28278 + Interview Questions in Maths in Class 12 Page 147 InterviewSolution

7301.	A fair coin is tossed once. If it shows head, then 2 fiar disc are thrown simultaneously otherwise 3 fair disc are thrown simultaneously. The probability that all the dice show different numbers is k, then 180 k is equal to
Answer» ANSWER :125

Discussion

7302.	Aray of light passing through the point(1, 2) reflects on the x-axis at point A and the reflected ray passes through the point (5,3). Find the coordinates of A.
Answer» ANSWER :`((13)/(5), 0)`

Discussion

7303.	{:([a xx b b xx c c xx a],a. 5),(II.[a + b b + c c + a],b. 1),(III. [a b c] [a' b' c'],c.[a b c]^(2)),(IV. [a - b b - c c -a],d. 0),(,e. 2[a b c]):}
Answer» C,c,B,d c,c,d,b b,c,d,a b,a,c,d Answer :A

Discussion

7304.	underset(xrarr0)lim((1)/(sin x)-(1)/(x))
Answer» ANSWER :`=(0)/(2)=0`

Discussion

7305.	Each of the two orthogonal circles C_(1) and C_(2) passes through both the points (2, 0) and (-2, 0). If y=mx+c is a common tangent to these circles, then
Answer» `C^(2)=4(1+2m^(2))` `c^(2)=2(1+2m^(2))` `c^(2)=1+m^(2)` `c^(2)m^(2)=4(1+m^(2))` ANSWER :A

Discussion

7306.	Differentiate the following functions with respect to x. y= (sin x)^(x) + sin x^(x)
Answer» Answer :`(sin x)^(x) [LOG sin x + x COT x] + x^(x) COS x^(x) (1+ log x)`

Discussion

7307.	If (1)/(""^(5)C_(r))+(1)/(""^(6)C_(r))=(1)/(""^(4)C_(r)), then the value of r equals to
Answer» 4 2 5 3 Answer :B

Discussion

7308.	(d(a^x))/dx =...a)a^x b)log(a^x) c)a^xlog a d)xa^(x-1)
Answer» `a^x` `LOG(a^x)` `a^xlog a` `XA^(x-1)` ANSWER :C

Discussion

7309.	If a,b and n are natural numbers, then a^(2n-1)+b^(2a-1) is divisible by
Answer» `a+B` `a-b` `a^(3)+b^(3)` `a^(2)+b^(2)` ANSWER :A

Discussion

7310.	Determine whether or not each of the definition of given below gives a binary operation. In the even that is not a binary operation , give justification for this . On Z^(+) , define ** by a" * " b = \|a-b\|
Answer» SOLUTION :N/A

Discussion

7311.	Determine whether or not each of the definition of given below gives a binary operation. In the even that is not a binary operation , give justification for this . On Z^(+) , define *by a" " b = a
Answer» SOLUTION :N/A

Discussion

7312.	Determine whether or not each of the definition of given below gives a binary operation. In the even that is not a binary operation , give justification for this . On R , define *by a" " b = ab^2
Answer» SOLUTION :N/A

Discussion

7313.	Let sequence (a_(n))be defined as a_(1)= pi/4,a_(n) = int_(0)^(1//2)(cos(pix)+a_(n+1)) cos pixdx, (n = 2,3,4,"......")then evaluate lim_(n to oo) a_(n)
Answer» SOLUTION :N//A

Discussion

7314.	An ellipse whose whose axis as x-axis and the centre (0,0) passes through (4,3) and (-1, 4). i. Find the equation of the ellipse. ii. Find its eccentricity.
Answer» ANSWER :i. `7x^2 + 15y^2 = 247` II. `SQRT(8/15)`.

Discussion

7315.	""^(15)C_(0)=
Answer»

Discussion

7316.	Determine the unit vector having the direction of the given vector in each of the following problems. 3hati+6hatj-hatk
Answer» Solution :LET `veca = 3hati+6hatj-hatk` \|veca\| = SQRT(9+36+1) = sqrt(46)` Unit VECTOR = `(3hati+6hatj-hatk)/sqrt(46)`.

