14949 + Interview Questions in Maths in Class 11 Page 212 InterviewSolution

10551.	Let n(A) = 6 and n(B) = p . Then , the total number of non - empty relations that can bedefinedfrom A to B is
Answer» <P>`6^(P)` `N^(P+1)` `6p-1` `2^(6p-1)` ANSWER :A

Discussion

10552.	If y = cos^(-1)""(9-x^2)/(9+x^2) then y^(1)(-1) is equal to
Answer» `-3//5` `3//5` `2//7` `3//8` ANSWER :B

Discussion

10553.	Ifcosh2x = 99, then tanhx =
Answer» `(5)/(7sqrt(2))` `(7)/(5sqrt(2))` `(5sqrt(7))/(2)` `(7sqrt(5))/(2)` ANSWER :B

Discussion

10554.	The sumof the distance of the any pointon the ellripse3x^(2) + 4y^(2) = 24from itsfoxi is
Answer» 4 `4sqrt(2)` `8sqrt(2)` `2sqrt(2)` ANSWER :B

Discussion

10555.	Find the mean deviation about the median for the given data:
Answer» ANSWER :4.97

Discussion

10556.	Find the number of different 8-letter arrangements that can be made from the letters of the word DAUGHTER so thatall vowels occur together .
Answer» ANSWER :4320

Discussion

10557.	Two coins (a one rupee coin and a two rupee coin)are tossed once. Write the sample space ?
Answer» ANSWER :S = {HH. HT, TH, TT}

Discussion

10558.	If bara, barb, barc are three non-coplanar vectors, barp=(barbxxbarc)/([barabarbbarc]),barq=(barcxxbara)/([barabarbbarc]),barr=(baraxxbarb)/([barabarbbarc]) then (2bara+3barb+4barc).barp+(2barb+3barc+4bara).barq+(2barc+3bara+4barb).barr=
Answer» `-6` 6 3 `-3` ANSWER :B

Discussion

10559.	Find the number of 4 letter words, with or without meaning, which can be formed out of the letters of the word ROSE, where the repetition of the letters is not allowed.
Answer» ANSWER :24

Discussion

10560.	The maximum value of f(x) =2x^3-21x^2+36x+20 , in the interval 0 le x le 2is
Answer» 37 44 32 30 Answer :A

Discussion

10561.	Find the number of different 8-letter arrangements that can be made from the letters of the word DAUGHTER so that all vowels do not occur together.
Answer» ANSWER :36000

Discussion

10562.	If the lines x+ay=a=0, bx+y+b=0, cx+cy+1=0 (a,b,c being distinct and !=1) are concurrent, then the value of (a/(a-1)+b/(b-1)+c/(c-1)) is
Answer» `-1` 0 1 3 Answer :C

Discussion

10563.	The rate of change of area of a square plate is equal to that of the rate of change of its perimeter. Then length of the side is
Answer» 2 units 3 units 4 units 6units Answer :A

Discussion

10564.	If the angles of a triangle are in the ration 4:1:1 then the ratio of the longest side to the perimeter is
Answer» `SQRT3 : (2 + sqrt3)` `1 : 6` `1 : 2 sqrt3` `2 : 3` ANSWER :A

Discussion

10565.	The smallest angle of the triangle whose sides are 6+sqrt12,sqrt48,sqrt24 is
Answer» `pi//3` `pi//4` `pi//6` `2pi//3` ANSWER :C

Discussion

10566.	Given r=0.8,Sigma xy=60,sigma_(y)=2.5 and Sigmax^(2)=90, find the number of items, if x and y are deviation from their respective means.
Answer» ANSWER :10

Discussion

10567.	sec ^(2) 2x =1-tan 2x
Answer» ANSWER :`X = (npi)/( 2), or (npi)/(2) + ( npi)/(2) + (3PI)/(8), N in Z`

Discussion

10568.	Let f_(k)(x)=(1)/(k)(sin^(k)x+cos^(k)x) wherex in R and k ge1, then f_(4)(x)-f_(6)(x) equals
Answer» `(1)/(6)` `(1)/(3)` `(1)/(4)` `(1)/(12)` ANSWER :D

Discussion

10569.	Solve sin x + sqrt(3) cos x = sqrt(2).
Answer» ANSWER :`{2NPI+(5PI)/(12)}or{2npi-(PI)/(12)}`

Discussion

10570.	If the transformed equation of curve is 17X^(2) - 16XY + 17y^(2) = 225 when the axes are rotated through an angle 45^(0), then the original equation of the curve is
Answer» ANSWER :`25 X^(2) + 9y^(2) = 225`

