14949 + Interview Questions in Maths in Class 11 Page 206 InterviewSolution

10251.	If sum_(r=1)^(n) a_(r) = (n (n+1)(n+2) )/( 6)AA n ge 1, then Lt_(n to oo) sum_(r=1)^(n) (1)/( a_r)=
Answer» `1` `3//2` `2` `3` ANSWER :C

Discussion

10252.	i) (costheta-sintheta)/(costheta+sintheta)=tan(pi/4-theta)=cot(pi/4+theta)=sqrt((1-sin2theta)/(1+sin2theta)) ii) (costheta+sintheta)/(costheta-sintheta)=tan(pi/4+theta)=cot(pi/4-theta)=sqrt((1+sin2theta)/(1-sin2theta))
Answer» ANSWER :(i)`= TAN (pi/4 -THETA)` (II) `COT (pi/4 +theta)`

Discussion

10253.	If (2,5,1) and (9,10,4) are ends of diagonal of a rectangular parallelepiped with its faces parallel to coordintates planes thenlengths of its edges are
Answer» 11,15,5 7,5,3 7,3,3 5,5,4 Answer :B

Discussion

10254.	Find the sum upto 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 :527

Discussion

10255.	The values of x for which the angle between the vectors bara = xbari -3barj-bark and 2xbari+xbarj-bark is acute, and the angle between the vector barb and the axis of ordinates is obtuse, are
Answer» `XGT0` `XLT0` x=0 `XGE0` ANSWER :B

Discussion

10256.	Find approximate value of cos(60^(@)1^(1))
Answer» ANSWER :0.4987

Discussion

10257.	A rod AB of length 30 cm moves such that its ends always touching the co-ordinate axes. Determine the locus of a point C of the rod if AC : BC = 2 : 1
Answer» ANSWER :`4X^(2)+y^(2)=400`

Discussion

10258.	The variance of observations 3,4,5,8 is
Answer» ANSWER :3.5

Discussion

10259.	If f: R rarr Rsuch that f(x)=ax+b, a != 0 andthe equation f(x)=f^(-1)(x) is satisfied by
Answer» `a=2, B = -1` `a = - 1, b in R` `a=1, b in R` `a = 1, b = -1` ANSWER :B

Discussion

10260.	Match from list I to list II
Answer» C, a, B, d a, c, b,d a, c, d, b c, a, d,b Answer :D

Discussion

10261.	The pth term of an A.P. is q and the qth term is p, show that the mth term is p + q -m.
Answer» ANSWER :C

Discussion

10262.	If the straight line ax+cy=2b, where a,b,c gt 0, makes a triangle of area 2 sq. units with the coordinate axes, then
Answer» a,B,C are in GP a,-b,c are in GP a, 2B,c are in GP a,-2b,c are in GP Answer :A

Discussion

10263.	The shortest distance betweenthe lines vecr = (2 veci -vecj - veck) + lamda ( 2 veci + vecj + 2 veck) and vecr = (veci + 2 vecj + veck) + mu ( veci - vecj + veck)is
Answer» `3//sqrt2` `3sqrt2` `2//sqrt3` `sqrt2//3` ANSWER :A

Discussion

10264.	Differentiate, f(x) = ax^(2) + (b)/(x) with respect to 'x' using first principle.
Answer» ANSWER :`2ax - (B)/(X^(2))`

Discussion

10265.	If (1+x^(2))^(2)(1+x)^(n)=a_(0)+a_(1)x+a_(2)x^(2)+…..+x^(n+4) and if a_(0), a_(1), a_(2) are in AP, then n is ………………
Answer» 1 2 3 4 Answer :B::C

Discussion

10266.	The period of function 2^({x})+sin pi x + 3^({x//2})+ cos 2 pi x ( where {x} denote the fractional part of x) is
Answer» 2 1 3 4 Answer :A

Discussion

10267.	Find the area of the parallelogram having 3bar(i)- bar(k) and 2bar(i)- 3bar(j) as adjacent sides
Answer» ANSWER :`sqrt94` SQ UNITS.

