14949 + Interview Questions in Maths in Class 11 Page 162 InterviewSolution

8051.	Number of solution (s) satisfying the equation (1)/(si x) - (1)/( sin 2 x) = (2)/( sin 4x)in [ 0, 4 pi] equals
Answer» 0 2 4 6 Answer :C

Discussion

8052.	Solve the following equations and write general solutions 1 + sin 2x = (sin 3x - cos 3 x)^(2)
Answer» ANSWER :`(N PI)/(4), n pi PM (pi)/(4)`

Discussion

8053.	Let f andg be inceasing and decreasing function respectively from [0,oo) to [0,oo), let h(x)=f(g(x)). If h(0)=0, then h(x)-h(1) is
Answer» ALWAYS zero always negative always positive strictly increasing Answer :A

Discussion

8054.	If cos theta=(-5)/(12), in which quadrant does theta lie ?
Answer» Answer :As cos `THETA` in NEGATIVE, `theta` can be EITHER in SECOND or third quadrant

Discussion

8055.	Prove that geometrically that cos (x+y)= cosx.cosy-sinx.siny and hence show that cos2x=cos^2x-sin^2x.
Answer» ANSWER :`=cos^2 X - sin^2 x`.

Discussion

8056.	An equilateral triangle ABC has its centroid at the origin and one side 'AC' isx+y=1Another point 'p' is taken in the plane of ABCP. (P being PA+PB+PC is maximum ). IfP^1A+P^1 B+P^1 C+P^1P=sqrt6+sqrt8, then locus of P^1 is
Answer» square circlel a point none of these Answer :C

Discussion

8057.	For the function f(x) = x^(x), find the points at which it is (i) increasing and (ii) decreasing. Hence determine which of e^(pi), pi^(e) is greater.
Answer» ANSWER :`rArre^pigtpi^e`

Discussion

8058.	Find the derivative of the w.r.to x. x ^(x) + (cot x) ^(x)
Answer» Answer :`X ^(x) (1+ log x) + (cot x ) ^(x) [log (cot x ) - (2X)/( SIN 2x) ]`

Discussion

8059.	A= {a, b, {c, d}, e} which of the following statements are correct? { {c, d} } sub A
Answer» ANSWER :CORRECT

Discussion

8060.	Coefficient of x^3 in expansion (1+x)^n is 20 then n = 6 .
Answer» ANSWER :FALSE STATEMENT

Discussion

8061.	If (1+sqrt(1+a)) tan alpha =1 + sqrt(1- alpha )then sin4 alpha =
Answer» 4x 2x x none of these ANSWER :C

Discussion

8062.	If sin 2 theta=k then the value of (tan^(3) theta)/(1+tan^(2) theta)+(cot^(3) theta)/(1+cot^(2) theta)=
Answer» `(1-K^(2))/(k)` `(2-k^(2))/(k)` `k^(2)+1` `2-k^(2)` ANSWER :B

Discussion

8063.	Evaluate the following limits : Lt_(xto0)(1+3x)^(4//x)
Answer» ANSWER :`E^(12)`

Discussion

8064.	If sin^(-1)x+4cos^(-1)x=pi, then x=
Answer» `1//2` `1/(SQRT(2))` `(sqrt(3))/2` `1` ANSWER :C

Discussion

8065.	Prove that (cos 7x + cos 5x)/( sin 7x - sin 5x) = cot x
Answer» ANSWER :`COT X = R.H.S.`

Discussion

8066.	For P(n):2^n = 0 ………..is true.
Answer» <P>P(1) P(3) P(10) `P(k) RARR P(k+1),k in N` Answer :D

Discussion

8067.	In DeltaABC , D, E and F are the mid points of the sides, then DeltaDEF=
Answer» D, E and F are the middle points of the sides of the TRIANGLE ABC, then orthocenter of the triangle DEF is the circumcentre of ABC orthocenter of the triangle DEF is the INCENTER of ABC centroid of the triangle DEF is not the same as that of ABC Answer :A::D

Discussion

8068.	Choose the correctoption for the following lim_(xrarr0)tan(x^5)/(tanx)^5 is ,
Answer» `(1/5)` 5 0 1 Answer :D

Discussion

8069.	Find the product of the following pairs 7a^(4),10b^(2)c^(2)
Answer» ANSWER :Inside the circle; since the distance of the POINT to the CENTRE of the circle is less than the radius of the circle.

