14949 + Interview Questions in Maths in Class 11 Page 176 InterviewSolution

8751.	Find the derivative of the function (sin r )/(x)
Answer» Answer :`(X COS x SIN x )/(C ^(2)) `

Discussion

8752.	Find the principal solutions of the equation six x = (sqrt3)/(2).
Answer» ANSWER :`X = PI /3 and (2PI)/(3).`

Discussion

8753.	Let f(x)=log(2x-x^(2))+"sin"(pix)/(2). Then which of the following is /are true ?
Answer» GRAPH of is symmetrical about the LINE x =1 MAXIMUM value of f is 1 Absolute minimum value of f does not exist Absolute maximum VALUEOF f does not exist Answer :A::B::C

Discussion

8754.	Let L _(1) : (x -1)/( 1) = (y+1)/(2) = (z-2)/(2) L _(2) : x - 2y -1 =0 lamda y - z + 2pi : 2x + y-z =0 If the line L _(1) and the line L _(2) are coplanar then lamda equals
Answer» 1 `-3` 2 4 Answer :D

Discussion

8755.	If (1)/(6!)+(1)/(7!)=(x)/(8!), find x
Answer» ANSWER :64

Discussion

8756.	baralpha=x(baraxxbarb)+y(barbxxbarc)+z(barcxxbara) and [barabarbbarc]=1//8 then x+y+z=
Answer» `8baralpha.(bara+barb+barc)` `BARALPHA.(bara+barb+barc)` `8.(bara+barb+barc)` `bara+barb+barc` ANSWER :A

Discussion

8757.	The real value of alpha for which the expression (1-sin alpha)/(1+2i sin alpha) is purely real is
Answer» `(n+1)(PI)/(2)` `(2n+1)(pi)/(2)` `npi` None of these Answer :C

Discussion

8758.	The maxmimum value of sin^(3)x+cos^(3)xis
Answer» 0 1 3 6 Answer :B

Discussion

8759.	If abs(cos^(-1)((1-x^(2))/(1+x^(2)))) lt pi/3, then
Answer» `x I [-1/3,1/(SQRT(3))]` `x in (-1/(sqrt(3)),1/(sqrt(3)))` `x in (0,1/(sqrt(3)))` NONE of these Answer :B

Discussion

8760.	Complete the following table (##ANE_PMP_MAT_0XI_C11_E02_017_Q01##)
Answer» SOLUTION :VERTEX : (0,0),(0,0), (0,0), (0,0) FOCUS : `(3,0), (-6,0), (0,4), [0,-9/4]` AXIS : y=0, y=0, x=0, x=0

Discussion

8761.	Iftan beta =(n tan alpha )/(1+(1-n) tan^(2) alpha ), then tan(alpha-beta)=
Answer» (1 + n) `TAN alpha` `(1- n) tan alpha` `-(1 + n) tan alpha` `(n - 1) tan alpha` Answer :B

Discussion

8762.	bara=bari-barj+3bark , barb =3bari-5barj+6bark. " the magnitude of the projection of " 2bara-barb " on " bara+barb is
Answer» `(22)/(SQRT10)` `(22)/(sqrt133)` `(11sqrt2)/(sqrt10)` `(22)/(SQRT5)` ANSWER :B

Discussion

8763.	Find the range of the following function f: N rarr R, f(x)= (1)/(x)
Answer» ANSWER :`{1, (1)/(2), (1)/(3)…..}`

Discussion

8764.	Find the common solutions of sin theta = -(1)/(2) and tan theta = (1)/(sqrt(3)).
Answer» ANSWER :`2n PI + (7pi)/(6), N in Z`

Discussion

8765.	Solve the following equations : sin^(-1)(1-x)-2sin^(-1)x=(pi)/2 then x is equal to
Answer» `{0,-1,2}` `{1//2,0}` `{0}` `{-1,0}` ANSWER :C

