14949 + Interview Questions in Maths in Class 11 Page 113 InterviewSolution

5601.	If (2,1,3), (3,2,5),(1,2,4) are the mid points of the sides BC,CA,AB, of DeltaABC respectively, then the vertex A is
Answer» (2,3,6) (0,2,2) (4,1,4) (2,5,4) ANSWER :A

Discussion

5602.	(a+2)sinalpha+(2a-1)cosalpha=(2a+1)iftan alpha is
Answer» `3//4` `4//3` `2A//(a^(2)+1)` `2a//(a^(2)-1)` ANSWER :B::D

Discussion

5603.	Draw the graphs of the following : y = 2x +1 if-2,2
Answer» ANSWER : `(##AKS_ELT_AI_MAT_XI_VIB_P02_C01_E01_017_A01##)`

Discussion

5604.	The range of the function f(x)=(x^(2)+x+2)/(x^(2)+x+1), x in R , is
Answer» `(1, OO)` `(1, 11//7)` `(1, 7/3]` `(1, 7//5)` ANSWER :C

Discussion

5605.	Let A and B denote the statements A:cosalpha+cosbeta+cosgamma=0""B:sinalpha+sinbeta+singamma=0 If cos(beta-gamma)+cos(gamma-alpha)+cos(alpha+beta)=-(3)/(2), then :
Answer» A is TRUE and B is FALSE A is false and B is true Both A and B are true Both A and B are false. ANSWER :C

Discussion

5606.	[bari-barjbark]+[-bari-barjbark]+[bari-barkbark]=
Answer» 0 1 `-1` 2 Answer :A

Discussion

5607.	If x^2+alphay^2+2betay=a^2 represents a pair of perpendicular lines, then beta=
Answer» a 2a 3a 4a Answer :A

Discussion

5608.	If \|z\| = 2 and arg z = (pi)/4 then z = ........
Answer» ANSWER :`SQRT2 +SQRT2I`

Discussion

5609.	Bhargav saves Rs 50 in first week. In each week after the first, he saved Rs 17.50 more than he did in the preceeding week. His savings at n^(th) week is Rs 207.50. Find n and also find his total savings.
Answer» ANSWER :n=10, RS 1287.50

Discussion

5610.	Let A={1,2,3,4,5,6}. Define a relation R form A to A by R= {(x,y) : y=x+1} (i) Depict this relation using an arrow diagram. (ii) Write down the domain, codmain and range of R.
Answer» ANSWER :{(1,2),(2,3),(3,4),(4,5),(5,6)}

Discussion

5611.	Find the radius of the circle in which a central angle of 60^(@) intercepts an arc of length 37.4 cm (use pi=22/7)
Answer» ANSWER :`35.7 CM`

Discussion

5612.	Let vecr=xveci+yvecj+zveck be the position vector of any point and letalpha,beta,gamma be the direction angle of vecr then sin^(2)alpha+sin^(2)beta+sin^(2)gamma is:
Answer» -2 0 2 1 Answer :C

Discussion

5613.	if f(x)=(1-cos ax)/(x sin x)" for "x ne 0, f(0)=1//2 is continuous at x=0 then a=
Answer» ANSWER :k=-2

Discussion

5614.	If exp [(sin^(2)x+sin^(4)x+sin^(6)x+……………."to"oo)"In"2] is a root of the equation y^(2)-9y+8=0 then the value of (cosx)/(cosx+sinx),0ltxlt(pi)/2 is
Answer» `SQRT(2)-1` `(sqrt(2)-1)/2` `(sqrt(3)-1)/2` `(sqrt(3),-sqrt(2))/2` ANSWER :C

Discussion

5615.	Let (x,y) be such that sin^(-1)(ax)+cos^(-1)(y)+cos^(-1)(bxy)=pi//2. Match the statements in column I which statements in column II.
Answer» ANSWER :A-p;B-q;C-p;D-s

Discussion

5616.	An urn contains 5 red and 5 black balls. A ball is drawn at random, its colour is noted and is returned to the urn. Moreover, 2 additional balls of the colour drawn are put in the urn and then a ball is drawn at random. The probability that the second ball drawn is red will be:
Answer» `(5)/(12)` `(1)/(2)` `(7)/(12)` `(1)/(4)` ANSWER :B

Discussion

5617.	How many words, with or without meaning, each of 2 vowels and 3 consonants can be formed from the letters of the word DAUGHTER ?
Answer» ANSWER :3600

Discussion

5618.	What is the periodof thefunctionsin^(4)x+cos^(4) x.
Answer» `2PI` `PI` `pi/2` `pi/4` ANSWER :C

Discussion

5619.	Findthe ratio in which the YZplane divides the linesegementformed by joining the points (-2,4,7) and (3,-5,8)
Answer» ANSWER :`2:3`

Discussion

5620.	At what distance does a man, whose hieght is2 metres, subtendan angle of 10 ?
Answer» ANSWER :687-3 METRES (NEARLY).

