14949 + Interview Questions in Maths in Class 11 Page 183 InterviewSolution

9101.	Find the vertices, transverse and conjugate axes, eccentricity, co-ordinates of foci, equation of directrices and length of latus rectum for each of the following hyperbola. (i) (x^(2))/(16)+(y^(2))/(9)=1 (ii) 9x^(2)-4y^(2)=36 (iii) 16y^(2)-9x^(2)=576 (vi) 49x^(2)-16y^(2)=784
Answer» Answer :(i) Vertices `=(pm4,0), transverse axis = 8, conjugate axis = 6, `e=(5)/(4)`, foci `=(pm5,0)`, equation of directrices `x=pm(16)/(5)`, latus rectum `=(9)/(2)` (ii) Vertices `=(pm2,0)`, transverse axis = 12, conjugate axis = 16 , `(sqrt(13))/(2)`, foci `=(pmsqrt(13),0)`, equation of directrices `x=pm(4)/(sqrt(13))`, latus rectum =9 (III) Vertices `=(0,pm6)`,transverse axis = 12 conjugate axis =16, `e=(5)/(3)`, foci = `(0,pm10)`, equation of directrices `y=pm(18)/(5)`, latus rectum `=(64)/(3)` (iv)Vertices `=(pm4,0)`, transverse axis = 8, conjugate axis = 14, `e=(sqrt(65))/(4),foci `=(pmsqrt(65),0)`, equation of directrices `x=pm(16)/(sqrt(65))`, latus rectum `=(49)/(2)`.

Discussion

9102.	sqrt((-x)/(4)) + sqrt((-x)/(16))- sqrt((-x)/(64)), where x is a positive real number
Answer» ANSWER :`(5)/(8) sqrtxi`

Discussion

9103.	Prove that, sin4A=4sinAcos^(3)A-4cosAsin^(3)A.
Answer» ANSWER :`THEREFORE LHS-RHS`

Discussion

9104.	Find the multiplicative invers of each of the complex number sqrt(5) + 3i
Answer» ANSWER :`(SQRT(5))/(14)-(3)/(14)i`

Discussion

9105.	If y= cos^(-1)sqrt((cos3x)/(cos^3x)) and (dy)/(dx)=sqrt((k)/(cos2x+cos4x))( sinx gt0) then k is
Answer»

Discussion

9106.	Ifcos^(6) theta + sin^(6) theta + k sin^(2) 2theta=1,thenk=
Answer» `3/4` 1 `3/2` 2 Answer :A

Discussion

9107.	Match the following .{:((1) tan(pi/4+theta)-tan(pi/4-theta)=,(a) 1),((b)tan(pi/4+theta)+cot(pi/4+theta)=,(b)4sec^(2)2theta),((c)tan(pi/4+theta).tan(pi/4-theta)=,(c)2sec2theta),((d)cosec^(2)(pi/4+theta)cosec^(2)(pi/4-theta)=,(d)2tan2theta):}
Answer» d,C,a,b a,d,b,c b,a,c,d c,b,d,a Answer :A

Discussion

9108.	In a triangle ABC, R(b+c)= a sqrt(bc) where R is the circum radius of the triangle. Then the triaangle is
Answer» ISOSCELES but not RIGHT right but not isosceles right isosceles equilateral ANSWER :C

Discussion

9109.	If N_(a)= {an : n in N}, then N_(5) cap N_(7)="………."
Answer» `N_7` `N_5` `N_(35)` `N_(12)` ANSWER :C

Discussion

9110.	Find the acute angle between pair of lines represented by following equations. y^(2)-xy-6x^(2)=0
Answer» ANSWER :`(PI)/(4)`

Discussion

9111.	Consider the function f (x) =(x^2 - 9)/(x-3), x ne 3 complete the following table
Answer» Solution :The MISSING VALUES of F(x) are 5.75,5.999,6.01,6.5 respectively

Discussion

9112.	Evaluate : lim_(xrarr0)(sqrt(1+x)-1)/(x)
Answer» `(1)/(2)` ANSWER :`(1)/(2)`

Discussion

9113.	Expand (3x-2y)^(4).
Answer» Answer :`=81X^(4) - 216x^(3) y + 216x^(2) y^(2) - 96xy^(3) + 16Y^(4)`.

Discussion

9114.	If \|vec(a)\|=sqrt3, \|vec(b)\|=2, (vec(a), vec(b))= (pi)/(3), then the area of the triangle with adjacent sides vec(a) + 2vec(b) and 2vec(a) + vec(b) (in sq.u) is
Answer» `(9 SQRT3)/(2)` `(9)/(2)` `(sqrt3)/(2)` `9sqrt3` ANSWER :A

Discussion

9115.	Solve the following equations and write general solutions sin 2 theta + cos 2 theta - sin theta - cos theta = 0
Answer» ANSWER :`{2NPI} CUP {(2npi)/(3) - (PI)/(6)}`

