14949 + Interview Questions in Maths in Class 11 Page 199 InterviewSolution

9901.	The range of y=(arc cosx)(arc sinx) is
Answer» `[-(pi)/(2),(pi)/(2)]` `(-(pi)/(2),(pi)/(2))` `[(-pi^(2))/(2),(pi^(2))/(16)]` `[0,(pi^(2))/(16)]` ANSWER :C

Discussion

9902.	If two angles of a DeltaABC are 45^(@) and 60^(@), then the ratio of the smallest and the greatest sides are
Answer» `(SQRT(3)-1):1` `sqrt(3):sqrt(2)` `1:sqrt(3)` `sqrt(3):1` ANSWER :A

Discussion

9903.	If f(x) - g(x)is constant then f'(x) = g'(x)
Answer» ANSWER :TRUE STATEMENT

Discussion

9904.	Area of the triangle with verticies (-4,1),(1,2) and (4,-3) is …......
Answer» `17` `16` `15` NONE of these Answer :A

Discussion

9905.	If cos 4 theta+sin 5 theta=2 then theta=
Answer» `2kpi+(pi)/2, kin Z` `2K pi +(pi)/3, K in Z` `2kpi+(pi)/6, k in Z` `2kpi+(pi)/4, kin Z` Answer :A

Discussion

9906.	If x, y, k, m, n are positive and x + y = k, then find the maximum value of x^(m)y^(n).
Answer» ANSWER :`(K^(m+N).m^(n).n^(n))/((m+n)^(m+n))`

Discussion

9907.	(sin (n +1) A + 2 sin n A + sin (n-1) A)/( cos ( n -1) A - cos (n +1) A)=
Answer» `TAN A //2` `COT A//2` `tan A` `cot A` ANSWER :B

Discussion

9908.	Find the value of sin((31pi)/(3)).
Answer» ANSWER :`(SQRT3)/(2)`

Discussion

9909.	A function defined by f(x)=(x^(2)-ax+1)/(x^(2)+ax+1),0ltalt2 Let g(x)=int_(0)^(e^(x))(f'(t))/(1+t^(2))dt Which of the following is true ?
Answer» `gcancelc(x)` is POSITIVE on `(-oo,0)` and negativeon `(0,oo)` `gcancelc(x)` is negative on `(-oo,0)` and positive on `(0,oo)` `gcancelc(x)` is negative on `(oo,0)` and positive on `(0,oo)` `gcancelc(x)` does not CHANGE sign on `(-oo,oo)` Answer :B

Discussion

9910.	If R = {(x,y): x, y in W, x^(2) + y^(2) = 25} , then find the domain and range of R .
Answer» ANSWER :DOMIAN = {0,3,4,5}, RANGE ={5,4,3,0}

Discussion

9911.	Statement-I: If sechx + cosechx ="k"(e^((k-1)x))/(e^(kx)-1) then k = 3 Statement-II : If sinh 9-k sinhk =(k+1)sinh^(3)k, then k = 2 Which of the above statement is correct?
Answer» only I only II Both I and II NEITHER I nor II ANSWER :D

Discussion

9912.	Find the co-ordinates of the point of intersection of the straight lines 3x-5y+5=0, 2x+3y-22=0
Answer» ANSWER : `(5, 4)`

Discussion

9913.	Solve the system of homogenous equations 3x+y-2z=0,x+y+z=0,x-2y+z=0
Answer» ANSWER :where K is any REAL NUMBER is the SOLUTION.

Discussion

9914.	If tan x = 3/4, pi lt x lt (3pi)/(2), find the vlaue of sin(x)/(2), cos "" pi/2 and tan "" x/2.
Answer» ANSWER :`-3`

Discussion

9915.	Let A={x//0 le x lt pi/2} and f: R rarr A is an onto function given by f(x)=tan^(-1) (x^(2)+x+lambda) where
Answer» `lambda GT 0` `lambda LE 1/4` `lambda = 1/4` `lambda ge 1/8` Answer :C

Discussion

9916.	Let f : N rarr N be defined by f(x)=x^(2)+x+1, x in N. Then f is
Answer» one-one onto many-one onto one-one but not onto into Answer :C

Discussion

9917.	If sin 2 A = 4/5, find the value of tan A, (0^(@) le A le (pi)/(3))
Answer» ANSWER :`1/2`

Discussion

9918.	A point P is such that the sum of the squares of its distances from the two axes of co-ordinates is equal to the square of its distance from the line x-y=1. Find the equation of the locus of P.
Answer» ANSWER : `X^(2)+y^(2)+2xy+2x-2y-1=0`

Discussion

9919.	A committee of 11 members sits at a round table. In how many ways can they be seated if the 'President' and the 'Secretary' choose to sit together?
Answer» ANSWER :` 9! " XX 2! = 2 (9!) `