Discussion

5621.	The value ofcos""(pi)/(7)+cos""(2pi)/(7)cos""(3pi)/(7)+cos""(4pi)/(7)+cos""(5pi)/(7)+cos""(6pi)/(7)+cos""(7pi)/(7) is
Answer» 1 -1 0 none of these Answer :B

Discussion

5622.	A card is drawn from a deck of 52 cards. Find the probability of getting a king or a heart of a red card.
Answer» ANSWER :`=(7)/(13)`

Discussion

5623.	Sin^(-1)x+sin^(-1)(1-x)=cos^(-1)ximpliesx in
Answer» `{1,0}` `{-1,1}` `{0,1/2}` `{2,0}` ANSWER :C

Discussion

5624.	Show that Lim_( xto 2) (\|x-2\|)/(x-2) does not exist .
Answer» ANSWER :L.H.E = - R.H.L = 1 Since L.H.L `!= ` R.H.L , THEREFORE ,limit does not EXIST .

Discussion

5625.	Find the derivative of x^(n)+ax^(n-1)+a^(2)x^(n-2)+…+a^(n-1)x+a^(n)for some fixed real number a.
Answer» ANSWER :`NX^(n-1)+a(n-1)X^(n-2)+a^(2).(n-2)x^(n-3)+………+a^(n-1)`

Discussion

5626.	Find the values of x for which the functions f(x)= 3x^(2)-1 and g(x)= 3 + x are equal
Answer» ANSWER :`-1, (4)/(3)`

Discussion

5627.	The sides of a triangles arex^(2) +3x + 3, 2x+ 3 and x^(2)+ 2xthen the greatestangle of the triangleis
Answer» `120 ^(@) ` ` 135^(@) ` ` 150 ^(@) ` ` 105 ^(@) ` ANSWER :A

Discussion

5628.	Theperiodof \|cot x\| +\|cos x\| + \| tan x\|+ \|sin x \|is
Answer» `PI` `(pi)/(2)` `2PI` `(pi)/(4)` Answer :B

Discussion

5629.	1-(sin^(2) theta)/(1+cos theta) + (1+cos theta)/(sin theta) - (sin theta)/(1-cos theta) - (1)/(sec theta)=
Answer» `SIN THETA` `COS theta` 0 1 Answer :C

Discussion

5630.	A line perpendicular to the line segment joining the points (1,0) and (2,3) divides it in the ratio 1 : n. Find the equation of the line.
Answer» ANSWER :`(1 + n) X + 3 (1 + n) y = n + 11`

Discussion

5631.	Find the co-ordinates of the points lying on parabola x^(2)=12y whose focal distance is 15.
Answer» ANSWER :(12, 12), (-12,-4)

Discussion

5632.	A point R with x-coordinate 4 lies on the line segment joining the points P(2, -3, 4) and Q(8, 0, 10). Find the coordinates of the point R.
Answer» Answer :COORDINATE of R = (4, -2, 6)

Discussion

5633.	For the equation 1 - 2 x - x^(2) = tan^(2) (x + y) + cot ^(2) (x + y)
Answer» exactly one value of X exists exactly two values of x exists `y = - 1 + n pi + pi //4, n in Z` `y = 1 + n pi + pi//4, n in Z` ANSWER :A

Discussion

5634.	If alpha, beta are complementary angles, sin alpha = (3)/(5) then cos alpha cos beta-sin alpha sin beta =
Answer» 1 2 `(4)/(5)` 0 Answer :D

Discussion

5635.	If f(x) = x^3 + x^2 f'(1) + xf^('')(2) + f^(''')(3), AA x in R then
Answer» `F(0) + f(2) = f(1)` `f(0) + f(3) = 0` `f(0) + f(3) = f(2)` `f(0) = f(3)` Answer :A::B

Discussion

5636.	Show that A ∩ B = A ∩ C need not imply B = C.
Answer» ANSWER :`B= C`.

Discussion

5637.	(d)/(dx) {Sin ^(-1) ((3x)/(2) - (x ^(3))/(2))}=
Answer» `3/(SQRT(1-x^2))` `1/(sqrt(4-x^2))` `3/(sqrt(4-x^2))` `(-3)/(sqrt(1-x^2))` ANSWER :C

Discussion

5638.	If 2Sin^(-1)x=Sin^(-1)2xsqrt(1-x^(2)) is valid find the interval in which x lies.
Answer» ANSWER :`[(-1)/(SQRT(2)),1/(sqrt(2))]`

