28278 + Interview Questions in Maths in Class 12 Page 226 InterviewSolution

11251.	A dice is thrown twice and the sum of the numbers appearing is observed to be 6. What is the conditional probability that the number 4 has appeared at least once ?
Answer» ANSWER :`(2)/(5)`

Discussion

11252.	Solve e^((dy)/(dx))=x+1, given that when x=0, y=3.
Answer» ANSWER :` y = (x+1) LOG (x+1)- x+3`

Discussion

11253.	Integrate the function (x+2)/(sqrt(x^(2)-1))
Answer» Answer :`SQRT(x^(2)-1)+2logabs(x+sqrt(x^(2)-1))+C`

Discussion

11254.	The normal at a point theta to the curve x=a(1+cos theta),y=a sin theta always passes through the fixed point
Answer» (0, a) (2A, 0) (a, 0) (a, a) ANSWER :C

Discussion

11255.	Which of thefollowingfunctionis notdifferentiableat x=1?
Answer» `F(x) =(x^(2)-1)\|(x-1)(x-2)\|` `f(x) = sin (\|x-1\|)-\|x-1\|` `f(x)= tan (\|x-1\|)+\|x-1\|` NONEOF these Answer :C

Discussion

11256.	int_(0)^(2) x sqrt(x+2) dx " (put x+2 " =t^(2)")"
Answer» Solution :`"LET B " x+2 =t^(2) rArr dx=2t dt` `x=0 rArr t= sqrt(0+2)=sqrt(2)` `x=2 rArr t=sqrt(2+2)=2` `=int_(sqrt(2))^(2)(t^(2)-2)sqrt(t^(2)).2t dt= 2 int_(sqrt(2))^(2)(t^(4)-2t^(2))dt` `=2[(t^(5))/(5)-(2t^(3))/(3)]_(sqrt(2))^(2)=(2)/(15)[3T^(5)-10t^(3)]_(sqrt(2))^(2)` `=(2)/(15)[(96-80)-(12sqrt(2)-20sqrt(2))]` `=(2)/(15)(16+8sqrt(2))=(16)/(15)(2+sqrt(2))`

Discussion

11257.	Coloured balls are distributed in four boxes as shown in the following table: A box is selected at random and then a ball is randomly drawn from the selected box. The colour of the ball is black, what is the probability that ball drawn is from the box III?
Answer» ANSWER :0.165

Discussion

11258.	Find the equation of the circle passing through the point (– 6, 0) if the power of the point (1, 1) w.r.t. the circle is 5 and it cuts the circle x^(2) + y^(2) – 4x – 6y – 3 = 0 orthogonally.
Answer» ANSWER :`x^(2) + y^(2) + 6x - 3Y = 0`

Discussion

11259.	Three urns A, Band C contain 6 red and 4 white, 2 red and 6 white, and 1 red and 5 white balls respectively. An um is chosen at random and a ball is drawn. If the ball drawn is found to be red, find the. probability that the ball was drawn from the urn A.
Answer» <P> SOLUTION :Let `E_1,E_2and E_3` be the events of choosing the urns A,B and C RESPECTIVELY, and let E be the event of drawing a red ball. Then, `P(E_1)=P(E_2)=P(E_3)=1/3` `P(E/E_1)=6/10,P(E/E_2)=2/8,and P(E/E_3)=1/6`. Required probability `=P(E_1/E)` `=(P(E_1)XXP(E/E_1))/(P(E_1)xxP(E/E_1)+P(E_2)xxP(E/E_2)+P(E_3)xxP(E/E_3))` `=((1/3xx6/10))/((1/3xx6/10)+(1/3xx2/8)+(1/3xx1/6))=36/61`.