Discussion

7317.	Determine the unit vector having the direction of the given vector in each of the following problems. 3hati+hatj-2hatk
Answer» SOLUTION :LET `veca = 3hati+hatj-2hatk` \|veca\| = SQRT(9+1+4) = sqrt(14)` Unit VECTOR = `(3hati+hatj-2hatk)/sqrt(14)`.

Discussion

7318.	Determine the unit vector having the direction of the given vector in each of the following problems: 5hati-12hatj
Answer» SOLUTION :Let `veca = 5hati-12hatj` `\|veca\| = SQRT(25+144) = 13` Unit VECTOR ALONG `veca` = `veca/\|veca\| = 5/13 HATI- (12)/13 hatj`.

Discussion

7319.	Determine the unit vector having the direction of the given vector in each of the following problems. 2hati+hatj
Answer» Solution :Let `VECA = 2hati+hatj` `\|veca\| = SQRT(4+1) = sqrt5` UNIT vector along `veca = (2hati+hatj)/sqrt5`.

Discussion

7320.	Find d.r. of the line frac{4-x}{2}=frac{y}{6}=frac{1-z}{3}
Answer» `larr2, 6, -3gt` `LT2, 6, -3gt` `lt2, 6, 3gt` `lt2, -6, -3gt` ANSWER :A

Discussion

7321.	int (1)/((16 + x^(2))^(3//2))dx =
Answer» `(1)/(16).(x)/(SQRT(16 + x^(2))) + C ` `-(1)/(16).(x)/(sqrt(16+x^(2))) + C` `(1)/(16).(1)/(sqrt(16 +x^(2))) +C` `-(1)/(16).(1)/(sqrt(16+x^(2))) + C` ANSWER :A

Discussion

7322.	(1)/(x)=("2 e")/("3 !")+("4 e")/("5 !")+("6 e")/("7 !")+….oo, then find int_(0)^(x)f(y)log_(y)x dy, y gt 1
Answer» `([f(e )]^(2))/(2)` `([f((1)/(e ))]^(2))/(2)` `([f(e^(2))]^(2))/(2)` NONE of these Answer :D

Discussion

7323.	Compute : [{:(1,-1),(0,2),(2,3):}]([{:(1" "0" "2),(2" "0" "1):}]-[{:(0""1""3),(1""0""2):}]).
Answer» ANSWER :`[{:(0,-1,0),(2,0,-2),(5,-2,-5):}]`

Discussion

7324.	If (1)/((1 - 2x)(1 + 3x)) is to tbe expanded as a power series of x, then
Answer» `\|X\| LT 1//2` `\|x\| lt 1//6` `-1//3 lt x lt 1//2` `\|x\| lt 1//3` ANSWER :D

Discussion

7325.	int_-a^ax^4dx
Answer» Solution :`int_-a^ax^4dx=2int_0^ax^4dx` [Here `F(X)=x^4` Then `f(-x)=x^4=f(x) So f(x) is even FUNCTION] =`2[x^5/5]_0^a=(2a^5)/5`

Discussion

7326.	If from the point (a,b,c) perpendiculars PL and PM be drawn to YOZ and ZOX then the equation of the plane OLM is ............
Answer» `(x)/(a) + (y)/(B) + (Z)/(c) =0` `x/a -y/b + z/c = 0` `x/a + y/b - z/c = 0` `x/a - y/b - z/c =0` ANSWER :C

Discussion

7327.	Let P(4,-4) and Q(9,6) be points on the parabola y^(2)=4a(x-b). Let R be a point on the arc of the parabola between P and Q. Then the area of DeltaPQR is largest when.
Answer» `anglePRQ=(pi)/(2)` the POINT R is `(4,4)` the point R is `((1)/(4),1)` NONE of these Solution :`(4,-4)` and `(9,6)` lie on `y^(2)=4A(x-b)` `implies 16=4a(4-b)` and `36=4a(9-b)impliesa=1,b=0` `therefore` Equation of PARABOLA is `y^(2)=4x` Let the point R be `(t^(2),2T)`, where `t in(-2,3)` `thereforeDeltaPQR=(1)/(2)\|(4,-4,1),(9,6,1),(t^(2),2t,1)\|` `DeltaPQR=(1)/(2)\|10t-10t^(2)+60\|=(1)/(4)\|125-5(2t-1)^(2)\|` `therefore` Area is largest when `t=(1)/(2){becauset in (-2,3)}` `thereforeR(t^(2),2t)=R((1)/(4),1)`