Discussion

5639.	IF the angles of a triangle are in the ratio 2:3:5, then the ratio of the greatest side to the least side is
Answer» ` 2: SQRT(10 - 2sqrt5)` ` 4: sqrt ( 10 -2 sqrt5) ` ` 2: sqrt ( 10 + 2sqrt5) ` ` 4:sqrt( 10 + 2sqrt5) ` Answer :B

Discussion

5640.	Express tan x as quotient of two trigonometric functions
Answer» SOLUTION :`TAN X = (SIN x)/(COS x)`

Discussion

5641.	Find the values of cos(2cos^(-1)x+sin^(-1)x) at x = 1/5, where 0 le cos^(-1)x le pi and -pi//2 le sin^(-1)x le pi//2.
Answer» `(2sqrt(6))/5` `-(2sqrt(6))/5` `SQRT(6)/5` `-sqrt(6)/5` ANSWER :B

Discussion

5642.	Assertion : If 0ltxlt(pi)/2 then sin^(-1)(cosx)+cos^(-1)(sinx)=pi-2x Reason : cos^(-1)x=(pi)/2-sin^(-1)x,AA x in [-1,1]
Answer» Both A and R are true and R is correct explanation of A Both A and R are true and R is not correct explanation of A A is true, R is FALSE A is false but R is true Answer :A

Discussion

5643.	If(x)/(a) cos theta + (y)/(b) sin theta = 1 , (x)/(a) sin theta - (y)/(b) cos theta =1then
Answer» 1 -1 2 3 Answer :C

Discussion

5644.	Solve the following equations and write general solutions tan theta + 3 cot theta = 5 sec theta
Answer» Answer :`NPI + (-1)^(N)(PI)/(6)`

Discussion

5645.	Evaluate the following limits : Lim_( x to 2) (e^(x)-e^(2))/(x-2)
Answer» ANSWER :`E^(2)`

Discussion

5646.	Let u(x) and v(x) are differentiable function such that (u(x))/(v(x))=7 . If (u'(x))/(v'(x))=p and ((u(x))/(v(x)))^'=q, then(p+q)/(p-q)=
Answer» 1 0 7 `-7` ANSWER :A

Discussion

5647.	sqrt2 + sqrt8 + sqrt18 + sqrt32 +…..up to n terms is…….
Answer» `(n(n+1))/(2)` `2N(n+1)` `(n(n+1))/(SQRT2)` 1 Answer :C

Discussion

5648.	If sinx + sin^(2) x = 1, then the value of cos^(12)x +3 cos^(10) x + 3 cos^(8) x + cos^(6) x - 2 is equal to
Answer» 0 1 -1 2 Answer :C

Discussion

5649.	Find what the following equation becomes when origin is shifted of the point (1,1). (iii) xy-x-y+1=0
Answer» Answer :New TRANSFORMED equation by shifting origin at `(1,1)` is as follows `xy=0`.

Discussion

5650.	If x,yin (0,2pi), then the number of distinct ordered pairs (x,y) satisfying the equation 9cos^(2)+sec^(2)y-6cosx-4secy+5=0 is
Answer» ANSWER :4

Discussion

Explore topic-wise InterviewSolutions in .

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

(a+2)sinalpha+(2a-1)cosalpha=(2a+1)iftan alpha is

Draw the graphs of the following : y = 2x +1 if-2,2

The range of the function f(x)=(x^(2)+x+2)/(x^(2)+x+1), x in R , is

Let A and B denote the statements A:cosalpha+cosbeta+cosgamma=0""B:sinalpha+sinbeta+singamma=0 If cos(beta-gamma)+cos(gamma-alpha)+cos(alpha+beta)=-(3)/(2), then :

[bari-barjbark]+[-bari-barjbark]+[bari-barkbark]=

If x^2+alphay^2+2betay=a^2 represents a pair of perpendicular lines, then beta=

If |z| = 2 and arg z = (pi)/4 then z = ........

Bhargav saves Rs 50 in first week. In each week after the first, he saved Rs 17.50 more than he did in the preceeding week. His savings at n^(th) week is Rs 207.50. Find n and also find his total savings.

Let A={1,2,3,4,5,6}. Define a relation R form A to A by R= {(x,y) : y=x+1} (i) Depict this relation using an arrow diagram. (ii) Write down the domain, codmain and range of R.

Find the radius of the circle in which a central angle of 60^(@) intercepts an arc of length 37.4 cm (use pi=22/7)

Let vecr=xveci+yvecj+zveck be the position vector of any point and letalpha,beta,gamma be the direction angle of vecr then sin^(2)alpha+sin^(2)beta+sin^(2)gamma is:

if f(x)=(1-cos ax)/(x sin x)" for "x ne 0, f(0)=1//2 is continuous at x=0 then a=

If exp [(sin^(2)x+sin^(4)x+sin^(6)x+……………."to"oo)"In"2] is a root of the equation y^(2)-9y+8=0 then the value of (cosx)/(cosx+sinx),0ltxlt(pi)/2 is

Let (x,y) be such that sin^(-1)(ax)+cos^(-1)(y)+cos^(-1)(bxy)=pi//2. Match the statements in column I which statements in column II.