Discussion

9920.	Find the distance between the parallel lines 3x - 4y + 7 = 0and 3x - 4y + 5 = 0
Answer» ANSWER :`= 2/5`

Discussion

9921.	Let f(x) = a_(1) cos (alpha_(1) + x) + a_(2) cos (alpha_(2) + x) +…+ a_(n) cos (alpha_(n) + x). If f(x) vanishes for x = 0 and x = x_(1) (where x_(1) ne k pi, k in Z) then
Answer» `a_(1) cos alpha_(1) + a_(2) cos alpha_(2) + …+ a_(n) cos alpha_(n) = 0` `a_(1) sin alpha_(1) + a_(2) sin alpha_(2) + …+ a_(n) sin alpha_(n) = 0` f(x) = 0 has only two solutions `0, x_(1)` f(x) is IDENTICALLY zero `AA x` ANSWER :A::B::D

Discussion

9922.	An equilateral triangle is inscribed in the parabola y^(2)=4ax, where one vertex is at the vertex of the parabola. Find the length of the side of the triangle.
Answer» ANSWER :`8sqrt(3)a`

Discussion

9923.	If the equation ax^3+3bx^2y+3cxy^2+dy^3=0 (a,b,c,d ne 0) represents three coincident lines then
Answer» a=C b=d `a/b=b/c=c/d` ac=bd Answer :C

Discussion

9924.	If veca,vecb,vecc,vecd are coplaner vectors, then (vecaxxvecb)xx(veccxxvecd)=
Answer» 1 `BARA` `BARB` `BAR0` ANSWER :D

Discussion

9925.	If sec h x = (3)/(5) then tan h (2x) =
Answer» `(40)/(41)` `(41)/(40)` `(21)/(41)` `(16)/(41)` ANSWER :A

Discussion

9926.	Conjugate of the complex number is 1/(1-i) then complex number is ............
Answer» ANSWER :`1/(1+i)`

Discussion

9927.	If a_(1) lt ( 257)^(1//4) -4 lt b _(1), then (a_(1) , b_(1) )( a_(1) , b_(1)) is
Answer» `((1)/( 257),(1)/(256))` `((1)/( 256),(1)/(257))` `(256,257)` `(255,256)` ANSWER :A

Discussion

9928.	The volume of a cube is increasing at a rate of 9 cubie centimeters per second. How fast is the surface area increasing when the length of edge is 10 cms?
Answer» ANSWER :`3.6cm^(2)//SEC`

Discussion

9929.	Find the area of the triangle formed by the lines x^(2)-4xy+y^(2)=0 and x+y=1
Answer» ANSWER :`(SQRT(3))/(2)`

Discussion

9930.	ABCD is a parallelogram and P is themid point of the side AD. The line BP meets the diagonal AC in Q. Then the ratio AQ : QC =
Answer» `1:2` `2:1` `1:3` `3:1` ANSWER :A

Discussion

9931.	Determine the conjugate and the reciprocal of each complex number given below: i
Answer» ANSWER :`-i, -i`

Discussion

9932.	Assertion (A): The area of the triangle with vertices (1,2,3), (2, 5, -1) and (-1, 1, 2) is (1)/(2) sqrt155 sq units. Reason (R ): The area of the triangle with vertices vec(a), vec(b), vec(c ) is (1)/(2) \|vec(a) xx vec(b) + vec(b) xx vec(c ) + vec(c ) xx vec(a)\| Which of the following is correct ?
Answer» Both (A) and (R ) are TRUE and (R ) is the CORRECT EXPLANATION of (A) Both (A) and (R ) are true and (R ) is not the correct explanation of (A) (A) is true, (R ) is FALSE (A) is false, (R ) is true Answer :A

Discussion

9933.	If tan5 theta = cot 2 theta " then " theta= ____
Answer» `THETA = (N PI)/((7)+(pi)/(14) , n in Z` `theta = (n pi)/( 7) - (pi)/(7) , n in Z` `theta = (n pi)/( 7) - (pi)/(14), n in Z` `theta = (n pi)/( 14) + (pi)/( 7) , n in Z` Answer :A

Discussion

9934.	Let a=2bari + barj-bark and barb = barI +3bark. If barc is a unit vectors such that [bara barb barc] is maximum, then barc is
Answer» `1/(SQRT14)(3bari+barj+2bark)` `1/(sqrt6)(2bari+barj-bark)` `1/(SQRT10)(bari+3bark)` `1/(SQRT(59))(3bari-7barj-bark)` Answer :D

Discussion

9935.	If the equationtan (P cot x) = cot (P tan x)has a solution in x in (0, pi) - {(pi)/( 2)} , then
Answer» `P ge (pi)/(4)` ` P le (pi)/( 4) ` ` P LT (pi)/( 2)` ` P GT (pi)/(2)` ANSWER :B

Discussion

9936.	If (x/3+1, y-2/3)=(5/3, 1/3), find the values of x and y.
Answer» ANSWER :x=2 and y=1

Discussion

9937.	The three axes {:(harr harr harr ),(OX"," OY ","OZ):} determine _____ .
Answer» ANSWER :`{:(HARR harr harr ),(OX"," OY ","OZ):}` REPRESENT COORDINATE planes.