Discussion

7328.	Let a,b,c be the sides of triangl whose perimeter is P and area is A, then
Answer» <P>`p^(3)LE 27 (b+C-a) (c+a-b) (a+b-c)` `p^(2)le 3 (a^(2)+b^(2) +c^(2))` `a^(2)+ b^(2) +c^(2) ge 4 sqrt3A` `p^(4) le 25 LTA` Answer :B::C

Discussion

7329.	Findthe areaofregionboundedby thetrianglewhoseverticesare A (-1,1),B ( 0,5) andC( 3,2)usingintegration .
Answer» ANSWER :`=15/2` SEQ . UNIT

Discussion

7330.	Let p and q stand for the statements: p: Monica is old . q: She needs medicine. Then negation of p ^^q is
Answer» Monica is neither old nor she needs MEDICINE Momca is not old or she doesn't need medicine Monica is not old but she needs medicine Monica is old but she needs medicine. Answer :B

Discussion

7331.	underset(r=)overset(6)(sum)(-1)^(r)((16),(r)) is divisible by
Answer» 5 7 11 13 Answer :A::B::C::D

Discussion

7332.	Find the inverse of the following using elementary transformations. A=[[2,1],[7,4]]
Answer» SOLUTION :`A^(-1) = [(4,-1),(-7,2)]`

Discussion

7333.	Write the component statement "All things have two eyes and two legs" compound statements and check whether the compound statement is true or false.
Answer» Solution :The component statements are p: All things have two EYES. Q :All things have two eyes The truth VALUE of the COMPOUND statement is .FALSE.

Discussion

7334.	Equation of line of projection of the line 3x-y+2z-1=0=x+2y-z=2 on the plane 3x+2y+z=0 is
Answer» `(x+1)/11=(y-1)/-9=(z-1)/-15` `3x-8y+7z+4=0=3x+2y+z` `(x+12)/11 = (y+8)/-9 = (z+14)/15` `(x+12)/11=(y+8)/-9=(z+14)/-15` Solution :Equation of a plane PASSING through the LINE `3x-y+2z-1=0=x+2y-z-2` is `3x-y+2z-1+lambda(x+2y-z-2)=0` `rArr (3+lambda)x+(-1+2lambda)y+(2-lambda)z+(-1-2lambda)` =0 Since it must be perpendicular to the given plane. `rArr (3+lambda)3+(-1+2lambda(x+2y-z-2)=0` `rArr (3+lambda)x+(-1+2lambda)2+(2-lambda)1=0` `rArr 6lambda-9 rArr lambda=-3//2` `rArr` Plane is `3x-8y+7z+4=0` Now line of projection is line of INTERSECTION of PLANES `3x-8y+7z+4=0` and `3x+2y+z=0`

Discussion

7335.	Express with rational denominator1/(3-sqrt(-2))
Answer» SOLUTION :`1/(3-sqrt(-2))=1/(3-sqrt(2I))=(3+sqrt(2i))/((3-sqrt(2i))(3+sqrt(2i))` `=(3+sqrt(2i))/(9-2i^2)=(3+sqrt(2i))/(9+2)=(3+isqrt2)/(11)`

Discussion

7336.	If I_(n)= intx^(n) e^(cx) dx for n ge 1, then c, I_(n) + nI_(n-1) is equal to
Answer» `X^(N)E^(CX)` `x^(n)` `e^(cx)` `x^(n) + e^(cx)` ANSWER :A

