28278 + Interview Questions in Maths in Class 12 Page 19 InterviewSolution

901.	Find the order and degree, if defined, of the differential equation. (d^4y)/(dx^4) + sin""((d^3y)/(dx^3))=0
Answer» ANSWER :ORDER `=4` DEGREE is not DEFINED.

Discussion

902.	intxtan^2xdx
Answer» SOLUTION :`intxtan^2xdx=intx(sec^2x-1)DX` =`intxsec^2xdx-intxdx` =`x.tanx-int1.tanxdx-1/2x^2` [x=1st `sec^2x=2nd`] =`xtanx+Inabs(COSX)-x^2/2+C`

Discussion

903.	Five balls of different colours are placed at random in fives boxes having colours as that of the balls. The probability that no ball goes into the box of same colour is
Answer» `(11)/(30)` `(119)/(120)` `(1)/(120)` `(19)/(30)` ANSWER :A

Discussion

904.	Let Q(x_(1), y_(1)) be a variable point and R(1,0) be a point on the circle x^(2) + y^(2) =1 and P be the mid -point of QR. Then, the locus of the point P is
Answer» `X^(2) + y^(2) -2X =0` `x^(2) + y^(2) + x=0` `x^(2) + y^(2) + 2x =0` `x^(2) + y^(2) -x = 0` ANSWER :D

Discussion

905.	Numbers 1, 2, 3, ………, 2n(ninN) are printed on 2n cards. The probability of drawing a number r is proportional to r. Then the probability of drawing an even number in one draw is
Answer» `(n+1)/(n+3)` `(n+1)/(n+3)` `(1)/(2)` `(n+1)/(2n+1)` ANSWER :D

Discussion

906.	f (x) =(x ^(2) - 1) ^(7)implies f ^((14))(x) =
Answer» 0 `2!` `7!` `14!` ANSWER :D

Discussion

907.	IF x yz are not equal to ne 0, ne 1 the value of \|{:(logx,,logy,,logz),(log2x,,log2y,,log2z),(log3x,,log3y,,log3z):}\| is equal to
Answer» a.`LOG(xyz)` B.`log(6XYZ)` c.0 d.`log(x+y+z)` ANSWER :C

Discussion

908.	The slope of the radical axis of the circles x^2+y^2+3x+4y-5=0 and x^2+y^2-5x+5y+6=0 is
Answer» 1 2 5 8 Answer :D

Discussion

909.	Let S be a non-empty subset of R. consider the following statement: P: There is a rational number x inS such that xgt0. Which of the following statements is the negation of the statement P?
Answer» There is a rational NUMBER `x in S` such that `XLE0` There is no rational number `x inS` such that `xle0` EVERY rational number `x inS` satisfies `xle0`. `x inS` and `xle0 impliesx` is not rational Answer :C

Discussion

910.	Differentiate.a^(sin^-1x^2)
Answer» SOLUTION :`y=a^(SIN^(-1))x^2` dy/dx=a^(sin^(-1))x^2cdotInacdotd/dx(sin^(-1))` `=a^(sin^(-1))x^2cdotInacdot1/(SQRT(1-x^4))cdotd/dx(x^2)` `=a^(sin^(-1))x^2cdotInacdot(2X)/(sqrt(1-x^4))`

Discussion

911.	The equation of the plane through the point (-1, 6, 2) and perpendicular to the planes x + 2y + 2z – 5 = 0 and 3x + 3y + 2z – 8 = 0 is
Answer» a, b, C b, c, a c, a, b c, b, a Answer :A

Discussion

912.	Statement-I : If (3x+4)/((x+1)^(2)(x-1))=(A)/(x-1)+(B)/(x+1)+(C)/((x+1)^(2)) then A=7//4 Statement-II : If (px+q)/((2x-3)^(2))=(1)/(2x-3)+(3)/((2x-3)^(2)) then p=2, q=3. Which of the above statements is true
Answer» only I is true only II is true both I & II are true neither I nor II true Answer :A

