28278 + Interview Questions in Maths in Class 12 Page 53 InterviewSolution

2601.	int (5x^(8)+7x^(6))/((x^(2)+1+2x^(7))^(2))dx=
Answer» `(x^(5))/(2x^(7)+x^(2)+1)+c` `(x^(7))/(2x^(7)+x^(2)+1)+c` `(x^(8)+x^(6))/(2x^(7)+x^(2)+1)+c` `(35x^(7))/(2x^(7)+x^(2)+1)+c` Answer :2

Discussion

2602.	P(theta ) and Q( phi )are two point onx^(2)//a^(2) -y^(2)//b^(2) =1such thattheta - phi = 2alpha .PQtouches the conic
Answer» ` (x^(2) cos ^(2) ALPHA )/( a^(2)) -(y^(2))/( B^(2)) =1` ` (x^(2))/( a^(2)) -(x^(2)cos ^(2) a)/( b^(2)) =1` ` (x^(2))/(a^(2)) =(y^(2))/(b^(2)) = cos ^(2) alpha ` none ANSWER :A

Discussion

2603.	C is the centre, AA' and BB' are major and minor axis of the ellipse. x^2/a^2+y^2/b^2=1. If PN is the ordinate f a point P on the ellipse then show that (PN)^2/((A'N)(AN))=(BC)^2/(CA)^2
Answer» ANSWER :`(BC)^2/(CA)^2=b^2/a^2implies (PN)^2/((A'N)(AN))=(BC)^2/(CA)^2`

Discussion

2604.	Find x , if [x-5-1][{:(1,0,2),(0,2,1),(2,0,3):}][{:(x),(4),(1):}]=O.
Answer» ANSWER :`thereforex^(2)=48=+-4sqrt(3)`

Discussion

2605.	By using elementary operations , find the inverse of the matrix A=[{:(1,2),(2,-1):}]
Answer» ANSWER :`=[{:((1)/(5),(2)/(5)),((2)/(5),(-1)/(5)):}]`

Discussion

2606.	From the following data, find () regression coefficients (ii) regression equations.
Answer» ANSWER :(i) ` b_(YX)= 0.74 b_(xy) =1.33` (II) Regressionequation of y or x : y= 0.74 x - 0. 5 Regression equation of x or y : x = 1.33y + 0. 72

Discussion

2607.	If (1 + x)^(n) = C_(0) + C_(1)x + C_(2)x + ….. + C_(n) x^(n) then show that the sum of the products of the C_(i) is taken two at a time represented by sum sum C_(i) C_(j) is equal to 0 le I lt j n 2^(2n - 1) - ((2n!))/(2(n!)^(2)).
Answer» Solution :We know that , `2SUM _(0) sum_(leile j lt n)sum C_i C_j=sum_(i=0)^(n)sum_(j=0)^(n)C_(i=0)^(n)sum_(j=0)^(n)C_i C_J- sum_(i=0)^(n)sum_(j=0)^(n)C_i C_j =sum_(i=0)^(n)C_i sum_(j=0)^(n)C_(j) -sum_(i=0)^(n)C_(i)^(2)` `=2^n 2^n -(.^2n C_n)=2^2n -.^2n C_n` `therefore sum sum_(0 LE i n j le n) C_iC_j=(2^2n -.^2n C_N)/(2)=2^(2n-1)-((2n)!)/(2(n!))`.

