28278 + Interview Questions in Maths in Class 12 Page 83 InterviewSolution

4101.	Let A, B, C be three points on bar(OX),bar(OY),bar(OZ)respectively at the distances 3, 6, 9 from origin. Let Q be the point (2, 5, 8) and P be the pointequidistant from O,A,B,C.Them,thecoordinates of the point R which divides PQ in the ratio : 2 is
Answer» `((17)/(10),(29)/(5),(43)/(10))` `((7)/(5),(16)/(5),5)` `((9)/(5),(21)/(5),(33)/(5))` `((8)/(5),(19)/(5),6)` ANSWER :C

Discussion

4102.	If A={1,2,3,4}B={1,2,3,4,5,6} and f :A to B is an injective mapping satisfying f (i) ne I, then number of such mappings are :
Answer» 182 181 183 None of these ANSWER :B

Discussion

4103.	A die 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

4104.	If vec(z_(1)) = a hat(i) + b hat(j) and vec(z_(2)) = c hat(i) + d hat(j)are two vectors in hat(i) and hat(j) system where \|vec(z_(1))\| = \|vec(z_(2))\| = rand vec(z_(1)).vec(z_(2)) = 0then vec(w_(1)) = ahat(i) + chat(j) and vec(w_(2)) = b hat(i) + d hat(j) satisfy .
Answer» `\|vec(w_(1))\| = R` `\|vec(w_(2))\| = r` `vec(w_(1)) .vec(w_(2)) = 0` NONE of these Answer :A::B::C

Discussion

4105.	If A=[{:(1,2,3),(2,3,1):}]andB=[{:(3,-1,3),(-1,0,2):}], then find 2A-B.
Answer» ANSWER :`[{:(-1,5,3),(5,6,0):}]`

Discussion

4106.	Let n(U) = 700 , n (A) = 200 , n (B) = 300 and n (A nn B) =100, then n(A' nn B')=
Answer» 90 40 10 20 Answer :C

Discussion

4107.	If z_1 andz_2are two non- zero comlex numbers such that \|z_1+z_2\|=\|z_1\|+\|z_2\| then arg (z_1)- arg (z_2) is equal to
Answer» `-pi` `-pi/2` 0 `pi/2` Solution :Given `\|z_1+z_2\|=\|z_1\|+\|z_2\|` On squaring both SIDES ,we GET `\|z_1\|^2 + \|Z_2\|^2+2\|z_1\|\|z_2\|cos (ARG z_1 - arg z_2)=\|z_1\|^2\|z_2\|^2+2\|z_1\|\|z_2\|` ` rArr2\|z_1\|\|z_2\|cos (arg z_1-arg z_2)=2\|z_1\|z_2\|` `rArrcos(arg z_1 - arg z_2)=1` `rArrarg(z_1)aargz_2)=0`

Discussion

4108.	Integrate the function is Exercise. cos^(3)x e^(log sinx)
Answer» ANSWER :`-(1)/(4)COS^(4)x+c`

Discussion

4109.	Let A,B,C be angles of triangles with vertex A -= (4,-1) and internal angular bisectors of angles B and C be x - 1 = 0 and x - y - 1 = 0 respectively. Slope of BC is
Answer» `1//2` 2 3 12 Solution : Image of `A(4,-1)` in bisectors of B and C lies on SIDE BC `rArr` Image of `A(4,-1)` with respect to `x-y -1 =0` is `(x-4)/(1) =(y+1)/(-1) =-(2(4+1-1))/(2) rArr (0,3)` Image of `A(4,-1)` with respect to `x -1 =0` is `(x-4)/(1) =(y+1)/(0) =- (2(4-1))/(1) rArr (-2,-1)` Hence, SLOPE of BC is `m = ((3+1)/(0+2)) =2`

Discussion

4110.	Let A,B,C be angles of triangles with vertex A -= (4,-1) and internal angular bisectors of angles B and C be x - 1 = 0 and x - y - 1 = 0 respectively. If A,B,C are angles of triangle at vertices A,B,C respectively then cot ((B)/(2))cot .((C)/(2)) =
Answer» 2 3 4 6 Solution :Angle between `X -1 =0` and BC is `(B)/(2) rArr TAN.(B)/(2) =(1)/(2)` Angle between `x -y -1 =0` and BC is `(C )/(2) rArr tan.(C )/(2) =(1)/(3)` `rArr cot.(B)/(2) cot.(C )/(2) =6`