Discussion

8766.	If alpha " and "beta are different complex numbers with \|beta\|=1, thenfind \|(beta - alpha)/(1-bar(alpha)beta)\|.
Answer» ANSWER :1

Discussion

8767.	A sperical balloon of radius r subtends an angle alpha at the eye of an observer, while the angle of elevation of its centre is beta. The height of the centre of the ballon is
Answer» `r COS(beta/2)sinalpha` `rcosec betasin(alpha/2)` `r cosec (alpha/2)sinbeta` `r cosec(alpha/2) sin(beta/2)` ANSWER :B

Discussion

8768.	If the pair of straight lines xy - x - y + 1 = 0 and the line ax+2y-3 = 0 are concurrent then a=
Answer» `-3` 3 1 0 Answer :C

Discussion

8769.	If the equation 2x^2+5xy+3y^2+6x+7y+=0 represents a pair of lines, then the equation of pair of lines parallel to then and passing through the point (0,1) is
Answer» `2x^2+5xy+3y^2+5x+6y=0` `2x^2+5xy+3y^2+5x+6y+3=0` `2x^2+5xy+3y^2+5x-6y+3=0` `2x^2+5xy+3y^2+5x+6y+3=0` ANSWER :C

Discussion

8770.	Lim_(x to pi) (1+sec^(3)x)/(tan^(2)x)
Answer» ANSWER :`-3/2 `

Discussion

8771.	Let f(x)=3x^(2) - 7x+ cwhere c is a veriable coefficient and x gt (7)/(6). Then the value of [c]such that f(x)touches f^(-1)(x)is where [.]represent greatest integer functions)………..
Answer» ANSWER :5

Discussion

8772.	Refer to question 6 above, state true or false : (give reason for your answer) A=B'
Answer» ANSWER :`:.` GIVEN STATEMENT is TRUE.

Discussion

8773.	If A gt 0, B gt 0 and A+B=(pi)/(3), then the maximum value of tan A tan B is
Answer» `1/2` `1/3` `1/4` `1/4` ANSWER :B

Discussion

8774.	If first term, second term and last term of an A.P are a,b and 2a respectively then there sum is……
Answer» `(AB)/(2(b-a))` `(ab)/(b-a)` `(3ab)/(2(b-a))` NONE of these Answer :C

Discussion

8775.	If a =7, b= 8 , c= 9then the length of the line joiningB to the middle point of AC is
Answer» `7` ` 8` ` 9 ` ` 6` ANSWER :A

Discussion

8776.	Solve[(x,0,-1)][(1,2,1),(1,1,2),(-2,1,0)][(x,1,0)]=0
Answer» ANSWER :x=+-i

Discussion

8777.	A bag contains 6 white ., 7 red and 5 black balls . Threeballs are drawn at random . Find the probability thatthey will be white .
Answer» Answer :`(""^(6)C_(3))/(""^(18)C_(3))=(5)/(204)`

Discussion

8778.	If a_(1),a_(2),a_(3),....,a_(n) is an A.P. with common difference d, then tan[Tan^(-1)(d/(1+a_(1)a_(2)))+Tan^(-1)(d/(1+a_(2)a_(3)))+...Tan^(-1)(d/(1+a_(n-1)a_(n)))=
Answer» `((N-1)d)/(a_(1)+a_(n))` `((n-1)d)/(1+a_(1)a_(n))` `(ND)/(1+a_(1)a_(n))` `(a_(n)-a_(1))/(a_(n)+a_(1))` ANSWER :B

Discussion

8779.	Passing through (2, 2 sqrt3) and inclined with the x-axis at an angle of 75^(@).
Answer» ANSWER :`(SQRT3 + 1) X - ( sqrt3 - 1) y = 4 (sqrt3- 1)`

