14949 + Interview Questions in Maths in Class 11 Page 196 InterviewSolution

9751.	The pair of lines h(x^(2)-y^(2))+pxy=0 bisects the angle betweenax^(2)+2hxy+by^(2)=0 then p=
Answer» a-b a+b b-a ab Answer :C

Discussion

9752.	Find a complex number whose modulus is 4 and principal argument is (5pi)/(6).
Answer» ANSWER :`-2 SQRT(3)+2I`

Discussion

9753.	A basket contains 20 apples and 10 oranges out of which 5 apples and 3 oranges are defective. If a person takes out 2 at random what is the probability that either are apples or both are good ?
Answer» ANSWER :`= 190/435 + 231/435 - 105/435 = (190 + 231 - 105)/(435) = 316/435`

Discussion

9754.	What is the geometric property possessed by the straight lines of each system given by y = 6x + 8
Answer» Solution :A straight line with SLOPE = 6 and y - intercept = 8

Discussion

9755.	Insert 3 arithmetic means between 2 and 10.
Answer» ANSWER :4,6,8

Discussion

9756.	Consider the circle x^2+y^2-4x-6y-3 = 0.What is the general form of the equation of a circle concentric with the given circle?
Answer» SOLUTION :`x^2+y^2-4x-6y+k = 0`

Discussion

9757.	Which of the following sets are empty sets ? {x : x in N, 5 lt x lt 6}
Answer» ANSWER :it is an emply SET

Discussion

9758.	If sin^(3) x cos 3x + cos^(3) x sin 3x = 3//8, then the value of 8 sin 4x is ____________.
Answer» ANSWER :4

Discussion

9759.	( r_1+ r_2) (r_2+r_3)(r_3+r_1)=
Answer» ` 4 R s^(2) ` ` 4RR^(2) ` ` R ` `0` ANSWER :A

Discussion

9760.	If f: R to R, g : R to R are defined by f(x) =3x-1, g(x) =x^(2)+1, then find (i) (fof)(x^(2)+1), (ii) (fog)(2), (iii) (gof)(2a-3)
Answer» Answer :(i) `16X^(2)-8X + 3`, (II) `a^(2)+2`, (III) `16x-5`, (iv) 27

Discussion

9761.	A+B = 90^(@) rArr cos A cos B in
Answer» `[ - (1)/(3) , (1)/(3) ]` `[ - (1)/(2) , (1)/(2)]` `[ - (1)/(4) , (1)/(4)]` `[ - (3)/(4) , (3)/(4)]` ANSWER :B

Discussion

9762.	Let f(x) = ab sin x+ b sqrt( 1-a^2) cos x+c, where \|a\| lt 1, b gt 0 then
Answer» maximum VALUE of F(x) is b if C = 0 difference of maximum and minimum values of f(x) is 2b f(x) = c if `x = -COS^(-1)a` f(x) = c if `x = cos^(-1)a` Answer :A::B::C

Discussion

9763.	A year is selected at random. What is the probability that (i)it contains 53 sundays,(ii)it is a leap year which contains 53 sundays.
Answer» ANSWER :(i)`(1)/(7)` (II)`(2)/(7)`

Discussion

9764.	If alpha,beta be the roots of the equation x^(2)-x-1=0, determine the value of i) alpha^(2)+beta^(2) and (ii) alpha^(3)+beta^(3).
Answer» ANSWER :(i) 3 (II) 4

Discussion

9765.	If Cot A Cot B = 2 & Cos (A+B) = 3/5 then Sin A Sin B
Answer» `2//5` `1//5` `4//5` `3//5` ANSWER :D

Discussion

9766.	The point of intersection of the plane bar(r)=(bar(a)-bar(b))+s(bar(a)+bar(b)+bar(c))+t(bar(a)-bar(b)+bar(c)) and the line bar(r)=(2bar(a)+3bar(b))+pbar(c) is
Answer» `2bar(a)-3BAR(B)+bar(C)` `2bar(a)-3bar(b)-bar(c)` `2bar(a)+3bar(b)+bar(c)` `2bar(a)+3bar(b)-bar(c)` ANSWER :C

Discussion

9767.	Find the point of intersection of lines x-3y+6=0, 2x+3y-10=0
Answer» ANSWER :`(4/3,22/9)`

Discussion

9768.	the system of equations x+y+z=4,2x+5y-2z=3,x+7y-7z=5 has no solution.
Answer» Both A and R are TRUE and R is the CORRECT EXPLANATION of A Both A and R are true but R is not correct explanation of A A is true but R is false A is false but R is true Answer :A