Discussion

10268.	Heights (in cm) of a sample of 12 fathers and their oldest sons are given below : Find Karl Pearson's correlation coefficient.
Answer» ANSWER :`0.7`

Discussion

10269.	If f(x) and g (x) are two positive and increasing funcreasing functions , then which of the following is not always true ?
Answer» `[F(x)]^(G(x))` is ALWAYS INCREASING. `[f(x)]^(g(x))` is decreasing , when `f(x)lt1`. If `[f(x)]^(g(x))` is increasing then `f(x)gt1`. If `f(x)gt1`, then `[f(x)gt1` , then `[f(x)]^(g(x))` is increasing . ANSWER :A::B::C

Discussion

10270.	From a point E on the horizontal due to east of a tree, the top of the tree makes an angle of elevation 60^(@).From a point S on thehorizsontal due west of the tree the same top makes an angle of elevation 30^(@). The angle of elevation made by the top of the tree at the mid point of ES is
Answer» `30^(@)` `60^(@)` `90^(@)` `40^(@)` ANSWER :B

Discussion

10271.	In triangle ABC, D is mid point of BC, if 'AD' is perpendicular to 'AC then cos A cos C
Answer» `(2(c^(2)-a^(2)))/(3ac)` `(c^(2)-a^(2))/(2ac)` `(c^(2)-a^(2))/(AC)` `(c^(2)+a^(2))/(2ac)` ANSWER :B

Discussion

10272.	Find the equation of the bisector of the acute angle between the lines 3x-4y+7=0,12x+5y-2=0
Answer» ANSWER :11x-3y+9=0

Discussion

10273.	If AsubBthen A - B= …….
Answer» ANSWER :`PHI`

Discussion

10274.	If \|bar(a)\| = 2, \|bar(b)\| = 3, \|bar(c )\| = 4 and each of bar(a), bar(b) , bar(c ) is perpendicular to the sum of the other two vectors, then find the magnitude of bar(a) + bar(b) + bar(c ).
Answer» ANSWER :`sqrt29`

Discussion

10275.	If f: R rarr R, f(x)= (4^(x))/(4^(x)+ 2) then,
Answer» `f(X)= f(1-x)` `f(x)+ f(1-x) = 0` `f(x) + f(1-x)= 1` `f(x)+ f(x-1)= 1` Answer :C

Discussion

10276.	Consider the equation int_(theta) ^(x) ( t ^(2) - 8 t + 13) dt = x sin (a / x)The number of real values of x for which the equation has solution is
Answer» 1 2 3 infinit Answer :A

Discussion

10277.	Solve the following equations : 4x^(2)+1=0
Answer» ANSWER :`(1)/(2)I,-(1)/(2)i`

Discussion

10278.	Find the sum of n terms of each of the following 1^(3) + 4^(3) + 7^(3)+……..
Answer» ANSWER :`(n)/(4) (27n^(3)-18n^(2)-9n+4)`

Discussion

10279.	A number is chosen at random from the numbers 20 to 50. What is the probability that the number chosen is a multiple of 3 or 5 or 7 ?
Answer» ANSWER :`(19)/(30)`

Discussion

10280.	The x co-ordinate of the incentre of the triangle that has the co-ordinates of mid points of its sides as (0, 1) (1, 1) (1, 0) is
Answer» `2+sqrt(2)` `2-sqrt(2)` `1+sqrt(2)` `1-sqrt(2)` ANSWER :B

Discussion

10281.	Ifangle C = 90 ^(@)," then "2(r + R) =
Answer» ` a-B` ` a+b ` ` 2( a+ b) ` ` 2(a-b)` ANSWER :B

Discussion

10282.	Find the standard deviation of the first five even natural numbers.
Answer» ANSWER :2.83 to 2DP.

Discussion

10283.	If two sides of triangle are given by x^(2)-xy-6y^(2)=0 and the centroid is ((11)/(3),-1) then equation of third side is
Answer» `x+y=8` `x+y=4` `3x+3y=4` `2x+y=5` ANSWER :A

Discussion

10284.	Differentiate the following functions w.r.t. x: sin (5x +9)
Answer» ANSWER :`5 COS (5X +9)`

Discussion

10285.	Find the slope of the lines : Passing through the points (3, - 2) " and " (3, 4)
Answer» ANSWER :`6/0`

Discussion

10286.	How many words can be formed out of the letters of the word 'ARTICLE' so that vowels may occupy even places ?
Answer» 144 48 36 120 Answer :A

Discussion

10287.	A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has (i) no girl ? (ii) at least one boy and one girl ? (iii) at least 3 girls ?
Answer» ANSWER :(i) 21 (ii) 441 (iii) 91

Discussion

10288.	Number of roots of cos^(2) x + (sqrt(3 + 1))/( 2) si x - (sqrt( 3))/( 4) - 1= 0which liein the interval [ - pi, pi] is
Answer» 2 4 6 8 Answer :B

Discussion

10289.	For the data given below, compute index numbers for various years by taking 1992 to 1994 as base period.
Answer» ANSWER :`(##SCH_OPM_ISC_MAT_XI_C30_SLV_005_A01##)`