Discussion

8780.	Evaluate the following limits : Lim_(x to oo) sqrt(x^(2) +x-1) - x
Answer» ANSWER :`1/2`

Discussion

8781.	If 27a+9b+3c+d=0, then the equation 4ax^(3)+3bx^(2)+2cx+d =0 has atleast one real root lying between
Answer» 0 and 1 1 and 3 0 and 3 0 and 2 Answer :C

Discussion

8782.	If the axes are translated to the point P(3,4) and then rotated through an angle 120^(0)about P. Then find the new coordinates of the point whose original coordinates are (1, -1)
Answer» ANSWER :`SQRT(3) + (5)/(2)`

Discussion

8783.	If f (x) = (x -1)/( 2x ^(2) - 7x + 5) for x ne 1, f (1) = (-1)/(3), find f '(1).
Answer» ANSWER :`-2/9`

Discussion

8784.	Equation x = 4 cos theta and y = 3 sin theta , theta in (-pi,pi)denotes ellipse .
Answer» ANSWER :TRUE STATEMENT

Discussion

8785.	IfLim_(x to 1) (x^(4)-1)/(x-1)=Lim_(x to k) (x^(3)-k^(3))/(x^(2)-k^(2)) , find the value of k .
Answer» ANSWER :`8/3`

Discussion

8786.	lim_(x to 0) (sin x^(@))/( x) is equal to
Answer» 1 `PI` `-pi` `(pi)/(180)` ANSWER :D

Discussion

8787.	Findthe meandeviationabout the mean for the folllowingdata ?
Answer» ANSWER :MEAN DEVIATION about the mean `BARX = 23`

Discussion

8788.	If""^(n)C_(8)=""^(n)C_(2)Find""^(n)C_(2) ?
Answer» ANSWER :45

Discussion

8789.	A plane is 1 km from one landmark and 2 km from another. Fromthe planes point of view the land between them subtends an angle of 45^(@) . How far apart are the landmarks?
Answer» ANSWER :c = `SQRT(5 - 2sqrt(2))`KM

Discussion

8790.	If alpha = Tan^(-1)((sqrt(1+x^2)-sqrt(1-x^2))/(sqrt(1+x^2)+sqrt(1-x^2))) then prove that x^(2) = sin 2alpha.
Answer» x `x^(3)` `x^(2)` `x^(4)` ANSWER :C

Discussion

8791.	Prove that, cos((pi)/(4)+x)+cos((pi)/(4)-x)=sqrt(2)cosx.
Answer» ANSWER :`SQRT2 COS X = R.H.S.`

Discussion

8792.	Statement 1 : The function f(x)=x^(2)+tan^(-1)x is a non -periodic function. Statement 2 : The sum of two non-periodic functions is always non-periodic.
Answer» Statement 1 is TRUE, statement 2 is true, statement 2 iscorrect explanation for statement 1. Statement 1 is true, statement 2 is true, statement 2 is NOTCORRECT explanation for statement 1. Statement1 is FALSE, but statement 2 is true Statement 1 is true, but statement 2 is false Answer :C

Discussion

8793.	The set builder form of (6,12) is a){x:x in RR, 6ltxle12}b){x:x in RR, 6ltxlt12}c){x:x in RR, 6lexle12}d){x:x in RR, 6lexlt12}
Answer» `{X:x in RR, 6ltxle12}` `{x:x in RR, 6ltxlt12}` `{x:x in RR, 6lexle12}` `{x:x in RR, 6LEXLT12}` ANSWER :B

Discussion

8794.	In triangle ABC the equation of side BC is 2x-y=3 and its circumecentre and orthocentre are at (2,4) and (1,2) respectively then match the itms of column I with item of column I I
Answer» ANSWER :A-q;B-S;C-p;D-r

Discussion

8795.	The sides of triangle are 4,5,6 then area is
Answer» `15/4 SQRT7` `15/2 sqrt7` `15 sqrt7` `15/4` ANSWER :A

Discussion

8796.	Check whether''Or'' used in the following compound statement is exclusive or inclusive? Write the component statements of the compound statements and use them to check whether the compound statement is true or not. Justify your answer. t: you are wet when it rains or you are in a river.
Answer» Answer :(i) Exclusive (ii) P: If it rains then you are WET. Q: When you are in river you BECOME wet. (III) COMPOUND statement is True.

