (2 + cos ^(2) alpha )` `sqrt (2 + sin ^(2) alpha )` Answer :B

Discussion

1035.	f(x) is a polynomial funciton, f : R to R, such that f(2x) = f'(x) f^('')(x) The value of f(3) is
Answer» `4` `12` `15` NONE of these Answer :B

Discussion

1036.	A container in the shape of an inverted cone has height 12 cm and radius 6cm at the top. If it is filled with water at the rate of 12cm^(3)//sec, what is the rate of change in the rate of change in the height of water level when the tank is filled 8 cm?
Answer» ANSWER :`(3)/(4PI)` cm/sec

Discussion

1037.	Intersecting the y-axis at a distance of 2 units above the origin and making an angle of 30^(@) with positive direction of the x-axis.
Answer» ANSWER :`X - SQRT3 y + 2 sqrt3 = 0 `

Discussion

1038.	If A=[(1,2-3i,3+4i),(2+3i,0,4-5i),(3-4i,4+5i,2)], then show that A is hermitian matrix.
Answer»

Discussion

1039.	If the system of equations 2x+3ky+(3k+4)z=0,x+(k+4)y+(4k+2)z=0,x+2(k+4)y+(3k+4)z=0 has non trivial solution then K =
Answer» `-8` or `1/2` 8 or `-1/2` `-4` or `1/2` 4 or `-1/2` ANSWER :A

Discussion

1040.	If A and B are two eventswithP(A) = (1)/(4), P(A//B) = (1)/(4) and P(B//A) = (1)/(2)then
Answer» A and B are mutuallyexclusive A and B are INDEPENDENT A is sub event of B B is sub - EVENTSA ANSWER :B

Discussion

1041.	A line L cuts the sides AB, BC of Delta ABC in theratio 2:5, 7:4 respectively then the line L cuts CA in the ratio
Answer» `7:10` `2:-5` `10:-7` `5:-2` ANSWER :C

Discussion

1042.	The sum of 20 observations of the deviation from 30 is 20. Their mean is
Answer» 30 30.1 29 31 Answer :D

Discussion

1043.	Find the derivative of the function (sin x )/( 1+ cos x)
Answer» ANSWER :`(1)/(1+ COS 1)`

Discussion

1044.	If f(x + y) = f(x) f(y) AA x, yand f(5) = 2,f'(0) = 3 then f'(5) =
Answer» `0` `1` `6` `2` ANSWER :C

Discussion

1045.	Distance between two foci is 8 unit, distance between two directrix is 18 Obtain equation of ellipse satisfying given conditions unit and X-axis as major axis.
Answer» ANSWER :`(x^(2))/(36) + (y^(2))/(20) =1`

Discussion

1046.	If f(x)=((x-3)(x+2)(x+5))/((x+1)(x-7))
Answer» `f(x) gt 0 AA x in (-5, -2) UU (-1, 3) uu (7, oo)` `f(x) lt 0 AA x in (-oo, -5) uu (-2, -1) uu (3, 7)` `f(x)gt 0 AA x in (-5, -2) uu (-1,3) uu(9, oo)` `f(x)lt 0 AA x in (-oo, -5) uu (-2, -1)uu (-2, -1) uu (3, 4)` Answer :A::B

Discussion

1047.	Find the derivative of (x+1)/(x-1)
Answer» ANSWER :`(-2)/((x-1)^(2))`

Discussion

1048.	If a= 3 , b =4 andsin A = 3//4 ,find B
Answer» ANSWER :` 90 ^(@) `

Discussion

1049.	Findn^(th) term of the series 1+(1+2)+(1+2+3)+....Find the sum to n terms of the series
Answer» SOLUTION :`n/6(n+1)(n+2)`

Discussion

1050.	Choose a new origin so thatthe equation 2x^(2) + 7y^(2) + 8x - 14y + 15 0 may be translated to the form in which the first degree terms be missing. Find the transformedequation also .
Answer» Answer :we get a = 2, B = 7, g = 4, F = - 7

Discussion

Explore topic-wise InterviewSolutions in .

From the following data compose price index by applying weighted average of price relatives method using arithmetic means:

If the slope of one of the lines represented by ax^(2) - 6xy + y^(2) = 0 is the square of the other, then the value of a is

If a_(ij)=(2i-j)^(2),find A_(32).

Statement -1 : For all n in N, x^( 2n+1) +y^(2n+1) is divisible by x+y Statement-2: If n in N, n^(3) + 2n is divisible by 6 Which of the above statement is true :

Compute :lim_(xto0)(e^(3x)-1)/(x)

"cosec" 10^(@) - sqrt(3)" sec" 10^(@) =

If sqrt(u/v)+sqrt(v/u)=6 , then (du)/(dv) =

If the projection of a line of length d on the coordinate axes ared_(1),d_(2),d_(3) " respectively then, prove that" d^(2) = (d_(1)^(2)+d_(2)^(2)+d_(3)^(2))/2

If A = (1,-1,0), B=(1,2,1), C=(2,3,0) andD=(0,1,t). Be four points. If the projection of bar(AB) " on " bar(CD)" is equal to that of " bar(CD) " on " bar(AB), then find t.