Discussion

10290.	How many strings are there using the letters of the word INTERMEDIATE, ifQ No two vowels are together.
Answer» ANSWER :43200

Discussion

10291.	cos^(6) A + sin^(6) A = 1 - k sin^2 (2A) implies k =
Answer» `1/4` `1/2` `3/4` 1 Answer :C

Discussion

10292.	Prove that :(i) ""^(n)P_(r )=""^(n-1)P_(r+r)""^(n-1)P_(r-1)(ii)""^(n)P_(r )=n ""^(n-1)P_(r-1)(iii)""^(n)P_(r )=(n-r+1)""^(n)P_(r-1),for all natural numbers n and r for which the symbols are defined.
Answer» <P> ANSWER :`""^(N)P_(R )`

Discussion

10293.	Let A and B are two symmetric matrices of same order.Then which one of the following statement is not true?
Answer»

Discussion

10294.	A plane meets the coordinate axes at A,B,C so that the centroid of the triangle ABC is (1,2,4) Then the equation of the plane is :
Answer» `x + 2y + 4z =12 ` `4X + 2y + z=12 ` `x + 2y + 4z =3` `4x + 2y + z=3` Answer :B

Discussion

10295.	Ratio of area of the incircle to the area of triangle ABC
Answer» `(PI)/(sinA sinB sinC)` `(pi)/("cot"(A)/(2)"cot"(B)/(2)"cot"(C)/(2))` `(pi)/("cot"(A)/(2)"cot"(B)/(2)"cot"(C)/(2))` `(pi)/(COSA COS B cosC)` Answer :B

Discussion

10296.	If (1, a), (3, 9a), (4, b), (6, 18) are collinear, then (a, (b)/(a))=
Answer» (6, 13) `((6)/(7), 13)` `((6)/(7), (13)/(7))` `(21, 13)` Answer :B

Discussion

10297.	Find the cartesian equation of the curve whose parametric equations are : x=t, y=t^(2)
Answer» ANSWER :`X^(2)=y`

Discussion

10298.	Determine k so that k + 2, 4k - 6 and 3k - 2 are three consecutive terms of an A.P
Answer» ANSWER :K =3

Discussion

10299.	The number of values ofx for which sin^(-1)(x^(2)-(x^(4))/3+(x^(6))/9………)+cos^(-1)(x^(4)-(x^(8))/3+(x^(12))/9………)=(pi)/2, where 0le\|x\|ltsqrt(3), is
Answer» ANSWER :3

Discussion

10300.	If bar(r)=sbar(a)+tbar(b) represents a line passing through the points bar(a), bar(b) then
Answer» s = t `s+t=0` `s+t=1` `s+t=-1` ANSWER :C

Discussion

Explore topic-wise InterviewSolutions in .

If sum_(r=1)^(n) a_(r) = (n (n+1)(n+2) )/( 6)AA n ge 1, then Lt_(n to oo) sum_(r=1)^(n) (1)/( a_r)=

i) (costheta-sintheta)/(costheta+sintheta)=tan(pi/4-theta)=cot(pi/4+theta)=sqrt((1-sin2theta)/(1+sin2theta)) ii) (costheta+sintheta)/(costheta-sintheta)=tan(pi/4+theta)=cot(pi/4-theta)=sqrt((1+sin2theta)/(1-sin2theta))

If (2,5,1) and (9,10,4) are ends of diagonal of a rectangular parallelepiped with its faces parallel to coordintates planes thenlengths of its edges are

Find the sum upto 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 values of x for which the angle between the vectors bara = xbari -3barj-bark and 2xbari+xbarj-bark is acute, and the angle between the vector barb and the axis of ordinates is obtuse, are

Find approximate value of cos(60^(@)1^(1))

A rod AB of length 30 cm moves such that its ends always touching the co-ordinate axes. Determine the locus of a point C of the rod if AC : BC = 2 : 1

The variance of observations 3,4,5,8 is

If f: R rarr Rsuch that f(x)=ax+b, a != 0 andthe equation f(x)=f^(-1)(x) is satisfied by

Match from list I to list II

The pth term of an A.P. is q and the qth term is p, show that the mth term is p + q -m.

If the straight line ax+cy=2b, where a,b,c gt 0, makes a triangle of area 2 sq. units with the coordinate axes, then

The shortest distance betweenthe lines vecr = (2 veci -vecj - veck) + lamda ( 2 veci + vecj + 2 veck) and vecr = (veci + 2 vecj + veck) + mu ( veci - vecj + veck)is

Differentiate, f(x) = ax^(2) + (b)/(x) with respect to 'x' using first principle.

