14949 + Interview Questions in Maths in Class 11

1.	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

2.	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

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

Discussion

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

Discussion

5.	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

6.	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

7.	(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

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

Discussion

9.	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

10.	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

11.	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

12.	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

13.	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

14.	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

15.	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

16.	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

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

Discussion

18.	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

19.	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

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

Discussion

21.	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

22.	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

23.	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

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

Discussion

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

Discussion

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

Discussion

27.	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

28.	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

29.	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

30.	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

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

Discussion

32.	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

33.	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

34.	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

35.	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

36.	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

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

Discussion

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

Discussion

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

Discussion

40.	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

41.	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

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

Discussion

43.	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

44.	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

45.	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

46.	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

47.	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

48.	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

49.	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

50.	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 Current Affairs.

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