Discussion

9938.	Find the derivative with respect to x of the following: (iv) (x^2 + 1)/( x)
Answer» ANSWER :`1- (1)/(x^2)`

Discussion

9939.	cosec15^(@)+sec15^(@)=
Answer» `2sqrt(2)` `SQRT(6)` `2sqrt(6)` `sqrt(6)+sqrt(2)` ANSWER :C

Discussion

9940.	A sum of रु6240 is paid off in 30 instalments, such that each instalment is 10 more than the preceding instalment. Calculate the value of the first instalment.
Answer» ANSWER :रु 63

Discussion

9941.	Which of the following are examples of the null set { x : x is a natural numbers, x < 5 and x > 7 }
Answer» ANSWER :it is an EMPTY SET

Discussion

9942.	solve the limit ;lim_(xto-1)(x^(10)+x^(5)+1)/(x-1)
Answer» ANSWER :`-(1)/(2)`

Discussion

9943.	A line passing through (1,0) intersects the curve 2x^(2)+5y^(2)-7x=0 in A and B then the angle substended by the line AB at the origin is
Answer» `(PI)/(4)` `(pi)/(3)` `(pi)/(2)` `(pi)/(6)` Answer :C

Discussion

9944.	A railroad curve is to be laid on a circle. What radius should be used if the track to change direction by 25^(@)in a distance of 40 meters?
Answer» ANSWER :91.636 METERS

Discussion

9945.	Write the negation of each of the following statements. My grade is an A or a B.
Answer» ANSWER :My GRADE is not an AAND it is not a B

Discussion

9946.	Range of f(x)=(1)/(1-2 cos x) is
Answer» `[1/3, 1]` `[-1, 1/3]` `(-OO, -1] UU [1/3, oo)` `[-1/3, 1]` ANSWER :C

Discussion

9947.	If tan((pi)/(4)+(y)/(2))=tan^(3)((pi)/(4)+(x)/(2)) then (3+sin^(2)x)/(1+3sin^(2)x)=
Answer» `(SIN X)/(sin y)` `(COS x)/(cos y)` `(cos y)/(cos x)` `(sin y)/(sin x)` ANSWER :D

Discussion

9948.	Solve the following equations by using matrix inversion method 3x+4y+5z=18 2x-y+8z=13 5x-2y+7z=20
Answer» ANSWER :`z=1`

Discussion

9949.	Letf(x) be a real valued functionwith domain R such that f(x+p)= 1 +[2-3f(x)+3(f(x))^(2)-(f(x))^(3)]^(1//3) holds good AA x in R and for some +ve constant 'p' then the period of f(x) is
Answer» `p/2` p 2p `p/3` ANSWER :C

Discussion

9950.	The values of x, between 0 and 2 pi, satisfying the equaion cos 3 x + cos 2 x = sin""(3x)/(2) + sin ""(x)/(2) are
Answer» `(PI)/(7)` `(5 pi)/(7)` `(9 pi)/(7)` `(13 pi)/(7)` Answer :A::B::C::D

Discussion

Explore topic-wise InterviewSolutions in .

The range of y=(arc cosx)(arc sinx) is

If two angles of a DeltaABC are 45^(@) and 60^(@), then the ratio of the smallest and the greatest sides are

If f(x) - g(x)is constant then f'(x) = g'(x)

Area of the triangle with verticies (-4,1),(1,2) and (4,-3) is …......

If cos 4 theta+sin 5 theta=2 then theta=

If x, y, k, m, n are positive and x + y = k, then find the maximum value of x^(m)y^(n).

(sin (n +1) A + 2 sin n A + sin (n-1) A)/( cos ( n -1) A - cos (n +1) A)=

Find the value of sin((31pi)/(3)).

A function defined by f(x)=(x^(2)-ax+1)/(x^(2)+ax+1),0ltalt2 Let g(x)=int_(0)^(e^(x))(f'(t))/(1+t^(2))dt Which of the following is true ?

If R = {(x,y): x, y in W, x^(2) + y^(2) = 25} , then find the domain and range of R .

Statement-I: If sechx + cosechx ="k"(e^((k-1)x))/(e^(kx)-1) then k = 3 Statement-II : If sinh 9-k sinhk =(k+1)sinh^(3)k, then k = 2 Which of the above statement is correct?