Discussion

2608.	If bar(x)_(1) and bar(x)_(2) are the means of two distribution such that bar(x_(1)) lt bar(x_(2)), bar(x) is mean of the combined distribution then
Answer» `BAR(X) lt bar(x_(1))` `bar(x) gt bar(x_(2))` `bar(x) = (bar(x)_(1) + bar(x)_(2))/(2)` `bar(x)_(1) lt bar(x) lt bar(x)_(2)` ANSWER :D

Discussion

2609.	int(a^2sin^2x+b^2cos^2x)/(sin^2x)dx
Answer» SOLUTION :`INT(a^2sin^2x+b^2cos^2x)DX/(sin^22x)`

Discussion

2610.	If the asymptotes of the hyperbolaperpendicular to the asymptotes of the hyperbola(x^(2))/(49)-(y^(2))/(b^(2))=1 then
Answer» `7apm6b=0` `6a+7b=0` `a^(2)-B^(2)=1` a-b=1 Answer :a

Discussion

2611.	Solve[x sin^(2)((y)/(x)) - y] dx + x dy = 0,
Answer»

Discussion

2612.	Find the coordinates of the point at unit distance from the lines 3x-4y + 1 = 0, 8x +6y +1 = 0
Answer» Answer :`(6/5,(-1)/10) ,((-2)/5,(-13)/10),(0,3/2),((-8)/5,3/10)`

Discussion

2613.	If p, q and r are perpendicular to q + r, r + p and p + q respectively and if \|p + q\| = 6, \|q + r\| = 4sqrt(3) and \|r + p\| = 4, then \|p + q + r\| is
Answer» `5sqrt(2)` 10 15 5 Solution :`\|p+q\|=6implies \|p+q\|^(2)=36` `implies p^(2) +q^(2)+2p.q=36` Similarly `q^(2)+r^(2)+2q.r=48` ` andr^(2) +p^(2)+2r .p =16` Addingall weget `2( p^(2)+q^(2)r^(2)+p.q+q.r+r.p)=36+48+16` `implies 2(p^(2)+q^(2)+r^(2))=100` `[ :'p.q+q.r+r.p=0]` `implies p^(2)+q^(2)+r^(2)=50` `=\|p+q+r\|^(2)=50` `implies \|p+q+r\|=5sqrt(2)`

Discussion

2614.	if x^(2)+3x+2 lt 0 and f(x)=x^(2)-3x+2, then
Answer» `0 lt f(x) lt 6` `f(x) ge (3)/(2)` `f(x) gt 12` `f(x)GT0` Solution :The problem is asking for the range of f(x) values for values of x that satisfy the inequality. FIRST GRAPH the inequality in `Y_(1)`, STARTING with the standardd window and zooming in until the x values for the portion of the graph that falls below the x-axis can be identified as the interval (-2,-1). then enter the formula for f(x0 in `Y_(2)`. although it can be done graphically, the simplest way to find the range of values of f(x) that correspond to `x epsi(-2,-1) ` is to use the TABLE function. deselct `Y_(1)` and enter TBLSET and set TblStart to -2, `DeltaTbl=0.1`, and Indpnt and Depend to Auto. then enter TABLE and observe that the `Y_(2)` values range from 12 to 6 as x ranges from -2 to 1, YIELDING the correct answer, choice E. The greatest integer less tha orr equal to x is int(x) on the graphing calculator. enter abs(x)+int(x) int `Y_(1)`. Return to the home screen, and enter `Y_(1)(-2.5)+Y_(1)(1.5)` to get the correct answer, choice D.

Discussion

2615.	Lt_(n rarr oo)(1)/(n)[e^((1)/(n))+e^((2)/(n))+....+e^((n)/(2))]
Answer» ANSWER :`e-1`

Discussion

2616.	Let alphaand betaare roots x^(2) - 7 . 32 x - 3 =0 and let A_(n) = alpha_(n) + beta_(n), "then " (A_(36) - 3 A_(35))/( A_(36)) isequal to _________
Answer» ANSWER :`7 . 32`

Discussion

2617.	If int(1)/((e^(x)-1)^(2))dx=f(x)-log\|g(x)\|+c, then :
Answer» `D_(F)=R` `D_(f)=R-{0}` `f(x)=1-e^(-x)` `G(x)=1-e^(x)`. ANSWER :B