Discussion

4111.	Let S = Set of all women in the world. Define R as follows: a, b in S, a Rb if a and b have at least one of the two parents in common, Then
Answer» R is REFLEXIVE and SYMMETRIC only R is reflexive and transitive only R is symmetric and transitive only R is an EQUIVALENCE relation Answer :A

Discussion

4112.	A student has obtained 75%, 80% and 855 in three subjects. If the marks of another subject are added then his average can not be less than
Answer» 0.6 0.65 0.8 0.9 Answer :A

Discussion

4113.	8-digit numbers are formed using the digits 1,1,2,2,2,3,4,4. Thenumber of such numbers in which the odd digits do not occupy odd places, is
Answer» 160 120 60 48 Answer :B

Discussion

4114.	Express as a sum of a symmetric and a skew symmetric matrix:[[0,1],[1,0]]
Answer» SOLUTION :`LET A=[[0,1],[1,0]]` `impliesA=[[0,1],[1,0]]=A` `:.`A is SYMMETRIC. Now A=A+0 where A is symmetric and O is SKEW symmetric.

Discussion

4115.	Find intervals in which the function given by f(x)=(3)/(10)x^(4)-(4)/(5)x^(3)-3x^(2)+(36)/(5)x+11is (a) Increasing (b) Decreasing.
Answer» Answer :Strickly INCREASES `(-2,1), (3,oo)`, Strickly DECREASES `(-oo, -2), (1,3)`

Discussion

4116.	Given two independent events A and B such that P(A)= 0.3, P(B)= 0.6. FindP(A or B)
Answer» ANSWER :0.72

Discussion

4117.	A house has an old gas furnace that is only 70% efficient . This means that only 70% of the heat produced by the gas goes into heating the house , while 30% of the least is lost . There is a constant charge per unit of gas , and the owner's gas bill is $1,200 per year . The owner is considering replacing the furnace witha new one that is 90 percent energy efficient . To the nearest dollar ,what would the gas bill be per year, assuming that the same amount of heat is required for the house ?
Answer» 896 901 933 947 Answer :C

Discussion

4118.	A house has an old gas furnace that is only 70% efficient . This means that only 70% of the heat produced by the gas goes into heating the house , while 30% of the least is lost . There is a constant charge per unit of gas , and the owner's gas bill is $1,200 per year . Instead of replacing the furnace , the owner keeps the old furnace but doubles the thicknessof insulation under the roof , thus cutting the heat loss by a factor of two . Assume that most of the heat supplied by the furnace goes into replacing the heat lost through the roof .If it costs $2,000 to install the insulation, how many years is the payback period , namely , after how many years would the cost of insulation equalthe savings on the gas bill ? Round your answer to the nearest tenth.
Answer» 2.7 3.6 3.3 4.3 Answer :C

Discussion

4119.	Evaluate lim_(n to oo) sum_(i=1)^(n)(1)/(n) [(n-i)/(n+i)] by using the method of finding definite integral as thelimit of a sum.
Answer» ANSWER :`-1+2log2`

Discussion

4120.	A family of curves has the differential equation xy(dy)/(dx)=2y^(2)-x^(2). Then, the family of curves is
Answer» `y^(2) = x + C x^(4)` `y^(2) = x^(2) + c x^(4)` `y^(2) = c x^(4) + x^(3)` `y^(2) = c x^(2) + x^(3)` ANSWER :B

Discussion

4121.	If f(x) is continuous atx=0, where f(x)=(sin(x^(2)-x))/(x), for x!=0, then f(0)=
Answer» -1 1 0 2 Answer :A

Discussion

4122.	If (alpha, beta) are the roots of the equation 15 x ^(2) - 22 x + 8=0 and (alpha', beta') are the roots of the equation 8x^(2) - 22x + 15=0, then the equation of the circle on A (alpha, alpha') and B (beta, beta') as diameter is
Answer» `120 (x ^(2) + y ^(2)) - 22 ( 8X + 15y) + 289 =0` `120 (x ^(2) + y ^(2)) - 22 ( 15 y + 8x) + 289 =0` `23 (x ^(2) +y ^(2)) + 22 (8x + 15y ) - 120 =0` none of these ANSWER :A

