28278 + Interview Questions in Maths in Class 12 Page 144 InterviewSolution

7151.	Find the mean deviation from the mean of observations -1, 0, 4 ?
Answer» ANSWER :2

Discussion

7152.	Let P denotes the plane consisting of all points that are equidistant from the points A(-4,2,1) and B(2,-4,3) and Q be the plane, x-y+cz=1 where c in R. If the angle between the planes P and Q is 45^(@) then the product of all possible values of c is
Answer» `-17` `-2` 17 `24//27` SOLUTION :`vecn_(1) = 3hati-3hatj+hatk` and `vecn_(2) = hati-hatj+chatk` `COS 45^(@) = \|(vecn_(1).vecn_(2))/(\|vecn_(1)\|\|vecn_(2)\|)\|=\|((3+3+c)/(sqrt(19)sqrt(2+c^(2))))\|` `THEREFORE 2(6+c)^(2) = 19(2+c^(2))` `rArr 2(36+c^(2)+12c)=38+19c^(2)` `rArr 17c^(2)-24c-34=0`

Discussion

7153.	Integrate the following functions xsqrt(x+2)
Answer» Solution :`xsqrt(x+2) = (x+2-2) sqrt(x+2)` =`(x+2) sqrt(x+2)-2sqrt(x+2)` =`(x+2)^(3/2) -2(x+2)^(1/2)` THEREFORE `int xsqrt(x+2) dx` =`(x+2)^(3/2+1)/(3/2+1) -2 (x+2)^(1/2+1)/(1/2+1) +C` =`2/5 (x+2)^(5/2) -4/3 (x=2)^(3/2) +c`

Discussion

7154.	If A(5, -4) and B(7, 6) are points in a plane, then the set of all points P(x, y) in the plane such that AP : PB = 2 : is
Answer» a CIRCLE a hyperbola an ellipse a parabola Answer :A

Discussion

7155.	Find all 8-digit numbers such that the sum of their digits is 14 and each of the digits 0,1,2,3,4 occurs at least once in them.
Answer» ANSWER :`""^(7)C_(2).(6!)/(3!).+ ""^(7)C_(2).(6!)/(2!.2!) + ""^(7)C_(3) (5!)/(2!).+ ""^(7)C_(1) .(7!)/(3!.2!)`

Discussion

7156.	Evaluate the following integrals. int(6x+5)sqrt(6+x-2x^(2))dx
Answer» Answer :`(6+x-2x^(2))^(3//2)+(13)/(2)(((4x-1)/8)sqrt(6+x-2x^(2))+(49)/(16sqrt(2))sin^(-1)((4x-1)/(7)))+C`

Discussion

7157.	(A) : If \|z+ 1\| - \|z - 1\| = (3)/(2) then least value of \|z\| is 3/4 (R) : If z_(1) , z_(2) are two complex numbers then \|z_(1) - z_(2)\| ge\|\|z_(1)\| - \|z_(2)\|\|
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 of A A is true R is FALSE A is false R is true Answer :B

Discussion

7158.	Evaluate the following integrals int_(a)^(b)sqrt((x-a)(b-x))dx
Answer» ANSWER :`pi/8 (b-a)^(2)`

Discussion

7159.	If the distance between the planes4x -2y - 4z +1 =0 and 4x -2y -4z + d=0 is 7, then d is
Answer» `41 or -42 ` `42 or -43 ` ` -41 or 43` ` -42 or 44` ANSWER :C

Discussion

7160.	Let A and B be square matrices of the order 3xx3 . Is (AB)^(2)=A^(2)B^(2) ? Given reasons .
Answer» ANSWER :`=B*A`.

Discussion

7161.	Prove that the sum of the vectors represented by the sides of a closed polygon taken in order is a zero vector.
Answer» Solution : Then by triangle law `VEC(AB)+vec(BC) = vec(AC), vec(AC)+vec(CD) = vec(AD)` `vec(AD)+vec(DE) = vec(AE), vec(EF)+vec(FA) = vec(EA)` ADDING the above RELATIONS we get `vec(AB)+vec(BC)+vec(AC)+vec(CD)+vec(AD)+vec(DE)+vec(EF)+vec(FA) = vec(AC)+vec(AD)+vec(AE)+vec(EA)` `implies vec(AB)+vec(BC)+vec(CD)+vec(DE)+vec(EF)+vec(FA)` =`vec(AE)+vec(EA) = 0`

Discussion

7162.	If veca=4hatj+5hatj-hatk,vecb=hati-4hatj+4hatk and vecc = 3hati+hatj+hatk Find a vector vecd which is perpendicualr to both veca and vecb and vecd.vecc = 21 .
Answer» ANSWER :`(21)/(10) (16hati- 17hatj- 21hatk)`

Discussion

7163.	Can the inverse of the following matric be found ? [[0,0],[0,0]]
Answer» Solution :LET A = `[[0,0],[0,0]]` `THEREFORE ABSA =0` `A^-1` can not be FOUND.