Discussion

11260.	When positive integer A is divided by positive integer B, the result is 4.35. Which of the following could be the remainder when A is divided by B?
Answer» 13 14 15 16 Answer :B

Discussion

11261.	Find the angle between the line oversettor=(overset^i+2overset^j-overset^k)+lambda(overset^i-overset^j+overset^k) and the plane oversettor(2overset^i-overset^j+overset^k)=4
Answer» Solution :For the line `oversettob=i-j+k` and NORMAL to the PLANE `=oversettoN=2i-j+k.` Let `THETA` is the ANGLE between the line and the plane. `thereforesintheta=(oversettob.oversettoN)/(\|b\|\|N\|)=(2+1+1)/(sqrt3sqrt6)=(2SQRT2)/3ifftheta=sin^(_1)((2sqrt2)/3)`

Discussion

11262.	Let f(x)=e^(x)cos x + 1. Which of the following statements is always true?
Answer» Between any two consecutive roots of `F (X)=0` there is always a root of `e^(x)SIN x+1=0` Between any two consecutive roots of `f(x)=0` there is always a root of `e^(x)sin x-1=0` Between any two consecutive roots of `f (x)=0` there is always a root of `e^(x) COS x=0` Between any two consecutive roots of `f(x)=0` there is always a roots of `e^(x)sin x=0` Answer :D

Discussion

11263.	Find (dy)/(dx) ify+siny=cosx
Answer» Solution :`y+siny=cosx` DIFFERENTIATING THROUGHOUT w.r.y.x we GET `(dy)/(DX)+cosy(dy)/(dx)=-sinx(dy)/(dx)(1+cosy)=-sinx(dy)/(dx)=(-sinx)/(1+cosy)` where `cosyne-1`

Discussion

11264.	A set A contains m elements another set B contains n elements. A relation is formed from A to B. Then the probability that the relation is a function is
Answer» <P>`(.^(n)P_(m))/(2^(MN))` `(n^(m))/(2^(mn))` `(m^(n))/(2^(mn))` `(m+n)/(2^(mn))` Answer :B

Discussion

11265.	If a matrix has 18 elements, what are the possible orders it can have? What if it has 5 elements?
Answer» ANSWER :`1xx18, 2xx9, 3xx6, 6xx3, 9xx2, 18xx1; 1xx5, 5xx1`

Discussion

11266.	Assertion (A): If the roots of (a^(2)+b^(2))x^(2)-2b(a+c)x+ (b^(2)+c^(2))=0are real and equal then a, b, c are in G.P. Reason (R): If the sum of two non-negative reals is zero then each of them is zero.
Answer» Both A, R are TRUE and R EXPLAIN Assertion Both A, R are true but R does't explain A A is true R is false A is false R is true Answer :A

Discussion

11267.	Show that (1 xx 2^(2) + 2 xx 3^(2) + ... +n xx (n + 1)^(2))/(1^(2) xx 2 + 2^(2) xx 3+ ... + n^(2) xx (n + 1)) = (3n + 5)/(3n + 1)
Answer» ANSWER :` = (3N + 5)/(3n + 1)`

Discussion

11268.	inttan^3theta d theta
Answer» SOLUTION :`inttan^3theta d THETA=inttantheta.(tan^2theta) d theta` =`inttantheta.(sec^2theta-1) d theta` =`inttantheta.sec^2theta d theta- inttantheta d theta` =`inttantheta d (TANTHETA)- inttantheta d theta` =`1/2tan^2theta+In abscostheta +C`

Discussion

11269.	If alpha, beta, gammaare the roots of the equation x^3 + px^2 + qx + r = n then the value of (alpha - 1/(beta gamma)) (beta -1/(gamma alpha)) (gamma-1/(alpha beta)) is:
Answer» ANSWER :`-(R+1)^(3)/r^(2)`

Discussion

11270.	In a book of 450 pages, it is found that there are 400 typing errors. Assume that poisson law holds for the number of errors per page, find the probability that a random sample of 5 pages will contain no errors.
Answer» ANSWER :`(E^(-8//9))^(5)`

Discussion

11271.	If \|z + 2- i\| = 5 then the maximum value of \|3z- 9 - 7i\| is
Answer» 18 19 20 8 Answer :C

Discussion

11272.	Two dice are thrown simultaneously. If X denotes the number of sixes. Find the mean (expectation) of X.
Answer» ANSWER :`1/3`