Discussion

9769.	The sides of a Delta ^("le') ABCbe 8, 7, 6 and smallest angle is C thenR/r =
Answer» `15/7` `31/15` `32/15` `40/19` ANSWER :C

Discussion

9770.	Find the sum of all the numbers between 100 and 200 which are divisible by 7.
Answer» ANSWER :2107

Discussion

9771.	Check the continuity of the function ‘f defined by f(x)={{:(cos x,if x ne 0),(1 ,if x=0):} at x=0
Answer» ANSWER :CONTINUOUS

Discussion

9772.	AA n in N; Which among these is true?
Answer» `\| sin (NX)\| lt \| sin X\|` `\| sin (nx) \| lt n \| sin x\|` `\| sin (nx) \| le n \| sin x\|` `sin (nx) le sin n` ANSWER :C

Discussion

9773.	How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that (i) repetition of the digits is allowed? (ii) repetition of the digits is not allowed?
Answer» ANSWER :HENCE, NUMBER of 3-digit number is =60

Discussion

9774.	Which of the following sentences are statements? Give reasons for your answer Mathematics is difficult.
Answer» Answer :This is not a STATEMENT because for some PEOPLE MATHEMATICS can be easy and for some others it can be DIFFICULT.

Discussion

9775.	Prove that tan^(-1)x+"tan"^(-1)(2x)/(1-x^(2))=tan^(-1)((3x-x^(3))/(1-3x^(2))),\|x\|lt1/(sqrt(3))
Answer» `(3x-x^(3))/(1-3x^(2))` `(3x+x^(3))/(1-3x^(2))` `(3x-x^(3))/(1+3x^(2))` `(3x+x^(3))/(1+3x^(2))` ANSWER :A

Discussion

9776.	The semivertical angle of a cone is 45^(@). The height of the cone is 30.05 cm. Find the approximate value of its volume
Answer» ANSWER :`9045pi` CUBIC CM

Discussion

9777.	The sum of the infinite series 1, 1/3, 1/9,……… Is…………….
Answer» `3/2` `5/2` `2/3` `7/2` ANSWER :A

Discussion

9778.	If the sum of the series cot^(-1)2+cot^(-1)8+cot^(-1)18+…+cot^(-1)2n^(2)+…… " upto "infty " is "(kpi)/4 then the value of K is
Answer» ANSWER :1

Discussion

9779.	If a triangle ABC, cos A + cos B + cos C
Answer» `LT ` `GT 1` `gt 1 ` but not `gt 2` `gt 1` but not `gt 3//2` ANSWER :D

Discussion

9780.	The upper (3)/(4)the portion of a verticalpole subtendsan angleTan ^(-1) ""(3)/(5)at a point in the horizontalplane throughits foot and at a distance40mfrom thefoot. Giventhat the verticalpole is at a heightless than 100 mfrom the ground. then its height is
Answer» `40 ` ` 80 ` ` 60 ` ` 20 ` ANSWER :A

Discussion

9781.	If tan""[(pi)/4 + theta ]+tan[(pi)/(4)- theta ]=a " then " tan^(3)[(pi)/(4)+ theta ] + tan^(3)[(pi)/(4)- theta]=
Answer» 0 a 3A `a^(3) - 3a` ANSWER :D

Discussion

9782.	Cos^(-1)((-1)/2)-2Sin^(-1)(1/2)+3Cos^(-1)((-1)/sqrt(2))-4Tan^(-1)(-1)=
Answer» `(19pi)/12` `(35pi)/12` `(47pi)/12` `(43pi)/12` ANSWER :D

Discussion

9783.	The mean and standard deviation of 100 observations were calculated as 40 and 5.1, respectively by a student who took by mistake 50 instead of 40 for one observation. What are the correct mean and standard deviation?
Answer» ANSWER :5

Discussion

9784.	A straight line through Q(sqrt(3),2) makes an angle pi//6 with positive direction of the X-axis. If the straight line intersects the line sqrt(3)x-4y+8=0 at P, find the distance PQ.
Answer» ANSWER :6

Discussion

9785.	lim_(xrarr0)(sin(x^@))/x = …. .
Answer» ANSWER :`pi/180`

Discussion

9786.	S.D. of the observation x_1, x_2, x_3 ..... x_nis 3.5 then S.D. of -2x _1-3,-2x_2-3,.........-2x_(n)-3 is ….........
Answer» ANSWER :7