If Pis a point on the altitude AD of the triangle ABC such that angleCBP =B//3, then AP is equal to

Write theconverse of the contrapositive of p implies q .

Identify the Quantifiers in the following statements: There exists a real number x such that x^(2)+1=0.

Differentiate the following functions: 15. sqrt ( 3 x +2).

If xsqrt(1+y)+ysqrt(1+x)=0 then (dy)/(dx)=

Equation of the line passing through (1, 2) and parallel to the line y=3x -1 is

Statement-I: Periodof [x]where[.]representstheintegral partof x is 1, Statement-II: Periodof x-[x]where [.] representsthe integralpart xis 1. Statement-III : A realfunction f : A toB issuch thatf(a+x) = f(x ) AA a E RthenF iscalledperiodicfunction.Whichof theabovestate mentsis correct.

The weightsof a coffeein 70jars are shownin the following table . .Determine variance and standard deviation of the above distribution.

If (1+x^2)^2(1+x)^n =a_0+a_1x+a_2x^2____ + x^(n+4) ____

If two pairs of straight lines with combinedequations xy + 4x - 3y - 12 = 0 and xy - 3x + 4y - 12 = 0 form a square. Then, the combined equation of its diagonals is

If vec(a) is a non zero vector and vec(a).vec(b)= vec(a).vec(c ), vec(a) xx vec(b)= vec(a) xx vec(c ), then

Find the distance between each of pair of point: (-4,-2,0) and (3,3,5)

Find anle between planes bar(r ).(2bar(i)-bar(j) + 2 bar(k)) = 3, bar(r ).(3bar(i)+6bar(j) + bar(k)) = 4

Maximum value of (x+5)^(4)(13-x)^(5)is

Examine whether the following statements are true or false : phi sub {x, y, z}

A light is at the top of 64m high. A ball is dropped from the same height from a point 20 m away from the light. Assuming that the ball falls according to the law s=5t^(2), how fast is the shadowof the ball moving along the ground 2 second later?

The maximum value of f(x)=tan^(-1)(((sqrt(12)-2)x^(2))/(x^(4)+2x^(2)+3)) is

Represent the complex number sqrt3+i in the polar form.

Let f(x)=a_(5)x^(5)+a_(4)x^(4)+a_(3)x^(3)+a_(2)x^(2)+a_(1)x, wherea_(i) s are real and f(x) =0 has a positive root alpha_(0) . Then

Centriod of triangle formed by lines 8x^(2)-14xy+5y^(2)=0, x-2y+3=0 is

If tantheta=(a)/(b), then bcos2theta+asin2theta is equal to

Find the angle between the planes x+2y+2z-5=0 and 3x+3y+2z-8=0.

Equation of a bisector of the angle between the line y-b=(2m)/(1-m^2)(x-a) and y-b=(2m')/(1-m^2)(x-a) is

If |cos theta (sin theta + sqrt( sin ^(2) theta + sin ^(2) alpha ) )| le kthen the value of k is

f(x) is a polynomial funciton, f : R to R, such that f(2x) = f'(x) f^('')(x) The value of f(3) is

A container in the shape of an inverted cone has height 12 cm and radius 6cm at the top. If it is filled with water at the rate of 12cm^(3)//sec, what is the rate of change in the rate of change in the height of water level when the tank is filled 8 cm?

Intersecting the y-axis at a distance of 2 units above the origin and making an angle of﻿ 30^(@) with positive direction of the x-axis.

If A=[(1,2-3i,3+4i),(2+3i,0,4-5i),(3-4i,4+5i,2)], then show that A is hermitian matrix.

If the system of equations 2x+3ky+(3k+4)z=0,x+(k+4)y+(4k+2)z=0,x+2(k+4)y+(3k+4)z=0 has non trivial solution then K =

If A and B are two eventswithP(A) = (1)/(4), P(A//B) = (1)/(4) and P(B//A) = (1)/(2)then

A line L cuts the sides AB, BC of Delta ABC in theratio 2:5, 7:4 respectively then the line L cuts CA in the ratio

The sum of 20 observations of the deviation from 30 is 20. Their mean is

Find the derivative of the function (sin x )/( 1+ cos x)

If f(x + y) = f(x) f(y) AA x, yand f(5) = 2,f'(0) = 3 then f'(5) =

Distance between two foci is 8 unit, distance between two directrix is 18 Obtain equation of ellipse satisfying given conditions unit and X-axis as major axis.

If f(x)=((x-3)(x+2)(x+5))/((x+1)(x-7))

Find the derivative of (x+1)/(x-1)

If a= 3 , b =4 andsin A = 3//4 ,find B

Findn^(th) term of the series 1+(1+2)+(1+2+3)+....Find the sum to n terms of the series

Choose a new origin so thatthe equation 2x^(2) + 7y^(2) + 8x - 14y + 15 0 may be translated to the form in which the first degree terms be missing. Find the transformedequation also .

If (1+x^2)^2(1+x)^n =a_0+a_1x+a_2x^2 + x^(n+4)

Intersecting the y-axis at a distance of 2 units above the origin and making an angle of 30^(@) with positive direction of the x-axis.