If (1+x^(2))^(2)(1+x)^(n)=a_(0)+a_(1)x+a_(2)x^(2)+…..+x^(n+4) and if a_(0), a_(1), a_(2) are in AP, then n is ………………

The period of function 2^({x})+sin pi x + 3^({x//2})+ cos 2 pi x ( where {x} denote the fractional part of x) is

Find the area of the parallelogram having 3bar(i)- bar(k) and 2bar(i)- 3bar(j) as adjacent sides

Heights (in cm) of a sample of 12 fathers and their oldest sons are given below : Find Karl Pearson's correlation coefficient.

If f(x) and g (x) are two positive and increasing funcreasing functions , then which of the following is not always true ?

From a point E on the horizontal due to east of a tree, the top of the tree makes an angle of elevation 60^(@).From a point S on thehorizsontal due west of the tree the same top makes an angle of elevation 30^(@). The angle of elevation made by the top of the tree at the mid point of ES is

In triangle ABC, D is mid point of BC, if 'AD' is perpendicular to 'AC then cos A cos C

Find the equation of the bisector of the acute angle between the lines 3x-4y+7=0,12x+5y-2=0

If AsubBthen A - B= …….

If |bar(a)| = 2, |bar(b)| = 3, |bar(c )| = 4 and each of bar(a), bar(b) , bar(c ) is perpendicular to the sum of the other two vectors, then find the magnitude of bar(a) + bar(b) + bar(c ).

If f: R rarr R, f(x)= (4^(x))/(4^(x)+ 2) then,

Consider the equation int_(theta) ^(x) ( t ^(2) - 8 t + 13) dt = x sin (a / x)The number of real values of x for which the equation has solution is

Solve the following equations : 4x^(2)+1=0

Find the sum of n terms of each of the following 1^(3) + 4^(3) + 7^(3)+……..

A number is chosen at random from the numbers 20 to 50. What is the probability that the number chosen is a multiple of 3 or 5 or 7 ?

The x co-ordinate of the incentre of the triangle that has the co-ordinates of mid points of its sides as (0, 1) (1, 1) (1, 0) is

Ifangle C = 90 ^(@)," then "2(r + R) =

Find the standard deviation of the first five even natural numbers.

If two sides of triangle are given by x^(2)-xy-6y^(2)=0 and the centroid is ((11)/(3),-1) then equation of third side is

Differentiate the following functions w.r.t. x: sin (5x +9)

Find the slope of the lines : Passing through the points (3, - 2) " and " (3, 4)

How many words can be formed out of the letters of the word 'ARTICLE' so that vowels may occupy even places ?

A group consists of 4 girls and 7 boys. In how many ways can a team of﻿ 5 members be selected if the team has (i) no girl ? (ii) at least one boy and one girl ?﻿ (iii) at least 3 girls ?﻿

Number of roots of cos^(2) x + (sqrt(3 + 1))/( 2) si x - (sqrt( 3))/( 4) - 1= 0which liein the interval [ - pi, pi] is

For the data given below, compute index numbers for various years by taking 1992 to 1994 as base period.

How many strings are there using the letters of the word INTERMEDIATE, ifQ No two vowels are together.

cos^(6) A + sin^(6) A = 1 - k sin^2 (2A) implies k =

Prove that :(i) ""^(n)P_(r )=""^(n-1)P_(r+r)""^(n-1)P_(r-1)(ii)""^(n)P_(r )=n ""^(n-1)P_(r-1)(iii)""^(n)P_(r )=(n-r+1)""^(n)P_(r-1),for all natural numbers n and r for which the symbols are defined.

Let A and B are two symmetric matrices of same order.Then which one of the following statement is not true?

A plane meets the coordinate axes at A,B,C so that the centroid of the triangle ABC is (1,2,4) Then the equation of the plane is :

Ratio of area of the incircle to the area of triangle ABC

If (1, a), (3, 9a), (4, b), (6, 18) are collinear, then (a, (b)/(a))=

Find the cartesian equation of the curve whose parametric equations are : x=t, y=t^(2)

Determine k so that k + 2, 4k - 6 and 3k - 2 are three consecutive terms of an A.P

The number of values ofx for which sin^(-1)(x^(2)-(x^(4))/3+(x^(6))/9………)+cos^(-1)(x^(4)-(x^(8))/3+(x^(12))/9………)=(pi)/2, where 0le|x|ltsqrt(3), is

If bar(r)=sbar(a)+tbar(b) represents a line passing through the points bar(a), bar(b) then

A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has (i) no girl ? (ii) at least one boy and one girl ? (iii) at least 3 girls ?