14949 + Interview Questions in Maths in Class 11 Page 80 InterviewSolution

3951.	Find the (3^(3) -2^(3)) + (5^(3)-4^(3)) + (7^(3) - 6^(3)) +……up to 10 terms
Answer» Answer :(i) `4n^(3) + 9N^(2) + 6n` (II) 4960

Discussion

3952.	\|{:(2013^(2),2014^(2),2015^(2)),(2016^(2),2017^(2),2018^(2)),(2019^(2),2020^(2),2021^(2)):}\|=
Answer» `-4024` `-216` 216 4042 Answer :B

Discussion

3953.	P is the circumcenter of an equilateral triangle ABC of side lengh sqrt3 " units then the value of " PA^2+PB^2+PC^2 is
Answer» ANSWER :C

Discussion

3954.	e_(1) and e_(2) are eccentricities of conies 5x^(2) + 9y^(2) = 45 and 5x^(2) - 4y^(2) = 45 then e_(1) .e_(2) = ……….
Answer» 9 4 5 1 Answer :D

Discussion

3955.	Given that (2 sqrt3 cos 30^(@) - 2i sin 30^(@))/(sqrt2 (cos 45^(@) + isin 45^(@)))=A + Bi, find the values of A and B.
Answer» ANSWER :`A= 1, B= -2`

Discussion

3956.	If e^x=(sqrt(1+t)-sqrt(1-t))/(sqrt(1+t)+sqrt(1-t)) and tan (y/2)=sqrt((1-t)/(1+t)) then (dy)/dxat t=1/2 is
Answer» `-1/2` `1/2` 0 2 Answer :A

Discussion

3957.	If a,b,c are the sides of Delta ABCand the lines ax+by+c=0, bx+cy+a=0, cx+ay+b=0 are concurrent, then Delta ABCis
Answer» RIGHT ANGLED equilateral isosceles scalene Answer :B

Discussion

3958.	If x = a cos^4 theta , y = a sin^4 theta then (dy)/(dx) at theta = (3 pi)/4 is
Answer» `a^2` `1` `-1` `-a^2` ANSWER :C

Discussion

3959.	Find the mean deviation about the mean for the data : 4,7,8,9,10,12,13,17
Answer» ANSWER :3

Discussion

3960.	The value of cos(67(1^(@))/(2)) is ………….
Answer» `(SQRT(2+sqrt(2)))/(2)` `(sqrt(2-sqrt(2)))/(2)` `sqrt(2)-1` `sqrt(2)+1` ANSWER :B

Discussion

3961.	If r is in radius of Delta^("le")ABC and R is its circum radius then Delta^("le")ABC is rightangled triangle then minimum value of (R)/(r)
Answer» `SQRT(2)` `sqrtt(2)-1` `sqrt(2)+1` 1 Answer :C

Discussion

3962.	If the mid-points of the sides of a triangle AB, BC, CA are D(1, 2, -3), E(3, 0, 1) and F(-1, 1, -4), then the centriod of the triangle ABC is ____ .
Answer» ANSWER :`DeltaABC=G(1,1,-2)`

Discussion

3963.	Value of 'c' of Lagrange's mean theorem for f(x) = {:{ (2+x^(3) ,","if xlt 1),(3x,","if x gt 1 ):} on [-1,2]
Answer» `+- ( SQRT(5))/( 3)` `+- ( sqrt(3))/( 2)` `+- (sqrt(2))/( 5)` `+- ( 3)/( sqrt(5))` ANSWER :A

Discussion

3964.	For function f(x)=x"cos"(1)/(x),xge1,(2009)
Answer» for atleast one x in INTERVAL `[1,oo),f(x+2)-f(x)lt2` `lim_(xto0)f'(x)=1` `[1,oo),f(x+2)-f(x)gt2` f(x) is strictly decreasing in the interval `[1,oo)` Answer :B::C::D

Discussion

3965.	Line makes right angled triangle with axis whose area is 6 unit and length of its hypoteneous is 5 unit. Find equation of line.
Answer» ANSWER :`3X + 4Y = PM 12, 4x+3y = pm 12`

Discussion

3966.	If tanx=(b)/(a), then find the value of sqrt((a+b)/(a-b))+sqrt((a-b)/(a+b)).
Answer» ANSWER :`(2COSX)/(SQRT(COS2X))`

