14949 + Interview Questions in Maths in Class 11 Page 285 InterviewSolution

14201.	Find the constant term in the expansion of (sqrt(x) -2/x^(2))^(20)
Answer» ANSWER :`16(""^(20)C_(4)`

Discussion

14202.	Find the transformed equation of x^(2) + 2 sqrt(3) xy - y^(2) = 2a^(2) when the axes are rotated through an angle 30^(0)
Answer» ANSWER :`X^(2) - Y^(2) = a^(2)`

Discussion

14203.	Find the locus of z if omega= (z)/(z- (1)/(3)i), \|omega\| =1
Answer» ANSWER :`y= (1)/(6)`, which is a st.line

Discussion

14204.	Find the number of ways in which (a) a selection ,(b)an arrangement of four letters can be made from the letters of the word 'PROPORTION' ?
Answer» ANSWER :` 53 , 78`

Discussion

14205.	If 4sinxcosx=sqrt(3), then x =
Answer» `npi+(-1)^(N)(PI)/(3)` `npi+(-1)^(n)(pi)/(6)` `(npi)/(2)+(-1)^(n)(pi)/(3)` `(npi)/(2)+(-1)^(n)(pi)/(6)` Answer :D

Discussion

14206.	Find the derivative of the function (cos x )/( sin x + cos x)
Answer» Answer :`(-1)/((sin X + COS 2) ^(2))`

Discussion

14207.	If A[(a,b,c),(0,c,b),(0,0,b)] then det a =
Answer» a 0 ABC `(abc)/(3)` ANSWER :C

Discussion

14208.	If (sin^(-1)a)^(2)+(cos^(-1)b)^(2)+(sec^(-1)c)^(2)+(cosec^(-1)d)^(2)=(5pi)^(2)/2, then the value of (sin^(-1)a)^(2)-(cos^(-1)b)^(2)+(sec^(-1)c)^(2)-(cosec^(-1)d)^(2) is equal to
Answer» `-PI^(2)` `-pi^(2)/2` 0 `pi^(2)/2` ANSWER :C

Discussion

14209.	The distance of pointP (1,2,3) from the coordinate axes are
Answer» ANSWER :`SQRT(41),sqrt(34),4`

Discussion

14210.	A functionfis defined by f(x)=2x-5. Write down the values of (i) f(0), (ii) f(7), (iii) f(-3)
Answer» ANSWER :`-11`

Discussion

14211.	(1-i)-(-1+i6)=.........
Answer» ANSWER :`2 - 7I`

Discussion

14212.	If A = {3, 6, 9, 12, 15, 18, 21}, B = { 4, 8, 12, 16, 20 }, C = { 2, 4, 6, 8, 10, 12, 14, 16 }, D = {5, 10, 15, 20 }, find A – B
Answer» Answer :`{3, 6, 9, 15, 18, 21}`

Discussion

14213.	Is 3! + 4! = 7!?
Answer» ANSWER :30, No

Discussion

14214.	Evaluate the following limits : Lim_(x to -1) (x^(2)-1)/(x+1)
Answer» ANSWER :`-2`

Discussion

14215.	How many 2 digit even numbers can be formed from the digits 1, 2, 3, 4, 5 if the digits can be repeated?
Answer» ANSWER :10

Discussion

14216.	Find the maximum value of f(x) = x^(3)(2-x)^(4)
Answer» ANSWER :`(2^(15)3^(3))/(7^(7))`

Discussion

14217.	Which of the following identities , wherever defined, hold (s) good ?
Answer» `COT alpha - TAN alpha = 2 cot 2 alpha` `tan (45^(0) + alpha) - tan (45^(0) - alpha) = "2 COSEC 2" alpha` `tan (45^(0) + alpha) + tan (45^(0) - alpha) = 2 SEC 2 alpha` `tan alpha + cot alpha = 2 tan 2 alpha` Answer :A::C

Discussion

14218.	Let f(x) = sinx + ax+b . Then which of the following is/are true ?
Answer» f(X) =0 has only one REAL ROOT which is positive if `agt1,blt0`. f(x)=0 has only one REALROOT which is negative if `agt1,BGT0` f(x)=0 has only one real root which is negative if `alt-1,blt0`. None of these Answer :A::B::C