Discussion

7164.	Suppose A and B are two square matrices of same order. If A, B are symmetricmatrices, then AB - BA is
Answer» SKEW symmetric MATRIX Symmetric matrix Zero matrix Identity matrix ANSWER :A

Discussion

7165.	Evaluate int(1)/(2 - 3 cos 2 x) dx
Answer» Answer :`(1)/(2sqrt(5))LOG\|(SQRT(5)tanx-1)/(sqrt(5)tanx+1)\|+C`

Discussion

7166.	Find the probability that a leap year will have 53 Mondays.
Answer» ANSWER :`(2)/(7)`

Discussion

7167.	Write Minors and Cofactors of the elements of following determinants: (i){:\|( 2,-4),(0,3)\|:}"" {:\|( a,c),( b,d) \|:}
Answer» ANSWER :` M_11 =3, M_12 =0, M_21 =-4 .M_22 = 2, A_11=3,A _12 = 0,A_21=4,A_22=2 ` (ii) ` M_11 =d,M_12=B,M_21 =C, M_22 =aA_11 =d,A_12 =-b,A_21 =-c ,A_22 =a `

Discussion

7168.	A radioactive isotope ._(Z)X^(A) is converting into ._(Z-8)Y^(A-16) by alpha-decay. If g-atoms._(Z)X^(A)produced 3 mole of He atoms in 20 hours, then calculate the half life of._(Z)X^(A)(in hours).
Answer» 10 5 2 1 Solution :`{:(._(Z)X^(A)to,Y+,4_(2)^(4)He,),("1 mole",,"4 mol",),(1-x,,4x,),(,,4x=3,),(,,x=(3)/(4),):}` `K=(1)/(20)ln4` `t_(1//2)=(LN2)/((1)/(10)ln2)` `t_(1//2)=10" hrs."]`

Discussion

7169.	f: Z rarrZ and g : Z rarrZ are defined as follow : f(n) ={:{(n+2," n even"),(2n-1," n odd"):}, g(n) ={{:(2n,"n even"),((n-1)/2,"n odd"):} Find fog and gof.
Answer» SOLUTION :N/A

Discussion

7170.	Consider the expansion of (a+b+c+d)^(6). Then thesum of all the coefficients of the term Which contains all of a,b,c, and d is
Answer» 4096 1560 3367 670 Solution :We have `(a+b+c+d)^(6)` SUM of coefficient which contains all of a,b,c and d = Number of ways of distributing six DISTINCT OBJECTS infourt boxes such that no box remains EMPTY `= 4^(6) - .^(4)C_(1)3^(6) +.^(4)C_(1) - .^(4)C_(1)1^(6) = 1560`

Discussion

7171.	Compute the volume of the solid obtained by revolving about the polar axis the cardioid rho = a (1 + cos varphi) shown in
Answer» ANSWER :`(8)/(30 pi a^(3) (u= cos varphi)`

Discussion

7172.	Equation of common tangent to y^(2)=32x and x^(2)=108 y is
Answer» 2x+3y-36=0 2x+3y + 36 =0 2x-3y + 36 =0 2x-3y-36 =0 ANSWER :B

Discussion

7173.	The ratio of men to women on a panel was 3 to 4 before one women was replaced by a man. {:("Quantity A","Quantity B"),("The number of men on the","The number of women on the"),("panel","panel"):}
Answer» ANSWER :The RELATIONSHIP cannot be DETERMINED from the INFORMATION GIVEN.