Discussion

3967.	Fine the value of : (i) log 3(ii) log 23.45(iii) log 4.17 (iv) log 0.325(iv) log 0.0954(vi) log 0.00056
Answer» Solution :USING LOG table, we have (i) log 3 = 0.4771 (II) log 23.45 = 1.3701 (iii) log 4.17 = 0.6201 (iv) log`0.325 = BAR(1).5119` (v) log `0.0954 = bar(2).9795` (vi) log `0.00056 = bar(4).7482`

Discussion

3968.	State which of the following sets are finite or infinite : {x : x in N and x is prime}
Answer» ANSWER :INFINITE

Discussion

3969.	Consider the expansion of (x+a)^n Find the 6th ,7th and 8th terms in the expansion
Answer» SOLUTION :^nC_5.x^(x-5)a^5,^nC_6x^(n-6)a^6,^nC_7x^(n-7)a^7

Discussion

3970.	Consider the following population and year graph (Fig 10.10), find the slope of the line AB and using it, find what will be the population in the year 2010?
Answer» ANSWER :`1/2 , 104.5` CRORES

Discussion

3971.	Find the mean deviation using arithmetic mean for the following observations: (a) 68,32,49,54,21,38,59,41,66,76 (b) 28,12,17,35,22,18,5,32
Answer» SOLUTION :NA

Discussion

3972.	IfABCD is a quadrilateral then Sec^(2) ((A+B)/(4))- Cot^(2) ((C+D)/(4))=
Answer» 0 1 -1 2 Answer :B

Discussion

3973.	Differentiate the following functions w.r.t. x: tan (4x -7)
Answer» Answer :`4 SEC^(2) (4X - 7)`

Discussion

3974.	Show that the area of a rectangle inscribed in a circle is maximum when it is a square.
Answer» ANSWER :SQUARE

Discussion

3975.	Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank spaces: 2. . .A
Answer» ANSWER :`∈`

Discussion

3976.	The minimum distance from the origin to a point on the curve x^(2//3) +y^(2//3)=a^(2//3) (a gt 0 ) is
Answer» a `a//2` `2A` `a^(2//3)` ANSWER :A

Discussion

3977.	The sums of n terms of two arithmetic progressions are in the ratio 5n + 4 : 9n + 6. Find the ratio of their 18^(th)terms.
Answer» ANSWER :`179/321`

Discussion

3978.	There are three events A, B and C of which one and only one can happpen. If the odds are 5 to 4 agains A and 2 toagainst B,then odds against C is:
Answer» `2:5` `5:2` `2:7` `7:2` ANSWER :D

Discussion

3979.	Compute the following limits. Lt_(xtooo)sqrt((x-sinx)/(x+cosx))
Answer» ANSWER :1

Discussion

3980.	If sin h^(-1) (x) = log_(e) (5 + sqrt(26)) then x =
Answer» `(1)/(2)(3sqrt(5) + 2sqrt(10))` `(1)/(2)(3sqrt(5) - 2sqrt(10))` `(1)/(2)(12 + 2sqrt(50))` `(1)/(2)(12 - 2sqrt(50))` Answer :C

Discussion

3981.	If probability of event A is (7)/(11), then give probability of its complement event A'?
Answer» <P> ANSWER :`P(A')=(4)/(11)`

Discussion

3982.	The sum of a series of terms in A.P. is 128. If the first term is 2 and the last term is 14, find the common difference.
Answer» ANSWER :`(4)/(5)`

Discussion

3983.	d/(dx){Cot^(-1)""(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))}
Answer» `1/(SQRT(1-x^2))` `(-1)/(2(sqrt(1-x^2)))` `(1)/(sqrt(1+x^2))` `(-1)/(2(1+x^2))` ANSWER :B

Discussion

3984.	From the employees of a company, 5 persons are selected to represent them in the managing committee of the company. Particulars of five persons are as follows: A person is selected at random from this group to act as a spokeperson. What is the probability that the spokesperson wil be either male or over 35 years?
Answer» <P> SOLUTION :Total MEMBER `=5` `implies` No. of ways of selecting one member `N(S)=5` Male member `=3impliesn(M)=3` Members over 35 YEARS of age are `P(T)=2` Now `n(MnnT)=1` `:.P(MuuT)=P(M)+P(T)-P(MnnT)` `=3/5+2/5-1/5=4/5` Here probability that the selected personwill be either male or over 35 years `=4/5`

Discussion

3985.	Find the mean deviation about the median for the following data:
Answer» ANSWER :4.97

Discussion

3986.	Period of cos(x+2x + 3x +…+n x) is
Answer» `(2PI)/(n(n+1))` `(4PI)/(n(n+1))` `(pi)/(n(n+1))` `(6PI)/(n(n+1))` Answer :B