Discussion

9787.	If A=[(-1,-2,3),(1,2,4),(2,-1,3)],B=[(1,-2,5),(0,-2,2),(1,2,-3)] and C=[(-2,1,2),(1,1,2),(2,0,1)] then A+B+C=
Answer» ANSWER :`[(-4,-3,10),(2,1,8),(5,1,1)]`

Discussion

9788.	Evaluate : lim_(xto 0)(3^(x)-2^(x))/(tanx)
Answer» ANSWER :`log_(E)=3/2 `

Discussion

9789.	If (10)^(9) + 2 (11)^(1)(10)^(8) + 3(11)^(2) ( 10)^(7) + …. =k ( 10)^(9), then k is equal to
Answer» `121/10` `121/10` `100` `110` ANSWER :C

Discussion

9790.	The solution set of the equation 2cos^(-1)x=cot^(-1)((2x^(2)-1)/(2xsqrt(1-x^(2)))) is
Answer» (0,1) (-1, 1)-{0} (-1, 0) [-1, 1] ANSWER :A

Discussion

9791.	root(7)(142.71)
Answer» ANSWER :2.032

Discussion

9792.	A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides having fence are of same length x. The maximum area enclosed by the park is
Answer» `sqrt((X^(3))/(8))` `(1)/(2)x^(2)` `PIX^(2)` `(3)/(2)x^(2)` ANSWER :B

Discussion

9793.	Evaluate the following limits : Lim_(xtoa) (sqrt(a+2x)-sqrt(3x))/(sqrt(3a+x)-2sqrt(x)), a != 0
Answer» ANSWER :`2/(3sqrt(3))`

Discussion

9794.	In triangle ABC r=(R)/(6) and r_(1)=7r. Then the mesaure of angle A=
Answer» `(pi)/(12)` `(pi)/(6)` `(pi)/(4)` `(pi)/(3)` Answer :D

Discussion

9795.	If (sin^(-1)x)^(2)+(sin^(-1)y)^(2)+(sin^(-1)z)^(2)=(3pi^(2))/4, then the value of (x-y+z) can be
Answer» 1 `-1` 3 `-3` ANSWER :A::B::C::D

Discussion

9796.	Differentiate the following functions w.r.t. x: sec (px + q)
Answer» ANSWER :`p SEC (PX +Q) tan (px +q)`

Discussion

9797.	Find the derivativ of the function from first principles : x sin x
Answer» ANSWER :`X COS + SIN x`

Discussion

9798.	Find (dy)/(dx)if x = 2 e ^(-t) , y = 4e ^(t)
Answer» ANSWER :`2E ^(2L)`

Discussion

9799.	The value of theta of mean value theorem for the function f(x) = ax^(2) + bx + cin [1,2] is
Answer» `(1)/(3)` `(3)/(2)` `(1)/(4)` `(1)/(5)` ANSWER :B

Discussion

9800.	Find out which of the following sentences are statements and which are not. Justify your answer .Who are you?
Answer» SOLUTION :NOTA STATEMENT

Discussion

Explore topic-wise InterviewSolutions in .

The pair of lines h(x^(2)-y^(2))+pxy=0 bisects the angle betweenax^(2)+2hxy+by^(2)=0 then p=

Find a complex number whose modulus is 4 and principal argument is (5pi)/(6).

A basket contains 20 apples and 10 oranges out of which 5 apples and 3 oranges are defective. If a person takes out 2 at random what is the probability that either are apples or both are good ?

What is the geometric property possessed by the straight lines of each system given by y = 6x + 8

Insert 3 arithmetic means between 2 and 10.

Consider the circle x^2+y^2-4x-6y-3 = 0.What is the general form of the equation of a circle concentric with the given circle?

Which of the following sets are empty sets ? {x : x in N, 5 lt x lt 6}

If sin^(3) x cos 3x + cos^(3) x sin 3x = 3//8, then the value of 8 sin 4x is ____________.

( r_1+ r_2) (r_2+r_3)(r_3+r_1)=

If f: R to R, g : R to R are defined by f(x) =3x-1, g(x) =x^(2)+1, then find (i) (fof)(x^(2)+1), (ii) (fog)(2), (iii) (gof)(2a-3)

A+B = 90^(@) rArr cos A cos B in

Let f(x) = ab sin x+ b sqrt( 1-a^2) cos x+c, where |a| lt 1, b gt 0 then

A year is selected at random. What is the probability that (i)it contains 53 sundays,(ii)it is a leap year which contains 53 sundays.

If alpha,beta be the roots of the equation x^(2)-x-1=0, determine the value of i) alpha^(2)+beta^(2) and (ii) alpha^(3)+beta^(3).