Discussion

913.	The shortest distance between the lines vecr=(hati-hatj)+lamda(hati+2hatj-3hatk) and vecr=(hati-hatj+2hatk)+mu(2hati+4hatj-5hatk) is
Answer» 6 `SQRT(5)` `(6)/(sqrt(5))` `6sqrt(5)` ANSWER :C

Discussion

914.	The product of the four values of (1/2+i(sqrt3)/(2))^(3//4) is
Answer» -1 1 i `-i` ANSWER :B

Discussion

915.	If alpha" and "beta are the roots of the equation x^(2)-7x+1=0, then the value of (1)/((alpha-7)^2)+(1)/((beta-7)^2) is
Answer» 45 47 50 51 Answer :B

Discussion

916.	hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1.
Answer» ANSWER :`a^(2) COS^(2) alpha-b^(2) SIN^(2) alpha=p^(2)`

Discussion

917.	If x^(2)+ax+10=0" and "x^(2)+bx-10=0 have a common root, then a^(2)-b^(2) is equal to
Answer» 10 20 30 40 Answer :D

Discussion

918.	The range of value's of k for which the equation2 cos^(4) x - sin^(4) x + k = 0has atleast one solution is[ lambda, mu]. Find the value of( 9 mu + lambda) .
Answer» ANSWER :7

Discussion

919.	A telephone company in the town has 5000 subscribers on its list and collects fiexed rent company proposes to increases annual rent and one subscriber will be discontinued. For maximum annual income to the company, the increased annual rent is
Answer» RS 2000 Rs 500 Rs 1500 Rs 1000 Answer :D

Discussion

920.	Find the equations of the circles for which the points given below are the end points of a diameter. (3,1),(2,7)
Answer» ANSWER :` X^(2) + y^(2) -5X - 8Y + 13=0 `

Discussion

921.	Let A and B be two 3xx3 real matrices such that AB = BA and det (A^(2)+AB+B^(2))=0 . If omega ne 1 is a cube root of unity then det (A-omega^(2)B) is equal to _______ .
Answer» ANSWER :`0.00`

Discussion

922.	It is not possible to find the equation of a cicle I: If radius centre of circle are given II: IF thre non collinear points on the circle are given III: If the centre and a tangent of the circle are known IV: If the centre and a chord length of the circle are known, the order of trueness, falseness of above statements is
Answer» T,T,T,T F,T,T,F F,F,F,T F,F,F,F Answer :C

Discussion

923.	Find veca.(vecbxxvecc),ifveca=2overset^^i+overset^^j+3overset^^k.vecb=-overset^^i+2overset^^j+overset^^k andvecc=3overset^^i+overset^^j+2overset^^k.
Answer» SOLUTION :We have `VECA.(VECBXXVECC)` `=\|(2,1,3),(-1,2,1),(3,1,2)\|=-10`

Discussion

924.	Differentiate tan^(-1) frac((cos x-sin x))((cos x+ sin x))
Answer» SOLUTION :`y = tan^(-1)((cos x- SIN x)/(cos x + sin x)) = tan^(-1)((1-tan x)/(1+tan x) = tan^(-1) tan(pi/2-x) = pi/4-x therefore dy/dx = -1`

Discussion

925.	If p _(1) =0 and p _(2) =0 be two non-parallel planes, then the equation p_(1) + lamda p _(2) =0, lamda in R represents the family of all planes through the line of intersection of the planes p _(1) =0 and p _(2) =0 except the plane :
Answer» `p _(1) =0` `p _(2) =0` `p _(1) + p _(2) =0` `p _(1) -p_(2) =0` Answer :B

Discussion

926.	Plane E_(1) is determined by the vectors I and i+j and plane E_(2) is determined by the vectors i-j and i+k. If barais a non-zero vector parallel to the line of intersection of E_(1) and E_(2), then the angle between bara and barb=i-2j+2k is
Answer» `pi/3` `pi/4` `pi/6` NONE of these ANSWER :B