Find the co-ordinates of the point of intersection of the straight lines 3x-5y+5=0, 2x+3y-22=0

Solve the system of homogenous equations 3x+y-2z=0,x+y+z=0,x-2y+z=0

If tan x = 3/4, pi lt x lt (3pi)/(2), find the vlaue of sin(x)/(2), cos "" pi/2 and tan "" x/2.

Let A={x//0 le x lt pi/2} and f: R rarr A is an onto function given by f(x)=tan^(-1) (x^(2)+x+lambda) where

Let f : N rarr N be defined by f(x)=x^(2)+x+1, x in N. Then f is

If sin 2 A = 4/5, find the value of tan A, (0^(@) le A le (pi)/(3))

A point P is such that the sum of the squares of its distances from the two axes of co-ordinates is equal to the square of its distance from the line x-y=1. Find the equation of the locus of P.

A committee of 11 members sits at a round table. In how many ways can they be seated if the 'President' and the 'Secretary' choose to sit together?

Find the distance between the parallel lines 3x - 4y + 7 = 0and 3x - 4y + 5 = 0

Let f(x) = a_(1) cos (alpha_(1) + x) + a_(2) cos (alpha_(2) + x) +…+ a_(n) cos (alpha_(n) + x). If f(x) vanishes for x = 0 and x = x_(1) (where x_(1) ne k pi, k in Z) then

An equilateral triangle is inscribed in the parabola y^(2)=4ax, where one vertex is at the vertex of the parabola. Find the length of the side of the triangle.

If the equation ax^3+3bx^2y+3cxy^2+dy^3=0 (a,b,c,d ne 0) represents three coincident lines then

If veca,vecb,vecc,vecd are coplaner vectors, then (vecaxxvecb)xx(veccxxvecd)=

If sec h x = (3)/(5) then tan h (2x) =

Conjugate of the complex number is 1/(1-i) then complex number is ............

If a_(1) lt ( 257)^(1//4) -4 lt b _(1), then (a_(1) , b_(1) )( a_(1) , b_(1)) is

The volume of a cube is increasing at a rate of 9 cubie centimeters per second. How fast is the surface area increasing when the length of edge is 10 cms?

Find the area of the triangle formed by the lines x^(2)-4xy+y^(2)=0 and x+y=1

ABCD is a parallelogram and P is themid point of the side AD. The line BP meets the diagonal AC in Q. Then the ratio AQ : QC =

Determine the conjugate and the reciprocal of each complex number given below: i

Assertion (A): The area of the triangle with vertices (1,2,3), (2, 5, -1) and (-1, 1, 2) is (1)/(2) sqrt155 sq units. Reason (R ): The area of the triangle with vertices vec(a), vec(b), vec(c ) is (1)/(2) |vec(a) xx vec(b) + vec(b) xx vec(c ) + vec(c ) xx vec(a)| Which of the following is correct ?

If tan5 theta = cot 2 theta " then " theta= ____

Let a=2bari + barj-bark and barb = barI +3bark. If barc is a unit vectors such that [bara barb barc] is maximum, then barc is

If the equationtan (P cot x) = cot (P tan x)has a solution in x in (0, pi) - {(pi)/( 2)} , then

If (x/3+1, y-2/3)=(5/3, 1/3), find the values of x and y.

The three axes {:(harr harr harr ),(OX"," OY ","OZ):} determine _____ .

Find the derivative with respect to x of the following: (iv) (x^2 + 1)/( x)

cosec15^(@)+sec15^(@)=

A sum of रु6240 is paid off in 30 instalments, such that each instalment is 10 more than the preceding instalment. Calculate the value of the first instalment.

Which of the following are examples of the null set { x : x is a natural numbers, x < 5 and x > 7 }

solve the limit ;lim_(xto-1)(x^(10)+x^(5)+1)/(x-1)

A line passing through (1,0) intersects the curve 2x^(2)+5y^(2)-7x=0 in A and B then the angle substended by the line AB at the origin is

A railroad curve is to be laid on a circle. What radius should be used if the track to change direction by 25^(@)in a distance of 40 meters?

Write the negation of each of the following statements. My grade is an A or a B.

Range of f(x)=(1)/(1-2 cos x) is

If tan((pi)/(4)+(y)/(2))=tan^(3)((pi)/(4)+(x)/(2)) then (3+sin^(2)x)/(1+3sin^(2)x)=

Solve the following equations by using matrix inversion method 3x+4y+5z=18 2x-y+8z=13 5x-2y+7z=20

Letf(x) be a real valued functionwith domain R such that f(x+p)= 1 +[2-3f(x)+3(f(x))^(2)-(f(x))^(3)]^(1//3) holds good AA x in R and for some +ve constant 'p' then the period of f(x) is

The values of x, between 0 and 2 pi, satisfying the equaion cos 3 x + cos 2 x = sin""(3x)/(2) + sin ""(x)/(2) are