Discussion

7337.	Find the values of each of the expression following : tan("sin"^(-1)3/5+"cot"^(-1)3/2)
Answer» ANSWER :`17/6`

Discussion

7338.	Let P(alpha,0)" and "Q(0,beta) be two-points on x-axis and y-axis respectively. Tangents from P touch the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 at M_1(x_1,y_1)" and "M_2(x_2,y_2), similarly tangent from Q to this hyperbola touches it at M_3(x_3,y_3)" and "M_4(x_4,y_4), then (given alpha,beta ne 0 )
Answer» `x_1=x_2" and "y_1+y_2=0` `x_1+x_2=0,y_1=y_2` `x_1+x_4=0,y_3=y_4` `x_3+x_4,y_3+y_4=0` ANSWER :A::C

Discussion

7339.	If there are 30 Railway stations on a Railway line, how many number of single second class tickets must be printed so as to enable a passenger to travel from one station to another.
Answer» ANSWER :870

Discussion

7340.	identify following statements for true (T) and and False (F): S_(1): An old man while dialing a 7-digit telephone number remembers that the first four digits consist of one 1's, one 2's and two 3's. he also remembers that the fifth digit is either a 4 or 5 while has no memory of the sixt digit, he remembers that the seventh digit is 9 minus the sixth digit, maximum number of distinct trials he has to try to make sure that he dials the correct telephone number, is 240. S_(2): A woman has 11 close friends. the number of ways in which she can invite 5 of them to dinner, if two of them are not on speaking terms and will not attend together is 378. S_(3): 10 IIT and 2 PET students sit in a row. if the total number of ways in which exactly 3 IIT students sit between 2 PET students is lamda xx10!, then lamda is 6. which of the following choice is correct?
Answer» TTT TTF TFF FTF Answer :B

Discussion

7341.	Fill in the blanks in the distance of the point P(x_0,y_0,z_0) "from z axis is :"[sqrt(x_0^2+y_0^2),sqrt(y_0^2+z_0^2),sqrt(x_0^2+z_0^2),sqrt((x-x_0)^2+(y-y_0)^2)]
Answer» SOLUTION :`SQRT(x^2+y^2)`

Discussion

7342.	Find the number of ways of selecting r objects from p identical thing and q identical things of other type (i) if p, q lt r "" (ii) " if" p, q gt r
Answer» <P> Solution :When `p, Q lt R`, we have SELECTION produre as FOLLOWS :

Discussion

7343.	int (x+4)/(6x-7-x^(2))dx=
Answer» ANSWER :`-(1)/(2)LOG\|6x-7-x^(2)\|-(7)/(2sqrt(2))log\|(x-3-sqrt(2))/(x-3+sqrt(2))\|+c`

Discussion

7344.	For what value of lamda is the function defined by f(x)= {(lamda(x^(2)-2x)",","if" x le 0),(4x+1",","if" x gt 0):} continuous at x=0 ? What about continuity at x=1?
Answer» ANSWER :5

Discussion

7345.	If locus of point P(z) in complex plane ils \|z+z_(1)\|+\|z+z_(2)\|=4 where A represents z_(1) as (1,0) and B represents z_(2) as (-1, 0) and Q(omega) is moving point inside the locus of P(z) such that all internal angle bisectors of triangle /_\PAB concurrent at Q. Then, answer the following questions if \|omega-omega_(1)\|+\|omega-omega_(2)\|=2 \|omega_(1)\|+\|omega_(2)\| is equal to
Answer» `2/(SQRT(3))` `sqrt(2/3)` `2 sqrt(2/3)` `(2sqrt(2))/3` SOLUTION :NA

Discussion

7346.	If f(x)={(1,xlt0),(1+sinx,0 le x le(pi)/2),(2+(x-(pi)/2),(pi)/2lex):} then which of the following is true for f(x)?
Answer» continuous at x=0 continuous at `x=(PI)/2` Non differentiable at x=0 Differentiable at `x=(pi)/2` ANSWER :A::B::C