Discussion

4123.	Show that y = (cos^(-1) x)^(2)is a solution of the differential equation . (1-x^(2))y '' - xy' - 2 = 0
Answer» ANSWER :`y = (COS^(-1)X)^(2)`

Discussion

4124.	C_0 + (C_1)/(2) (4) + (C_2)/(3) (16) + …………..+(C_n)/(n + 1) (2^(2n))
Answer» `(5^(N+1) + 1)/(n-1)` `(5^(n+1) - 1)/(4(n+ 1))` `(5^(n+1) + 1)/(4(n + 1))` `(5^(n+1) + 1)/(4(n -1))` Answer :B

Discussion

4125.	Determine the unknown coordinates of the S(7,y,z) in x-"axis"
Answer» SOLUTION :y=0,z=0,

Discussion

4126.	If f(x)=\|{:(cosx,1,0),(1,2cosx,1),(0,1,2cosx):}\|" then "int_(0)^(pi//2)f(x)dx=
Answer» `1/2` `- 1/2` `- 1/3` `1/3` ANSWER :C

Discussion

4127.	Find the area of the smaller part of the circle x^(2) + y^(2) = a^(2) cut off by the line x = (a)/(sqrt(2)).
Answer» ANSWER :`a^(2)/2 (pi/2-1)`

Discussion

4128.	If x ge 0, y ge 0, 2x+y ge 0, x+2y ge 10, x+y le 10, then the minimum value of f=x-y is
Answer» 5 10 `5//2` `10//3` ANSWER :B

Discussion

4129.	Write the following function in the simplest form : "tan"^(-1)(sqrt(1+x^(2))-1)/x, x!=0
Answer» ` ANSWER :`1/2tan^(-1)X`

Discussion

4130.	Find the area of the parallelogram whose adjacent sides are determined by the vectors veca=hati-hatj+3hatkandvecb=2veci-7hatj+hatk.
Answer» ANSWER :`15sqrt2` SQ. UNITS

Discussion

4131.	The sum of the numbers formed by taking all the digits at a time from 0, 2, 3, 4 is
Answer» 57996 756993 99657 57699 Answer :A

Discussion

4132.	54/7 pi radians is approximately equal to how many degrees?
Answer» `8^@` `694^@` `1,389^@` `2,777^@` ANSWER :C

Discussion

4133.	underset( x to oo)("lim") [(x^(2) + x + 3)/(x^(2) - x + 2)]^(x) is equal to
Answer» `OO` E `e^(4)` `e^(2)` ANSWER :d

Discussion

4134.	Find the volume of the following parallelo-piped whose the coterminous edges are:veca=3overset^^i+4overset^^j,vecb=2overset^^i+3overset^^j+4overset^^k,vecc=5overset^^k
Answer» SOLUTION :`=\|(3,4,0),(2,3,4),(0,0,5)\|` `5(9-8)=5"UNIT"^3`

Discussion

4135.	ABCD is a rectangular park with AB = a. A tower standing at C makes angles alpha and beta at A and B respectively, the height of the tower is
Answer» `(a)/(SQRT(cot^(2)ALPHA+cot^(2)beta))` `(a)/(sqrt(cot^(2)alpha-cot^(2)beta))` `(a tan alpha tan beta)/(sqrt(tan^(2)beta + tan^(2)alpha))` `(a cot alpha cot beta)/(sqrt(cot^(2) alpha - cot^(2) beta))` ANSWER :B

Discussion

4136.	A company manufactures two types of toys A and B. Type A requires 5 minutes each for cutting and 10 minutes each for assembling. Type B requires 8 minutes each for cutting and 8 minutes each for assembling. There are 3 hours available for cutting and 4 hours available for assembling in a day. He earns a profit of Rs.50 each on type A and Rs.60 each on type. B. How many toys of each type should the company manufacture in a day to maximize the profit ?
Answer» SOLUTION :Maximize `Z=50x+60y,` subject ot the constraints `5x+8yle180,` `5x+4yge120,` `x ge 0and YGE0.` The corner points of the feasible region are `O(0,0),C(24,0),D(0,22.5)and E(12,15).` z is MAXIMUM at `E(12,15).`