Discussion

11273.	For n in N, the value of int_(0)^(pi) sin^(n) x*cos^(2n-1)x dx is
Answer» 0 N `2n-1` `(n PI)/(8)` ANSWER :A

Discussion

11274.	Find the second order derivatives of the functions. e^(6x) cos 3x.
Answer» Answer :`9E^(6X) (3 cos 3X-4 sin 3x)`

Discussion

11275.	If 7x+4y le 28, 2y le 7, x ge 0then the maximum value of f=4x-2y is
Answer» 16 28 42 56 Answer :A

Discussion

11276.	Rain falling vertically is appeared to fall at 37^@ with vertical for a man running on horizontal ground with 8 m/s. What is the speed of rain ( in m/s) relative to ground.
Answer» ANSWER :10.66 to 10.67

Discussion

11277.	Find tha area of theregion containing the points (x, y) satisfying 4 le x^(2) + y^(2) le 2 (\|x\|+ \|y\|).
Answer» Solution :The points in the required region satisfy `""4le x^(2) + y^(2) le 2 (\|x\| + \|y\|)""` (i) Since curve (i) is symmetrical about both the AXES, the required area is 4 times the area of the region in the first quadrant. Therefore, it is sufficient to sketch the region and to find the area in the first quadrant. In the first quadrant, curve (i) consists of two curves : `""x^(2) + y^(2) ge 4 ""(C_(1))""and x^(2)+y^(2)-2x -2Y ge0""(C_(2))` `therfore ""` Required area = 4 area ABCDA = 4 (area of semi-circle ABCA)- (area of sector ADCA) = 4 (area of semi-circle ABCA)-(area of sector sector OADCO- area of triangle OAC) `= 4 {pi- (pi-2)}= 8` sq. units

Discussion

11278.	If A , B are event such that P(A)=0.6, P(B)=0.4 and P(A cap B)=0.2, then find P(B \| A)
Answer» <P> SOLUTION :`P(B/A)=(P(A capB))/(P(A))=0.2/0.6=2/6=1/3`

Discussion

11279.	Let F be the set of all 4 digited numbers whose sum is 34. If a number is selected from F then find the probability that the selected number is even.
Answer» ANSWER :`(3)/(10)`

Discussion

11280.	Ifveca,vecb,veccare three vectors, prove that[veca+vecc,veca+vecb,veca+vecb+vecc]=-[veca,vecb,vecc]
Answer» ANSWER : ` -[VECA,VECB,VECC] `

Discussion

11281.	If the line 4x + 4y - 11 = 0 intersects the circle x^(2)+y^(2)-4x-6y+4=0 at A and B, then the point of intersection of the tangents drawn at A, B is
Answer» `(-1,2)` `(-1,-2)` (2, 1) `(-2,-1)` ANSWER :D

Discussion

11282.	The mean deviatons about the median of the data set 4,10,6,4,13,11,19,m,8,7, where m ge 11 is an integer is 4, Then m is equal to:
Answer» 14 15 16 17 Answer :C

Discussion

11283.	" If" f(x) =int_(0)^(x)" t sin t dt tehn " f(x) is
Answer» x SIN x x cos x sin x+xcos x Solution :` f(x) = int_(0)^(x) TSIN t DT` Usingpartialintegration `f(x) =[intsintdt -INT [((d)/(dt)t) int sin t dt ]dt]_(0)^(x)` `= [t( -cos t)]_(0)^(x) - int_(0)^(x) (-cos t)dt` `=[-t cos t + sin t]_(0)^(x)` `rArr f(x) =-x cos x + sin x` Nowdifferebntiate withrespect to x . f(x) = -[{x(-sin x)}+cos x] +cos x `= sin x- cos x + cos x =x sin x`