Discussion

7347.	The three normals from a point to the parabola y^(2)=4axcut the axes in points whose distance from vertex are in in A.R then the loous of the point is
Answer» 27A`y^(2)=2(x-2a)^(3)` 27a`y^(3)=2(x-2a)^(2)` 9A`y^(2)=2(x-2a)^(3)` 9a`y^(3)=2(x-2a)^(2)` ANSWER :A

Discussion

7348.	If the position vectors of two points A and B are 3hati + hatk and 2hati+hatj-hatk, then the vector vec(BA) is
Answer» `-hati+hatj-2hatk` `hati+hatj` `hati-hatj+2hatk` `hati-hatj-2hatk` ANSWER :C

Discussion

7349.	Find the second order derivatives of the function. sin (log x).
Answer» ANSWER :`-(SIN (LOG X)+COS (log x))/(x^2)`

Discussion

7350.	sin(cot^(-1)((2x)/(1-x^(2)))+cos^(-1)((1-x^(2))/(1+x^(2))))=
Answer» 1 `X` `1/x` `SQRT(1-x^(2))` ANSWER :A

Discussion

Explore topic-wise InterviewSolutions in .

A fair coin is tossed once. If it shows head, then 2 fiar disc are thrown simultaneously otherwise 3 fair disc are thrown simultaneously. The probability that all the dice show different numbers is k, then 180 k is equal to

Aray of light passing through the point(1, 2) reflects on the x-axis at point A and the﻿ reflected﻿ ray passes through the point (5,3). Find the coordinates of A.

{:([a xx b b xx c c xx a],a. 5),(II.[a + b b + c c + a],b. 1),(III. [a b c] [a' b' c'],c.[a b c]^(2)),(IV. [a - b b - c c -a],d. 0),(,e. 2[a b c]):}

underset(xrarr0)lim((1)/(sin x)-(1)/(x))

Each of the two orthogonal circles C_(1) and C_(2) passes through both the points (2, 0) and (-2, 0). If y=mx+c is a common tangent to these circles, then

Differentiate the following functions with respect to x. y= (sin x)^(x) + sin x^(x)

If (1)/(""^(5)C_(r))+(1)/(""^(6)C_(r))=(1)/(""^(4)C_(r)), then the value of r equals to

(d(a^x))/dx =...a)a^x b)log(a^x) c)a^xlog a d)xa^(x-1)

If a,b and n are natural numbers, then a^(2n-1)+b^(2a-1) is divisible by

Determine whether or not each of the definition of ** given below gives a binary operation. In the even that ** is not a binary operation , give justification for this . On Z^(+) , define ** by a" * " b = |a-b|

Determine whether or not each of the definition of ** given below gives a binary operation. In the even that ** is not a binary operation , give justification for this . On Z^(+) , define **by a" * " b = a

Determine whether or not each of the definition of ** given below gives a binary operation. In the even that ** is not a binary operation , give justification for this . On R , define **by a" * " b = ab^2

Let sequence (a_(n))be defined as a_(1)= pi/4,a_(n) = int_(0)^(1//2)(cos(pix)+a_(n+1)) cos pixdx, (n = 2,3,4,"......")then evaluate lim_(n to oo) a_(n)

An ellipse whose whose axis as x-axis and the centre (0,0) passes through (4,3) and (-1, 4). i. Find the equation of the ellipse. ii. Find its eccentricity.

""^(15)C_(0)=

Determine the unit vector having the direction of the given vector in each of the following problems. 3hati+6hatj-hatk

Determine the unit vector having the direction of the given vector in each of the following problems. 3hati+hatj-2hatk

Determine the unit vector having the direction of the given vector in each of the following problems: 5hati-12hatj

Determine the unit vector having the direction of the given vector in each of the following problems. 2hati+hatj

Find d.r. of the line frac{4-x}{2}=frac{y}{6}=frac{1-z}{3}

int (1)/((16 + x^(2))^(3//2))dx =

(1)/(x)=("2 e")/("3 !")+("4 e")/("5 !")+("6 e")/("7 !")+….oo, then find int_(0)^(x)f(y)log_(y)x dy, y gt 1

Compute : [{:(1,-1),(0,2),(2,3):}]([{:(1" "0" "2),(2" "0" "1):}]-[{:(0""1""3),(1""0""2):}]).