Discussion

8070.	An enquiry into the budget of the middle class families in a city in England gave the followinginformation: What is thecost of living index of 2004 as compared with that of 1995 are seen?
Answer» Answer :Index NUMBER for 1929 is equal to 97.86. It MEANS that the LIVING in 1929 was CHEAPER than the living in 1928.

Discussion

8071.	Lim_(x to1) (1-1/x)/(sin pi (x-1))
Answer» ANSWER :`1/pi`

Discussion

8072.	A(2,0), B(-2, 0) are two points. The locus of the point P which moves such that PA-PB=2 is
Answer» `3X^(2)+y^(2)=3` `3x^(2)-y^(2)=3` `X^(2)+3y^(2)=3` `x^(2)-3y^(2)=3` ANSWER :2

Discussion

8073.	If the circum circle and nine pointcircle intersect such that the common chord is largest then sum (cos 2A) =
Answer» 0 `1/2` `-1` 1 Answer :a

Discussion

8074.	Factorise x^3 - 6x^2 + 11x - 6 into two factors so that one factor is x - 2.
Answer» SOLUTION :`X^3 - 6x^2 + 11X - 6 = (x -2)(x^2 - 4x + 3)`

Discussion

8075.	Ifthe d.c's (l,m,n) of two lines are connected by the relations 7l^(2) + 5m^(2) - 3n^(2) = 0, l - 5m + 3n = 0 then the d.c's of the two lines are
Answer» Answer :`((-1)/(SQRT(6)),(1)/(sqrt(6)),(2)/(sqrt(6)))((1)/(sqrt(14)),(2)/(sqrt(14)),(3)/(sqrt(14)))`

Discussion

8076.	Find the angle between the x-axis and the line joining the points (3, -1) " and " (4, -2) .
Answer» ANSWER :`135^(@)`

Discussion

8077.	If x, y, z are natural numbers such that cot^(-1)x+cot^(-1)y=cot^(-1)z then the number of ordered triplets (x, y, z) that satisfy the equation is
Answer» 0 1 2 infinite solutions Answer :D

Discussion

8078.	Find the derivatives of the function tan ^(-1) (log x)
Answer» ANSWER :`(1)/( X [1 + (LOG x ) ^(2)])`

Discussion

8079.	Thetangent function whoseperiodis 7 is
Answer» `TAN ((pi)/(7) x)` `tan (-(pi)/(7) x)` `tan (+-(pi)/(7)x)` `TAN7 pi x` Answer :3

Discussion

8080.	If 0ltalphaltpi/2 and cos^(6)alpha+sin^(6)alpha+Ksin^(2)2alpha=1. Then find the value of K.
Answer» ANSWER :`3/4`

Discussion

8081.	If (cos alpha, cos beta) are new co-ordinates of P when the axes are translated to the point (1,1) then original co-ordinates of P are .
Answer» `(2 COS^(2)"" (alpha)/(2), 2 cos^(2)""(beta)/(2))` `(2 SIN^(2)"" (alpha)/(2), 2 sin^(2)""(beta)/(2))` `(2 cos""(alpha)/(2), 2 cos""(beta)/(2))` `(2 sin""(alpha)/(2), 2 sin""(beta)/(2))` Answer :A

Discussion

8082.	If 0^(@) lt A, B lt 90^(@), such that cos A = 5/13, sin B = 4/5, find sin (A-B).
Answer» ANSWER :`(16)/(65)`

Discussion

8083.	Find the length of latus rectum of the hyperbola 4x^2-9y^2+8x+36y=68.
Answer»

Discussion

8084.	n gt 1, neven rArr digit in the units place of 2^(2n)+1
Answer» `5` `7` `6` `1` Answer :B

Discussion

8085.	Differentiate the following functions: 3+ 4x - 7x^(2) - sqrt(2) x^(3) + pi x^(4) - (2)/(5) x^(5) + (4)/(3)
Answer» Answer :`4-14x-3 SQRT(2) X^(2) + 4pix^(3) - 2X^(4)`

Discussion

8086.	Evaluate the following limits : Lim_( x to 0) (x^(2))/(1- cos x)
Answer» ANSWER :2

Discussion

8087.	Find the sum to infinity in each of the following G.P 5, (20)/(7), (80)/(49),……
Answer» ANSWER :`(35)/(3)`

Discussion

8088.	The value of (z+3)(barz+3) is equivalent to
Answer» `\|Z+3\|^(2)` `\|z-3\|` `z^(2)+3` NONE of these Answer :A

Discussion

8089.	If alpha, beta, gamma are lenghts of internal bisectors of angles A,B,C respectively of DeltaABC, then sum (1)/(alpha) "cos" (A)/(2) is
Answer» a+B+C `(1)/(a)+(1)/(b)+(1)/(c)` `2((1)/(a)+(1)/(b)+(1)/(c))` `2(a+b+c)` ANSWER :B