Discussion

14219.	The medians AD and BE of the triangle with vertices A(0, b), B(0, 0) and C(a, 0) are mutually perpendicular if
Answer» `B=sqrt(2)a` `a=sqrt(2)b` `b=-sqrt(2)a` `a=-sqrt(b)` ANSWER :B

Discussion

14220.	If sin h^(3)x-cos h^(3)x=(ke^(x)-e^(-kx))/(1-k) then k=
Answer» `-1` 0 `-3` 2 Answer :C

Discussion

14221.	Find the value of 2(sin^(6)theta+cos^(6)theta)-3(sin^(4)theta+cos^(4)theta)
Answer» ANSWER :-1

Discussion

14222.	Find the equation of a circle passing through the point (7,3) having radius 3 units and whose centre lies on the line y = x -1.
Answer» Answer :CENTRE will be (4,3) `x^(2) + y^(2) - 8X - 6y + 16 = 0`

Discussion

14223.	Expand the following expressions : (1-2x+x^(2))^(3)
Answer» Answer :`1-6X+15X^(2)-0x^(3)+15x^(4)-6x^(5)+X^(6)`

Discussion

14224.	f (x) = (cos x) ( cos 2x ) …( cos nx) implies f' (x) + sum ^(n) (r tan rx) f (x) =
Answer» `f(X)` 0 `-f(x)` `2F(x)` ANSWER :B

Discussion

14225.	Find the modulus of the following complex numbers 8-6i^(7)
Answer» ANSWER :10

Discussion

14226.	Write the contrapositive and converse of the following statement "x isan even numberimplies that x is divisible by 4"
Answer» Answer :This STATEMENT can be written as ''If X is an even number, then x is DIVISIBLE by 4''. The CONTRAPOSITIVE is, If x is not divisible by 4, then x is not an even number. The converse is, If x is divisible by 4, then x is an even number.

Discussion

14227.	Find the modulus of 8-6i^(7)?
Answer» ANSWER :0.1

Discussion

14228.	Let 'f' be a real valued function defined for all x in Rsuch that for some fixed a gt 0, f(x+a)= 1/2 + sqrt(f(x)-(f(x))^(2)) for all 'x' then the period of f(x) is
Answer» `a/4` `a/3` 2a 3a Answer :C

Discussion

14229.	Find the derivative of cos x +1 .
Answer» ANSWER :`-SINX`

Discussion

14230.	If f and g are two decreasing functions such that fog exists then fog is
Answer» an INCREASING FUNCTION a decreasing function neither increasing nor decreasing function cannot be determined Answer :A

Discussion

14231.	The value of f(0) so that the function f(x)=((27-2x)^(1//3)-3)/(9-3(243+5x)^(1//5))" is continuous at x=0 is "
Answer» ANSWER :2

Discussion

14232.	Solve 3x-6=0
Answer»

Discussion

14233.	lim_(x rarr 1)(x^(1//3) - 1)/(x^(1//6)-1) is equal to
Answer» 1 4 3 2 Answer :D

Discussion

14234.	Internal bisectors of DeltaABC meet the circumcircle at points D, E and F then Length of side EF is
Answer» `2R"COS"(A)/(2)` `2Rsin((A)/(2))` `2R cos ((C)/(2))` `2R cos((B)/(2))cos ((C)/(2))` Answer :A

Discussion

14235.	Evaluate : lim_(xto0)(sin4x)/(sin2x)
Answer» ANSWER :2

Discussion

14236.	Which of the following pairs of functions is/are identical ?
Answer» `f(x)=TAN(tan^(-1)x)` and `g(x)=cot(cot^(-1)x)` `f(x)=sin(x)` and `g(x)=sin(sin(x))` `f(x)=cot^(2) x.cos^(2)x` and `g(x)=cot^(2)x - cos^(2)x` `f(x)=e^(ln SEC^(-1)x)` and `g(x)=sec^(-1)x` Answer :A::B::C::D