If Cot A Cot B = 2 & Cos (A+B) = 3/5 then Sin A Sin B

The point of intersection of the plane bar(r)=(bar(a)-bar(b))+s(bar(a)+bar(b)+bar(c))+t(bar(a)-bar(b)+bar(c)) and the line bar(r)=(2bar(a)+3bar(b))+pbar(c) is

Find the point of intersection of lines x-3y+6=0, 2x+3y-10=0

the system of equations x+y+z=4,2x+5y-2z=3,x+7y-7z=5 has no solution.

The sides of a Delta ^("le') ABCbe 8, 7, 6 and smallest angle is C thenR/r =

Find the sum of all the numbers between 100 and 200 which are divisible by 7.

Check the continuity of the function ‘f defined by f(x)={{:(cos x,if x ne 0),(1 ,if x=0):} at x=0

AA n in N; Which among these is true?

How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5﻿ assuming that ﻿ (i) repetition of the digits is allowed?﻿ (ii) repetition of the digits is not allowed?﻿

Which of the following sentences are statements? Give reasons for your answer Mathematics is difficult.

Prove that tan^(-1)x+"tan"^(-1)(2x)/(1-x^(2))=tan^(-1)((3x-x^(3))/(1-3x^(2))),|x|lt1/(sqrt(3))

The semivertical angle of a cone is 45^(@). The height of the cone is 30.05 cm. Find the approximate value of its volume

The sum of the infinite series 1, 1/3, 1/9,……… Is…………….

If the sum of the series cot^(-1)2+cot^(-1)8+cot^(-1)18+…+cot^(-1)2n^(2)+…… " upto "infty " is "(kpi)/4 then the value of K is

If a triangle ABC, cos A + cos B + cos C

The upper (3)/(4)the portion of a verticalpole subtendsan angleTan ^(-1) ""(3)/(5)at a point in the horizontalplane throughits foot and at a distance40mfrom thefoot. Giventhat the verticalpole is at a heightless than 100 mfrom the ground. then its height is

If tan""[(pi)/4 + theta ]+tan[(pi)/(4)- theta ]=a " then " tan^(3)[(pi)/(4)+ theta ] + tan^(3)[(pi)/(4)- theta]=

Cos^(-1)((-1)/2)-2Sin^(-1)(1/2)+3Cos^(-1)((-1)/sqrt(2))-4Tan^(-1)(-1)=

The mean and standard deviation of 100 observations were calculated as 40 and 5.1, respectively by a student who took by mistake 50 instead of 40 for one observation. What are the correct mean and standard deviation?

A straight line through Q(sqrt(3),2) makes an angle pi//6 with positive direction of the X-axis. If the straight line intersects the line sqrt(3)x-4y+8=0 at P, find the distance PQ.

lim_(xrarr0)(sin(x^@))/x = …. .

S.D. of the observation x_1, x_2, x_3 ..... x_nis 3.5 then S.D. of -2x _1-3,-2x_2-3,.........-2x_(n)-3 is ….........

If A=[(-1,-2,3),(1,2,4),(2,-1,3)],B=[(1,-2,5),(0,-2,2),(1,2,-3)] and C=[(-2,1,2),(1,1,2),(2,0,1)] then A+B+C=

Evaluate : lim_(xto 0)(3^(x)-2^(x))/(tanx)

If (10)^(9) + 2 (11)^(1)(10)^(8) + 3(11)^(2) ( 10)^(7) + …. =k ( 10)^(9), then k is equal to

The solution set of the equation 2cos^(-1)x=cot^(-1)((2x^(2)-1)/(2xsqrt(1-x^(2)))) is

root(7)(142.71)

A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides having fence are of same length x. The maximum area enclosed by the park is

Evaluate the following limits : Lim_(xtoa) (sqrt(a+2x)-sqrt(3x))/(sqrt(3a+x)-2sqrt(x)), a != 0

In triangle ABC r=(R)/(6) and r_(1)=7r. Then the mesaure of angle A=

If (sin^(-1)x)^(2)+(sin^(-1)y)^(2)+(sin^(-1)z)^(2)=(3pi^(2))/4, then the value of (x-y+z) can be

Differentiate the following functions w.r.t. x: sec (px + q)

Find the derivativ of the function from first principles : x sin x

Find (dy)/(dx)if x = 2 e ^(-t) , y = 4e ^(t)

The value of theta of mean value theorem for the function f(x) = ax^(2) + bx + cin [1,2] is

Find out which of the following sentences are statements and which are not. Justify your answer .Who are you?

How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that (i) repetition of the digits is allowed? (ii) repetition of the digits is not allowed?