Discussion

8090.	Reduce the following equations to the normal form and find the values of p and alpha. sqrt(3)x-y+2=0
Answer» Answer : `X"cos"150^(@)+y"sin"150^(@)=1, p=1, alpha=150^(@)`

Discussion

8091.	If f(x) =x^4 tan(x^3)-x1n(1+x^2) , then the value of (d^4(f(x)))/(dx^4) at x = 0 is
Answer» 0 6 12 24 Answer :A

Discussion

8092.	A sports team of 11 students is to be constituted, choosing alteast 5 from class XI and atleast 5 from class XII. If there are 20 students in each of these classes, in how many ways can the team be constituted ?
Answer» ANSWER :`= 2{(""_20P_5}/{5!)}{(""_20P_6}/{6!)}`

Discussion

8093.	Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king.
Answer» ANSWER :`""^(4)C_(1) XX ""^(48)C_(4)`

Discussion

8094.	If the area of the rhombus enclosed by the lines lxpmmypmn=0 be 2 sp units, then
Answer» L, m,N are in G.P l,n,m are in GP lm =n l n = -m Answer :B

Discussion

8095.	O is the circumcentre of the triangle ABC and R_(1), R_(2), R_(3)are the radii of the circumcircles of the triangles OBC, OCA and OAB respectively, thena/R_(1) + b/R_(2) + c/R_(3)is equal to
Answer» `(ABC)/R ` `(abc)/R^(3)` `(abc)/R^(4)` None ANSWER :B

Discussion

8096.	Find the eccentricity of the ellipse of which the major axis is double the minor axis.
Answer» ANSWER :`SQRT(3)/2`

Discussion

8097.	Evaluate (563.4 xx root(3)(0.4773))/((6.15)^(3)).
Answer» Solution :Let `x = (563.4 xx ROOT(3)(0.4773))/((6.15)^(3)).` Then, log x = log `563.4 + 1/3` log (0.4573) - 3 log (6.15) `= 2.7508 + 1/3 (bar(1).6602) - 3 xx 0.7889` `= 2.7508 + 1/3 (-3398) - 2.3667` `= 2.7508 - 0.1133 - 2.3667` = 0.2708 `rArr` x = ANTILOG (0.2708) = 1.865. HENCE, the value of the given expression is 1.865.

Discussion

8098.	Write each sentence in the " If ................Then " form. A racer wins the race only if he runs fast.
Answer» ANSWER :Only if he RUNS fast, then a RACER wins the RACE.

Discussion

8099.	The values of 'x' at which f(x) = sinx is stationary are given by
Answer» `NPI,AAN in Z` `(2n+1)(pi)/(2),AAn in Z` `(npi)/(4),AAn inZ` `(npi)/(2),AAn inZ` ANSWER :B

Discussion

8100.	cos 56 ^(@) + cos 58^(@) - cos 66^(@) - 4 cos 28^(@) cos 29^(@) sin 33 ^(@) =
Answer» 0 1 `-1` 2 Answer :C

Discussion

Explore topic-wise InterviewSolutions in .

Number of solution (s) satisfying the equation (1)/(si x) - (1)/( sin 2 x) = (2)/( sin 4x)in [ 0, 4 pi] equals

Solve the following equations and write general solutions 1 + sin 2x = (sin 3x - cos 3 x)^(2)

Let f andg be inceasing and decreasing function respectively from [0,oo) to [0,oo), let h(x)=f(g(x)). If h(0)=0, then h(x)-h(1) is

If cos theta=(-5)/(12), in which quadrant does theta lie ?

Prove that geometrically that cos (x+y)= cosx.cosy-sinx.siny and hence show that cos2x=cos^2x-sin^2x.

An equilateral triangle ABC has its centroid at the origin and one side 'AC' isx+y=1Another point 'p' is taken in the plane of ABCP. (P being PA+PB+PC is maximum ). IfP^1A+P^1 B+P^1 C+P^1P=sqrt6+sqrt8, then locus of P^1 is

For the function f(x) = x^(x), find the points at which it is (i) increasing and (ii) decreasing. Hence determine which of e^(pi), pi^(e) is greater.