Discussion

8797.	Use the graph to find the limits (if it exists).If the limit does not exist ,explain why? 7. lim_(xrarr3)(4-x)
Answer» ANSWER :1

Discussion

8798.	If the foot of the perpendicular from (0,0,0) to a plane is (1, 2, 2), then the equation of the plane is
Answer» `-X + 2y + 8Z -9=0` `x + 2y + 2Z - 9=0` `x + y + z -5=0` `x + 2y - 3Z + 1=0` Answer :B

Discussion

8799.	Two adjacent sides of the parallogram are 4x + 5y = 0 and 7x + 2y = 0 one diagonal ofthe parallogram is along line 11x + 7y = 9. Then find equation of other diagonal.
Answer» ANSWER :`y = X`

Discussion

8800.	If P= {x: x lt 3, x in N}, Q = {x : x le 2, x in W} then find (P uu Q) xx (P nn Q), where W is the set of whole numbers.
Answer» ANSWER :`{(0, 1), (0, 2), (1,1), (1,2), (2, 1), (2,2)}`

Discussion

Explore topic-wise InterviewSolutions in .

Find the derivative of the function (sin r )/(x)

Find the principal solutions of the equation six x = (sqrt3)/(2).

Let f(x)=log(2x-x^(2))+"sin"(pix)/(2). Then which of the following is /are true ?

Let L _(1) : (x -1)/( 1) = (y+1)/(2) = (z-2)/(2) L _(2) : x - 2y -1 =0 lamda y - z + 2pi : 2x + y-z =0 If the line L _(1) and the line L _(2) are coplanar then lamda equals

If (1)/(6!)+(1)/(7!)=(x)/(8!), find x

baralpha=x(baraxxbarb)+y(barbxxbarc)+z(barcxxbara) and [barabarbbarc]=1//8 then x+y+z=

The real value of alpha for which the expression (1-sin alpha)/(1+2i sin alpha) is purely real is

The maxmimum value of sin^(3)x+cos^(3)xis

If abs(cos^(-1)((1-x^(2))/(1+x^(2)))) lt pi/3, then

Complete the following table (##ANE_PMP_MAT_0XI_C11_E02_017_Q01##)

Iftan beta =(n tan alpha )/(1+(1-n) tan^(2) alpha ), then tan(alpha-beta)=

bara=bari-barj+3bark , barb =3bari-5barj+6bark. " the magnitude of the projection of " 2bara-barb " on " bara+barb is

Find the range of the following function f: N rarr R, f(x)= (1)/(x)

Find the common solutions of sin theta = -(1)/(2) and tan theta = (1)/(sqrt(3)).

Solve the following equations : sin^(-1)(1-x)-2sin^(-1)x=(pi)/2 then x is equal to

If alpha " and "beta are different complex numbers with |beta|=1, thenfind |(beta - alpha)/(1-bar(alpha)beta)|.

A sperical balloon of radius r subtends an angle alpha at the eye of an observer, while the angle of elevation of its centre is beta. The height of the centre of the ballon is

If the pair of straight lines xy - x - y + 1 = 0 and the line ax+2y-3 = 0 are concurrent then a=

If the equation 2x^2+5xy+3y^2+6x+7y+=0 represents a pair of lines, then the equation of pair of lines parallel to then and passing through the point (0,1) is

Lim_(x to pi) (1+sec^(3)x)/(tan^(2)x)

Let f(x)=3x^(2) - 7x+ cwhere c is a veriable coefficient and x gt (7)/(6). Then the value of [c]such that f(x)touches f^(-1)(x)is where [.]represent greatest integer functions)………..