Discussion

11284.	Circles C_(1) and C_(2) are externally tangent and they are both internally tangent to the circle C_(3). The radii of C_(1) and C_(2) are 4 and 10, respectively and the centres of the three circles are collinear. A chord of C_(3) is also a common internal tangent of C_(1) and C_(2). Given that the length of the chord is (msqrt(n))/(p) where m, n and p are positive integers, m and p are relatively prime and n is not divisible by the square of any prime, find the value of (m + n + p).
Answer» ANSWER :19

Discussion

11285.	A particle of mass m is moving in a straight line is acted on by an attractive force( m k^2 a^2)/(x^2) forx ge aand( 2m K ^2 x)/( a) forx lt2.If the particle starts from rest at the point x = 2a, then it will reach the point x = 0 with a speed
Answer» `k sqrt(a)` `k` `k sqrt(3a)` `1 / ksqrt(a)` Answer :C

Discussion

11286.	The orbit of the Earth is an ellipse with eccentricity 1/60 with the sun at one of its foci, the major axis being approximately 186times10^6 miles in length. Find the shortest and longest distance of the Earth from the sun.
Answer» ANSWER :`9145times10^4` MILES

Discussion

11287.	If (z-1)/(z+3)=(3+4i)/(2) find barz
Answer» ANSWER :`(17+68i)/(40)`

Discussion

11288.	The pole of a straight line with respect to the circle x^(2)+y^(2)=a^(2) lies on the circle x^(2)+y^(2)=9a^(2). If the straight line touches the circle x^(2)+y^(2)=r^(2), then
Answer» `9A^(2)=R^(2)` `9r^(2)=a^(2)` `r^(2)=a^(2)` `3r^(2)=a^(2)` ANSWER :B

Discussion

11289.	Draw aroughsketch of thecurvey= sqrt(x-1)in theintervalx in[ 1,5]. Findtheareaunder the curveand betweenthe linesx=1andx=5 .
Answer» ANSWER :`=16/3` SEQ . UNIT

Discussion

11290.	Let S, be a conic whose centre is M(p, q). Locus of middle points of chords of this conic, which passes through a fixed point N(alpha,beta) is:
Answer» ANOTHER conic which has a CENTRE Another conic with same focus Another conic with centre as `((alpha+p)/(2),(beta+p)/(2))` Another conic with centre as `((alpha-p)/(2),(beta-p)/(2))` ANSWER :A::C

Discussion

11291.	Integration using rigonometric identities : int (sinx- cos x)/(x^(2)+x sin x)dx=....+c
Answer» `LOG\|x+sinx\|` `log\|(x)/(x+sinx)\|` `log\|x^(2)+x sinx\|` `log\|(x+sinx)/(x)\|` ANSWER :B

Discussion

11292.	A postman has to deliver five letters to five different houses. Mischievously, he posts one letter through each door without looling to see if it is the correct address. In how many different ways could he do this so that exactly two of the five houses receive the correct letters?
Answer» ANSWER :20

Discussion

11293.	If a point P is moving such that the lengths of the tangents drawn form P to the circles x^(2) + y^(2) + 8x + 12y + 15 = 0 and x^(2) + y^(2)- 4 x - 6y - 12 = 0are equal then find theequation of the locus of P
Answer» ANSWER :` 4X + 6Y + 9=0`

Discussion

11294.	If the third term of a G.P is P. Then the Product of the first 5 terms of the G.P is
Answer» <P>`p^(3)` `p^(2)` `p^(10)` `p^(5)` Answer :D

Discussion

11295.	If(1-x+6x^(2))/(x-x^(3))=A/x +(B)/(1-x)+(C)/(1+x), then A=
Answer» 1 2 3 4 Answer :A

Discussion

11296.	Let f(x) =a_0+a_1x^2+a_2x^4+…….+a_nx^(2n) be a polynomial in x in R with 0lta_0lta_1lt……lta_n then f(x) has
Answer» neither a maximum nor a MINIMUM only ONE maximum only one minimum none Answer :C