Discussion

9116.	For the curve y=3 sin theta cos theta, x=e^(theta) sin theta, 0 le theta le pi, the tangent is paralle to x-axis when theta is
Answer» `3pi//4` `pi//2` `pi//4` `pi//6` ANSWER :C

Discussion

9117.	If the graph of a function f(x) is symmetrical about the line x=a then
Answer» `F(a+X)=f(a-x)` `f(a+x)=f(x-a)` `f(x)=f(-x)` `f(x)=f(-x)` ANSWER :A

Discussion

9118.	If OABC, OCDE, OEFA are adjacent faces of a cube OABCDEF then bar(OB)+bar(OD)+bar(OF) interms of bar(OA), bar(OE), bar(OC) is
Answer» `2(BAR(OA)+bar(OC)+bar(OE))` `2(bar(OA)+bar(OB)+bar(OC))` `2(bar(OA)-bar(OC)+bar(OE))` `bar(OA)-bar(OC)-bar(OE)` ANSWER :A

Discussion

9119.	Find the value of x for which the points (x,-1) (2,1) and (4,5) are collinear
Answer» ANSWER :`X = 1`

Discussion

9120.	How many terms of the G.P.3,(3)/2,3/4 ..........are needed to give the sum (3069)/512 ?
Answer» ANSWER :10

Discussion

9121.	Find the domains of the following functionsf(x) =e^((1)/( x))
Answer» ANSWER :`R - { 0 }`

Discussion

9122.	If A=((cosx,sinx,0),(-sinx,cosx,0),(0,0,1))=f(x) then A^(-1)=
Answer» `F(-X)` `f(x)` `-f(x)` `-f(-x)` ANSWER :A

Discussion

9123.	Determine mean and standard deviation of first n terms of an A.P. whose first term is a and common difference is d.
Answer» ANSWER :`simga^2 = d .SQRT((n^2 - 1)/(12)) `

Discussion

9124.	Express (1-i)(sqrt3+i) in polar form
Answer» ANSWER :`2sqrt2[COS((-pi)/12) + isin((-pi)/12)]`

Discussion

9125.	(1+ sec 20^(0))(1+sec40^(0))(1+ sec80^(0))=
Answer» `COT^(2)20^(0)` `cot^(2)10^(0)` `tan^(2)10^(0)` `tan^(2)20^(0)` Answer :B

Discussion

9126.	If u=tan^(-1)(1/(sqrt(cos 2 theta)))-tan^(-1)(sqrt(cos 2 theta)), then sin u=
Answer» 1)`cot^(2)theta` 2)`sin^(2) theta` 3)`COS^(2) theta` 4)`tan^(2) theta` Answer :D

Discussion

9127.	The rootsofx^(2) - 2 sqrt 3 x+ 2=0representtwo sides of a triangle . If the angle betweenthemis(pi)/(3), then the perimeter of the trianglesis
Answer» ` 2 sqrt3 +6` ` 2 sqrt3 +sqrt6` ` 3 sqrt2 +6` ` 3 sqrt2 +6` Answer :B

Discussion

9128.	A = {1, 2, 3, 4, 5}, S= {(x,y) : x in A, y in A}, then find the ordered which satisfy the conditions given below. x+ y gt 8
Answer» ANSWER :`{(4,5),(5,4),(5,5)}`

Discussion

9129.	Find the range of the following function f(x)=1- \|x-2\|, x in R
Answer» ANSWER :`(-OO, 1]`

Discussion

9130.	If the angle between the lines respresented by 2x^2+5xy+3y^2+6x+7y+4=0 is tan^(-1)(m) and a^2+b^2-ab-a-b+1le0, then 2a+3b=
Answer» `1//3` m `-m` `m^2` ANSWER :A

Discussion

9131.	Ifa_0 = x, a_( n+1) = f(a_n) , " where"n = 0,1,2……… then answer the following questions Iff : R to Ris given by f(x) = 3 +4 x and a_n =A+ Bxthe whichof the following is not true ?
Answer» `A+B+1=2^(2n+1)` `\|A-B\|=1` `lim_(N rarr oo) "" A/B = -1` None of these Answer :C

Discussion

9132.	cos 36^@ - cos72^@ =
Answer» `1/4` `1/2` `1/2` `3/2` ANSWER :B

Discussion

9133.	Simplify : i^(38)
Answer» ANSWER :`-1`

Discussion

9134.	Find the derivative of the function x ^(2) 2 log x (x gt 0)
Answer» ANSWER :`X 2 ^(x) [1+ 2 LOG x + (log 2) x log x]`

Discussion

9135.	Solvex^(2)-x + 2=0
Answer» ANSWER :`(1+-sqrt(7)i)/2`

Discussion

9136.	Express ((1)/(3)+3i)^3 in the form a+ib.
Answer» ANSWER :`-242/27 - 26 i`

Discussion

9137.	Find two positive integers whose sum is 16 and the sum of squares is minimum.
Answer» ANSWER :8, 8

Discussion

9138.	Three coins are tossed . Describe Two events which are not mutually exclusive.
Answer» ANSWER :`:.` A and B are not MUTUALLY EXCLUSIVE.