Discussion

10571.	(sinx)/(sinx//8) =
Answer» `8 COS""x/8cos""x/4cos""x/2` `8 cos""x/8sin""x/4sin""x/2` `8 SIN""x/8sin""x/4sin""x/2` `8 sin""x/8sin""x/4cos""x/2` ANSWER :A

Discussion

10572.	The vertex of a equilateral triangle is at (2,-1) and the side opposite to it has the equation x+y=2 then orthocenre of the triangle if
Answer» `(1/3,1/3)` `((SQRT(2))/3,(sqrt(2))/3)` `(7/2,(-2)/3)` `(1,1)` ANSWER :C

Discussion

10573.	The vector equation of a straight line passing through bara and perpendicular to barb and barc is
Answer» `barr-bara=t(BARBXXBARC)` `barr=baraxx(barbxxbarc)` `barr-barb=t(baraxxbarc)` `barr=barbxx(baraxxbarc)` ANSWER :A

Discussion

10574.	Let sets R and T be defined as R= {x in Z\|x is divisible by 2} T= {x in Z\| x is divisible by 6}. Then T sub R.
Answer» ANSWER :1

Discussion

10575.	Let 0ltalphaltpi/2 " be a fixed angle.If " P(costheta,sintheta) and Q(cos(alpha-theta),sin(alpha-theta)) then Q is obtained from P by
Answer» CLOCKWISE rotation AROUND origin through an angle`alpha` ANTICLOCKWISE rotation around origin through an angle `alpha` REFLECTION in the line through origin with slop that `alpha` reflection in the line through origin with slope `tan " alpha/2` Answer :D

Discussion

10576.	The range of f(x)=Sin^(-1)[1/2 +x^(2)] is ([.] denotes greatest integer function)
Answer» `{-PI/2, 0, pi/2}` `{0, pi/2}` `{pi/2}` `{0, pi}` ANSWER :B

Discussion

10577.	Prove that ((A cupB' cap C) cap (A cap B' cap C')) cup ((A cup B cup C') cap (B' cap C'))=B' cap C'
Answer» ANSWER :`B' CAP C'`

Discussion

10578.	Write the following as intervals : {x : x ∈ R, 0 ≤ x < 7}
Answer» ANSWER :`=(0, 7)`

Discussion

10579.	If x in R and P=(x^(2))/(x^(4)-2x^(2)+4), then P lies interval
Answer» `[0, 1/2]` `[3/4, 4/5]` `[0, 1/3]` `[0, 1/4]` ANSWER :A

Discussion

10580.	A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected.
Answer» ANSWER :200

Discussion

10581.	Expresseach ofthe followingas aproduct :
Answer» `" sin10x +SIN 6x "` ` " sin 7X- sin3x "` `" COS 7x + cos5x"` `"cos 2x - cos 4x"` ANSWER :B::C

Discussion

10582.	(cot x)/(cotx-cot3x)+(tanx)/(tanx-tan3x)=
Answer» 0 1 2 3 Answer :B

Discussion

10583.	Discuss the continulity off(x) = (e^(1/x) -1)/(e^(1/x) + 1) , x ne 0and f(0) = 0 at x = 0 .
Answer» ANSWER :` thereforef(X) ` is DISCONTINUOUS at x = 0 .

Discussion

10584.	The value of the expression tan^(6) 20^(@) - 33 tan^(4) 20^(@) + 27 tan^(2) 20^(@) is
Answer» 0 1 2 3 Answer :D

Discussion

10585.	At which origin will be shifted so, that new coordinate at point (4,5) will be (-3,9) ?
Answer» ANSWER :`(7,-4)`

Discussion

10586.	Find all other trigonometric ratios:cos x =- 1/2, x lies in third quadrant.
Answer» ANSWER :`SIN x = - (sqrt3)/(2), COSEC x =- (2)/( sqrt3), sec x =-2 , TAN x = sqrt3 ,cot x = (1)/(sqrt3)`

Discussion

10587.	If log_(tan x) (2 + 4 cos^(2) x) = 2then x=
Answer» `npi +-(PI)/6, n in Z` `n pi +-(pi)/3, n in Z` `n pi +-(pi)/4, n in Z` `(2n+1)+-(pi)/2, n in Z` Answer :B

Discussion

10588.	Find the value of tan(2"Tan"^(-1)(1/5)-(pi)/4)
Answer» `(-7)/17` `(-8)/17` `(-9)/17` `(-6)/17` ANSWER :A

Discussion

10589.	If x = cos(Theta), y = sin p(theta). Show that (1-x^(2))y_(2) - xy_(1) + p^(2)y = 0.
Answer» ANSWER :`(1-x^(2))y_(2) - xy_(1) + p^(2)y = 0`