Find the derivative of the w.r.to x. x ^(x) + (cot x) ^(x)

A= {a, b, {c, d}, e} which of the following statements are correct? { {c, d} } sub A

Coefficient of x^3 in expansion (1+x)^n is 20 then n = 6 .

If (1+sqrt(1+a)) tan alpha =1 + sqrt(1- alpha )then sin4 alpha =

If sin 2 theta=k then the value of (tan^(3) theta)/(1+tan^(2) theta)+(cot^(3) theta)/(1+cot^(2) theta)=

Evaluate the following limits : Lt_(xto0)(1+3x)^(4//x)

If sin^(-1)x+4cos^(-1)x=pi, then x=

Prove that (cos 7x + cos 5x)/( sin 7x - sin 5x) = cot x

For P(n):2^n = 0 ………..is true.

In DeltaABC , D, E and F are the mid points of the sides, then DeltaDEF=

Choose the correctoption for the following lim_(xrarr0)tan(x^5)/(tanx)^5 is ,

Find the product of the following pairs 7a^(4),10b^(2)c^(2)

An enquiry into the budget of the middle class families in a city in England gave the followinginformation: What is thecost of living index of 2004 as compared with that of 1995 are seen?

Lim_(x to1) (1-1/x)/(sin pi (x-1))

A(2,0), B(-2, 0) are two points. The locus of the point P which moves such that PA-PB=2 is

If the circum circle and nine pointcircle intersect such that the common chord is largest then sum (cos 2A) =

Factorise x^3 - 6x^2 + 11x - 6 into two factors so that one factor is x - 2.

Ifthe d.c's (l,m,n) of two lines are connected by the relations 7l^(2) + 5m^(2) - 3n^(2) = 0, l - 5m + 3n = 0 then the d.c's of the two lines are

Find the angle between the x-axis and the line joining the points (3, -1) " and " (4, -2) .

If x, y, z are natural numbers such that cot^(-1)x+cot^(-1)y=cot^(-1)z then the number of ordered triplets (x, y, z) that satisfy the equation is

Find the derivatives of the function tan ^(-1) (log x)

Thetangent function whoseperiodis 7 is

If 0ltalphaltpi/2 and cos^(6)alpha+sin^(6)alpha+Ksin^(2)2alpha=1. Then find the value of K.

If (cos alpha, cos beta) are new co-ordinates of P when the axes are translated to the point (1,1) then original co-ordinates of P are .

If 0^(@) lt A, B lt 90^(@), such that cos A = 5/13, sin B = 4/5, find sin (A-B).

Find the length of latus rectum of the hyperbola 4x^2-9y^2+8x+36y=68.

n gt 1, neven rArr digit in the units place of 2^(2n)+1

Differentiate the following functions: 3+ 4x - 7x^(2) - sqrt(2) x^(3) + pi x^(4) - (2)/(5) x^(5) + (4)/(3)

Evaluate the following limits : Lim_( x to 0) (x^(2))/(1- cos x)

Find the sum to infinity in each of the following G.P 5, (20)/(7), (80)/(49),……

The value of (z+3)(barz+3) is equivalent to

If alpha, beta, gamma are lenghts of internal bisectors of angles A,B,C respectively of DeltaABC, then sum (1)/(alpha) "cos" (A)/(2) is

Reduce the following equations to the normal form and find the values of p and alpha. sqrt(3)x-y+2=0

If f(x) =x^4 tan(x^3)-x1n(1+x^2) , then the value of (d^4(f(x)))/(dx^4) at x = 0 is

A sports team of 11 students is to be constituted, choosing alteast 5 from class XI and atleast 5 from class XII. If there are 20 students in each of these classes, in how many ways can the team be constituted ?

Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king.

If the area of the rhombus enclosed by the lines lxpmmypmn=0 be 2 sp units, then

O is the circumcentre of the triangle ABC and R_(1), R_(2), R_(3)are the radii of the circumcircles of the triangles OBC, OCA and OAB respectively, thena/R_(1) + b/R_(2) + c/R_(3)is equal to

Find the eccentricity of the ellipse of which the major axis is double the minor axis.

Evaluate (563.4 xx root(3)(0.4773))/((6.15)^(3)).

Write each sentence in the " If ................Then " form. A racer wins the race only if he runs fast.

The values of 'x' at which f(x) = sinx is stationary are given by

cos 56 ^(@) + cos 58^(@) - cos 66^(@) - 4 cos 28^(@) cos 29^(@) sin 33 ^(@) =