Discussion

927.	The value of lambda for which the straight line (x-lambda)/(3)=(y-1)/(2+lambda)=(z-3)/(-1) may lie on the plane x-2y=0 is
Answer» 1 0 `-(1)/(2)` there is no such `LAMBDA` Answer :C

Discussion

928.	A vector perpendicular to the vectors hati+hatj and hati+hatk is ____
Answer» `hati-hatj-hatk` `hatj-hatk+hati` `hatk-hatj-hati` `hatj+hatk+hati` ANSWER :A

Discussion

929.	Using the property of determinants andd without expanding in following exercises 1 to 7 prove that \|{:(y+k,y,y),(y,y+k,y),(y,y,y+k):}\|=k^2(3y+k)
Answer» ANSWER :`k^2(3y+k)`

Discussion

930.	VarifyA (adjA)=(adjA)A[{:(1,-1,2),(3,0,-2),(1,0,3):}]=
Answer» Solution :`therefore""\|A\|=[{:(1,-1,2),(3,0,-2),(1,0,3):}]=0` =1(0-0)-(-1)(9+2)+2(0-0)=11 `rArr""\|A\|.I_(3)=11[{:(1,0,0),(0,1,0),(0,0,1):}]=[{:(11,0,0),(0,11,0),(0,0,11):}]` `A_(11)=(-1)^(1+1)\|{:(0,-2),(0,3):}\|` `A_(12)=(-1)^(1+2)[{:(3,-2),(1,3):}]=-11,` `A_(13)=(-1)^(1+3)[{:(3,0),(1,3):}]=0,` `A_(21)=(-1)^(2+1)[{:(-1,2),(0,3):}]=1,` `A_(22)=(-1)^(2+2)[{:(1,2),(1,3):}]=1,` `A_(23)=(-1)^(2+3)[{:(1,-1),(1,0):}]=2,` `A_(31)=(-1)^(3+1)[{:(-1,2),(0,-2):}]=8,` `A_(32)=(-1)^(3+2)[{:(1,2),(3,-2):}]=8,` `A_(33)=(-1)^(3+3)[{:(1,-1),(3,0):}]=3,` `therefore"adj A"=[{:(0,-11,0),(3,1,-1),(2,8,3):}]=[{:(0,3,2),(-11,1,8),(0,-1,3):}]` `"Now A. (adj A)"=[{:(0,-1,2),(3,1,-2),(1,0,3):}]=[{:(0,3,2),(-11,1,8),(0,-1,3):}]` `=[{:(0+11+0,3-1-2,2-8+6),(0+0+0,9+0+2,6+0-6),(0+0+0,3+0=3,2+0+9):}]` `=[{:(11,0,0),(0,11,0),(0,0,11):}]` `"(adj A).A"=[{:(0,3,2),(-11,1,8),(0,-1,3):}]=[{:(1,-1,2),(3,0,-2),(1,0,3):}]` `=[{:(0+9+2,0+0+0,0-6+6),(-11+3+8,11+0+0,-22-2+24),(0-3+3,0+0+0,0+2+9):}]` `=[{:(11,0,0),(0,11,0),(0,0,11):}]` `therefore`A.(adj A)=(adjA)A=\|A\|.`I_(3)`

Discussion

931.	Which is not the property of diamond ?
Answer» It is insoluble in all solvents It is oxidised with a mixture of `k_(2)Cr_(2)O_(7)` and `H_(2)SO_(4)` at `200^(@)C`. Being hardest, it is used an abrasive for SHARPENING hard TOOLS `Delta_(f)H^(@)` value of diamond is `1.90 KJ mol^(-1)`. Solution :Diamond is almost chemically inert.

