14949 + Interview Questions in Maths in Class 11 Page 44 InterviewSolution

2151.	lim_(x to (pi)/(2))([1-tan((x)/(2))][1-sinx])/([1+tan((x)/(2))][pi-2x]^(3))=
Answer» `OO` `(1)/(8)` 0 `(1)/(32)` ANSWER :D

Discussion

2152.	Consider the sets A and B of Example 12. Find A ∩ B.
Answer» ANSWER :`= {6, 8}`

Discussion

2153.	Number of solutions of the equation tan x+tan 2x +tan3x=tanx tan 2x tan 3x,x in [0,pi] ils
Answer» `(pi)/6, (2PI)/3, pi` `(pi)/3, (2pi)/3, pi` `(pi)/3, (pi)/2, 2pi` `(pi)/2, (3PI)/2, pi` Answer :B

Discussion

2154.	Let f(x) be non-constant differentiable function for all real x and f(x) = f(1-x) Then Roole's theorem is notapplicable for f(x) on
Answer» [0,1] [-1,2] [-2,3] `[0,(2)/(3)]` ANSWER :D

Discussion

2155.	From the data given below state which group is more variable A or B?
Answer» Solution :Let ASSUMED MEAN `A=45` and `h=10` For group A Variance `SIGMA^(2)=h^(2)[(sumf_(i)d_(i)^(2))/N-((sumf_(i)d_(i))/N)^(2)]` `=10^(2)[342/150-((-6)/150)^(2)]` `=100[(51300-36)/(150xx150)]` `=51264/225=227.84` For group B Variance `sigma^(2)=h^(2)[(sumf_(i)d_(i)^(2))/N-((sumf_(i)d_(i))/N)^(2)]` `=10^(2)[366/100-((-6)/150)^(2)]` `=100[(54900-36)/(150xx150)]` `=54864/225=243.84` `:.` The variance of group B is more `:.` The data of group B is more variable.

Discussion

2156.	One side of an equilateral triangle is 3x+4y=7 and its vertex is (1,2). Then the length of the side of the triangle is
Answer» `(4sqrt3)/17` `(3SQRT3)/16` `(8sqrt3)/15` `(4sqrt3)/15` Answer :B

Discussion

2157.	Point R(h,k) divides a line segment between the axes in the ratio 1:2. Find equation of the line.
Answer» ANSWER :`2KX + HY = 3KH`

Discussion

2158.	DeltaABCis formed by a (1,8,4), B (0, -11,4) and C(2,-3,1) . If D is the foot of the perpendicular from A to BC . Then the coordinates of D are
Answer» ANSWER :(4,5,-2)

Discussion

2159.	If (2,1,1) is the centroid of the triangle for which (3,2,-1) ,(2,-2,5) are two vertices then the third vertex is
Answer» (1,2,9) (-10,4,-9) (-1,-5,-2) (1,3,-1) ANSWER :B

Discussion

2160.	Find the trace of [(1,3,-5),(2,-1,5),(2,0,1)]
Answer» ANSWER :1

Discussion

2161.	If x+y+z =xyz,then sum(2x)/(1-x^(2))=
Answer» `PI((2X)/(1+x))` `Pi((2x)/(1-x))` `Pi((1+x^(2))/2)` `Pi(1-x^(2))` ANSWER :B

Discussion

2162.	If asec theta + b tan theta = c then ( theta + bsec theta)^(2) =
Answer» `a^(2) + B^(2) + C^(2)` `-a^(2) + b^(2) + c^(2)` `a^(2) - b^(2) + c^(2)` `a^(2) + b^(2) - c^(2)` ANSWER :B

Discussion

2163.	Which point lies on the origin side of the plane x-2y+2z+3=0
Answer» `(1,2,-7)` `(2,3,-2)` `(1,1,-1)` `(2,1,3)` ANSWER :D

Discussion

2164.	i) In DeltaABC, if b=17, c=11 and angleA=60^(@), find tan(B-C)/(2) ii) In DeltaABC, angleB=90^(@), then prove that: tanA/2=sqrt((b-c)/(b+c))
Answer» SOLUTION :`(3sqrt(3))/14`

Discussion

2165.	Write the negation of the following statements. p: I went to my class yesterday
Answer» <P> SOLUTION :~ p : I didnot GO to my CLASS YESTERDAY