Discussion

4137.	Find a unit vector parallel to the vector veca+vecb where veca=3hati+2hatj+2hatk and vecb=hati+2hatj-2hatk.
Answer»

Discussion

4138.	8 coins are tossed simultaneously. Find the probability of getting at least 6 heads.
Answer» ANSWER :`(37)/(2^(8))`

Discussion

4139.	C_0C_2 + C_1C_3 +C_2C_4+……..+C_(n-2) C_n =
Answer» `""^(2N)C_(n-2)` `""^(2n)C_n` `""^(2n)C_(n-1))` `""^(2n)C_(2n -2)` ANSWER :A

Discussion

4140.	If (1)/(2)(z-4)(z+4)=m, then,in term of z, what is the value of z^(2)-16?
Answer» `SQRT(m)` `(m)/(2)` `m` `2M` ANSWER :D

Discussion

4141.	If Delta=\|(1+y,1-y,1-y),(1-y,1+y,1-y),(1-y,1-y,1+y)\|=0, then value of y are
Answer» 0,3 2,-1 `-1,3` 0,2 Answer :A

Discussion

4142.	If three numbers are drawn at random successively without replacement from a set S={1,2,…..10}, then the probability that the minimum of the chosennumbers is 3 or their maximum is 7 is
Answer» `(1)/(40)` `(3)/(40)` `(5)/(40)` `(11)/(40)` ANSWER :D

Discussion

4143.	Let alpha,beta,gamma be the roots of x^(3)+x+10=0 and alpha_(1)=(alpha+beta)/(gamma^(2)),beta_(1)=(beta+gamma)/(alpha^(2)),gamma_(1)=(gamma+alpha)/(beta^(2)). Then, the value of (alpha_(1)^(3)+beta_(1)^(3)+gamma_(1)^(3))-(1)/(10)(alpha_(1)^(2)+beta_(1)^(2)+gamma_(1)^(2)) is
Answer» `(1)/(10)` `(1)/(5)` `(3)/(10)` `(1)/(2)` ANSWER :3

Discussion

4144.	Which of the following is a homogenous differential equation ?
Answer» `(4x+6y+5)dy-(3y+2x+4)dx=0` `(xy)dx-(x^(3)+y^(3))dy=0` `(x^(3)+2Y^(2))dx+2xydy=0` `y^(2)dx+(x^(2)-xy-y^(2))dy=0` Solution :`(a)` Given equation `(4x+6y+5)dy-(3y+2x+4)dx=0` can be written as `(dy)/(dx)=(3y+2x+4)/(4x+6y+5)IMPLIES(dy)/(dx)=(x(3*(y)/(x)+2+(4)/(x))/(x(4+6(y)/(x)+(5)/(x))` whichis non-homogenous differential equation. `(b)` Given differential equation `xydx-(x^(3)+y^(3))dy=0` from the separating of VARIABLES, `(x^(3)+y^(3))dy=xydximplies(dy)/(dx)=(xy)/(x^(3)+y^(3))` `implies (dy)/(dx)=((y)/(x^(2)))/(1+((y)/(x))^(3))` which is non-homogenous differential equation `(c )` Given differential EQAUTION `(x^(3)+2y^(2))dx+2 xy dy=0` `2xy dy=-(x^(3)+2y^(2))dx` From the separating of variables, `(dy)/(dx)=-(x^(3)+2y^(2))/(2xy)implies(dy)/(dx)=(1+(2y^(2))/(x^(3)))/((2y)/(x^(2)))` which is non-homogenous differential equation. `(d)` Given differential equation `y^(2)dx+(x^(2)-xy-y^(2))dy=0` From the separating of variables, `(x^(2)-xy-y^(2))dy=-y^(2)dx` `implies (dy)/(dx)=-(y^(2))/(x^(2)-xy-y^(2))` `implies (dy)/(dx)=-(((y)/(x))^(2))/([1-(y)/(x)-((y)/(x))^(2)])` which is a homogenous differential equation.