Discussion

932.	A wire of length 20cm is cut into two parts which are bent in the form of a square and a circle, then the least value of the sum of areas so formed is
Answer» `(400)/(pi+4)` `(20)/(pi+4)` `5/(pi+4)` `(100)/(pi+4)` ANSWER :D

Discussion

933.	Find minors and cofactors of the elements of the determinant \|{:(2,-3,5),(6,0,4),(1,5,-7):}\| and verify that a_(11)A_(31)+a_(12)A_(32)+a_(13)A_(33)=0
Answer» ANSWER :`a_(11)A_(31)+a_(12)A_(32)+a_(13)A_(33)=0`

Discussion

934.	If a+b+c ne 0 and \|{:(a,b,c),(b,c,a),(c,a,b):}\|=0 then prove that a=b=c
Answer» ANSWER :a=b=c

Discussion

935.	Let e(lambda)be eccentricity of the hyperbola (x^(2))/(a^(2)+lambda)-(y^(2))/(b^(2)+gamma)=1 where a^(2) gtb^(2) and gammage1 if e(lambda) is least when lambda=lambda_(0) then lambda_(0) is equal to
Answer» ANSWER :1

Discussion

936.	Let z_1 , z_2 and z_3 be three distinct complex numbers satisfying \|z_1\|=\|z_2\|=\|z_3\|=1. Which of the following is/aretrue ?
Answer» If arg`(z_1/z_2)=pi/2` then arg `((z-z_1)/(z-z_2)) gt pi/4` where \| z\| gt 1 `\|z_1z_2+z_2z_3 + z_3z_1\|=\|z_1+z_2+z_3\|` `LIM(((z_1+z_2)(z_2+z_3)(z_3+z_1))/(z_1.z_2.z_3))=0` If `\|z_1-z_2\|=sqrt2\|z_1-z_3\|=sqrt2\| z_2-z_3\|`, then Re `((z_3-z_1)/(z_3-z_2))` = 0 ANSWER :B::C::D

Discussion

937.	Using the method of differentials, find the approximate value of sqrt(0.24).
Answer» SOLUTION :N/A

Discussion

938.	int_(0)^(pi) (cos x + \|cos x\|)dx=
Answer» 2 0 1 `1/2` ANSWER :A

Discussion

939.	If A and B are independent events , then P(B/A)=
Answer» <P>`P(A)` `(P(B))/(P(A))` `P(B)` `P(A) P(B)` ANSWER :C

Discussion

940.	If z_1, z_2, z_3 are the vertices of an equilateral triangle inscribed in the circle \|z\|=1 then the area of thetriangle having z_1 , z_2, z_3 as its vertices is
Answer» `(sqrt3)/(2)` `(sqrt3)/(4)` `( 3 sqrt3)/(4)` NONE of these Answer :B

Discussion

941.	The set of point on the axis of the parabola y^(2) -2y -4x + 5=0 from which all the three normals to the parabola are real is:
Answer» ` { (X,1 ) : XGE 3}` ` { (x,-1) : xge 1}` ` { (x,3) : XGE1}` ` { ( x,- 3) : xge3} ` Answer :A

Discussion

942.	Slope of tangent to the curve 'y = x^2-2x+1' at x=3 is :
Answer» 4 6 0 2 Answer :A

Discussion

943.	Let f: R rarr R be defined by f(x)= (1)/(x) AA x inR, then f is _______
Answer» 1)F is not defined 2)bijective 3)onto 4)one-one Answer :A

Discussion

944.	int_(0)^(4) (x + e^(2x)) dx.
Answer» ANSWER :`(15+e^(8))/2`

Discussion

945.	((1+isqrt3)/(1-isqrt3))^6+((1-isqrt3)/(1+isqrt3))^6=
Answer» 2 -2 1 0 Answer :A

Discussion

946.	Two numbers are selected at random from 1, 2, 3,…., 100 without replacement. Find the probability that the minimum of the two numbers is less than 70.
Answer» ANSWER :`1- (30C_(2))/(100C_(2))`

