28278 + Interview Questions in Maths in Class 12

1.	If alpha_(1), alpha_(2), alpha_(3), alpha_(4) are the roots of the equation x^(4)+(2-sqrt(3))x^(2)+2+sqrt(3)=0, then the value of (1-alpha_(1))(1-alpha_(2))(1-alpha_(3))(1-alpha_(4)) is
Answer» `1` `4` `0` `5` ANSWER :D

Discussion

2.	Find the maximum and minimum values of x+sin(2x) on [0, 2pi].
Answer» ANSWER :`0, 2PI`

Discussion

3.	Examine the following functions for continuity : f(x)=(x^(2)-25)/(x+5),xne-5
Answer» ANSWER :CONTINUOUS EXCEPT at X = -5

Discussion

4.	{:(" "Lt),(n rarr oo):} 1/n [Sin^(2). (pi)/(2n)+Sin^(2). (2pi)/(2n)+...+Sin^(2). (npi)/(2n)]=
Answer» ANSWER :`(1)/(2)`

Discussion

5.	Find the area of the region enclosed by the parabola x^(2) = y and the line y = x + 2 and the x-axis.
Answer» ANSWER :`5/6`

Discussion

6.	An aeroplane flying at a height of 3000 m above the ground passes vertically another place at an instant when the angle of elevation of the two planes from the same point on the ground are 60^(@) and 45^(@)respectively. The height of the lower plane from the ground is :
Answer» 500 m 1000 `1000 sqrt3m` `100 (SQRT3 +1)m.` Answer :C

Discussion

7.	If bar(x) and bar(y) are non zero, non collinear vector then the number of unit vectors which are perpendicular to both bar(x) and bar(y) is ……………
Answer» 2 4 Do not GET INFINITE ANSWER :A

Discussion

8.	Solve system of linear equations ,using matrix methodx-y +z= 4 2x+y-3z =0x+y+z=2
Answer» ANSWER :`x=2,y=-1,z=1 `

Discussion

9.	In the given figure AB, BC, BD cannot be in
Answer» A.P. G.P. H.P. None of these Answer :A

Discussion

10.	If A= [(alpha,2),(2,alpha)] and \|A^(3)\|= 27, then alpha= _______
Answer» `+- SQRT5` `+- SQRT7` `+- 2` `+- 1` Answer :B

Discussion

11.	Bag 4 contains 3 red and 2 white balls, and Bag B contains 2 red and 5 white balls. A bag is selected at random, a ball is drawn and put into the other bag, then a ball is drawn from the second bag. Find the probability that both balls drawn are of the same colour.
Answer» ANSWER :`(901)/(1680) ~~0.54`

Discussion

12.	{:(" "Lt),(n rarr oo):}(((2n)!)/(n!n^(n)))^(1/n)=
Answer» `2/e` `3/e` `4/e` `1/e` ANSWER :C

Discussion

13.	Integrate the followingint2xcot(x^2+3)dx
Answer» Solution :`int2xcot(x^2+3)DX` [PUT `x^2+3=z` then 2xdx=dz] `intcotdz` Inabs(SINZ)+C` `In abs(SIN(x^2+3)+C`

Discussion

14.	Which of the followingis/are correct .
Answer» `(tanx)^(In (sin x)) gt ( COT x )^(In sin x), AA x in (0,pi//4)` `4^(In "cosec"x) lt 5^(In "cosec"x),AA x in(0,pi//2)` `(1//2)^(In (cos x)) lt (1//3)^(In(cosx)),AA x in (0,pi//2) ` `2^(In ( TAN x )) gt 2^(In ( tan x )), AA x in (0,pi//2)` Answer :A::B::C::D

Discussion

15.	Find theequation of the tangent and normal at (1, 1) to the circle 2x^(2) + 2 y^(2) - 2x - 5y + 3 = 0
Answer» ANSWER :` 2x-y -1=0 , X+ 2Y -3=0 `

Discussion

16.	Using elementary row transformations , find the inverse of[{:(2,1),(1,1):}]
Answer» ANSWER :`thereforeA^(-1)=[{:(1,-1),(-1,2):}]"" (becauseI=A^(-1).A)`

Discussion

17.	Findavalueof "x"forwhichx(hati+ hatj+ hatk)isaunitvector .
Answer» `PM(1)/(sqrt(3))` `pmsqrt(3)` `PM3` `pm(1)/(3)` Answer :A

Discussion

18.	N is the set of natural numbers and R is a relation on N xx N defined by (a, b)R(c, d) if an only if a+d=b+c then R is
Answer» only reflexive only SYMMETRIC only transitive EQUIVALENCE RELATION ANSWER :D

Discussion

19.	A manufacturer produces three products x, y, z which he sells in two markets. Annual sales are indicated below: {:("Market",,"Products",),(I,"10,000","2,000","18,000"),(II,"6,000","20,000","8,000"):} (a) If unit sale prices of x, y and z are Rs. 2.50, Rs. 1.50 and Rs. 1.00, respectively, find the total revenue in each market with the help of matrix algebra. (b) If the unit costs of the above three commodities are Rs. 2.00, Rs. 1.00 and 50 paise respectively. Find the gross profit.
Answer» ANSWER :(a) Total revenue in the MARKET - `I=Rs. 46000` Total revenue in the market - `II=Rs. 53000` (b) Rs. 15000, Rs. 17000

Discussion

20.	Find the term independent of x in (1+3x)^(n)(1+(1)/(3x))^(n).
Answer» ANSWER :`""^(2N)C_n`

Discussion

21.	Find the maximum profit that a company can make, if the profit function is given by p(x) = 41 – 72x – 18x^(2)
Answer» ANSWER :MAXIMUM PROFIT = 113 UNIT.