Discussion

2166.	Statement -I: f: A to B is one -one and g: B to C is a one-one function, then gof : A to C is one-one Statement-II: If f: A to B, g : B to A are two functions such that gof=I_(A) and fog=I_(B), then f=g^(-1). Statement-III: f(x) =sec^(2)x- tan^(2)x, g(x) ="cosec"^(2)x-cot^(2)x, then f=g. Which of the above statements is/are true:
Answer» only III both I & III both I & II I, II, III Answer :C

Discussion

2167.	barixx(barixxbara)+barjxx(barjxxbara)+barkxx(barkxxbara)=
Answer» `BARA` `-bara` `-2bara` `2bara` ANSWER :C

Discussion

2168.	underset(n to oo)(Lt) (3^(3)+6^(3)+...+(3n)^(3))/(3n^(4))=
Answer» `(1)/(2)` `(9)/(4)` `(27)/(4)` `(81)/(4)` ANSWER :B

Discussion

2169.	Find the domains of the following functionsf(x) = sqrt( 4- x^(2))
Answer» ANSWER :[-2,2]

Discussion

2170.	If sin A : sin B : sin C = 3: 4: 5 thentan ""(A)/(2) : tan ""(B)/(2) : tan "" (C ) /(2)=
Answer» 2 : 3: 6 2 : 3: 5 2:3: 4 2: 3: 7 Answer :A

Discussion

2171.	A committee of 3 persons is to be constituted from a group of 2 men and 3 women. In how many ways can this be done? How many of these committees would consist of 1 man and 2 women?
Answer» ANSWER :6

Discussion

2172.	If an equation of tangent to the curve, y=cos(x+y), -1I le x le 1+pi, is x+2y=k then k is equal to :
Answer» 1 2 `(PI)/(4)` `(pi)/(2)` ANSWER :D

Discussion

2173.	Find the derivative of the function sin x (tan ^(-1) x) ^(2)
Answer» ANSWER :`cos X ( tan ^(-1) x ) ^(2) + (2 SIN x tan ^(-1)x)/( (1+ x ^(2)))`

Discussion

2174.	If x=a cos^(3) theta sin^(2) theta, y= a sin^(3) theta cos^(2) theta and ((x^(2)+y^(2))^(p))/((xy)^(q))(p, q, in N) is independent of theta, then
Answer» `4p=5q` `5p=4q` `p+q=9` `pq=20` ANSWER :A

Discussion

2175.	If f^(11)(x)lt0(gt0) on an interval (a,b) then the curve y=f(x) on this interval is convex (concave) i.e it is below (above) any of its tangent lines If f^(11)(x_(0))=0 or does not exist and the second derivative changes sign when passing through the point x_(0) then the point (x_(0),f(x))is the = point of inflection of the curve y=f(x) If y=x^(4)+x^(3)-18x^(2)+24x-12 then
Answer» `(-2,-24)` is a point of inflection `(-2,3//2)` is a point of inflection `((3)/(2),-8(1)/(16))` is a point of inflection y is convex on `((3)/(2),oo)` ANSWER :C

Discussion

2176.	If f^(11)(x)lt0(gt0) on an interval (a,b) then the curve y=f(x) on this interval is convex (concave) i.e it is below (above) any of its tangent lines If f^(11)(x_(0))=0 or does not exist and the second derivative changes sign when passing through the point x_(0) then the point (x_(0),f(x))is the = point of inflection of the curve y=f(x) If y=xsin(logx) then
Answer» y has only teo points of inflection y has only 4 points of inflection `(PI)/(4)` is the only POINT of inflection y has INFINITE number of points of inflection Answer :D

Discussion

2177.	If f^(11)(x)lt0(gt0) on an interval (a,b) then the curve y=f(x) on this interval is convex (concave) i.e it is below (above) any of its tangent lines If f^(11)(x_(0))=0 or does not exist and the second derivative changes sign when passing through the point x_(0) then the point (x_(0),f(x))is the = point of inflection of the curve y=f(x) y=x^(4)+ax^(3)+(3)/(2)x^(2)+1 is concave along the entire number scale then
Answer» `\|a\|\|ge1` `\|a\|le1` `\|a\|le2` `\|a\|gt2` ANSWER :C