Discussion

9139.	If sin x gt - (1)/(2) then x lies between
Answer» `2 N pi - (pi)/( 3) lt x lt 2 n pi + (4 pi)/( 3),n in Z` `2 n pi - (pi)/( 6) lt x lt 2 n pi + ( 7 pi )/( 6) , n in Z` `2 n pi - (pi)/(6) lt x lt 2 pi + (5 pi)/(6) , n in Z` `2 n pi - (pi)/(3) lt x lt 2 n pi + (2 pi)/( 3) , n in Z` Answer :B

Discussion

9140.	The minimum value of (px+qy)when xy=n^(2) is equal to .
Answer» `2nsqrt(PQ)` `2pqsqrt(N)` `2sqrt(NPQ)` `2pqn` ANSWER :A

Discussion

9141.	If tan 69^(@) + tan 66^(@) - tan 69^(@)tan 66^(@) = 2kthen k =(a)-(1)/(2)(b)(1)/(2)(c)-1(d)None of these
Answer» `-(1)/(2)` `(1)/(2)` `-1` NONE of these ANSWER :A

Discussion

9142.	If""^(4)P_2= n.""^(4)C_2. Find the value on f.
Answer» ANSWER :` n=2`

Discussion

9143.	Area of triangle formed by pair of lines (x+2a)^2-3y^2=0 and x=a is
Answer» `3a^2` `3sqrt3a` `3sqrt3a^2` `SQRT(3/4a^2` ANSWER :A

Discussion

9144.	A standard obtained the mean and standard deviation of 100 observations as 40 and 5.1 respectively. Later it was discovered that he had wrongly copied down and observation as 50 instead of 40. Calculate the true mean and standard deviation.
Answer» ANSWER :5

Discussion

9145.	Evaluate the following Lt_(xto0)(tanx-sinx)/x^(3)
Answer» ANSWER :`1/2`

Discussion

9146.	If cos^(-1)(5/13)+cos^(-1)(3/5)=cos^(-1)x then x=
Answer» 1)`3/65` 2)`(-36)/65` 3)`(-33)/65` 4)`-1` ANSWER :C

Discussion

9147.	Find the nth term and the sum to n terms of the series 1.2+ 2.3 +3.4 + ...
Answer» ANSWER :`T_(N) = n(n+1); S_(n) = (n)/(3) (n+2)(n+1)`

Discussion

9148.	In (0,(pi)/(2)),f(x)=xsinx+cosx+(1)/(2)cos^(2)x is
Answer» increasing Decreasing Constant NOTHING can be DETERMINED ANSWER :A

Discussion

9149.	Equations of diagonals of the square formed by the lines x=0, y=0, x=1 and y=1 are
Answer» `y=X, y+x=1` `y=x, x+y=2` `2Y= x, y+x = (1)/(3)` `y=2 x, y+ 2X =1` Answer :A

Discussion

9150.	A(3,0) and B(6,0) are two fixed points and U(x_1,y_1) is a variable point of the plane. AU and BU meet the Y-axis at C and D respectively. AD meets OU at V The coordinates of V are
Answer» (6,0) (2,0) (1,0) (1,1) ANSWER :B

Discussion

Explore topic-wise InterviewSolutions in .

Find the vertices, transverse and conjugate axes, eccentricity, co-ordinates of foci, equation of directrices and length of latus rectum for each of the following hyperbola. (i) (x^(2))/(16)+(y^(2))/(9)=1 (ii) 9x^(2)-4y^(2)=36 (iii) 16y^(2)-9x^(2)=576 (vi) 49x^(2)-16y^(2)=784

sqrt((-x)/(4)) + sqrt((-x)/(16))- sqrt((-x)/(64)), where x is a positive real number

Prove that, sin4A=4sinAcos^(3)A-4cosAsin^(3)A.

Find the multiplicative invers of each of the complex number sqrt(5) + 3i

If y= cos^(-1)sqrt((cos3x)/(cos^3x)) and (dy)/(dx)=sqrt((k)/(cos2x+cos4x))( sinx gt0) then k is

Ifcos^(6) theta + sin^(6) theta + k sin^(2) 2theta=1,thenk=

Match the following .{:((1) tan(pi/4+theta)-tan(pi/4-theta)=,(a) 1),((b)tan(pi/4+theta)+cot(pi/4+theta)=,(b)4sec^(2)2theta),((c)tan(pi/4+theta).tan(pi/4-theta)=,(c)2sec2theta),((d)cosec^(2)(pi/4+theta)cosec^(2)(pi/4-theta)=,(d)2tan2theta):}

In a triangle ABC, R(b+c)= a sqrt(bc) where R is the circum radius of the triangle. Then the triaangle is

If N_(a)= {an : n in N}, then N_(5) cap N_(7)="………."