Discussion

11297.	The valueoftan 31^@ tan33 ^@tan35 ^@ tan 50^@is
Answer» 0 1 2 `- SQRT(2)` ANSWER :B

Discussion

11298.	Obtain the following integrals : int(cos(5x)+cos(4x))/(1-2cos(3x))dx
Answer» ANSWER :`:. I=-{(SIN(2))/(2)+SINX}+C`

Discussion

11299.	Two particles A and B move from rest along a straight line with constant accelerationsfand h respectively.If A takes m seconds more than B and describes n units more than that of B acquiring the same speed then
Answer» `(f+h)m^(2)=FHN` `(f-fh)m^(2)=fhn` `(h-f)N=(1)/(2)FHM^(2)` `(1)/(2)(f+h)n=fhm^(2)` ANSWER :C

Discussion

11300.	Let f, g, and h be functions from R to R. Show that (f + g) o h = foh + goh
Answer» Solution :[ (F + g) o H ] (x) = (f + g) (h(x)) =f(h(x)) + g (h(x)) (f o h) (x) + (g o h) (x)) (FOH + GOH) (x), for all `x in R` Thus, (f + g) o h = f o h + g o h

Discussion

Explore topic-wise InterviewSolutions in .

A dice is thrown twice and the sum of the numbers appearing is observed to be 6. What is the conditional probability that the number 4 has appeared at least once ?

Solve e^((dy)/(dx))=x+1, given that when x=0, y=3.

Integrate the function (x+2)/(sqrt(x^(2)-1))

The normal at a point theta to the curve x=a(1+cos theta),y=a sin theta always passes through the fixed point

Which of thefollowingfunctionis notdifferentiableat x=1?

int_(0)^(2) x sqrt(x+2) dx " (put x+2 " =t^(2)")"

Coloured balls are distributed in four boxes as shown in the following table: A box is selected at random and then a ball is randomly drawn from the selected﻿ box. The colour of the ball is black, what is the probability that ball drawn is from the﻿ box III?﻿

Find the equation of the circle passing through the point (– 6, 0) if the power of the point (1, 1) w.r.t. the circle is 5 and it cuts the circle x^(2) + y^(2) – 4x – 6y – 3 = 0 orthogonally.

Three urns A, Band C contain 6 red and 4 white, 2 red and 6 white, and 1 red and 5 white balls respectively. An um is chosen at random and a ball is drawn. If the ball drawn is found to be red, find the. probability that the ball was drawn from the urn A.

When positive integer A is divided by positive integer B, the result is 4.35. Which of the following could be the remainder when A is divided by B?

Find the angle between the line oversettor=(overset^i+2overset^j-overset^k)+lambda(overset^i-overset^j+overset^k) and the plane oversettor(2overset^i-overset^j+overset^k)=4

Let f(x)=e^(x)cos x + 1. Which of the following statements is always true?

Find (dy)/(dx) ify+siny=cosx

A set A contains m elements another set B contains n elements. A relation is formed from A to B. Then the probability that the relation is a function is

If a matrix has 18 elements, what are the possible orders it can have? What if it has 5 elements?

Assertion (A): If the roots of (a^(2)+b^(2))x^(2)-2b(a+c)x+ (b^(2)+c^(2))=0are real and equal then a, b, c are in G.P. Reason (R): If the sum of two non-negative reals is zero then each of them is zero.

Show that (1 xx 2^(2) + 2 xx 3^(2) + ... +n xx (n + 1)^(2))/(1^(2) xx 2 + 2^(2) xx 3+ ... + n^(2) xx (n + 1)) = (3n + 5)/(3n + 1)

inttan^3theta d theta

If alpha, beta, gammaare the roots of the equation x^3 + px^2 + qx + r = n then the value of (alpha - 1/(beta gamma)) (beta -1/(gamma alpha)) (gamma-1/(alpha beta)) is:

In a book of 450 pages, it is found that there are 400 typing errors. Assume that poisson law holds for the number of errors per page, find the probability that a random sample of 5 pages will contain no errors.

If |z + 2- i| = 5 then the maximum value of |3z- 9 - 7i| is

Two dice are thrown simultaneously. If X denotes the number of sixes. Find the mean (expectation) of X.