If (1)/((1 - 2x)(1 + 3x)) is to tbe expanded as a power series of x, then

int_-a^ax^4dx

If from the point (a,b,c) perpendiculars PL and PM be drawn to YOZ and ZOX then the equation of the plane OLM is ............

Let P(4,-4) and Q(9,6) be points on the parabola y^(2)=4a(x-b). Let R be a point on the arc of the parabola between P and Q. Then the area of DeltaPQR is largest when.

Let a,b,c be the sides of triangl whose perimeter is P and area is A, then

Findthe areaofregionboundedby thetrianglewhoseverticesare A (-1,1),B ( 0,5) andC( 3,2)usingintegration .

Let p and q stand for the statements: p: Monica is old . q: She needs medicine. Then negation of p ^^q is

underset(r=)overset(6)(sum)(-1)^(r)((16),(r)) is divisible by

Find the inverse of the following using elementary transformations. A=[[2,1],[7,4]]

Write the component statement "All things have two eyes and two legs" compound statements and check whether the compound statement is true or false.

Equation of line of projection of the line 3x-y+2z-1=0=x+2y-z=2 on the plane 3x+2y+z=0 is

Express with rational denominator1/(3-sqrt(-2))

If I_(n)= intx^(n) e^(cx) dx for n ge 1, then c, I_(n) + nI_(n-1) is equal to

Find the values of each of the expression following : tan("sin"^(-1)3/5+"cot"^(-1)3/2)

Let P(alpha,0)" and "Q(0,beta) be two-points on x-axis and y-axis respectively. Tangents from P touch the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 at M_1(x_1,y_1)" and "M_2(x_2,y_2), similarly tangent from Q to this hyperbola touches it at M_3(x_3,y_3)" and "M_4(x_4,y_4), then (given alpha,beta ne 0 )

If there are 30 Railway stations on a Railway line, how many number of single second class tickets must be printed so as to enable a passenger to travel from one station to another.

Fill in the blanks in the distance of the point P(x_0,y_0,z_0) "from z axis is :"[sqrt(x_0^2+y_0^2),sqrt(y_0^2+z_0^2),sqrt(x_0^2+z_0^2),sqrt((x-x_0)^2+(y-y_0)^2)]

Find the number of ways of selecting r objects from p identical thing and q identical things of other type (i) if p, q lt r "" (ii) " if" p, q gt r

int (x+4)/(6x-7-x^(2))dx=

For what value of lamda is the function defined by f(x)= {(lamda(x^(2)-2x)",","if" x le 0),(4x+1",","if" x gt 0):} continuous at x=0 ? What about continuity at x=1?

If f(x)={(1,xlt0),(1+sinx,0 le x le(pi)/2),(2+(x-(pi)/2),(pi)/2lex):} then which of the following is true for f(x)?

The three normals from a point to the parabola y^(2)=4axcut the axes in points whose distance from vertex are in in A.R then the loous of the point is

If the position vectors of two points A and B are 3hati + hatk and 2hati+hatj-hatk, then the vector vec(BA) is

Find the second order derivatives of the function. sin (log x).

sin(cot^(-1)((2x)/(1-x^(2)))+cos^(-1)((1-x^(2))/(1+x^(2))))=

Aray of light passing through the point(1, 2) reflects on the x-axis at point A and the reflected ray passes through the point (5,3). Find the coordinates of A.

Determine whether or not each of the definition of given below gives a binary operation. In the even that is not a binary operation , give justification for this . On Z^(+) , define ** by a" * " b = |a-b|

Determine whether or not each of the definition of given below gives a binary operation. In the even that is not a binary operation , give justification for this . On Z^(+) , define **by a" * " b = a

Determine whether or not each of the definition of given below gives a binary operation. In the even that is not a binary operation , give justification for this . On R , define **by a" * " b = ab^2