Discussion

10590.	If bara.barb= 0and bara+barb " makes an angle of" 30^(@) with bara , then
Answer» 1)`absbarb =2absbara` 2)`ABSBARA =2absbarb` 3)`absbara =sqrt3absbarb` 4)`absbara =absbarb` Answer :C

Discussion

10591.	If bara, barb, barc are three non-coplanar vectors, barp=(barbxxbarc)/([barabarb barc]),barq=(barcxxbara)/([bara barb barc]),barr=(baraxxbarb)/([bara barb barc]) then (bara+barb).barp+(barb+barc).barq+(barc+bara).barr=
Answer» 0 6 3 `-4` ANSWER :D

Discussion

10592.	Range of Sin^(-1)x+Cos^(-1)x+Tan^(-1)x is
Answer» `(PI/4, (3PI)/4)` `(0, pi)` `[pi/4, (3pi)/4]` `[0, pi]` Answer :C

Discussion

10593.	If sin A , sin B are roots ofc^(2)x^(2) - c ( a+b)x + ab = 0 ,then the Deltale is
Answer» EQUILATERAL ISOSCELES Right ANGLED ACUTE angled Answer :C

Discussion

10594.	Three forces having magnitudes 5,4 and 3 units act on a particle in the directions 2bari-2barj-bark , bari+2barj+2bark and 2bari+barj-2bark respectively and the particele gets displaced from the point A whose position vector is6bari-2barj+3bark to the point B whose position vector is 9bari+7barj+5bark then the work done by these forces is
Answer» 9 UNIT 21 unit 30 unit 45 unit Answer :A

Discussion

10595.	Find the domain of the function f(x) =(x^(2)+2x+1)/(x^(2)-8x+12)
Answer» ANSWER :`R - {2,6}`

Discussion

10596.	Write the following sets in the roaster from. F= {x"/"x^(4)-5x^(2)+6=0, x in R}
Answer» ANSWER :`= {-SQRT(3), -sqrt(2), sqrt(2), sqrt(3)}`

Discussion

10597.	Find the variance of the following data:6,8,10,12,14,16,18,20,22,24
Answer» ANSWER :5.74

Discussion

10598.	Find (dy)/(dx) in the following : y = tan^(-1)((3x-x^(3))/(1-3x^(2))), -(1)/(sqrt(3)) lt x lt (1)/(sqrt(3)).
Answer» ANSWER :`(3)/(1 + X ^(2))`

Discussion

10599.	Between any two real roots of the equation e^(x) sin x =1, the equation e^(x) cos x = -1 has
Answer» ATLEAST ONE ROOT EXACTLY one root Atmost one root Not root ANSWER :A

Discussion

10600.	No. of terms in the expansion of (1+3x+3x^(2)+x^(3))^(10) is:
Answer» 31 32 10 11 Solution :N/a

Discussion

Explore topic-wise InterviewSolutions in .

Let n(A) = 6 and n(B) = p . Then , the total number of non - empty relations that can bedefinedfrom A to B is

If y = cos^(-1)""(9-x^2)/(9+x^2) then y^(1)(-1) is equal to

Ifcosh2x = 99, then tanhx =

The sumof the distance of the any pointon the ellripse3x^(2) + 4y^(2) = 24from itsfoxi is

Find the mean deviation about the median for the given data:

Find the number of different 8-letter arrangements that can be made﻿ from the letters of the word DAUGHTER so that﻿all vowels occur together .

Two coins (a one rupee coin and a two rupee coin)are tossed once. Write the sample space ?

If bara, barb, barc are three non-coplanar vectors, barp=(barbxxbarc)/([barabarbbarc]),barq=(barcxxbara)/([barabarbbarc]),barr=(baraxxbarb)/([barabarbbarc]) then (2bara+3barb+4barc).barp+(2barb+3barc+4bara).barq+(2barc+3bara+4barb).barr=

Find the number of 4 letter words, with or without meaning, which can be﻿ formed out of the letters of the word ROSE, where the repetition of the letters is not﻿ allowed.

The maximum value of f(x) =2x^3-21x^2+36x+20 , in the interval 0 le x le 2is

Find the number of different 8-letter arrangements that can be made﻿ from the letters of the word DAUGHTER so that﻿ all vowels do not occur together.