Discussion

3987.	Evaluate Lt_(xtooo)(sqrt(x^(2)+x)-x)
Answer» ANSWER :`1/2`

Discussion

3988.	If \|z-(9)/(z)\|=6 then maximum value of \|z\| is ....
Answer» `2sqrt(3)+i3` `3+3sqrt(2)` `sqrt(3)+sqrt(2)` `3-3sqrt(2)` ANSWER :B

Discussion

3989.	Find the values of sin 2 theta, cos 2 theta, and tan 2 theta, given : (i)sin theta = (3)/(5) , thetain Quadrant I. (ii) sin theta = 3/5 , thetain Quadrant II. (iii)sin theta= - (1)/(2), thetain Quadrant IV. (iv) tan theta =- (1)/(5) , theta in Quadrant II.
Answer» ANSWER :`SQRT3`

Discussion

3990.	The sides of a triangle are three consecutive natural numbers and its largest angle is twice the smallerst one. Determine the sides of the triangle.
Answer» 5, 6, 4 6, 5, 4 4, 5, 6 4, 6, 5 ANSWER :C

Discussion

3991.	Given that N= {1, 2, 3, 4,……….., 100}. Then, write The subset of N whose elements are perfect square numbers.
Answer» ANSWER :`{1, 4, 9, 16, 25, 36, 49, 64, 81, 100}`

Discussion

3992.	cos 36^(@) - cos 72^(@) =
Answer» 1 `(1)/(2)` `(1)/(4)` `(1)/(8)` Answer :B

Discussion

3993.	Write down the negation of following compound statements. x=2 and x=3 are roots of the quadratic equation x^(2)-5x+6=0
Answer» ANSWER :QUADRATIC EQUATION.

Discussion

3994.	The triangle formed by 2x+3y+7=0 and the pair (2x+3y)^(2)-3(3x-2y)^(2)=0 is
Answer» Isosceles Equilateral RIGHT ANGLED scalane ANSWER :A

Discussion

3995.	If Tan A = (4)/(3), Tan B = (1)/(7) then A - B =
Answer» `(pi)/(4)` `(pi)/(2)` `pi` `(2PI)/(3)` ANSWER :A

Discussion

3996.	Find the modulus of the following using the property of modulus (3+2i)/(2-5i) + (3-2i)/(2+5i)
Answer» ANSWER :`(8)/(29)`

Discussion

3997.	Find the domain of each of the following functions given by f(x)= (3x)/(28-x)
Answer» ANSWER :`R- {28}`

Discussion

3998.	The negation of the statement 7 is greater than 8" is …………
Answer» 7 is EQUAL to 8 6 is not GREATER than 8 8 is LESS than 6 None of these Answer :B

Discussion

3999.	Find the term independent of x in the expansion of (3/2x^(2) - 1/(3x))^(6).
Answer» ANSWER :`5/12`

Discussion

4000.	Evaluate : lim_(x to 0) (e^(cos x)-1)/(cos x)
Answer» Answer :`[ " USING " Lim_(xto0) (E^(X)-1)/x = 1] `

Discussion

Explore topic-wise InterviewSolutions in .

Find the (3^(3) -2^(3)) + (5^(3)-4^(3)) + (7^(3) - 6^(3)) +……up to 10 terms

|{:(2013^(2),2014^(2),2015^(2)),(2016^(2),2017^(2),2018^(2)),(2019^(2),2020^(2),2021^(2)):}|=

P is the circumcenter of an equilateral triangle ABC of side lengh sqrt3 " units then the value of " PA^2+PB^2+PC^2 is

e_(1) and e_(2) are eccentricities of conies 5x^(2) + 9y^(2) = 45 and 5x^(2) - 4y^(2) = 45 then e_(1) .e_(2) = ……….

Given that (2 sqrt3 cos 30^(@) - 2i sin 30^(@))/(sqrt2 (cos 45^(@) + isin 45^(@)))=A + Bi, find the values of A and B.

If e^x=(sqrt(1+t)-sqrt(1-t))/(sqrt(1+t)+sqrt(1-t)) and tan (y/2)=sqrt((1-t)/(1+t)) then (dy)/dxat t=1/2 is

If a,b,c are the sides of Delta ABCand the lines ax+by+c=0, bx+cy+a=0, cx+ay+b=0 are concurrent, then Delta ABCis

If x = a cos^4 theta , y = a sin^4 theta then (dy)/(dx) at theta = (3 pi)/4 is

Find the mean deviation about the mean for the data : 4,7,8,9,10,12,13,17

The value of cos(67(1^(@))/(2)) is ………….

If r is in radius of Delta^("le")ABC and R is its circum radius then Delta^("le")ABC is rightangled triangle then minimum value of (R)/(r)

If the mid-points of the sides of a triangle AB, BC, CA are D(1, 2, -3), E(3, 0, 1) and F(-1, 1, -4), then the centriod of the triangle ABC is ____ .

Value of 'c' of Lagrange's mean theorem for f(x) = {:{ (2+x^(3) ,","if xlt 1),(3x,","if x gt 1 ):} on [-1,2]

For function f(x)=x"cos"(1)/(x),xge1,(2009)

Line makes right angled triangle with axis whose area is 6 unit and length of its hypoteneous is 5 unit. Find equation of line.

If tanx=(b)/(a), then find the value of sqrt((a+b)/(a-b))+sqrt((a-b)/(a+b)).

Fine the value of : (i) log 3(ii) log 23.45(iii) log 4.17 (iv) log 0.325(iv) log 0.0954(vi) log 0.00056

State which of the following sets are finite or infinite : {x : x in N and x is prime}

Consider the expansion of (x+a)^n Find the 6th ,7th and 8th terms in the expansion

Consider the following population and year graph (Fig 10.10), find the slope of the line AB and using it, find what will be the population in the year 2010?

Find the mean deviation using arithmetic mean for the following observations: (a) 68,32,49,54,21,38,59,41,66,76 (b) 28,12,17,35,22,18,5,32

IfABCD is a quadrilateral then Sec^(2) ((A+B)/(4))- Cot^(2) ((C+D)/(4))=

Differentiate the following functions w.r.t. x: tan (4x -7)

Show that the area of a rectangle inscribed in a circle is maximum when it is a square.

Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank spaces: 2. . .A

The minimum distance from the origin to a point on the curve x^(2//3) +y^(2//3)=a^(2//3) (a gt 0 ) is

The sums of n terms of two arithmetic progressions are in the ratio 5n + 4 : 9n + 6. Find the ratio of their 18^(th)terms.

There are three events A, B and C of which one and only one can happpen. If the odds are 5 to 4 agains A and 2 toagainst B,then odds against C is:

Compute the following limits. Lt_(xtooo)sqrt((x-sinx)/(x+cosx))

If sin h^(-1) (x) = log_(e) (5 + sqrt(26)) then x =

If probability of event A is (7)/(11), then give probability of its complement event A'?

The sum of a series of terms in A.P. is 128. If the first term is 2 and the last term is 14, find the common difference.

d/(dx){Cot^(-1)""(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))}

Find the mean deviation about the median for the following data:

Period of cos(x+2x + 3x +…+n x) is

Evaluate Lt_(xtooo)(sqrt(x^(2)+x)-x)

If |z-(9)/(z)|=6 then maximum value of |z| is ....

Find the values of sin 2 theta, cos 2 theta, and tan 2 theta, given : (i)sin theta = (3)/(5) , thetain Quadrant I. (ii) sin theta = 3/5 , thetain Quadrant II. (iii)sin theta= - (1)/(2), thetain Quadrant IV. (iv) tan theta =- (1)/(5) , theta in Quadrant II.

The sides of a triangle are three consecutive natural numbers and its largest angle is twice the smallerst one. Determine the sides of the triangle.

Given that N= {1, 2, 3, 4,……….., 100}. Then, write The subset of N whose elements are perfect square numbers.

cos 36^(@) - cos 72^(@) =

Write down the negation of following compound statements. x=2 and x=3 are roots of the quadratic equation x^(2)-5x+6=0

The triangle formed by 2x+3y+7=0 and the pair (2x+3y)^(2)-3(3x-2y)^(2)=0 is

If Tan A = (4)/(3), Tan B = (1)/(7) then A - B =

Find the modulus of the following using the property of modulus (3+2i)/(2-5i) + (3-2i)/(2+5i)

Find the domain of each of the following functions given by f(x)= (3x)/(28-x)

The negation of the statement 7 is greater than 8" is …………

Find the term independent of x in the expansion of (3/2x^(2) - 1/(3x))^(6).

Evaluate : lim_(x to 0) (e^(cos x)-1)/(cos x)