Discussion

4145.	Two balls , projected at different times so they don't collide, have trajectories A and B , as shown below . Which statement is correct ?
Answer» If `v_(0A)` and `v_(0B)` are initial speeds of A & B respectively then `v_(0B)` must be greater then `v_(0A)`. Ball A is in the air for a longer TIME then ball B. Ball B is in the air for a longer time than ball A. Ball B has a greater acceleration than ball A.

Discussion

4146.	If f(x) = (log x)/(x^(3)) = then its antiderivative F(x) given by
Answer» `C - (1)/(2x^(2)) log (xsqrt E)` `C + (1)/(2x^(2)) log X` `C - (1)/(2x^(2)) log (x e)` `C + (1)/(2x^(3)) log ( x e)` ANSWER :A

Discussion

4147.	Evaluate int(xe^(x))/((1+x)^(2))dx
Answer» ANSWER :`I= E^(X)(1)/(1+x)+C`

Discussion

4148.	int(dx)/(x^(2)+2x+2)=
Answer» `XTAN^(-1)(x+1)+C` `tan^(-1)(x+1)+C` `(x+1)tan^(-1)x+C` `tan^(-1)x+C` ANSWER :B

Discussion

4149.	Find the distance between the parallel planes x + y - z + 4 = 0 and x + y - z + 5 = 0.
Answer» ANSWER :`(1)/(SQRT3)`

Discussion

4150.	intsin^3xsec^14xdx
Answer» SOLUTION :`intsin^3xsec^14xdx` =`intsin^3x/cos^14x dx` =`int((1-cos^2x)sinx)/cos^14x dx` [PUT cosx=t Then sinxdx=-DT] =`int(t^2-1)/t^14 dt=int(t^-12-t^-14)dt` =`-1/11t^-11+1/13t^-13+C` =`1/13sec^13x-1/11sec^11x+C`

Discussion

Explore topic-wise InterviewSolutions in .

Let A, B, C be three points on bar(OX),bar(OY),bar(OZ)respectively at the distances 3, 6, 9 from origin. Let Q be the point (2, 5, 8) and P be the pointequidistant from O,A,B,C.Them,thecoordinates of the point R which divides PQ in the ratio : 2 is

If A={1,2,3,4}B={1,2,3,4,5,6} and f :A to B is an injective mapping satisfying f (i) ne I, then number of such mappings are :

A die 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?

If vec(z_(1)) = a hat(i) + b hat(j) and vec(z_(2)) = c hat(i) + d hat(j)are two vectors in hat(i) and hat(j) system where |vec(z_(1))| = |vec(z_(2))| = rand vec(z_(1)).vec(z_(2)) = 0then vec(w_(1)) = ahat(i) + chat(j) and vec(w_(2)) = b hat(i) + d hat(j) satisfy .

If A=[{:(1,2,3),(2,3,1):}]andB=[{:(3,-1,3),(-1,0,2):}], then find 2A-B.

Let n(U) = 700 , n (A) = 200 , n (B) = 300 and n (A nn B) =100, then n(A' nn B')=

If z_1 andz_2are two non- zero comlex numbers such that |z_1+z_2|=|z_1|+|z_2| then arg (z_1)- arg (z_2) is equal to

Integrate the function is Exercise. cos^(3)x e^(log sinx)

Let A,B,C be angles of triangles with vertex A -= (4,-1) and internal angular bisectors of angles B and C be x - 1 = 0 and x - y - 1 = 0 respectively. Slope of BC is

Let A,B,C be angles of triangles with vertex A -= (4,-1) and internal angular bisectors of angles B and C be x - 1 = 0 and x - y - 1 = 0 respectively. If A,B,C are angles of triangle at vertices A,B,C respectively then cot ((B)/(2))cot .((C)/(2)) =

Let S = Set of all women in the world. Define R as follows: a, b in S, a Rb if a and b have at least one of the two parents in common, Then

A student has obtained 75%, 80% and 855 in three subjects. If the marks of another subject are added then his average can not be less than

8-digit numbers are formed using the digits 1,1,2,2,2,3,4,4. Thenumber of such numbers in which the odd digits do not occupy odd places, is

Express as a sum of a symmetric and a skew symmetric matrix:[[0,1],[1,0]]

Find intervals in which the function given by f(x)=(3)/(10)x^(4)-(4)/(5)x^(3)-3x^(2)+(36)/(5)x+11is (a) Increasing (b) Decreasing.