Refer to question 6 above, state true or false : (give reason for your answer) A=B'

If A gt 0, B gt 0 and A+B=(pi)/(3), then the maximum value of tan A tan B is

If first term, second term and last term of an A.P are a,b and 2a respectively then there sum is……

If a =7, b= 8 , c= 9then the length of the line joiningB to the middle point of AC is

Solve[(x,0,-1)][(1,2,1),(1,1,2),(-2,1,0)][(x,1,0)]=0

A bag contains 6 white ., 7 red and 5 black balls . Threeballs are drawn at random . Find the probability thatthey will be white .

If a_(1),a_(2),a_(3),....,a_(n) is an A.P. with common difference d, then tan[Tan^(-1)(d/(1+a_(1)a_(2)))+Tan^(-1)(d/(1+a_(2)a_(3)))+...Tan^(-1)(d/(1+a_(n-1)a_(n)))=

Passing through (2, 2 sqrt3) and inclined with the x-axis at an angle of 75^(@).

Evaluate the following limits : Lim_(x to oo) sqrt(x^(2) +x-1) - x

If 27a+9b+3c+d=0, then the equation 4ax^(3)+3bx^(2)+2cx+d =0 has atleast one real root lying between

If the axes are translated to the point P(3,4) and then rotated through an angle 120^(0)about P. Then find the new coordinates of the point whose original coordinates are (1, -1)

If f (x) = (x -1)/( 2x ^(2) - 7x + 5) for x ne 1, f (1) = (-1)/(3), find f '(1).

Equation x = 4 cos theta and y = 3 sin theta , theta in (-pi,pi)denotes ellipse .

IfLim_(x to 1) (x^(4)-1)/(x-1)=Lim_(x to k) (x^(3)-k^(3))/(x^(2)-k^(2)) , find the value of k .

lim_(x to 0) (sin x^(@))/( x) is equal to

Findthe meandeviationabout the mean for the folllowingdata ?

If""^(n)C_(8)=""^(n)C_(2)Find""^(n)C_(2) ?

A plane is 1 km from one landmark and 2 km from another. Fromthe planes point of view the land between them subtends an angle of 45^(@) . How far apart are the landmarks?

If alpha = Tan^(-1)((sqrt(1+x^2)-sqrt(1-x^2))/(sqrt(1+x^2)+sqrt(1-x^2))) then prove that x^(2) = sin 2alpha.

Prove that, cos((pi)/(4)+x)+cos((pi)/(4)-x)=sqrt(2)cosx.

Statement 1 : The function f(x)=x^(2)+tan^(-1)x is a non -periodic function. Statement 2 : The sum of two non-periodic functions is always non-periodic.

The set builder form of (6,12) is a){x:x in RR, 6ltxle12}b){x:x in RR, 6ltxlt12}c){x:x in RR, 6lexle12}d){x:x in RR, 6lexlt12}

In triangle ABC the equation of side BC is 2x-y=3 and its circumecentre and orthocentre are at (2,4) and (1,2) respectively then match the itms of column I with item of column I I

The sides of triangle are 4,5,6 then area is

Check whether''Or'' used in the following compound statement is exclusive or inclusive? Write the component statements of the compound statements and use them to check whether the compound statement is true or not. Justify your answer. t: you are wet when it rains or you are in a river.

Use the graph to find the limits (if it exists).If the limit does not exist ,explain why? 7. lim_(xrarr3)(4-x)

If the foot of the perpendicular from (0,0,0) to a plane is (1, 2, 2), then the equation of the plane is

Two adjacent sides of the parallogram are 4x + 5y = 0 and 7x + 2y = 0 one diagonal ofthe parallogram is along line 11x + 7y = 9. Then find equation of other diagonal.

If P= {x: x lt 3, x in N}, Q = {x : x le 2, x in W} then find (P uu Q) xx (P nn Q), where W is the set of whole numbers.