Discussion

947.	Find the number of 4 letter words that can he formed using one vowel and 3 consonants from the letters of the word 'ARTICLE'.
Answer» ANSWER :288

Discussion

948.	Find the equation of the circle which passes through the point (0,-3) and intersects the circles given by the equation x^2 + y^2 - 6x + 3y + 5 = 0 and x^2 + y^2 - x - 7y = 0 orthogonally.
Answer» ANSWER :(or)`3x^2 + 3y^2 + 2X + 4Y - 15 = 0 `

Discussion

949.	A triangle ABC exists such that
Answer» `(b+C+a)(b+c-a)=5bc` the sides are of lengths `sqrt19, sqrt38, sqrt116` `cos ((b ^(2)-c^(2))/(a ^(2)))+((c^(2)-a^(2))/(b ^(2)))+((a^(2)-b^(2))/(c^(2)))=0` `cos ((B-C)/(2))=(SIN B+ sin C) cos ((B+C)/(2))` Answer :D

Discussion

950.	Point of contact of the line kx + y-4 =0, w.r.t.the parabola y=x -x^(2)is
Answer» ` (-2,2) ` `(2,-2) ` ` ( -2,6) ` `( 2,-6) ` ANSWER :B

Discussion

Explore topic-wise InterviewSolutions in .

Find the order and degree, if defined, of the differential equation. (d^4y)/(dx^4) + sin""((d^3y)/(dx^3))=0

intxtan^2xdx

Five balls of different colours are placed at random in fives boxes having colours as that of the balls. The probability that no ball goes into the box of same colour is

Let Q(x_(1), y_(1)) be a variable point and R(1,0) be a point on the circle x^(2) + y^(2) =1 and P be the mid -point of QR. Then, the locus of the point P is

Numbers 1, 2, 3, ………, 2n(ninN) are printed on 2n cards. The probability of drawing a number r is proportional to r. Then the probability of drawing an even number in one draw is

f (x) =(x ^(2) - 1) ^(7)implies f ^((14))(x) =

IF x yz are not equal to ne 0, ne 1 the value of |{:(logx,,logy,,logz),(log2x,,log2y,,log2z),(log3x,,log3y,,log3z):}| is equal to

The slope of the radical axis of the circles x^2+y^2+3x+4y-5=0 and x^2+y^2-5x+5y+6=0 is

Let S be a non-empty subset of R. consider the following statement: P: There is a rational number x inS such that xgt0. Which of the following statements is the negation of the statement P?

Differentiate.a^(sin^-1x^2)

The equation of the plane through the point (-1, 6, 2) and perpendicular to the planes x + 2y + 2z – 5 = 0 and 3x + 3y + 2z – 8 = 0 is

Statement-I : If (3x+4)/((x+1)^(2)(x-1))=(A)/(x-1)+(B)/(x+1)+(C)/((x+1)^(2)) then A=7//4 Statement-II : If (px+q)/((2x-3)^(2))=(1)/(2x-3)+(3)/((2x-3)^(2)) then p=2, q=3. Which of the above statements is true

The shortest distance between the lines vecr=(hati-hatj)+lamda(hati+2hatj-3hatk) and vecr=(hati-hatj+2hatk)+mu(2hati+4hatj-5hatk) is

The product of the four values of (1/2+i(sqrt3)/(2))^(3//4) is

If alpha" and "beta are the roots of the equation x^(2)-7x+1=0, then the value of (1)/((alpha-7)^2)+(1)/((beta-7)^2) is

hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1.

If x^(2)+ax+10=0" and "x^(2)+bx-10=0 have a common root, then a^(2)-b^(2) is equal to

The range of value's of k for which the equation2 cos^(4) x - sin^(4) x + k = 0has atleast one solution is[ lambda, mu]. Find the value of( 9 mu + lambda) .

