28278 + Interview Questions in Maths in Class 12 Page 557 InterviewSolution

27801.	Find the maximum number of points into which 4 circles and 4 straight lines intersect
Answer» ANSWER :50

Discussion

27802.	int_1^2xlogxdx
Answer» Solution :`int_1^2xlogxdx` [CHOOSE logx =IST x=2nd function] [logx CDOT (x^2/2)]_1^2-int_1^2(1/x) cdot(x^2/2) dx` 2log2 -1/4(4-1) =2log2-(3/4)

Discussion

27803.	If a= .^(20)C_(0) + .^(20)C_(3) + .^(20)C_(6) + .^(20)C_(9) + "…..", b = .^(20)C_(1) + .^(20)C_(4) + .^(20)C_(7) + "……"' and c = .^(20)C_(2) + .^(20)C_(5) + .^(20)C_(8) + "…..", then Value of a^(3) + b^(3) + c^(3) - 3abc is
Answer» Solution :We have `a+b+c = 2^(30)` Now, `a^(3) + b^(3) + c^(3) - c^(3) - 3abc` `= (a+b+c) (a+BOMEGA + comega^(2)) (a +bomega^(2) + comega)` `= 2^(20) (1+omega)^(20) (1+omega^(2))^(20)` `= 2^(20)`

Discussion

27804.	Find the value of k so that the lines (1-x)/(3) = (y-2)/(2k) = (z-3)/(2) and (1+x)/(3k) = (y-1)/(1) = (6-z)/(7) are perpendicular to each other.
Answer» ANSWER :K = -2

Discussion

27805.	If (sqrt(3)-i)^(50)= 2^(48)(x-iy), then x^(2)+y^(2) is equal to
Answer» `2` `4` `8` `16` ANSWER :D

Discussion

27806.	. Which of the following is the CORRECT combination ?
Answer» <P>(III) (II) (S) (IV) (i) ( R) (I) (ii) (P) (II) (ii) (Q) Answer :A

Discussion

27807.	int (1)/((2x+1)^((5)/(6))(3x+5)^((7)/(6)))dx=
Answer» `(6)/(7)((2x+1)/(3x+5))^(6)+C` `(6)/(7)((3x+5)/(2x+1))^((1)/(6))+c` `-(6)/(7)((2x+1)/(3x+5))^((1)/(6))+c` `-(6)/(7)((3x+5)/(3x+1))^((1)/(6))+c` ANSWER :1

Discussion

27808.	Locus of mid point of AB is
Answer» `X^(2) = - 2y ` `2X^(2) = - y` `x^(2) = - 4Y` `x^(2)/2 - y^(2)/1 = - 1` SOLUTION :N/A

Discussion

27809.	. Which of the following is the CORRECT combination ?
Answer» <P>(I) (III) (P) (IV) (ii) (P) (II) (iii) (Q) (III) (i) (S ) ANSWER :C

Discussion

27810.	A fair die is rolled. Consider events E = {1,3,5}, F = {2,3} and G = {2,3,4,5} Find (i) P(E\|F) and P(F\|E) (ii) P(E\|G) and P(G\|E) (iii) P((E cup F)\|G) and P((E cap F)\|G)
Answer» ANSWER :`(3)/(4)` and `(1)/(4)`

Discussion

27811.	. Which of the following is the CORRECT combination ?
Answer» (II) (i) (S) (L) (i) (R ) (IV) (iii) ( P) (III) (ii) (Q) Answer :B

Discussion

27812.	Find the maximum value of 2x^(3)-24x+107 in the interval [1, 3]. Find the maximum value of the same function in [-3,-1].
Answer» ANSWER :89, 139

Discussion

27813.	Ifa ne bthen theexpressionx^2- (a +b)x+ ( a^2- ab +b^2 )___negativevaluesforanyrealvalueofx
Answer» does not TAKE take none cannotbe determined Answer :A

Discussion

27814.	If x=2at, y=4/t." Find "(dy)/(dx)
Answer» ANSWER :`(DY)/(DX)=(-2)/(at^(2))`

Discussion

27815.	A : If x+y =12 then the minimum value of x^2+y^2 is 72 R : If x+y=k then the maximum value of xy is k^2
Answer» Both A and R are true and R is correct explanation of A Both A and R are true but R is not correct explanation of A A is true R is FALSE A is false but R is true Answer :A

Discussion

27816.	If a circle passes through the point (a,b)and cuts the circles x^(2) +y^(2) =4 orthogonally then the locus of its centre is
Answer» ` 2ax+ 2BY + a^(2) +b^(2) + 4= 0` ` 2ax-2by -(a^(2) +b^(2) +4) =0 ` ` 2ax -2by +(a^(2) +b^(2) +4) =0` ` 2ax+2by -(a^(2) +b^(2) +4) =0 ` Answer :D