For n in N, the value of int_(0)^(pi) sin^(n) x*cos^(2n-1)x dx is

Find the second order derivatives of the functions. e^(6x) cos 3x.

If 7x+4y le 28, 2y le 7, x ge 0then the maximum value of f=4x-2y is

Rain falling vertically is appeared to fall at 37^@ with vertical for a man running on horizontal ground with 8 m/s. What is the speed of rain ( in m/s) relative to ground.

Find tha area of theregion containing the points (x, y) satisfying 4 le x^(2) + y^(2) le 2 (|x|+ |y|).

If A , B are event such that P(A)=0.6, P(B)=0.4 and P(A cap B)=0.2, then find P(B | A)

Let F be the set of all 4 digited numbers whose sum is 34. If a number is selected from F then find the probability that the selected number is even.

Ifveca,vecb,veccare three vectors, prove that[veca+vecc,veca+vecb,veca+vecb+vecc]=-[veca,vecb,vecc]

If the line 4x + 4y - 11 = 0 intersects the circle x^(2)+y^(2)-4x-6y+4=0 at A and B, then the point of intersection of the tangents drawn at A, B is

The mean deviatons about the median of the data set 4,10,6,4,13,11,19,m,8,7, where m ge 11 is an integer is 4, Then m is equal to:

" If" f(x) =int_(0)^(x)" t sin t dt tehn " f(x) is

A particle of mass m is moving in a straight line is acted on by an attractive force( m k^2 a^2)/(x^2) forx ge aand( 2m K ^2 x)/( a) forx lt2.If the particle starts from rest at the point x = 2a, then it will reach the point x = 0 with a speed

The orbit of the Earth is an ellipse with eccentricity 1/60 with the sun at one of its foci, the major axis being approximately 186times10^6 miles in length. Find the shortest and longest distance of the Earth from the sun.

If (z-1)/(z+3)=(3+4i)/(2) find barz

The pole of a straight line with respect to the circle x^(2)+y^(2)=a^(2) lies on the circle x^(2)+y^(2)=9a^(2). If the straight line touches the circle x^(2)+y^(2)=r^(2), then

Draw aroughsketch of thecurvey= sqrt(x-1)in theintervalx in[ 1,5]. Findtheareaunder the curveand betweenthe linesx=1andx=5 .

Let S, be a conic whose centre is M(p, q). Locus of middle points of chords of this conic, which passes through a fixed point N(alpha,beta) is:

Integration using rigonometric identities : int (sinx- cos x)/(x^(2)+x sin x)dx=....+c

A postman has to deliver five letters to five different houses. Mischievously, he posts one letter through each door without looling to see if it is the correct address. In how many different ways could he do this so that exactly two of the five houses receive the correct letters?

If a point P is moving such that the lengths of the tangents drawn form P to the circles x^(2) + y^(2) + 8x + 12y + 15 = 0 and x^(2) + y^(2)- 4 x - 6y - 12 = 0are equal then find theequation of the locus of P

If the third term of a G.P is P. Then the Product of the first 5 terms of the G.P is

If(1-x+6x^(2))/(x-x^(3))=A/x +(B)/(1-x)+(C)/(1+x), then A=

Let f(x) =a_0+a_1x^2+a_2x^4+…….+a_nx^(2n) be a polynomial in x in R with 0lta_0lta_1lt……lta_n then f(x) has

The valueoftan 31^@ tan33 ^@tan35 ^@ tan 50^@is

Obtain the following integrals : int(cos(5x)+cos(4x))/(1-2cos(3x))dx

Two particles A and B move from rest along a straight line with constant accelerationsfand h respectively.If A takes m seconds more than B and describes n units more than that of B acquiring the same speed then

Let f, g, and h be functions from R to R. Show that (f + g) o h = foh + goh

Coloured balls are distributed in four boxes as shown in the following table: A box is selected at random and then a ball is randomly drawn from the selected box. The colour of the ball is black, what is the probability that ball drawn is from the box III?