Discussion

2178.	If A = {x: x in W, x lt 2}, B= {x: x in N, 1 lt x lt 5} and C= {3, 5}, then findA xx (B nn C)
Answer» ANSWER :{2, 3, 4, 5}

Discussion

2179.	If the complexnumbers sin x + I cos 2 x and cos x - I sin 2 xare conjugate to each other, then the set of
Answer» `N pi, n in Z` `(2 n + 1) (pi)/(2), n in Z` {0} `phi` Answer :D

Discussion

2180.	If D(x_(1),y_(1),z_(1)), E(x_(2),y_(2),z_(2)) and F(x_(3),y_(3),z_(3)) are the midpoints of the sides BC, CA and AB respectively of a triangle, find its vertices A, B and C.
Answer» ANSWER :`A=(x_(2)+x_(3)-x_(1),y_(2)+y_(3)-y_(1),z_(2)+z_(3)-z_(1))` `B=(x_(3)+x_(1)-x_(2),y_(3)+y_(1)-y_(2),z_(3)+z_(1)-z_(2))` `C=(x_(1)+x_(2)-x_(3),y_(1)+y_(2)-y_(3),z_(1)+z_(2)-z_(3))`

Discussion

2181.	If a^(2)+2bc,b^(2)+2ca,c^(2)+2ab are in A.P., then prove that (1)/(b-c),(1)/(c-a),(1)/(a-b) are also in A.P.
Answer» SOLUTION :N/a

Discussion

2182.	How many permutations of the letters of the word 'MADHUDANI' do not begin with M but end with I.
Answer» ANSWER :17640

Discussion

2183.	(1+ x + x^(2))^(n) = a_(0) +a_(1)x + a_(2) x^(2) +...+ a_(2n )x^(2n) , thena_(0) a_(2n) - a_(1) a_(2r+1) + a_(2) a_(2r+2) - a_(3) a_(2r+3) +...+a_(2n-2r)a_(2n)= .
Answer» 0 1 `a_(n-r)` `a_(n+r)` Solution :On EQUATING the coefficients of `x^(2N +1)` on both sides of (v) in illustration 25, we GET `a_(0) a_(2n) - a_(1) a_(2r+1) + a_(2) a_(2r+2) - a_(3) a_(2r+3) +...+a_(2n-2r)a_(n+r)`.

Discussion

2184.	An equilateral triangle has its incentre at the origin and one side as x+y-2=0.Find the vertex opposite to x+y-2=0
Answer» ANSWER :REQUIRED VERTEX.

Discussion

2185.	Determine whether p,q and "If p, then q " are true or false in each case given below : (P) 3 is a prime number
Answer» <P> ANSWER :`{:(p,Q,p =>q),(T,F,F):}`

Discussion

2186.	If y=(2x+3)/(4x+5) then find y''.
Answer» ANSWER :`(16)/((4X +5)^(3))`

Discussion

2187.	If sin^(-1)(a-a^(2)/3+a^(3)/9+…..)+cos^(-1)(1+b+b^(2)+…..)=pi/2, then
Answer» `B=(2A-3)/(3A)` `b=(3a-2)/(2a)` `a=3/(2-3b)` `a=2/(3-2b)` ANSWER :A::C

Discussion

2188.	Statement-I: If \|vec(a).vec(b)\|= \|vec(a) xx vec(b)\| then (vec(a), vec(b))= (pi)/(4) or (3pi)/(4) Statement-II: If vec(a).vec(b)= \|vec(a) xx vec(b)\| then (vec(a), vec(b))= (pi)/(4) or (3pi)/(4) Which of the above two statements are true?
Answer» only I only II both I and II neither I nor II Answer :A

Discussion

2189.	The locus of the point, the sum of the squares of whose distance from the planes x+y+z=0, x-y=0,x+y-2z=0 is 7 is
Answer» `X^(2)+y^(2)+z^(2)=7` `x^(2)+y^(2)+z^(2)=5` `x+y+z=sqrt(5)` `x^(2)+y^(2)+z^(2)=25` Answer :A