Discussion

7174.	Evaluate the following improper integrals (or prove their divergence) : (a) int_(0)^(1//2)(dx)/(x1nx), (b) int_(1)^(2)(dx)/(xsqrt(1nx)), (c ) int_(0)^(1)(3x^(2)+2)/(root3(x^(2)))dx.
Answer» ANSWER :(a) It diverges; (B) `2sqrt(1N2);` (C ) `(51)/(7)`

Discussion

7175.	Which of the following expressions is equivalent to the expression above, assuming that I = sqrt-1, ?
Answer» `1/5` `5/7` `(13+ 18I)/(20)` `(13+ 18i)/(29)` ANSWER :D

Discussion

7176.	(a + b). A' + (b + c). B' + (c + a). C' =
Answer» 0 1 2 3 Answer :D

Discussion

7177.	Distance between two parallel planes: 2x + y + 2z = 8 and 4x + 2y + 4z +5=0 is:
Answer» `5/2` `7/2` `9/2` `3/2` ANSWER :B

Discussion

7178.	int_(1)^(3)(1)/(sqrt(x+1)-sqrt(x-1))dx=
Answer» `4/3` `5/3` `7/3` `8/3` ANSWER :D

Discussion

7179.	The side of an equilateral triangle expands at the rate of sqrt(3) cm/sec. When the side is 12 cm, the rate of increase of its area is ……….
Answer» `12CM^(2)//sec` `18 CM^(2)//sec` `3sqrt(3)cm^(2)//sec` `10cm^(2)//sec` Answer :B

Discussion

7180.	IFalpha, betabe theroots of theequation(x-a) ( x-b) +c=0 (c ne 0) thentheroots of theequation(x-c-alpha ) (x-c-beta )=c are
Answer» a andb+C a+c and b a+candb+c a-c andb-c Answer :C

Discussion

7181.	Prove that the sum of any two of roots of the equation x^4+px^3+qx^2+rx+s=0 is equal to the sum of the remaining two roots of the equation iff p^3 -4pq+8r=0
Answer» ANSWER :WE have `alpha_1+beta_1=-b=gamma_1+delta_1`

Discussion

7182.	int_0^oox^2/(1+x^6)^ndx
Answer» Solution :`I=int_0^oox^2/(1+x^6)^ndx` <BR> Let `x^3=tantheta` `rArr3x^2dx=sec^2thetad THETA` `x=0rArrtheta=0` ,br> `x=oorArrtheta=pi//2` `therefore I=1/3int_0^(pi/2)(sec^2thetad theta)/(sec^2theta)^N` =`1/3int_0^(pi/2)COS^(2n-2)thetad theta` =`1/3(2n-3)/(2n-2)CDOT(2n-5)/(2n-4)...1/2cdotpi/2`

Discussion

7183.	Find order and degree of given differential equation y" + 2y' + sin y = 0
Answer» ANSWER :ORDER 2; DEGREE 1

Discussion

7184.	Evalute the following integral int" x sinh"^(-1)x dx
Answer» ANSWER :`(1)/(4)(2X^(2)+1)sinh^(-1)x-xsqrt(1+x^(2))]+C`

Discussion

7185.	The plane passing through the intersection of the planes x+y +z =1 and 2x+3y -z + 4 = 0 and parallel to Y - axis is also passing through ....... Point.
Answer» (-3,0,1) (3,2,2) `(-3,1,1)` `(3,3,-1)` ANSWER :B

Discussion

7186.	Compute the product A xx B when A = {0} = B
Answer» SOLUTION :A = {0} = B `THEREFORE A XX B` = {(0,0)}

Discussion

7187.	Statement - I : The variance of first n even natural numbers is (n^(2) - 1)/(4) Statement - II : The sum of first n natural numbers is (n(n+1))/(2) and the sum of the squares of first n natural numbers is (n(n+1)(2n+1))/(6)
Answer» Statement-I is TRUE, Statement-II is true, Statement -II is not a CORRECT EXPLANATION for statement - I Statement-I is true, Statement-II is false Statement-I is false, Statement-II is true Statement-I is true, Statement-II is true, Statement -II is a correct explanation for statement - I Answer :C

Discussion

7188.	Find x,y if (x+y1) = (1, x-y)
Answer» SOLUTION :`therefore x + y =1 , x-y = 1` `therefore` 2x = 2 or , x=1 `therefore` y = 0

Discussion

7189.	If y=1-x+(x^(2))/(2!)-(x^(3))/(3!)+(x^(4))/(4!)- . . . . then (d^(2)y)/(dx^(2))=
Answer» `-X` `x` y `-y` ANSWER :C

Discussion

7190.	The rangeof(x^2-2x+3)/(x^(2)-2x-8) is
Answer» `[-9//2,1//2]` `(-OO,1] CUP [2,oo)` `(-oo ,-9 ] cup[-1,oo)` R Answer :D