Given two independent events A and B such that P(A)= 0.3, P(B)= 0.6. FindP(A or B)

Evaluate lim_(n to oo) sum_(i=1)^(n)(1)/(n) [(n-i)/(n+i)] by using the method of finding definite integral as thelimit of a sum.

A family of curves has the differential equation xy(dy)/(dx)=2y^(2)-x^(2). Then, the family of curves is

If f(x) is continuous atx=0, where f(x)=(sin(x^(2)-x))/(x), for x!=0, then f(0)=

If (alpha, beta) are the roots of the equation 15 x ^(2) - 22 x + 8=0 and (alpha', beta') are the roots of the equation 8x^(2) - 22x + 15=0, then the equation of the circle on A (alpha, alpha') and B (beta, beta') as diameter is

Show that y = (cos^(-1) x)^(2)is a solution of the differential equation . (1-x^(2))y '' - xy' - 2 = 0

C_0 + (C_1)/(2) (4) + (C_2)/(3) (16) + …………..+(C_n)/(n + 1) (2^(2n))

Determine the unknown coordinates of the S(7,y,z) in x-"axis"

If f(x)=|{:(cosx,1,0),(1,2cosx,1),(0,1,2cosx):}|" then "int_(0)^(pi//2)f(x)dx=

Find the area of the smaller part of the circle x^(2) + y^(2) = a^(2) cut off by the line x = (a)/(sqrt(2)).

If x ge 0, y ge 0, 2x+y ge 0, x+2y ge 10, x+y le 10, then the minimum value of f=x-y is

Write the following function in the simplest form : "tan"^(-1)(sqrt(1+x^(2))-1)/x, x!=0

Find the area of the parallelogram whose adjacent sides are determined by the vectors veca=hati-hatj+3hatkandvecb=2veci-7hatj+hatk.

The sum of the numbers formed by taking all the digits at a time from 0, 2, 3, 4 is

54/7 pi radians is approximately equal to how many degrees?

underset( x to oo)("lim") [(x^(2) + x + 3)/(x^(2) - x + 2)]^(x) is equal to

Find the volume of the following parallelo-piped whose the coterminous edges are:veca=3overset^^i+4overset^^j,vecb=2overset^^i+3overset^^j+4overset^^k,vecc=5overset^^k

ABCD is a rectangular park with AB = a. A tower standing at C makes angles alpha and beta at A and B respectively, the height of the tower is

Find a unit vector parallel to the vector veca+vecb where veca=3hati+2hatj+2hatk and vecb=hati+2hatj-2hatk.

8 coins are tossed simultaneously. Find the probability of getting at least 6 heads.

C_0C_2 + C_1C_3 +C_2C_4+……..+C_(n-2) C_n =

If (1)/(2)(z-4)(z+4)=m, then,in term of z, what is the value of z^(2)-16?

If Delta=|(1+y,1-y,1-y),(1-y,1+y,1-y),(1-y,1-y,1+y)|=0, then value of y are

If three numbers are drawn at random successively without replacement from a set S={1,2,…..10}, then the probability that the minimum of the chosennumbers is 3 or their maximum is 7 is

Let alpha,beta,gamma be the roots of x^(3)+x+10=0 and alpha_(1)=(alpha+beta)/(gamma^(2)),beta_(1)=(beta+gamma)/(alpha^(2)),gamma_(1)=(gamma+alpha)/(beta^(2)). Then, the value of (alpha_(1)^(3)+beta_(1)^(3)+gamma_(1)^(3))-(1)/(10)(alpha_(1)^(2)+beta_(1)^(2)+gamma_(1)^(2)) is

Which of the following is a homogenous differential equation ?

Two balls , projected at different times so they don't collide, have trajectories A and B , as shown below . Which statement is correct ?

If f(x) = (log x)/(x^(3)) = then its antiderivative F(x) given by

Evaluate int(xe^(x))/((1+x)^(2))dx

int(dx)/(x^(2)+2x+2)=

Find the distance between the parallel planes x + y - z + 4 = 0 and x + y - z + 5 = 0.

intsin^3xsec^14xdx

A die 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?