An urn contains 5 red and 5 black balls. A ball is drawn at random, its colour is noted and is returned to the urn. Moreover, 2 additional balls of the colour drawn are put in the urn and then a ball is drawn at random. The probability that the second ball drawn is red will be:

How many words, with or without meaning, each of 2 vowels and 3 consonants﻿ can be formed from the letters of the word DAUGHTER ?﻿

What is the periodof thefunctionsin^(4)x+cos^(4) x.

Findthe ratio in which the YZplane divides the linesegementformed by joining the points (-2,4,7) and (3,-5,8)

At what distance does a man, whose hieght is2 metres, subtendan angle of 10 ?

The value ofcos""(pi)/(7)+cos""(2pi)/(7)cos""(3pi)/(7)+cos""(4pi)/(7)+cos""(5pi)/(7)+cos""(6pi)/(7)+cos""(7pi)/(7) is

A card is drawn from a deck of 52 cards. Find the probability of getting a king or a heart of a red card.

Sin^(-1)x+sin^(-1)(1-x)=cos^(-1)ximpliesx in

Show that Lim_( xto 2) (|x-2|)/(x-2) does not exist .

Find the derivative of x^(n)+ax^(n-1)+a^(2)x^(n-2)+…+a^(n-1)x+a^(n)for some fixed real number a.

Find the values of x for which the functions f(x)= 3x^(2)-1 and g(x)= 3 + x are equal

The sides of a triangles arex^(2) +3x + 3, 2x+ 3 and x^(2)+ 2xthen the greatestangle of the triangleis

Theperiodof |cot x| +|cos x| + | tan x|+ |sin x |is

1-(sin^(2) theta)/(1+cos theta) + (1+cos theta)/(sin theta) - (sin theta)/(1-cos theta) - (1)/(sec theta)=

A line perpendicular to the line segment joining the points (1,0) and (2,3) divides it in the ratio 1 : n. Find the equation of the line.

Find the co-ordinates of the points lying on parabola x^(2)=12y whose focal distance is 15.

A point R with x-coordinate 4 lies on the line segment joining the points P(2, -3, 4) and Q(8, 0, 10). Find the coordinates of the point R.

For the equation 1 - 2 x - x^(2) = tan^(2) (x + y) + cot ^(2) (x + y)

If alpha, beta are complementary angles, sin alpha = (3)/(5) then cos alpha cos beta-sin alpha sin beta =

If f(x) = x^3 + x^2 f'(1) + xf^('')(2) + f^(''')(3), AA x in R then

Show that A ∩ B = A ∩ C need not imply B = C.

(d)/(dx) {Sin ^(-1) ((3x)/(2) - (x ^(3))/(2))}=

If 2Sin^(-1)x=Sin^(-1)2xsqrt(1-x^(2)) is valid find the interval in which x lies.

IF the angles of a triangle are in the ratio 2:3:5, then the ratio of the greatest side to the least side is

Express tan x as quotient of two trigonometric functions

Find the values of cos(2cos^(-1)x+sin^(-1)x) at x = 1/5, where 0 le cos^(-1)x le pi and -pi//2 le sin^(-1)x le pi//2.

Assertion : If 0ltxlt(pi)/2 then sin^(-1)(cosx)+cos^(-1)(sinx)=pi-2x Reason : cos^(-1)x=(pi)/2-sin^(-1)x,AA x in [-1,1]

If(x)/(a) cos theta + (y)/(b) sin theta = 1 , (x)/(a) sin theta - (y)/(b) cos theta =1then

Solve the following equations and write general solutions tan theta + 3 cot theta = 5 sec theta

Evaluate the following limits : Lim_( x to 2) (e^(x)-e^(2))/(x-2)

Let u(x) and v(x) are differentiable function such that (u(x))/(v(x))=7 . If (u'(x))/(v'(x))=p and ((u(x))/(v(x)))^'=q, then(p+q)/(p-q)=

sqrt2 + sqrt8 + sqrt18 + sqrt32 +…..up to n terms is…….

If sinx + sin^(2) x = 1, then the value of cos^(12)x +3 cos^(10) x + 3 cos^(8) x + cos^(6) x - 2 is equal to

Find what the following equation becomes when origin is shifted of the point (1,1). (iii) xy-x-y+1=0

If x,yin (0,2pi), then the number of distinct ordered pairs (x,y) satisfying the equation 9cos^(2)+sec^(2)y-6cosx-4secy+5=0 is

How many words, with or without meaning, each of 2 vowels and 3 consonants can be formed from the letters of the word DAUGHTER ?