Discussion

7191.	Let p and q be two statements, then ~ p rarr q ^^ (~q)is equivalent to
Answer» <P>p `p^^Q` q p `VEE `q Answer :A

Discussion

7192.	If f(x) = {:{((sqrt(1+ + kx ) - sqrt(1-kx))/x , " for"-1le x lt 0) , ( 2x^(2) + 3x -2," for "0 le x le 1):} continuousat x = 0 ,then k is equal to
Answer» `-1` `-2` `-3` `-4` ANSWER :B

Discussion

7193.	If 0 lt y lt 1, then sum_(n=1)^(oo)(1)/(2n-1)*y^(n+1)=……
Answer» `(y^(3//2))/(2) LOG((1+sqrt(y))/(1-sqrt(y)))` `y^(3//2)log((1-sqrt(y))/(1+sqrt(y)))` `y^(1//2)log((1+sqrt(y))/(1-sqrt(y)))` `y^(1//2)log((1-sqrt(y))/(1+sqrt(y)))` ANSWER :A

Discussion

7194.	If a,b,c are in A.P. then the determinant {:[( x+2,x+3,x+2a),( x+3,x+4,x+2b),( x+4,x+5,x+2c)]:} is
Answer» `0` `1` `X` `2X` ANSWER :A

Discussion

7195.	Resolve (3x-2)/((x^(2)+4)^(2)(x-1)) into partial fractions.
Answer» ANSWER :`:. (3x-2)/((x^(2)+4)^(2)(x-1))=(-(x+1))/(25(x^(2)+4)^(2))+(1)/(25(x-1))`

Discussion

7196.	Differentiate e^(log(e^(x)), x gt 0 with respect to x.
Answer» ANSWER :`= 1`

Discussion

7197.	Find the maximum value of the 24sinx-7cosx
Answer» Solution :MAXIMUM value of 24 sinx-7cosx is `SQRT(24^2+(-7)^2)=sqrt625=25`

Discussion

7198.	If int(2e^(x)+3e^(-x))/(3e^(x)+4e^(-x))dx=Ax+B log(3e^(2x)+4), then
Answer» `A=-(3)/(4), B=(1)/(24)` `A=(3)/(4), B=-(1)/(24)` `A=(1)/(4), B=(1)/(24)` `A=-(3)/(4), B=(1)/(4)` Answer :B

Discussion

7199.	The maximum value of \|z\| when z satisfies the condition \|z+2/z\|=2 is
Answer» `sqrt(3)-1` `sqrt(3)+1` `sqrt(2)+sqrt(3)` `sqrt(3)` Answer :B

Discussion

7200.	Sum to n terms of the series :1 + 2 (1 + (1)/(n)) + 3 (1 + (1)/(n )) ^(2) + ………
Answer» ANSWER :`N ^(2)`

Discussion

Explore topic-wise InterviewSolutions in .

Find the mean deviation from the mean of observations -1, 0, 4 ?

Let P denotes the plane consisting of all points that are equidistant from the points A(-4,2,1) and B(2,-4,3) and Q be the plane, x-y+cz=1 where c in R. If the angle between the planes P and Q is 45^(@) then the product of all possible values of c is

Integrate the following functions xsqrt(x+2)

If A(5, -4) and B(7, 6) are points in a plane, then the set of all points P(x, y) in the plane such that AP : PB = 2 : is

Find all 8-digit numbers such that the sum of their digits is 14 and each of the digits 0,1,2,3,4 occurs at least once in them.

Evaluate the following integrals. int(6x+5)sqrt(6+x-2x^(2))dx

(A) : If |z+ 1| - |z - 1| = (3)/(2) then least value of |z| is 3/4 (R) : If z_(1) , z_(2) are two complex numbers then |z_(1) - z_(2)| ge||z_(1)| - |z_(2)||

Evaluate the following integrals int_(a)^(b)sqrt((x-a)(b-x))dx

If the distance between the planes4x -2y - 4z +1 =0 and 4x -2y -4z + d=0 is 7, then d is

Let A and B be square matrices of the order 3xx3 . Is (AB)^(2)=A^(2)B^(2) ? Given reasons .

Prove that the sum of the vectors represented by the sides of a closed polygon taken in order is a zero vector.

If veca=4hatj+5hatj-hatk,vecb=hati-4hatj+4hatk and vecc = 3hati+hatj+hatk Find a vector vecd which is perpendicualr to both veca and vecb and vecd.vecc = 21 .

Can the inverse of the following matric be found ? [[0,0],[0,0]]

Suppose A and B are two square matrices of same order. If A, B are symmetricmatrices, then AB - BA is

Evaluate int(1)/(2 - 3 cos 2 x) dx

Find the probability that a leap year will have 53 Mondays.