Discussion

2618.	A tangent is drawn to the ellipse(x^(2))/( 27 ) +y^(2) =1 at the point (3sqrt3 cos theta, sin theta) "where"0 lt theta lt (pi )/(2)then the sum of the intercepts of the tangent with the coordinate axes is least when theta =
Answer» `(PI )/( 6) ` ` ( pi )/(3) ` ` ( pi )/(8) ` ` ( pi )/(4) ` Answer :A

Discussion

2619.	Find the centre, eccentricity, foci directrices and the length of the latus rectum of the following hyperbolas(i) 4x^(2) - 9y^(2) - 8x - 32 = 0 (ii)4(y + 3)^(2) + 9(x - 2)^(2) = 1
Answer» ANSWER :`(4)/(9)`

Discussion

2620.	Let S and S' be the two foci of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 if the circle described on SS' as diameter: to ches the ellipse in real point, then find the eccentricity of the ellipse.
Answer» ANSWER :`(1)/(SQRT(2))`

Discussion

2621.	Let A=[[1,2,3,4,1], [4,5,6,1,2], [3,9,1,1,6]]What is the order of A?
Answer» SOLUTION :ORDER of A is `(3xx5)`

Discussion

2622.	Show that the number of ways to select 'r' objects from ndistinct objects which are arranged along a row so that no two of the selected objects are consecutive is ""^((n-r+1))C_r," where "ge2r-1
Answer» ANSWER :`""^((n-r+1))C_r," where "ge2r-1`

Discussion

2623.	Evaluate int(a tan x - b cot x)^(2) dx
Answer» Answer :`a^(2) tan X + B^(2) (-COT x) - (a + b)^(2) x + c`

Discussion

2624.	If z= x+iy , z^(1//3) = a- ib and (x)/(a) - (y)/(b) = lambda (a^(y)-b^(y) ), then lambda is equal to
Answer» 1 2 3 4 Answer :D

Discussion

2625.	Two persons A and B stand in a row with 10 other persons. What is the probability that three are exactly two persons between A and B.
Answer» ANSWER :`(3)/(22)`

Discussion

2626.	int (dx)/(cos x - sin x )=
Answer» `(1)/(SQRT(2)) log \| tan ((X)/(2) - (pi)/(8))\| +C ` `(1)/(sqrt(2)) log \| tan ((x)/(2) + (3pi)/(8))\| +c ` `(1)/(sqrt(2)) log \| tan ((x)/(2) - (3pi)/(8))\| +c ` `(1)/(sqrt(2)) log \|COT""(x)/(2) \|+c` Answer :A

Discussion

2627.	Two dice are thrown simultaneously. The events A, B, C, D are described as follows: A = Getting an even number on the first die B = Getting an odd number on the first die C = Getting atmost 5 as sum of the numbers on the two dice D = Getting the sum of the numbers on the dice greater than 5 but less than 10 Which of the following statements is true?
Answer» A and D are MUTUALLY exclusive A and B are mutually exclusive and EXHAUSTIVE events A and C are mutually exclusive events C and D are mutually exclusive and exhaustive events Answer :B

Discussion

2628.	If the sine of the angles of DeltaABC satisfy the equation c^(3)x^(3)-c^(2) (a+b+c)x^(2)+lx +m=0 (where a,b,c are the sides of DeltaABC), then DeltaABC is
Answer» ALWAYS right angled for any L, m right angled only when `l=c (AB+bc+ca) =c sum ab, m=-abc` right angled only when `l= (c sum ab)/(4) , m=-(abc)/(8)` NEVER right angled Answer :B

Discussion

2629.	Compute the (10!)/(5i)
Answer» Solution :`(10!)/(5!)=109876=30240`

Discussion

2630.	Let f(x)=x^(2)+4x+1. Then
Answer» `f(X) gt 0` for all x `f(x) gt 1` when `x ge 0` `f(x) ge 1` when `x le -4` `f(x) = f(-x)` for all x. ANSWER :C

Discussion

2631.	Let A=[[1,2,3,4,1], [4,5,6,1,2], [3,9,1,1,6]]Write down A^T.
Answer» SOLUTION :`A^T=[[1,4,3],[2,5,9],[3,6,1],[4,1,1],[1,2,6]]`

Discussion

2632.	Three vectors veca,vecbandvecc satisfy the condition veca+vecb+vecc=vec0 . Evaluate the quantity mu=vecavecb+vecbvecc+vecc*veca,if \|veca\|=3,\|vecb\|=4and\|vecc\|=2.
Answer» ANSWER :`-(21)/2`

Discussion

2633.	Evaluate the following integrals intxlog(1+x)dx
Answer» ANSWER :`(x^(2))/(2)log(1+x)-(x^(2))/(4)+(x)/(2)-(1)/(2)-log(1+x)+C`

Discussion

2634.	If the third term in the expansion of ((1)/(x)+x^(log_10 x) x)^5 is 1000, then x=
Answer» 100 10 1 `1//sqrt10` ANSWER :A

Discussion

2635.	Evalute the following integrals int (1)/((1 + sqrt(x)) sqrt(x - x^(2)) )dx on (0,1)
Answer» Answer :`(2(SQRT(X)-1))/(sqrt(1-x)) + C `

Discussion

2636.	Angle between tangents drawn at ends of focal chord of parabola y^(2) = 4ax is
Answer» `(PI)/(2)` `(pi)/(3)` `(pi)/(4)` `(pi)/(6)` Answer :A

Discussion

2637.	Ifonerootof x^3- 12x^2 +kx -18=0is thricethe sumof remainingtworootsthenk=
Answer» 29 `-29` `19` `15` ANSWER :A

Discussion

2638.	Show that semi - vertical angle of right circular cone of given surface area and maximum volume is sin^(-1)((1)/(3)).
Answer» ANSWER :`ALPHA = SIN^(-1)((1)/(3))`

Discussion

2639.	If 'c' is small in comparison with l then ((l)/(l+c))^(1//2) + ((l)/(l-c))^(1//2)=
Answer» `2 + (3c)/(4L)` `2 + (3c^2)/(4l^2)` `l + (3c^2)/(4l^2)` `l + (3c)/(4l)` ANSWER :B

Discussion

2640.	p : sqrt(39) is irrational To check the validity of statement p , which of the following method we can use
Answer» DIRECT method Conteapositive method Contrapositive method By GIVING a counter EXAMPLE Answer :C

Discussion

2641.	If the expansion (4a - 8x)^(1//2) were to possible then
Answer» `2LT \|a/x\|` `2 GT \|a/x\|` `2lt \|x/a\|` `2gt\|x/a\|` ANSWER :A

Discussion

2642.	Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P(E cap F) = 0.2, find P(E\|F) and P(F\|E).
Answer» <P> ANSWER :`P(E\|F)=(2)/(3), P(F\|E)=(1)/(3)`

Discussion

2643.	(sqrt(2)-1)/(sqrt(2))+(3-2sqrt(2))/(4)+(5sqrt(2)-7)/(6sqrt(2))+……oo=
Answer» log 2 log 3 `log sqrt(2)` `log sqrt(3)` ANSWER :C

Discussion

2644.	Form the differential equation by eliminating a, b from y = ae^(3x) + be^(4x)
Answer» `(d^(2)y)/(DX^(2)) + 7 (dy)/(dx) + 12Y = 0` `(d^(2) y)/(dx^(2)) - 7 (dy)/(dx) - 12y =0` `(d^(2) y)/(dx^(2)) - 7 (dy)/(dx) + 12 y = 0` `(d^(2) y)/(dx^(2)) + 7 (dy)/(dx) + 12y = 0` Answer :C

Discussion

2645.	Evaluateintx^(5) e^(x) dx
Answer» Answer :`e^(x)[x^(5)-5X^(4)+20x^(3)-60X^(2)+120x-120]+c`

Discussion

2646.	if underset(r=1)overset(m)Sigma(r^(2)+1)r! =100xx101! then m equals
Answer» 100 101 102 None of these Answer :A

Discussion

2647.	Which of the following equation (s) is/ are linear?
Answer» `dy/dx + y /X = LOG x` `y(dy/dx) + 4X =0` ` (2X + y^(3))(dy/dx) = 3y ` `dy/dx = ((AX^(3) - 2x^(2) y + y ))/ (x(1 - x^(2))` Answer :A::B::C::D

Discussion

2648.	If A,B,C are the angles of a triangle, then the value of cot.(A)/(2)+cot.(B)/(2)+cot.(C )/(2) is
Answer» `(R)/(s)` `(s)/(R)` `(DELTA)/(s^(2))` `(s^(2))/(Delta)` ANSWER :D

Discussion

2649.	int (dx)/( e^(x) + e^(-x) +2) is equal to
Answer» `(1)/( E^(X) +1) +C` `(1)/( 1 + e^(-x)) + C` `- ( 1)/( e^(x) +1) + C` NONE of these Answer :C

Discussion

2650.	int_(0)^(1)sqrt((1+x)/(1-x))dx=
Answer» 1)`pi/2` 2)`pi/2-1` 3)`pi/2` 4)`pi/2+1` ANSWER :D

Discussion

Explore topic-wise InterviewSolutions in .

int (5x^(8)+7x^(6))/((x^(2)+1+2x^(7))^(2))dx=

P(theta ) and Q( phi )are two point onx^(2)//a^(2) -y^(2)//b^(2) =1such thattheta - phi = 2alpha .PQtouches the conic

C is the centre, AA' and BB' are major and minor axis of the ellipse. x^2/a^2+y^2/b^2=1. If PN is the ordinate f a point P on the ellipse then show that (PN)^2/((A'N)(AN))=(BC)^2/(CA)^2

Find x , if [x-5-1][{:(1,0,2),(0,2,1),(2,0,3):}][{:(x),(4),(1):}]=O.

By using elementary operations , find the inverse of the matrix A=[{:(1,2),(2,-1):}]

From the following data, find () regression coefficients (ii) regression equations.

If (1 + x)^(n) = C_(0) + C_(1)x + C_(2)x + ….. + C_(n) x^(n) then show that the sum of the products of the C_(i) is taken two at a time represented by sum sum C_(i) C_(j) is equal to 0 le I lt j n 2^(2n - 1) - ((2n!))/(2(n!)^(2)).

If bar(x)_(1) and bar(x)_(2) are the means of two distribution such that bar(x_(1)) lt bar(x_(2)), bar(x) is mean of the combined distribution then

int(a^2sin^2x+b^2cos^2x)/(sin^2x)dx

If the asymptotes of the hyperbolaperpendicular to the asymptotes of the hyperbola(x^(2))/(49)-(y^(2))/(b^(2))=1 then

Solve[x sin^(2)((y)/(x)) - y] dx + x dy = 0,

Find the coordinates of the point at unit distance from the lines 3x-4y + 1 = 0, 8x +6y +1 = 0

If p, q and r are perpendicular to q + r, r + p and p + q respectively and if |p + q| = 6, |q + r| = 4sqrt(3) and |r + p| = 4, then |p + q + r| is

if x^(2)+3x+2 lt 0 and f(x)=x^(2)-3x+2, then

Lt_(n rarr oo)(1)/(n)[e^((1)/(n))+e^((2)/(n))+....+e^((n)/(2))]

Let alphaand betaare roots x^(2) - 7 . 32 x - 3 =0 and let A_(n) = alpha_(n) + beta_(n), "then " (A_(36) - 3 A_(35))/( A_(36)) isequal to _________

If int(1)/((e^(x)-1)^(2))dx=f(x)-log|g(x)|+c, then :

A tangent is drawn to the ellipse(x^(2))/( 27 ) +y^(2) =1 at the point (3sqrt3 cos theta, sin theta) "where"0 lt theta lt (pi )/(2)then the sum of the intercepts of the tangent with the coordinate axes is least when theta =

Find the centre, eccentricity, foci directrices and the length of the latus rectum of the following hyperbolas(i) 4x^(2) - 9y^(2) - 8x - 32 = 0 (ii)4(y + 3)^(2) + 9(x - 2)^(2) = 1

Let S and S' be the two foci of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 if the circle described on SS' as diameter: to ches the ellipse in real point, then find the eccentricity of the ellipse.

Let A=[[1,2,3,4,1], [4,5,6,1,2], [3,9,1,1,6]]What is the order of A?

Show that the number of ways to select 'r' objects from ndistinct objects which are arranged along a row so that no two of the selected objects are consecutive is ""^((n-r+1))C_r," where "ge2r-1

Evaluate int(a tan x - b cot x)^(2) dx

If z= x+iy , z^(1//3) = a- ib and (x)/(a) - (y)/(b) = lambda (a^(y)-b^(y) ), then lambda is equal to

Two persons A and B stand in a row with 10 other persons. What is the probability that three are exactly two persons between A and B.

int (dx)/(cos x - sin x )=

If the sine of the angles of DeltaABC satisfy the equation c^(3)x^(3)-c^(2) (a+b+c)x^(2)+lx +m=0 (where a,b,c are the sides of DeltaABC), then DeltaABC is

Compute the (10!)/(5i)

Let f(x)=x^(2)+4x+1. Then

Let A=[[1,2,3,4,1], [4,5,6,1,2], [3,9,1,1,6]]Write down A^T.

Three vectors veca,vecbandvecc satisfy the condition veca+vecb+vecc=vec0 . Evaluate the quantity mu=veca*vecb+vecb*vecc+vecc*veca,if |veca|=3,|vecb|=4and|vecc|=2.

Evaluate the following integrals intxlog(1+x)dx

If the third term in the expansion of ((1)/(x)+x^(log_10 x) x)^5 is 1000, then x=

Evalute the following integrals int (1)/((1 + sqrt(x)) sqrt(x - x^(2)) )dx on (0,1)

Angle between tangents drawn at ends of focal chord of parabola y^(2) = 4ax is

Ifonerootof x^3- 12x^2 +kx -18=0is thricethe sumof remainingtworootsthenk=

Show that semi - vertical angle of right circular cone of given surface area and maximum volume is sin^(-1)((1)/(3)).

If 'c' is small in comparison with l then ((l)/(l+c))^(1//2) + ((l)/(l-c))^(1//2)=

p : sqrt(39) is irrational To check the validity of statement p , which of the following method we can use

If the expansion (4a - 8x)^(1//2) were to possible then

Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and﻿ P(E cap F) = 0.2, find P(E|F) and P(F|E)﻿.

(sqrt(2)-1)/(sqrt(2))+(3-2sqrt(2))/(4)+(5sqrt(2)-7)/(6sqrt(2))+……oo=

Form the differential equation by eliminating a, b from y = ae^(3x) + be^(4x)

Evaluateintx^(5) e^(x) dx

if underset(r=1)overset(m)Sigma(r^(2)+1)r! =100xx101! then m equals

Which of the following equation (s) is/ are linear?

If A,B,C are the angles of a triangle, then the value of cot.(A)/(2)+cot.(B)/(2)+cot.(C )/(2) is

int (dx)/( e^(x) + e^(-x) +2) is equal to

int_(0)^(1)sqrt((1+x)/(1-x))dx=

Three vectors veca,vecbandvecc satisfy the condition veca+vecb+vecc=vec0 . Evaluate the quantity mu=vecavecb+vecbvecc+vecc*veca,if |veca|=3,|vecb|=4and|vecc|=2.

Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P(E cap F) = 0.2, find P(E|F) and P(F|E).