Discussion

14237.	(cosh x_(1)+sinhx_(1)) (cosh x_(2)+sinhx_(2))….. (coshx_(n)+sinhx_(n))=
Answer» `cosh(n(x_(1)+x_(2)+…..+x_(n)) +SINH(n(x_(1)+x_(2)+…..+x_(n)))` `cosh(x_(1)+x_(2)+…..+x_(n)) +sinh(x_(1)+x_(2)+…..+x_(n))` `cosh(x_(1)+x_(2)+..+x_(n))-sinh(x_(1)+x_(2)+…..x_(n))` `cosh(x(x_(1)+x_(2)+…..+x_(n))) -sinh(n(x_(1)+x_(2)+…..x_(n)))` ANSWER :B

Discussion

14238.	Find the centre and radius of the circle x^(2) + y^(2) + 8x + 10y - 8 = 0
Answer» Answer :CENTRE at `(-4,-5)` and RADIUS `7`.

Discussion

14239.	What is the general value of theta which satisfies both the equations sin theta =- (1)/(2) and cos theta = - (sqrt3)/(2) ?
Answer» ANSWER :`(7pi)/(6), N in I`

Discussion

14240.	If the arcs of the same lengths in two circles subtends angles 65^(@)and110^(@) at the centre, find the ratio of their radii.
Answer» ANSWER :`22:13`

Discussion

14241.	If the slopes of the lines represented by ax^(2)+2hxy+by^(2)=0 are in the ratio m:n then ((m+n)^(2))/(mn)=
Answer» ANSWER :`(4H^(2))/(AB)`

Discussion

14242.	Express each of the following in the form b or bi, where b is a real number (1)/(2) sqrt((-3)/(4))
Answer» ANSWER :`(1)/(4) SQRT3I`

Discussion

14243.	Solve the following system of equations by using Cramer,s ruel . 3x+4y+5z=18,2x-y+8z=13,5x-2y+7z=20
Answer» ANSWER :`z=1`

Discussion

14244.	The smallest positive value of x (in radians ) satisfying the equation log_(cos x) ((sqrt(3))/(2) sin x) = 2 + log _(sec x) tan x)
Answer» `(pi)/(12)` `(pi)/(6)` `(pi)/(4)` `(pi)/(3)` ANSWER :B

Discussion

14245.	Find the mode for the following distribution.
Answer» ANSWER :`346.19`

Discussion

14246.	If x=log[y+sqrt(y^(2)-1)], then y =
Answer» TANH(x) COTH(x) SINH(x) COSH(x) Answer :D

Discussion

14247.	If x, y in R then x+iy is a non-real complex number, if
Answer» X=0 `y=0` `x NE 0` `y NE0` ANSWER :D

Discussion

14248.	Minimum value of (Sinx)^(Sinx) is
Answer» `(e)^((-1)/(e))` 1 `(PI)/(2)` `(1)/(e)` Answer :B

Discussion

14249.	For some integer k, i^(4k)+i^(4k+1)+i^(4k+2)+i^(4k+3) = ..........
Answer» ANSWER :ZERO

Discussion

14250.	If a straight line L is perpendicular to the line 4x-2y=1 and forms a triangle of area 4 square units with the coordinate axes, then an equation of the line L is
Answer» `2x+4y+8=0` `2x-4y+8=0` `2x+4y+7=0` `4x-2y-7=0` ANSWER :A

Discussion

Explore topic-wise InterviewSolutions in .

Find the constant term in the expansion of (sqrt(x) -2/x^(2))^(20)

Find the transformed equation of x^(2) + 2 sqrt(3) xy - y^(2) = 2a^(2) when the axes are rotated through an angle 30^(0)

Find the locus of z if omega= (z)/(z- (1)/(3)i), |omega| =1

Find the number of ways in which (a) a selection ,(b)an arrangement of four letters can be made from the letters of the word 'PROPORTION' ?

If 4sinxcosx=sqrt(3), then x =

Find the derivative of the function (cos x )/( sin x + cos x)

If A[(a,b,c),(0,c,b),(0,0,b)] then det a =

If (sin^(-1)a)^(2)+(cos^(-1)b)^(2)+(sec^(-1)c)^(2)+(cosec^(-1)d)^(2)=(5pi)^(2)/2, then the value of (sin^(-1)a)^(2)-(cos^(-1)b)^(2)+(sec^(-1)c)^(2)-(cosec^(-1)d)^(2) is equal to

The distance of pointP (1,2,3) from the coordinate axes are

A functionfis defined by f(x)=2x-5. Write down the values of (i) f(0), (ii) f(7), (iii) f(-3)

(1-i)-(-1+i6)=.........