Discussion

2190.	If xcostheta=ycos(theta+120^(@))=z cos (theta+240^(@)) then xy+yz+zx=
Answer» `-1` 1 0 `3//4` ANSWER :C

Discussion

2191.	Curve having eccentricity sqrt2 is a rectangular hyperbola.
Answer» ANSWER :`SQRT2`

Discussion

2192.	Period of tan(x+4x+9x+…+ n^(2)x) is
Answer» `(2PI)/(N(n+1)(2n+1))` `(4PI)/(n(n+1)(2n+1))` `(6PI)/(n(n+1)(2n+1))` `(8pi)/(n(n+1)(2n+1))` ANSWER :C

Discussion

2193.	Find perpendicular distance from the origin of the line joining the points (cos theta, sin theta) and (cos phi, sin phi).
Answer» ANSWER :`\|COS ((PHI - THETA)/2)\|`

Discussion

2194.	The range of f(x)=sin^(-1)(sqrt(x^(2)+x+1)) is
Answer» `[0, pi/2]` `[0, pi/3]` `[pi/3, pi/2]` `[pi/6, pi/2]` ANSWER :C

Discussion

2195.	If A=340^(@) then 2 sin A//2=
Answer» `SQRT(1+sinA)+sqrt(1-sinA)` `sqrt(1+sinA)-sqrt(1-sinA)` `-sqrt(1+sinA)-sqrt(1-sinA)` `-sqrt(1+sinA)+sqrt(1-sinA)` ANSWER :D

Discussion

2196.	If the amplitude of z-2-3i " is " (pi)/(4), then find the locus of z= x+ yi
Answer» ANSWER :`x-y+ 1= 0`

Discussion

2197.	Write the ascending order of the distance between the parallel lines (A) 2x+3y+1=0, 2x+3y+14=0 (B) 3x+4y+10=0, 3x+4y+5=0 (C) x+y+1=0, x+y+3=0 (D) 2x+y+1=0, 2x+y+6=0
Answer» B,C,D,A A,B,C,D B,D,C,A B,C,A,D Answer :A

Discussion

2198.	Which of the following pairs of sets are disjoint : {2, 4, 6, 8, 10}" and "{2, 3, 5, 7, 11}
Answer» ANSWER :it is dispoint SET

Discussion

2199.	Find the bisector of the acute angle between the lines : 5x=12y+24 and 12x=5y+10
Answer» ANSWER : `x-y-2=0`

Discussion

2200.	Solve 2 cos^(2) theta+3 sin theta=0
Answer» ANSWER :`X = NPI + (-1) ^(N)`

Discussion

Explore topic-wise InterviewSolutions in .

lim_(x to (pi)/(2))([1-tan((x)/(2))][1-sinx])/([1+tan((x)/(2))][pi-2x]^(3))=

Consider the sets A and B of Example 12. Find A ∩ B.

Number of solutions of the equation tan x+tan 2x +tan3x=tanx tan 2x tan 3x,x in [0,pi] ils

Let f(x) be non-constant differentiable function for all real x and f(x) = f(1-x) Then Roole's theorem is notapplicable for f(x) on

From the data given below state which group is more variable A or B?

One side of an equilateral triangle is 3x+4y=7 and its vertex is (1,2). Then the length of the side of the triangle is

Point R(h,k) divides a line segment between the axes in the ratio 1:2. Find equation of the line.

DeltaABCis formed by a (1,8,4), B (0, -11,4) and C(2,-3,1) . If D is the foot of the perpendicular from A to BC . Then the coordinates of D are

If (2,1,1) is the centroid of the triangle for which (3,2,-1) ,(2,-2,5) are two vertices then the third vertex is

Find the trace of [(1,3,-5),(2,-1,5),(2,0,1)]

If x+y+z =xyz,then sum(2x)/(1-x^(2))=

If asec theta + b tan theta = c then ( theta + bsec theta)^(2) =

Which point lies on the origin side of the plane x-2y+2z+3=0

i) In DeltaABC, if b=17, c=11 and angleA=60^(@), find tan(B-C)/(2) ii) In DeltaABC, angleB=90^(@), then prove that: tanA/2=sqrt((b-c)/(b+c))

Write the negation of the following statements. p: I went to my class yesterday

barixx(barixxbara)+barjxx(barjxxbara)+barkxx(barkxxbara)=

underset(n to oo)(Lt) (3^(3)+6^(3)+...+(3n)^(3))/(3n^(4))=

Find the domains of the following functionsf(x) = sqrt( 4- x^(2))