Discussion

27817.	If the area bounded by the curves y=ax^2 and x=ay^2,(a gt 0) is 3.sq. units then the value of a is
Answer» `(2)/(3)` `(1)/(3)` 1 4 Answer :B

Discussion

27818.	Bag I contains 3 red and 4 black balls and Bag II contains 4 red and 5 black balls. One ball is transferred from Bag I to Bag II and then a ball is drawn from Bag II. The ball so drawn is found to be red in colour. Find the probability that the transferred ball is black.
Answer» ANSWER :`(16)/(31)`

Discussion

27819.	From 1,2,3,…..20 if two natural numbers are selected, find the probability of getting both even if sum of the selected numbers is even.
Answer» ANSWER :`(1)/(2)`

Discussion

27820.	If polars of A,B w.r.t to the circle having centre O and radius r intersect at P then OA^(2)-OB^(2)=AP^(2)-BP^(2)
Answer» ANSWER :`=AP^(2)-BP^(2)`

Discussion

27821.	Find the particular solution of the differential equations log((dy)/(dx)) = 3x + 4y given that y = 0 when x = 0.
Answer» ANSWER :`4e^(3x) + 3e^(-4Y) - 7 = 0`

Discussion

27822.	Write solution ofdy/dx=2/y,y(0)=0
Answer» SOLUTION :`dy/dx=2/yrArrintydy=int2dxrArry^2/2=2x+C` Using the CONDITION y (0)=0 we get C = 0 `therefore` The requaid solution is `y^2/2=2x"i.e",y^2=4x`

Discussion

27823.	Examine that sin \|x\| is a continuous function.
Answer» ANSWER :`SIN \|X\|`

Discussion

27824.	Draw the graph of y = e^(x) sin 2pix.
Answer» Solution :We have `y = f(x) = e^(x) sin 2PIX` First draw the GRAPH of `y = +-e^(x).` Now `sin 2pix = 0` when `2pix = npi` or x = n/2, where `n in Z` Also `sin 2pix = 1` for `2 pix = (4n + 1) (PI)/(2)` or `x = n + (1)/(4), n in Z` and `sin 2pix = - 1` for `2 pix = (4n - 1) (pi)/(2)` or `x = n - (1)/(4), n in Z` For `f(n + (1)/(4)) = e^(n + (1)/(4))` and `f(n - (1)/(4)) = -e^(n + (1)/(4))` All points `f(n + (1)/(4), e^(n + (1)/(4)))` lie on the graph of `y = e^(x)` and all points `f(n - (1)/(4), -e^(n - (1)/(4)))` lie on the graph of `y = -e^(x)` Thus, the graph of the function is as shown in the following figure.

Discussion

27825.	The order and degree of the differential equation (1+3y_(1))^(2//3) = 4y_(3) are
Answer» `2//3` 3,1 3,3 1,2 Answer :C

Discussion

27826.	If log_2 log_3 log_4 (x+1) =0, then x is greater than :-
Answer» 63 62 65 66

Discussion

27827.	Let g(x)=xf(x), where f(x)={{:(x^(2)sin.(1)/(x),":",x ne0),(0,":",x=0):}. At x=0,
Answer» G is DIFFERENTIABLE but g' is not g is differentiable while F is not differentiable both f and g are NON differentiable g is differentiable and g' is continuous Answer :D

Discussion

27828.	3+5+7+ …..sum to n terms
Answer» `N(n+2)` `n(n-2)` `n^(2)` `(n+1)^(2)` ANSWER :A

Discussion

27829.	From the employees of a company, 5 persons are selected to represent then in the managing committee of the company. The particulars of 5 persons are as follows : {:("S.No.","Name","Sex","Age in years"),(1,"Harish",M,""30),(2,"Rohan",M,""33),(3,"Sheetala",F,""46),(4,"Alis",F,""28),(5,"Salim",M,""41):} A person is selected at random from this group to act as spokesperson. Find the probability that the spokesperson will be either male or above 35 years.
Answer» ANSWER :`(4)/(5)`

Discussion

27830.	f (x) = lim _(x to oo) (x ^(2) + 2 (x+1)^(2n))/((x+1) ^(2n+1) + x^(2) +1),n in N and g (x) =tan ((1)/(2)sin ^(-1)((2f (x))/(1+f ^(2) (x)))), then lim _(x to 0^(-)){(f (x))/(tna ^(2)x)} +\|lim _(x to 2 ^(-))f (x)\|+ lim _(x to 2 ^(+)) (5 f (x)) is equal to (where {.} denotes fraction part function)
Answer» 7 8 12 Non-existent ANSWER :A