If the lines x+ay=a=0, bx+y+b=0, cx+cy+1=0 (a,b,c being distinct and !=1) are concurrent, then the value of (a/(a-1)+b/(b-1)+c/(c-1)) is

The rate of change of area of a square plate is equal to that of the rate of change of its perimeter. Then length of the side is

If the angles of a triangle are in the ration 4:1:1 then the ratio of the longest side to the perimeter is

The smallest angle of the triangle whose sides are 6+sqrt12,sqrt48,sqrt24 is

Given r=0.8,Sigma xy=60,sigma_(y)=2.5 and Sigmax^(2)=90, find the number of items, if x and y are deviation from their respective means.

sec ^(2) 2x =1-tan 2x

Let f_(k)(x)=(1)/(k)(sin^(k)x+cos^(k)x) wherex in R and k ge1, then f_(4)(x)-f_(6)(x) equals

Solve sin x + sqrt(3) cos x = sqrt(2).

If the transformed equation of curve is 17X^(2) - 16XY + 17y^(2) = 225 when the axes are rotated through an angle 45^(0), then the original equation of the curve is

(sinx)/(sinx//8) =

The vertex of a equilateral triangle is at (2,-1) and the side opposite to it has the equation x+y=2 then orthocenre of the triangle if

The vector equation of a straight line passing through bara and perpendicular to barb and barc is

Let sets R and T be defined as R= {x in Z|x is divisible by 2} T= {x in Z| x is divisible by 6}. Then T sub R.

Let 0ltalphaltpi/2 " be a fixed angle.If " P(costheta,sintheta) and Q(cos(alpha-theta),sin(alpha-theta)) then Q is obtained from P by

The range of f(x)=Sin^(-1)[1/2 +x^(2)] is ([.] denotes greatest integer function)

Prove that ((A cupB' cap C) cap (A cap B' cap C')) cup ((A cup B cup C') cap (B' cap C'))=B' cap C'

Write the following as intervals : {x : x ∈ R, 0 ≤ x < 7}

If x in R and P=(x^(2))/(x^(4)-2x^(2)+4), then P lies interval

A bag contains 5 black and 6 red balls. Determine the number of ways in which﻿ 2 black and 3 red balls can be selected.﻿

Expresseach ofthe followingas aproduct :

(cot x)/(cotx-cot3x)+(tanx)/(tanx-tan3x)=

Discuss the continulity off(x) = (e^(1/x) -1)/(e^(1/x) + 1) , x ne 0and f(0) = 0 at x = 0 .

The value of the expression tan^(6) 20^(@) - 33 tan^(4) 20^(@) + 27 tan^(2) 20^(@) is

At which origin will be shifted so, that new coordinate at point (4,5) will be (-3,9) ?

Find all other trigonometric ratios:cos x =- 1/2, x lies in third quadrant.

If log_(tan x) (2 + 4 cos^(2) x) = 2then x=

Find the value of tan(2"Tan"^(-1)(1/5)-(pi)/4)

If x = cos(Theta), y = sin p(theta). Show that (1-x^(2))y_(2) - xy_(1) + p^(2)y = 0.

If bara.barb= 0and bara+barb " makes an angle of" 30^(@) with bara , then

If bara, barb, barc are three non-coplanar vectors, barp=(barbxxbarc)/([barabarb barc]),barq=(barcxxbara)/([bara barb barc]),barr=(baraxxbarb)/([bara barb barc]) then (bara+barb).barp+(barb+barc).barq+(barc+bara).barr=

Range of Sin^(-1)x+Cos^(-1)x+Tan^(-1)x is

If sin A , sin B are roots ofc^(2)x^(2) - c ( a+b)x + ab = 0 ,then the Deltale is

Find the domain of the function f(x) =(x^(2)+2x+1)/(x^(2)-8x+12)

Write the following sets in the roaster from. F= {x"/"x^(4)-5x^(2)+6=0, x in R}

Find the variance of the following data:6,8,10,12,14,16,18,20,22,24

Find (dy)/(dx) in the following : y = tan^(-1)((3x-x^(3))/(1-3x^(2))), -(1)/(sqrt(3)) lt x lt (1)/(sqrt(3)).

Between any two real roots of the equation e^(x) sin x =1, the equation e^(x) cos x = -1 has

No. of terms in the expansion of (1+3x+3x^(2)+x^(3))^(10) is:

Find the number of different 8-letter arrangements that can be made from the letters of the word DAUGHTER so thatall vowels occur together .

Find the number of 4 letter words, with or without meaning, which can be formed out of the letters of the word ROSE, where the repetition of the letters is not allowed.

Find the number of different 8-letter arrangements that can be made from the letters of the word DAUGHTER so that all vowels do not occur together.

A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected.