28278 + Interview Questions in Maths in Class 12 Page 138 InterviewSolution

6851.	The value of (cos2 theta + i sin 2 theta)^5(sin theta+i cos theta)^4 is
Answer» `cos10 theta+i sin 10 theta` `COS6 theta-i sin6theta` `cos6 theta+i sin6 theta` `COS 10 theta-i sin 10 theta` ANSWER :C

Discussion

6852.	Integrate the following functions. int(dx)/(sin^(3)xcos^(5)x)
Answer» ANSWER :`-(1)/(2)cot^(2)x+(1)/(4)tan^(4)x+3log\|tanx\|+(3)/(2)+tan^(2)x+c`

Discussion

6853.	The sum of the series1 + 2.2 + 3.2^(2) + 4.2^(3) + 5.2^(4) + ……… + 100.2^(99) is
Answer» `99.2^(100)` `100.2^(100)` `99.2^(100) + 1` `1000.2^(100)` ANSWER :C

Discussion

6854.	Two systems of rectangular axis have the same origin. If a plane cuts them at distances a, b, c and a', b', c', respectively from the origin, then prove that (1)/(a^2)+(1)/(b^2)+(1)/(c^2)=(1)/((a')^2)+(1)/((b')^2)+(1)/((c')^2).
Answer» ANSWER :`(1)/(a^2)+(1)/(b^2)+(1)/(C^2)=(1)/((a')^2)+(1)/((b')^2)+(1)/((c')^2)` which is REQUIRED RESULT

Discussion

6855.	One ticket is selected at random from 50 tickets numbered 00, 01, 02, ……49. Then the probability that the sum of the digites on the selected ticket is 8, given that the product of these digits is zero, equals
Answer» `(1)/(4)` `(5)/(14)` `(1)/(50)` `(1)/(14)` Answer :D

Discussion

6856.	Verify that\|P({a,b})\|=2^2
Answer» <P> SOLUTION :LET `A={a,B}` then ,`P(A)={{a},{b},{a,b},PHI}` `:.P(A)=4=2^2`

Discussion

6857.	Find the number of ways of arranging 7 persons around a circle.
Answer» ANSWER :720

Discussion

6858.	A value of n such that ((sqrt3)/(2)+(i)/(2))^(n)=1 is
Answer» 12 3 2 1 Answer :A

Discussion

6859.	Show that x = 2 is a root of the equation\|{:(x, -6, -1),(2,- 3x,x-3),(-3," "2x,x+2):}\| = 0 and solve it completely.
Answer» ANSWER :`X = 1, 2, - 3 `

Discussion

6860.	Let vec a=3hat i+2hat j+4hat k, vec b=2(hat i+hat k) and vec c=4hat i+2hat j+3hat k .Sum of the values of alpha for which the equation xvec a+yvec b+zvec c=alpha(xhat i+yhat j+zhat k) has non-trivial solution is:
Answer» -1 4 7 8 Answer :C

Discussion

6861.	If the equation formed by decreasing each root of ax^(2) + bx + c = 0"by 1 is " 2 x^(2) + 6x + 2 = 0 , then the value of a, b and cis _______
Answer»

Discussion

6862.	Find the domain of continuityof f(x)=sin^(-1) x - [x], []represents greatest integer function .
Answer» ANSWER :`(-1,0) U (0,1)`

Discussion

6863.	C (18, r) = C (18, r + 2). Then C(r, 5) =
Answer» 56 21 126 6 Answer :A

Discussion

6864.	Integrate the following function : int(cosec^(2)x)/(1-cot^(2)x)dx
Answer» ANSWER :`-(1)/(2)LOG\|(1+cotx)/(1-cotx)\|+C`

Discussion

6865.	Expand the following using binomial theorem. ((2)/(3)x+(7)/(4)y)^(5)
Answer» SOLUTION :N/A

Discussion

6866.	{:(" " Lt),(n rarroo):}[(1^(2))/(n^(3)+1^(3))+(2^(2))/(n^(3)+2^(3))+......+(1)/(2n)]=
Answer» `1/2 LOG 2` `1/3 log 3` `1/3 log 2` `1/2 log 3` ANSWER :C

Discussion

6867.	A and B are two independent events such that P(A)= 0.8 and P(A nn vec B ) = 0.3Find P(B)
Answer» ANSWER :`(5)/(8)`

Discussion

6868.	The vertices of the rectangle ABCD are A(-1,0), B(2, 0), C(a, b) and D(-1, 4). Then the length of the diagonal AC is
Answer» 2 3 4 5 Answer :D

Discussion

6869.	Find adjoint of each of the matrices [{:(1,1,1),(1,0,2),(3,1,1):}]
Answer» ANSWER :`[{:(-2,0,2),(5,-2,-1),(1,2,-1):}]`

Discussion

6870.	Integrate the following functions : int(dx)/(1+e^(x))
Answer» ANSWER :`X-log\|1+e^(x)\|+C`

Discussion

6871.	Write the value of x-intercept of the plane x+y+2z=1.
Answer» SOLUTION :The EQUATION `ax+by+c=0` is a PLANE PARALLEL to z-axis.

Discussion

6872.	f: R rarr R , f(x) = x^(2)+2 and g :Rrarr R , g (x) = x/(x-1) then find fog and gof.
Answer» SOLUTION :N/A

Discussion

6873.	Given the circle C with the equation x^(2)+y^(2)-2x+10y-38=0 Match the List-I with the List-II given below concening C:
Answer» I) c. II). a, III). E, iv). b I) d. ii). e, iii). a, iv). B I) c. ii). e, iii). a, iv). b I) d. ii). b, iii). a, iv). e ANSWER :A

Discussion

6874.	Old hens can be bought for ₹ 2.00 each and young ones at ₹. 5.00 each.The old hens lay 3 eggs per week and the young hens 5 eggs per week, each egg being worth 30 paise.A hen costs ₹ 1.00 per week to feed.A man has only ₹ 80 to spend for hens.Formulate the problem for maximum profit per week, assuming that he cannot house more than 20 hens.
Answer» Answer : Maximize `Z = (5y - X)/(10)` SUBJECT to : `x GE 0, y ge 0, x+y le 20` and `2x + 5y le 80`

Discussion

6875.	Determine the truth of falsity of the Every set is a proper subset of same setpropositions with reasons.
Answer» Solution :Every SET is a PROPER SUBSET of same set is FALSE.

Discussion

6876.	Differentiate the following w.r.t x: (i) e^(-x) (ii) sin (log x), x gt 0 (iii) cos^(-1) (e^(x)) (iv) e^(cos x)
Answer» Answer :(i) `-e^(-x)` (II) `(cos (log x))/(x)` (iii) `-(e^(x))/(SQRT(1-e^(2x)))` (IV) `-(SIN x) e^(cos x)`

Discussion

6877.	Locus of the point of intersection of perpendicular tangents drawn one of each of the circles x^(2)+y^(2)=8 and x^(2)+y^(2)=12 is
Answer» `x^(2)+y^(2)=4` `x^(2)+y^(2)=20` `x^(2)+y^(2)=208` `x^(2)+y^(2)=16` Answer :B

Discussion

6878.	Assertion (A) : If alpha=cos((2pi)/(7))+isin((2pi)/(7)),p=alpha+alpha^2+alpha^4,q=alpha^3+alpha^5+alpha^6 then the equation whose roots are p and q is x^2+x+2=0Reason (R) : If alpha is a roots of z^7=1 then 1+alpha+alpha^2+…...+alpha^6=0
Answer» Both A and R are true R is CORRECT EXPLANATION to A Both A and R are true but R is not correct explanation to A A is true R is FALSE A is false R is true Answer :A

Discussion

6879.	Solve the following differential equation : x.(dy)/(dx) + y - x + xy cot x = 0, x != 0.
Answer» ANSWER :`y = (1)/(x) - cot x + (C)/(x sin x)`

Discussion

6880.	If bar(a)+bar(b)+bar( c )=bar(0) and \|bar(a)\|=3,\|bar(b)\|=5,\|bar( c )\|=7 and (bar(a)""_(,)^(hat)bar(b))alpha then alpha=……………. .
Answer» `(PI)/(3)` `(pi)/(6)` `(2pi)/(3)` `(5pi)/(6)` ANSWER :A

Discussion

6881.	A binary operation * on the set {0,1,2,3,4,5} is defined as a*b = {{:(a+b, if a+blt6),(a+b-6 if a+b ge 6):} Show that 0 is the identity for this operation and each element a has an inverse(6-a)
Answer» SOLUTION :a0=a+0=a ltrbvgt so 0 is the IDENTITY `a(6-a)=a+(6-a)-6=0 [therefore a+(6-a)ge6]` `therefore`The inverse of a is (6-a)

Discussion

6882.	Find the maximum and minimum values of Z=2x+y, subject to the constraintsx+3y ge6, x+3y le3,3x+4yle24,-2x+2yle6,5x+yge5,x ge0and y ge0.
Answer» ANSWER :Maximum `Z=14(1)/(3)at ((84)/(13),(15)/(13))"and minimum"Z=3(1)/(14)at ((9)/(14),(25)/(14))`

Discussion

6883.	If int_(a)^(b)f(dx)dx=l_(1), int_(a)^(b)g(x)dx = l_(2) then :
Answer» `int_(a)^(B)(f(x)+g(x))dx = l_(1)+l_(2)` `int_(a)^(b)(f(x).g(x))dx=l_(1)l_(2)` `int_(a)^(b)(f(x))/(g(x))dx = (l_(1))/(l_(2))` ANSWER :A

Discussion

6884.	Two cards are drawn from a well shuffled deck of 52 playing cards with replacement. The probability, that both cards are queens, is .......
Answer» `((1)/(13))((1)/(13))` `(1)/(13) +(1)/(13)` `((1)/(13)) ((1)/(17))` `((1)/(13)) ((4)/(51))` ANSWER :A

Discussion

6885.	The partial fractions of ((x+1)^(2))/(x(x^(2)+1)) are
Answer» `(1)/(2X)+(X)/(x^(2)+1)` `(1)/(x)-(2)/(x^(2)+1)` `(1)/(x)+(1)/(x^(2)+1)` `(1)/(x)+(2)/(x^(2)+1)` ANSWER :D

Discussion

6886.	Using proper substitution, find (dy)/(dx) if y = tan^(-1)(sqrt(1+b^(2)x^(2)) - bx).
Answer» Answer :`(dy)/(DX) = -(b)/(2).(1)/(1+b^(2)X^(2))`

Discussion

6887.	If alphaand beta are roots of the equation ax^(2)+bx+c=0 and if px^(2)+qx+r=0 has roots (1-alpha)/(alpha) and (1-beta)/(beta), then r is equal to
Answer» `a+2b` `a+B+c` `ab+bc+ca` `ABC` ANSWER :B

Discussion

6888.	Let A, B and C be three non-empty sets. Suppose f : A to B and g: B to C are two functions such that g o f: A to Cis one-to-one, then
Answer» F and G are both one-to-one f is one-to-one g MAY not be one-to-one f may not be one-to-one but g is one-to-one both f and g NEED not be one-to-one Answer :B

Discussion

6889.	If b and c are the lengths of the segments of any focal chord of a parabola y^(2)=4ax, then the length of the semilatusrectum is
Answer» `(BC)/(b+c)` `sqrtbc` `(b+c)/(2)` `(2BC)/(b+c)` ANSWER :D

Discussion

6890.	Translate "If the government cannot solve the unemployment problem, then public opinion will rise against it which will lead to a strengthening of opposition" propositions into symbolic form, stating the prime components
Answer» Solution :Let p:The GOVERNMENT can solve the unemployment PROBLEM. q :Public OPINION will rise against it. It will LEAD to a strengthening of OPPOSITION. `:.` Answer is (p rarrq ) rarrr.

Discussion

6891.	The value of sin(2 sin^(-1) 0.8) is equal to
Answer» `0.48` `SIN 1.2^(@)` `sin 1.6^(@)` `0.96` ANSWER :D

Discussion

6892.	Evaluate (ii) int_(1)^(2)x dx
Answer» ANSWER :1

Discussion

6893.	if theta and phi areeccentricanglesof theendsof a pairofconjugatediameters of theellipse(x^(2))/(a^(2))+(y^(2))/(b^(2))=1then( theta - phi)is equalto
Answer» `+- PI //2` `+- pi` 0 none of these Answer :A

Discussion

6894.	The polar of a point with respect to y^2=4x touches x^2=4y. If the locus of this point is xy=lambda, then the value of \|lambda\| is
Answer» 1 2 3 4 Answer :B

Discussion

6895.	Find derivatives of the following functions.sqrt(ax^2 + bx + c)
Answer» SOLUTION :`y = sqrt(ax^2 + BX + c) dy/dx = d/dx(ax^2 + bx + c)^(1/2) 1/2(ax^2 + bx +c)^(1/2-1)xx d/dx(ax^2 + bx+ c) (2ax + B)/{2sqrt (ax^2 + bx + c)}`

Discussion

6896.	For the ellipse (x^(2))/(25)+(y^(2))/(16) = 1, a list of lines given in List-I are to be matched with their equation given in list II {:(list I,list II),("directrix corresponding to the focus" (-3,0),y=4),("tangent at the vertex" (0,4),3x=25),("latus rectum through" (3,0),x=3),("" ,y+4=0 ),("" ,x+3=0),("" ,3x+25=0):}
Answer» B a e f a c b d c f a e Answer :B

Discussion

6897.	If y= (sin ^(-1) x) ^(x) + (x) ^(cos ^(-1)x) ,then ( dy)/(dx)
Answer» ` (sin ^(-1)x) ^(x) (LOG sin ^(-1) x-(x)/( SQRT(1-x^(2)sin x ))) +x^(cos ^(-1)x) ((cos ^(-1)x+ )/( x )+(logx )/( sqrt( 1-x^(2))))` ` (sin ^(-1)x) ^(x) (log sin ^(-1) x-(x)/( sqrt(1-x^(2)sin x ))) -x^(cos ^(-1)x) ((cos ^(-1)x+ )/( x )+(logx )/( sqrt( 1-x^(2))))` ` (sin ^(-1)x) ^(x) (log sin ^(-1) x-(x)/( sqrt(1-x^(2)sin x ))) + x^(cos ^(-1)x) ((cos ^(-1)x+ )/( x )-(logx )/( sqrt( 1-x^(2))))` Answer :C

Discussion

6898.	int_(0)^(pi) (x tan x)/( sec x + tan x) dx=
Answer» `PI/2 +1` `pi/2 -1` `pi (pi/2 -1)` `pi(pi/2 +1)` ANSWER :C

Discussion

6899.	If two lines represented by ax^(3)+bx^(2)y+cxy^(2)+dy^(3)=0 are at right anlges then a^(2)+d^(2)+ac+bd equals
Answer» 0 1 `-1` ab+cd Answer :A

Discussion

6900.	Let S be the sample space of the random experiment of throwing simultaneously two unbaised dice with six faces (numbered1 to 6) and let E_(k) = {(a,b) in S : ab = k} for k ge 1. IfP_(k) = P(E_(k)) for kge 1 then the correct, amongthe following is
Answer» `P_(1) LT P_(30)lt P_(4)lt P_(6)` `P_(36) lt P_(6)lt P_(2)lt P_(4)` `P_(1) lt P_(11)lt P_(4)lt P_(6)` `P_(36) lt P_(11)lt P_(6)lt P_(4)` Answer :A

Discussion

Explore topic-wise InterviewSolutions in .

The value of (cos2 theta + i sin 2 theta)^5(sin theta+i cos theta)^4 is

Integrate the following functions. int(dx)/(sin^(3)xcos^(5)x)

The sum of the series1 + 2.2 + 3.2^(2) + 4.2^(3) + 5.2^(4) + ……… + 100.2^(99) is

Two systems of rectangular axis have the same origin. If a plane cuts them at distances a, b, c and a', b', c', respectively from the origin, then prove that (1)/(a^2)+(1)/(b^2)+(1)/(c^2)=(1)/((a')^2)+(1)/((b')^2)+(1)/((c')^2).

One ticket is selected at random from 50 tickets numbered 00, 01, 02, ……49. Then the probability that the sum of the digites on the selected ticket is 8, given that the product of these digits is zero, equals

Verify that|P({a,b})|=2^2

Find the number of ways of arranging 7 persons around a circle.

A value of n such that ((sqrt3)/(2)+(i)/(2))^(n)=1 is

Show that x = 2 is a root of the equation|{:(x, -6, -1),(2,- 3x,x-3),(-3," "2x,x+2):}| = 0 and solve it completely.

Let vec a=3hat i+2hat j+4hat k, vec b=2(hat i+hat k) and vec c=4hat i+2hat j+3hat k .Sum of the values of alpha for which the equation xvec a+yvec b+zvec c=alpha(xhat i+yhat j+zhat k) has non-trivial solution is:

If the equation formed by decreasing each root of ax^(2) + bx + c = 0"by 1 is " 2 x^(2) + 6x + 2 = 0 , then the value of a, b and cis _______

Find the domain of continuityof f(x)=sin^(-1) x - [x], []represents greatest integer function .

C (18, r) = C (18, r + 2). Then C(r, 5) =

Integrate the following function : int(cosec^(2)x)/(1-cot^(2)x)dx

Expand the following using binomial theorem. ((2)/(3)x+(7)/(4)y)^(5)

{:(" " Lt),(n rarroo):}[(1^(2))/(n^(3)+1^(3))+(2^(2))/(n^(3)+2^(3))+......+(1)/(2n)]=

A and B are two independent events such that P(A)= 0.8 and P(A nn vec B ) = 0.3Find P(B)

The vertices of the rectangle ABCD are﻿ A(-1,0), B(2, 0), C(a, b) and D(-1, 4).﻿ Then the length of the diagonal AC is﻿

Find adjoint of each of the matrices [{:(1,1,1),(1,0,2),(3,1,1):}]

Integrate the following functions : int(dx)/(1+e^(x))

Write the value of x-intercept of the plane x+y+2z=1.

f: R rarr R , f(x) = x^(2)+2 and g :Rrarr R , g (x) = x/(x-1) then find fog and gof.