Discussion

27831.	If a, b and c are non-coplanar vectors and r is a real number, then the vectors a+2b+3c, lambdab+4c and (2lambda-1)c are non-coplanar for
Answer» no value of `lambda` all except ONE value of `lambda` all except two value of `lambda` all values of `lambda` SOLUTION :LET `alpha=a+2b+3c, beta=lambdab+4c` and `GAMMA (2lambda-1)c` Then,`[ alpha, beta, gamma] = \| (1, 2 , 3),(0 ,lambda, 4),(0,0,(2lambda-1))\|[ "a b c"]` `(alpha, beta, gamma] = lambda (2 lambda -1) [abc] ` Now, consider `lambda (2 lambda -1) =0` `lambda =0,(1)/(2) "" [ because [abc] ne 0]` Hence, `alpah, beta and gamma ` are non-coplanar for all value of `lambda` expcepttwo values`0 and (1)/(2)`.

Discussion

27832.	Solve the following equations. x^(5) + 1 = 0
Answer» ANSWER :`CIS(2k+1)pi/5,k=0,1,2,3,4`

Discussion

27833.	Coefficient of x^50 in (1+x)^1000 + 2x (1+x)^(999)+3x^2 (1+x)^(999) +…...+ 1001 x^(1000) is
Answer» `""^(1001) C_50` `""^(1000) C_(50)` `""^(1002) C_(50)` `""^(1002) C_(51)` Answer :C

Discussion

27834.	What do the {z:\|z-a\|+\|z+a\|=2c} "where" \|a\|lt c represent?
Answer» Solution :`{z:\|z-a\|+\|z+a\=2e}` `"where " \|a\|lt` ` Here z is a COMPLEX number . Let `z=x=iy.` `:.(xy)` is the point corresponding the complex number z. 'a' and '-a' be TWO fixed points. `:.`Eqn.(1) implies that the SUM of the distancer of the point (x,y) from two points a' and '-a` is CONSTANT i.e.2c `:.` The locat is an ellipse.

Discussion

27835.	Compute the following: [[cos^2x, sin^2x],[sin^2x, cos^2x]]+[[sin^2x, cos^2x],[cos^2x, sin^2x]]
Answer» SOLUTION :GIVEN SUM=`[[cos^2x+sin^2x, sin^2x+cos^2x],[sin^2x+cos^2x, cos^2x+sin^2x]]=[[1,1],[1,1]]`

Discussion

27836.	If the line (x-3)/2=(y+k)/(-1)=(z+1)/(-5) lies on the plane 2x-y+z-7 = 0, then k = - (2,-1,-2)
Answer» ANSWER :2

Discussion

27837.	Derivative of tan2x6xtan8xw.r.t.x is
Answer» `8SEC^(2)8x+6sec^(2)6x+sec^(2)2X` `sec^(2)8x+6sec^(2)6x+sec^(2)2x` `8sec^(2)8x-sec6sec^(2)6x-2sec^(2)2x` `sec^(2)8x-sec^(2)6x-sec^(2)2x` ANSWER :C

Discussion

27838.	The solution of (x+3)/(x-2) le 2is
Answer» `(-oo ,oo)` `(-oo, 2] uu (7, oo)` `(-oo, 2) uu [7 , oo)` `[7,oo)` ANSWER :C

Discussion

27839.	Find the number· of proper divisors of 15!
Answer» ANSWER :4030

Discussion

27840.	If \|(a^(2)+lamda^(2),ab+clamda,ca-blamda),(ab-clamda,b^(2)+lamda^(2),bc+alamda),(ca+blamda,-bc+alamda, c^(2)+lamda^(2))\|\|(lamda,c,-b),(-c,lamda,a),(b,-a,lamda)\|=(1+a^(2)+b^(2)+c^(2))^(3), then find the value of lamda.
Answer» Solution :We observe that the elements in the prefactor are the cofactors of the corresponding elements of the post factor. Hence L.H.S. `=\|(lamda, C, -b),(-c, lamda, a),(b, -a, lamda)\|^(3)=[lamda(lamda^(2)+a^(2)+b^(2)+c^(2))]^(3)=(1+a^(2)+b^(2)+c^(2))^(2)implieslamda=1`

Discussion

27841.	Assertion (A): The number of ways in which 4 sovereings can be given away when there are 6 applicants and any applicant may have either 0, 1, 2, 3 or 4 sovereigns is 126. Reason (R) : The number of ways that n sovereigns can be given away when there are k applicants and any applicant may have either 0,1,2,.... or n sovereigns is ""^((n+k-1))C_(k-1). The correct answer is
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

27842.	Evaluate the following determinates \|{:(0,1,sectheta),(tantheta,-sectheta,tantheta):}\|
Answer» ANSWER :`sec^2theta`

Discussion

27843.	If two dice are thrown simultaneously, then the probability that the sum of the numbers which come up on the dice to be more than 5 is_________
Answer» `(13)/(18)` `(5)/(18)` `(1)/(6)` `(5)/(36)` ANSWER :A

Discussion

27844.	sec^2(tan^(-1)(2))+"cosec"^2(cos^(-1)(3)) is equal to
Answer» 3 10 15 20 Answer :C

Discussion

27845.	Find thescalar and vector components of the vector withinitial point (2,1) and terminal point (-5,7).
Answer» ANSWER :VECTOR `VEC(AB)` are `7hati,6hatj`.

Discussion

27846.	Find AB, if A=[(6,9),(2,3)] and B=[(2,6,0),(7,9,8)].
Answer» ANSWER :`[{:(75,117,72),(25,39,24):}]`

Discussion

27847.	int e^(x^3) . 5^(x^2) . x. [2log 5+ 3x] dx = …...... + C.
Answer» `E^( X^3) . 5^(x^2) .x` `(1)/(6).e^(x^3) . 5^(x^2)` `(1)/(6) .e^(x^3) . 5^(x^2) .x` `e^(x^3) . 5^(x^2)` ANSWER :D

Discussion

27848.	Let A = ((a,b),(c,d)) where a,b,c,d in R . Ad ne 0 If (a+d) A-A^(2) =A then
Answer» a=d a=d=1 a+d=0 a+d=1 Answer :B

Discussion

27849.	Differentiate the functionsx^(x cos x) + (x^(2) + 1)/(x^(2)-1)
Answer» Answer :`x^(x cos x) [cos x. (LOG +1)-x.log x.sin x] - (4X)/((x^(2)-1)^(2))`

Discussion

27850.	Find the area bounded by curves y=[cosA+cosS+cosC] and y=[7sin.(A)/(2)sin.(B)/(2)sin.(C )/(2)] (where [.] denotes the greatest integer function and A,B, C are angles of a triangle) and curve \|x-4\|+\|y\|=2.
Answer» ANSWER :3

Discussion

Explore topic-wise InterviewSolutions in .

Find the maximum number of points into which 4 circles and 4 straight lines intersect

int_1^2xlogxdx

If a= .^(20)C_(0) + .^(20)C_(3) + .^(20)C_(6) + .^(20)C_(9) + "…..", b = .^(20)C_(1) + .^(20)C_(4) + .^(20)C_(7) + "……"' and c = .^(20)C_(2) + .^(20)C_(5) + .^(20)C_(8) + "…..", then Value of a^(3) + b^(3) + c^(3) - 3abc is

Find the value of k so that the lines (1-x)/(3) = (y-2)/(2k) = (z-3)/(2) and (1+x)/(3k) = (y-1)/(1) = (6-z)/(7) are perpendicular to each other.

If (sqrt(3)-i)^(50)= 2^(48)(x-iy), then x^(2)+y^(2) is equal to

. Which of the following is the CORRECT combination ?

int (1)/((2x+1)^((5)/(6))(3x+5)^((7)/(6)))dx=

Locus of mid point of AB is

. Which of the following is the CORRECT combination ?

A fair die is rolled. Consider events E = {1,3,5}, F = {2,3} and G = {2,3,4,5} Find﻿ (i) P(E|F) and P(F|E) (ii) P(E|G) and P(G|E)﻿ (iii) P((E cup F)|G) and P((E cap F)|G)﻿

. Which of the following is the CORRECT combination ?

Find the maximum value of 2x^(3)-24x+107 in the interval [1, 3]. Find the maximum value of the same function in [-3,-1].

Ifa ne bthen theexpressionx^2- (a +b)x+ ( a^2- ab +b^2 )___negativevaluesforanyrealvalueofx

If x=2at, y=4/t." Find "(dy)/(dx)

A : If x+y =12 then the minimum value of x^2+y^2 is 72 R : If x+y=k then the maximum value of xy is k^2

If a circle passes through the point (a,b)and cuts the circles x^(2) +y^(2) =4 orthogonally then the locus of its centre is

If the area bounded by the curves y=ax^2 and x=ay^2,(a gt 0) is 3.sq. units then the value of a is

Bag I contains 3 red and 4 black balls and Bag II contains 4 red and 5 black balls.﻿ One ball is transferred from Bag I to Bag II and then a ball is drawn from Bag II.﻿ The ball so drawn is found to be red in colour. Find the probability that the﻿ transferred ball is black.﻿

From 1,2,3,…..20 if two natural numbers are selected, find the probability of getting both even if sum of the selected numbers is even.

If polars of A,B w.r.t to the circle having centre O and radius r intersect at P then OA^(2)-OB^(2)=AP^(2)-BP^(2)

Find the particular solution of the differential equations log((dy)/(dx)) = 3x + 4y given that y = 0 when x = 0.

Write solution ofdy/dx=2/y,y(0)=0

Examine that sin |x| is a continuous function.

Draw the graph of y = e^(x) sin 2pix.

The order and degree of the differential equation (1+3y_(1))^(2//3) = 4y_(3) are

If log_2 log_3 log_4 (x+1) =0, then x is greater than :-

Let g(x)=xf(x), where f(x)={{:(x^(2)sin.(1)/(x),":",x ne0),(0,":",x=0):}. At x=0,

3+5+7+ …..sum to n terms

f (x) = lim _(x to oo) (x ^(2) + 2 (x+1)^(2n))/((x+1) ^(2n+1) + x^(2) +1),n in N and g (x) =tan ((1)/(2)sin ^(-1)((2f (x))/(1+f ^(2) (x)))), then lim _(x to 0^(-)){(f (x))/(tna ^(2)x)} +|lim _(x to 2 ^(-))f (x)|+ lim _(x to 2 ^(+)) (5 f (x)) is equal to (where {.} denotes fraction part function)

If a, b and c are non-coplanar vectors and r is a real number, then the vectors a+2b+3c, lambdab+4c and (2lambda-1)c are non-coplanar for

Solve the following equations. x^(5) + 1 = 0

Coefficient of x^50 in (1+x)^1000 + 2x (1+x)^(999)+3x^2 (1+x)^(999) +…...+ 1001 x^(1000) is

What do the {z:|z-a|+|z+a|=2c} "where" |a|lt c represent?

Compute the following: [[cos^2x, sin^2x],[sin^2x, cos^2x]]+[[sin^2x, cos^2x],[cos^2x, sin^2x]]

If the line (x-3)/2=(y+k)/(-1)=(z+1)/(-5) lies on the plane 2x-y+z-7 = 0, then k = - (2,-1,-2)

Derivative of tan2x6xtan8xw.r.t.x is

The solution of (x+3)/(x-2) le 2is

Find the number· of proper divisors of 15!

If |(a^(2)+lamda^(2),ab+clamda,ca-blamda),(ab-clamda,b^(2)+lamda^(2),bc+alamda),(ca+blamda,-bc+alamda, c^(2)+lamda^(2))||(lamda,c,-b),(-c,lamda,a),(b,-a,lamda)|=(1+a^(2)+b^(2)+c^(2))^(3), then find the value of lamda.

Evaluate the following determinates |{:(0,1,sectheta),(tantheta,-sectheta,tantheta):}|

If two dice are thrown simultaneously, then the probability that the sum of the numbers which come up on the dice to be more than 5 is_________

sec^2(tan^(-1)(2))+"cosec"^2(cos^(-1)(3)) is equal to

Find thescalar and vector components of the vector withinitial point (2,1) and terminal point (-5,7).

Find AB, if A=[(6,9),(2,3)] and B=[(2,6,0),(7,9,8)].

int e^(x^3) . 5^(x^2) . x. [2log 5+ 3x] dx = …...... + C.

Let A = ((a,b),(c,d)) where a,b,c,d in R . Ad ne 0 If (a+d) A-A^(2) =A then

Differentiate the functionsx^(x cos x) + (x^(2) + 1)/(x^(2)-1)

Find the area bounded by curves y=[cosA+cosS+cosC] and y=[7sin.(A)/(2)sin.(B)/(2)sin.(C )/(2)] (where [.] denotes the greatest integer function and A,B, C are angles of a triangle) and curve |x-4|+|y|=2.

A fair die is rolled. Consider events E = {1,3,5}, F = {2,3} and G = {2,3,4,5} Find (i) P(E|F) and P(F|E) (ii) P(E|G) and P(G|E) (iii) P((E cup F)|G) and P((E cap F)|G)

Bag I contains 3 red and 4 black balls and Bag II contains 4 red and 5 black balls. One ball is transferred from Bag I to Bag II and then a ball is drawn from Bag II. The ball so drawn is found to be red in colour. Find the probability that the transferred ball is black.