A telephone company in the town has 5000 subscribers on its list and collects fiexed rent company proposes to increases annual rent and one subscriber will be discontinued. For maximum annual income to the company, the increased annual rent is

Find the equations of the circles for which the points given below are the end points of a diameter. (3,1),(2,7)

Let A and B be two 3xx3 real matrices such that AB = BA and det (A^(2)+AB+B^(2))=0 . If omega ne 1 is a cube root of unity then det (A-omega^(2)B) is equal to _______ .

Find veca.(vecbxxvecc),ifveca=2overset^^i+overset^^j+3overset^^k.vecb=-overset^^i+2overset^^j+overset^^k andvecc=3overset^^i+overset^^j+2overset^^k.

Differentiate tan^(-1) frac((cos x-sin x))((cos x+ sin x))

If p _(1) =0 and p _(2) =0 be two non-parallel planes, then the equation p_(1) + lamda p _(2) =0, lamda in R represents the family of all planes through the line of intersection of the planes p _(1) =0 and p _(2) =0 except the plane :

Plane E_(1) is determined by the vectors I and i+j and plane E_(2) is determined by the vectors i-j and i+k. If barais a non-zero vector parallel to the line of intersection of E_(1) and E_(2), then the angle between bara and barb=i-2j+2k is

The value of lambda for which the straight line (x-lambda)/(3)=(y-1)/(2+lambda)=(z-3)/(-1) may lie on the plane x-2y=0 is

A vector perpendicular to the vectors hati+hatj and hati+hatk is ____

Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(y+k,y,y),(y,y+k,y),(y,y,y+k):}|=k^2(3y+k)

VarifyA (adjA)=(adjA)A[{:(1,-1,2),(3,0,-2),(1,0,3):}]=

Which is not the property of diamond ?

A wire of length 20cm is cut into two parts which are bent in the form of a square and a circle, then the least value of the sum of areas so formed is

Find minors and cofactors of the elements of the determinant |{:(2,-3,5),(6,0,4),(1,5,-7):}| and verify that a_(11)A_(31)+a_(12)A_(32)+a_(13)A_(33)=0

If a+b+c ne 0 and |{:(a,b,c),(b,c,a),(c,a,b):}|=0 then prove that a=b=c

Let e(lambda)be eccentricity of the hyperbola (x^(2))/(a^(2)+lambda)-(y^(2))/(b^(2)+gamma)=1 where a^(2) gtb^(2) and gammage1 if e(lambda) is least when lambda=lambda_(0) then lambda_(0) is equal to

Let z_1 , z_2 and z_3 be three distinct complex numbers satisfying |z_1|=|z_2|=|z_3|=1. Which of the following is/aretrue ?

Using the method of differentials, find the approximate value of sqrt(0.24).

int_(0)^(pi) (cos x + |cos x|)dx=

If A and B are independent events , then P(B/A)=

If z_1, z_2, z_3 are the vertices of an equilateral triangle inscribed in the circle |z|=1 then the area of thetriangle having z_1 , z_2, z_3 as its vertices is

The set of point on the axis of the parabola y^(2) -2y -4x + 5=0 from which all the three normals to the parabola are real is:

Slope of tangent to the curve 'y = x^2-2x+1' at x=3 is :

Let f: R rarr R be defined by f(x)= (1)/(x) AA x inR, then f is _______

int_(0)^(4) (x + e^(2x)) dx.

((1+isqrt3)/(1-isqrt3))^6+((1-isqrt3)/(1+isqrt3))^6=

Two numbers are selected at random from 1, 2, 3,…., 100 without replacement. Find the probability that the minimum of the two numbers is less than 70.

Find the number of 4 letter words that can he formed using one vowel and 3 consonants from the letters of the word 'ARTICLE'.

Find the equation of the circle which passes through the point (0,-3) and intersects the circles given by the equation x^2 + y^2 - 6x + 3y + 5 = 0 and x^2 + y^2 - x - 7y = 0 orthogonally.

A triangle ABC exists such that

Point of contact of the line kx + y-4 =0, w.r.t.the parabola y=x -x^(2)is