If A = {3, 6, 9, 12, 15, 18, 21}, B = { 4, 8, 12, 16, 20 }, C = { 2, 4, 6, 8, 10, 12, 14, 16 }, D = {5, 10, 15, 20 }, find A – B

Is 3! + 4! = 7!?

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

How many 2 digit even numbers can be formed from the digits﻿ 1, 2, 3, 4, 5 if the digits can be repeated?

Find the maximum value of f(x) = x^(3)(2-x)^(4)

Which of the following identities , wherever defined, hold (s) good ?

Let f(x) = sinx + ax+b . Then which of the following is/are true ?

The medians AD and BE of the triangle with vertices A(0, b), B(0, 0) and C(a, 0) are mutually perpendicular if

If sin h^(3)x-cos h^(3)x=(ke^(x)-e^(-kx))/(1-k) then k=

Find the value of 2(sin^(6)theta+cos^(6)theta)-3(sin^(4)theta+cos^(4)theta)

Find the equation of a circle passing through the point (7,3) having radius 3 units and whose centre lies on the line y = x -1.

Expand the following expressions : (1-2x+x^(2))^(3)

f (x) = (cos x) ( cos 2x ) …( cos nx) implies f' (x) + sum ^(n) (r tan rx) f (x) =

Find the modulus of the following complex numbers 8-6i^(7)

Write the contrapositive and converse of the following statement "x isan even numberimplies that x is divisible by 4"

Find the modulus of 8-6i^(7)?

Let 'f' be a real valued function defined for all x in Rsuch that for some fixed a gt 0, f(x+a)= 1/2 + sqrt(f(x)-(f(x))^(2)) for all 'x' then the period of f(x) is

Find the derivative of cos x +1 .

If f and g are two decreasing functions such that fog exists then fog is

The value of f(0) so that the function f(x)=((27-2x)^(1//3)-3)/(9-3(243+5x)^(1//5))" is continuous at x=0 is "

Solve 3x-6=0

lim_(x rarr 1)(x^(1//3) - 1)/(x^(1//6)-1) is equal to

Internal bisectors of DeltaABC meet the circumcircle at points D, E and F then Length of side EF is

Evaluate : lim_(xto0)(sin4x)/(sin2x)

Which of the following pairs of functions is/are identical ?

(cosh x_(1)+sinhx_(1)) (cosh x_(2)+sinhx_(2))….. (coshx_(n)+sinhx_(n))=

Find the centre and radius of the circle x^(2) + y^(2) + 8x + 10y - 8 = 0

What is the general value of theta which satisfies both the equations sin theta =- (1)/(2) and cos theta = - (sqrt3)/(2) ?

If the arcs of the same lengths in two circles subtends angles 65^(@)and110^(@) at the centre, find the ratio of their radii.

If the slopes of the lines represented by ax^(2)+2hxy+by^(2)=0 are in the ratio m:n then ((m+n)^(2))/(mn)=

Express each of the following in the form b or bi, where b is a real number (1)/(2) sqrt((-3)/(4))

Solve the following system of equations by using Cramer,s ruel . 3x+4y+5z=18,2x-y+8z=13,5x-2y+7z=20

The smallest positive value of x (in radians ) satisfying the equation log_(cos x) ((sqrt(3))/(2) sin x) = 2 + log _(sec x) tan x)

Find the mode for the following distribution.

If x=log[y+sqrt(y^(2)-1)], then y =

If x, y in R then x+iy is a non-real complex number, if

Minimum value of (Sinx)^(Sinx) is

For some integer k, i^(4k)+i^(4k+1)+i^(4k+2)+i^(4k+3) = ..........

If a straight line L is perpendicular to the line 4x-2y=1 and forms a triangle of area 4 square units with the coordinate axes, then an equation of the line L is

How many 2 digit even numbers can be formed from the digits 1, 2, 3, 4, 5 if the digits can be repeated?