Find the acute angle between pair of lines represented by following equations. y^(2)-xy-6x^(2)=0

Consider the function f (x) =(x^2 - 9)/(x-3), x ne 3 complete the following table

Evaluate : lim_(xrarr0)(sqrt(1+x)-1)/(x)

Expand (3x-2y)^(4).

If |vec(a)|=sqrt3, |vec(b)|=2, (vec(a), vec(b))= (pi)/(3), then the area of the triangle with adjacent sides vec(a) + 2vec(b) and 2vec(a) + vec(b) (in sq.u) is

Solve the following equations and write general solutions sin 2 theta + cos 2 theta - sin theta - cos theta = 0

For the curve y=3 sin theta cos theta, x=e^(theta) sin theta, 0 le theta le pi, the tangent is paralle to x-axis when theta is

If the graph of a function f(x) is symmetrical about the line x=a then

If OABC, OCDE, OEFA are adjacent faces of a cube OABCDEF then bar(OB)+bar(OD)+bar(OF) interms of bar(OA), bar(OE), bar(OC) is

Find the value of x for which the points (x,-1) (2,1) and (4,5) are collinear

How many terms of the G.P.3,(3)/2,3/4 ..........are needed to give the sum (3069)/512 ?

Find the domains of the following functionsf(x) =e^((1)/( x))

If A=((cosx,sinx,0),(-sinx,cosx,0),(0,0,1))=f(x) then A^(-1)=

Determine mean and standard deviation of first n terms of an A.P. whose first term is a and common difference is d.

Express (1-i)(sqrt3+i) in polar form

(1+ sec 20^(0))(1+sec40^(0))(1+ sec80^(0))=

If u=tan^(-1)(1/(sqrt(cos 2 theta)))-tan^(-1)(sqrt(cos 2 theta)), then sin u=

The rootsofx^(2) - 2 sqrt 3 x+ 2=0representtwo sides of a triangle . If the angle betweenthemis(pi)/(3), then the perimeter of the trianglesis

A = {1, 2, 3, 4, 5}, S= {(x,y) : x in A, y in A}, then find the ordered which satisfy the conditions given below. x+ y gt 8

Find the range of the following function f(x)=1- |x-2|, x in R

If the angle between the lines respresented by 2x^2+5xy+3y^2+6x+7y+4=0 is tan^(-1)(m) and a^2+b^2-ab-a-b+1le0, then 2a+3b=

Ifa_0 = x, a_( n+1) = f(a_n) , " where"n = 0,1,2……… then answer the following questions Iff : R to Ris given by f(x) = 3 +4 x and a_n =A+ Bxthe whichof the following is not true ?

cos 36^@ - cos72^@ =

Simplify : i^(38)

Find the derivative of the function x ^(2) 2 log x (x gt 0)

Solvex^(2)-x + 2=0

Express ((1)/(3)+3i)^3 in the form a+ib.

Find two positive integers whose sum is 16 and the sum of squares is minimum.

Three coins are tossed . Describe Two events which are not mutually exclusive.

If sin x gt - (1)/(2) then x lies between

The minimum value of (px+qy)when xy=n^(2) is equal to .

If tan 69^(@) + tan 66^(@) - tan 69^(@)tan 66^(@) = 2kthen k =(a)-(1)/(2)(b)(1)/(2)(c)-1(d)None of these

If""^(4)P_2= n.""^(4)C_2. Find the value on f.

Area of triangle formed by pair of lines (x+2a)^2-3y^2=0 and x=a is

A standard obtained the mean and standard deviation of 100 observations as 40 and 5.1 respectively. Later it was discovered that he had wrongly copied down and observation as 50 instead of 40. Calculate the true mean and standard deviation.

Evaluate the following Lt_(xto0)(tanx-sinx)/x^(3)

If cos^(-1)(5/13)+cos^(-1)(3/5)=cos^(-1)x then x=

Find the nth term and the sum to n terms of the series 1.2+ 2.3 +3.4 + ...

In (0,(pi)/(2)),f(x)=xsinx+cosx+(1)/(2)cos^(2)x is

Equations of diagonals of the square formed by the lines x=0, y=0, x=1 and y=1 are

A(3,0) and B(6,0) are two fixed points and U(x_1,y_1) is a variable point of the plane. AU and BU meet the Y-axis at C and D respectively. AD meets OU at V The coordinates of V are