Write Minors and Cofactors of the elements of following determinants: (i){:|( 2,-4),(0,3)|:}"" {:|( a,c),( b,d) |:}

A radioactive isotope ._(Z)X^(A) is converting into ._(Z-8)Y^(A-16) by alpha-decay. If g-atoms._(Z)X^(A)produced 3 mole of He atoms in 20 hours, then calculate the half life of._(Z)X^(A)(in hours).

f: Z rarrZ and g : Z rarrZ are defined as follow : f(n) ={:{(n+2," n even"),(2n-1," n odd"):}, g(n) ={{:(2n,"n even"),((n-1)/2,"n odd"):} Find fog and gof.

Consider the expansion of (a+b+c+d)^(6). Then thesum of all the coefficients of the term Which contains all of a,b,c, and d is

Compute the volume of the solid obtained by revolving about the polar axis the cardioid rho = a (1 + cos varphi) shown in

Equation of common tangent to y^(2)=32x and x^(2)=108 y is

The ratio of men to women on a panel was 3 to 4 before one women was replaced by a man. {:("Quantity A","Quantity B"),("The number of men on the","The number of women on the"),("panel","panel"):}

Evaluate the following improper integrals (or prove their divergence) : (a) int_(0)^(1//2)(dx)/(x1nx), (b) int_(1)^(2)(dx)/(xsqrt(1nx)), (c ) int_(0)^(1)(3x^(2)+2)/(root3(x^(2)))dx.

Which of the following expressions is equivalent to the expression above, assuming that I = sqrt-1, ?

(a + b). A' + (b + c). B' + (c + a). C' =

Distance between two parallel planes: 2x + y + 2z = 8 and 4x + 2y + 4z +5=0 is:

int_(1)^(3)(1)/(sqrt(x+1)-sqrt(x-1))dx=

The side of an equilateral triangle expands at the rate of sqrt(3) cm/sec. When the side is 12 cm, the rate of increase of its area is ……….

IFalpha, betabe theroots of theequation(x-a) ( x-b) +c=0 (c ne 0) thentheroots of theequation(x-c-alpha ) (x-c-beta )=c are

Prove that the sum of any two of roots of the equation x^4+px^3+qx^2+rx+s=0 is equal to the sum of the remaining two roots of the equation iff p^3 -4pq+8r=0

int_0^oox^2/(1+x^6)^ndx

Find order and degree of given differential equation y" + 2y' + sin y = 0

Evalute the following integral int" x sinh"^(-1)x dx

The plane passing through the intersection of the planes x+y +z =1 and 2x+3y -z + 4 = 0 and parallel to Y - axis is also passing through ....... Point.

Compute the product A xx B when A = {0} = B

Statement - I : The variance of first n even natural numbers is (n^(2) - 1)/(4) Statement - II : The sum of first n natural numbers is (n(n+1))/(2) and the sum of the squares of first n natural numbers is (n(n+1)(2n+1))/(6)

Find x,y if (x+y1) = (1, x-y)

If y=1-x+(x^(2))/(2!)-(x^(3))/(3!)+(x^(4))/(4!)- . . . . then (d^(2)y)/(dx^(2))=

The rangeof(x^2-2x+3)/(x^(2)-2x-8) is

Let p and q be two statements, then ~ p rarr q ^^ (~q)is equivalent to

If f(x) = {:{((sqrt(1+ + kx ) - sqrt(1-kx))/x , " for"-1le x lt 0) , ( 2x^(2) + 3x -2," for "0 le x le 1):} continuousat x = 0 ,then k is equal to

If 0 lt y lt 1, then sum_(n=1)^(oo)(1)/(2n-1)*y^(n+1)=……

If a,b,c are in A.P. then the determinant {:[( x+2,x+3,x+2a),( x+3,x+4,x+2b),( x+4,x+5,x+2c)]:} is

Resolve (3x-2)/((x^(2)+4)^(2)(x-1)) into partial fractions.

Differentiate e^(log(e^(x)), x gt 0 with respect to x.

Find the maximum value of the 24sinx-7cosx

If int(2e^(x)+3e^(-x))/(3e^(x)+4e^(-x))dx=Ax+B log(3e^(2x)+4), then

The maximum value of |z| when z satisfies the condition |z+2/z|=2 is

Sum to n terms of the series :1 + 2 (1 + (1)/(n)) + 3 (1 + (1)/(n )) ^(2) + ………