If sin A : sin B : sin C = 3: 4: 5 thentan ""(A)/(2) : tan ""(B)/(2) : tan "" (C ) /(2)=

A committee of 3 persons is to be constituted from a group of 2 men and﻿ 3 women. In how many ways can this be done? How many of these committees would﻿ consist of 1 man and 2 women?﻿

If an equation of tangent to the curve, y=cos(x+y), -1I le x le 1+pi, is x+2y=k then k is equal to :

Find the derivative of the function sin x (tan ^(-1) x) ^(2)

If x=a cos^(3) theta sin^(2) theta, y= a sin^(3) theta cos^(2) theta and ((x^(2)+y^(2))^(p))/((xy)^(q))(p, q, in N) is independent of theta, then

If A = {x: x in W, x lt 2}, B= {x: x in N, 1 lt x lt 5} and C= {3, 5}, then findA xx (B nn C)

If the complexnumbers sin x + I cos 2 x and cos x - I sin 2 xare conjugate to each other, then the set of

If D(x_(1),y_(1),z_(1)), E(x_(2),y_(2),z_(2)) and F(x_(3),y_(3),z_(3)) are the midpoints of the sides BC, CA and AB respectively of a triangle, find its vertices A, B and C.

If a^(2)+2bc,b^(2)+2ca,c^(2)+2ab are in A.P., then prove that (1)/(b-c),(1)/(c-a),(1)/(a-b) are also in A.P.

How many permutations of the letters of the word 'MADHUDANI' do not begin with M but end with I.

(1+ x + x^(2))^(n) = a_(0) +a_(1)x + a_(2) x^(2) +...+ a_(2n )x^(2n) , thena_(0) a_(2n) - a_(1) a_(2r+1) + a_(2) a_(2r+2) - a_(3) a_(2r+3) +...+a_(2n-2r)a_(2n)= .

An equilateral triangle has its incentre at the origin and one side as x+y-2=0.Find the vertex opposite to x+y-2=0

Determine whether p,q and "If p, then q " are true or false in each case given below : (P) 3 is a prime number

If y=(2x+3)/(4x+5) then find y''.

If sin^(-1)(a-a^(2)/3+a^(3)/9+…..)+cos^(-1)(1+b+b^(2)+…..)=pi/2, then

Statement-I: If |vec(a).vec(b)|= |vec(a) xx vec(b)| then (vec(a), vec(b))= (pi)/(4) or (3pi)/(4) Statement-II: If vec(a).vec(b)= |vec(a) xx vec(b)| then (vec(a), vec(b))= (pi)/(4) or (3pi)/(4) Which of the above two statements are true?

The locus of the point, the sum of the squares of whose distance from the planes x+y+z=0, x-y=0,x+y-2z=0 is 7 is

If xcostheta=ycos(theta+120^(@))=z cos (theta+240^(@)) then xy+yz+zx=

Curve having eccentricity sqrt2 is a rectangular hyperbola.

Period of tan(x+4x+9x+…+ n^(2)x) is

Find perpendicular distance from the origin of the line joining the points (cos theta, sin theta) and﻿ (cos phi, sin phi).

The range of f(x)=sin^(-1)(sqrt(x^(2)+x+1)) is

If A=340^(@) then 2 sin A//2=

If the amplitude of z-2-3i " is " (pi)/(4), then find the locus of z= x+ yi

Write the ascending order of the distance between the parallel lines (A) 2x+3y+1=0, 2x+3y+14=0 (B) 3x+4y+10=0, 3x+4y+5=0 (C) x+y+1=0, x+y+3=0 (D) 2x+y+1=0, 2x+y+6=0

Which of the following pairs of sets are disjoint : {2, 4, 6, 8, 10}" and "{2, 3, 5, 7, 11}

Find the bisector of the acute angle between the lines : 5x=12y+24 and 12x=5y+10

Solve 2 cos^(2) theta+3 sin theta=0

A committee of 3 persons is to be constituted from a group of 2 men and 3 women. In how many ways can this be done? How many of these committees would consist of 1 man and 2 women?

Find perpendicular distance from the origin of the line joining the points (cos theta, sin theta) and (cos phi, sin phi).