Given the circle C with the equation x^(2)+y^(2)-2x+10y-38=0 Match the List-I with the List-II given below concening C:

Determine the truth of falsity of the Every set is a proper subset of same setpropositions with reasons.

Differentiate the following w.r.t x: (i) e^(-x) (ii) sin (log x), x gt 0 (iii) cos^(-1) (e^(x)) (iv) e^(cos x)

Locus of the point of intersection of perpendicular tangents drawn one of each of the circles x^(2)+y^(2)=8 and x^(2)+y^(2)=12 is

Assertion (A) : If alpha=cos((2pi)/(7))+isin((2pi)/(7)),p=alpha+alpha^2+alpha^4,q=alpha^3+alpha^5+alpha^6 then the equation whose roots are p and q is x^2+x+2=0Reason (R) : If alpha is a roots of z^7=1 then 1+alpha+alpha^2+…...+alpha^6=0

Solve the following differential equation : x.(dy)/(dx) + y - x + xy cot x = 0, x != 0.

If bar(a)+bar(b)+bar( c )=bar(0) and |bar(a)|=3,|bar(b)|=5,|bar( c )|=7 and (bar(a)""_(,)^(hat)bar(b))alpha then alpha=……………. .

A binary operation * on the set {0,1,2,3,4,5} is defined as a*b = {{:(a+b, if a+blt6),(a+b-6 if a+b ge 6):} Show that 0 is the identity for this operation and each element a has an inverse(6-a)

Find the maximum and minimum values of Z=2x+y, subject to the constraintsx+3y ge6, x+3y le3,3x+4yle24,-2x+2yle6,5x+yge5,x ge0and y ge0.

If int_(a)^(b)f(dx)dx=l_(1), int_(a)^(b)g(x)dx = l_(2) then :

Two cards are drawn from a well shuffled deck of 52 playing cards with replacement. The probability, that both cards are queens, is .......

The partial fractions of ((x+1)^(2))/(x(x^(2)+1)) are

Using proper substitution, find (dy)/(dx) if y = tan^(-1)(sqrt(1+b^(2)x^(2)) - bx).

If alphaand beta are roots of the equation ax^(2)+bx+c=0 and if px^(2)+qx+r=0 has roots (1-alpha)/(alpha) and (1-beta)/(beta), then r is equal to

Let A, B and C be three non-empty sets. Suppose f : A to B and g: B to C are two functions such that g o f: A to Cis one-to-one, then

If b and c are the lengths of the segments of any focal chord of a parabola y^(2)=4ax, then the length of the semilatusrectum is

Translate "If the government cannot solve the unemployment problem, then public opinion will rise against it which will lead to a strengthening of opposition" propositions into symbolic form, stating the prime components

The value of sin(2 sin^(-1) 0.8) is equal to

Evaluate (ii) int_(1)^(2)x dx

if theta and phi areeccentricanglesof theendsof a pairofconjugatediameters of theellipse(x^(2))/(a^(2))+(y^(2))/(b^(2))=1then( theta - phi)is equalto

The polar of a point with respect to y^2=4x touches x^2=4y. If the locus of this point is xy=lambda, then the value of |lambda| is

Find derivatives of the following functions.sqrt(ax^2 + bx + c)

If y= (sin ^(-1) x) ^(x) + (x) ^(cos ^(-1)x) ,then ( dy)/(dx)

int_(0)^(pi) (x tan x)/( sec x + tan x) dx=

If two lines represented by ax^(3)+bx^(2)y+cxy^(2)+dy^(3)=0 are at right anlges then a^(2)+d^(2)+ac+bd equals

Let S be the sample space of the random experiment of throwing simultaneously two unbaised dice with six faces (numbered1 to 6) and let E_(k) = {(a,b) in S : ab = k} for k ge 1. IfP_(k) = P(E_(k)) for kge 1 then the correct, amongthe following is

The vertices of the rectangle ABCD are A(-1,0), B(2, 0), C(a, b) and D(-1, 4). Then the length of the diagonal AC is