Discussion

22.	There are 8 pairs of shoes in a cupboard. Find the number of ways of selecting 4 shoes so that there is no pair ?
Answer» ANSWER :1120

Discussion

23.	Chords AB and CD of parabola y^(2)=8x intersect at E(2,0). Tangents at A and B intersect at P(x_(1),y_(1)) and those at C and D intersect at Q (x_(2),y_(2)).Then \|x_(1)-x_(2)\|=
Answer» 0 1 2 3 Solution :`because ""y+z=a+2x` `""z+x=b+2y` `""x+y=c+2z` `THEREFORE "" "by adding we get "a+b+c=0` ALSO `b=4a+(c)/(4)implies 16a-4b+c=0` implies x = 1 and `x = - 4` are roots of equation `AX^(2)+bx+c=0` `therefore "" "sum of roots" = 1+(-4)=-3`

Discussion

24.	Prove that : Find the 9^("th")" term of "(2+(x)/(3))^(-5)
Answer» SOLUTION :N/A

Discussion

25.	If p=4sqrt(3q), what is 3q, in terms of p?
Answer» `(p^(2))/(16)` `(p^(2))/(4)` `16P^(2)` `(p)/(4)` ANSWER :A

Discussion

26.	If S and S^(1) are the foci BB^(1) is the minor axis such that Ang(SBS^(1)) = sin^(-1) (3/5)then e =
Answer» `(1)/sqrt(3)` `(1)/sqrt(5)` `(1)/sqrt(10)` `(1)/sqrt(2)` Answer :C

Discussion

27.	Evaluation of definite integrals by subsitiution and properties of its : I_(1)=int_(a)^(pi-a)xf(sinx)dx,I_(2)=int_(a)^(pi-a)f(sinx)dx then I_(2)=……..
Answer» `(pi)/(2)I_(1)` `piI_(1)` `(2)/(pi)I_(1)` `2I_(1)` Answer :C

Discussion

28.	int_(-1)^(1)(sqrt(1+x+x^(2))-sqrt(1-x+x^(2)))/(sqrt(1+x+x^(2))+sqrt(1-x+x^(2)))dx=
Answer» 2 4 6 0 Answer :D

Discussion

29.	If (1+x)^(n)=C_(0)+C_(1)+x+C_(2)x^(2)+...+C_(n) x^(n) Show that C_(1)-(1)/(2)C_(2)+(1)/(3)C_(3)-...+(-1)^(n-1)*(1)/(n)C_(n)=1+(1)/(2)+(1)/(3)+...+ (1)/(n)
Answer» ANSWER :`N(1+x)^(n-2)(1+nx);0`

Discussion

30.	A line makesan angle (pi)/(4) with each y-axis and z-axis. The angle that it makes with the x - axis is
Answer» `(PI)/(2)` `(pi)/(4)` `pi` `(pi)/(6)` ANSWER :A

Discussion

31.	Find all the values of following . (-32)^(1//5)
Answer» ANSWER :`2cis(2k+1)(PI)/(5),k=0,1,2,3,4`

Discussion

32.	A firm has to transport 1200 packages using large vans which can carry 200 packages each and small vans which can take 80 packages each. The cost for engaging each large van is Rs. 400 and each small van is Rs. 200. Not more than Rs. 3000 is to be spent on the job and the number of large vans can not exceed the number of small vans. Formulate this problem as a LPP given that the objective is to minimize cost.
Answer» Answer :Minimum cost of OBJECTIVE function z = 400X + 200y subject to `5x+2y GE 30, 2x+y lt 15, X le y" and "x ge 0, y ge 0`

Discussion

33.	Solve : (x+y)^(2//3)+2(x-y)^(2//3)=3(x^2-y^2)^(1//3) and 3x-2y=13.
Answer» ANSWER :X = 9 , y = 7

Discussion

34.	\|z-4\|lt\|z-2\| represents the region given by
Answer» Re `(Z) gt 3` Re `(z) LT 3` IM `(z) gt 3` Im `(z) lt 3` Answer :A

Discussion

35.	If the straight line mx-y=1+2x intersects the circle x^2+y^2=1at least at one point , thenthe set of values of m is
Answer» `[-4/3,0]` `[-4/3,4/3]` `[0,4/3]` all of these ANSWER :D

Discussion

36.	Evaluate:int ( dx)/( sqrt(x+1) +""^(3) sqrt(x+1))
Answer» ANSWER :` 2 sqrt (x+1)- 3 ""^(3) sqrt( x+1) +6 ""^(6) sqrt(x+1) -6 log \|""^(6) sqrt(x+1) +1\| +C`

Discussion

37.	Fill int the blanks choosing correct answer from the bracket. In a Delta ABC if b sinC + c sinB = 2 then b sinC = _____.
Answer» 0 1 2 Answer :B

Discussion

38.	Find the vector equation of the plane which is at a distance of (6)/(sqrt(29)) the from the origin and its normal vector from the origin is 2hati-3hatj+4hatk. Also find its cartesian form.
Answer» Answer :`vecr((2)/(sqrt(29))hati+((-3))/(sqrt(29))HATJ+(4)/(sqrt(29))hatk)=(6)/(sqrt(29))`

Discussion

39.	int (overset(oo)underset(r=o)sum(x^(r)2^(r))/(r!))dx=
Answer» `E^(X)` + C `(1)/(2) e^(2x) + C ` `2 e^(2x)+ C` `(1)/(2) e^(x) + C ` ANSWER :B

Discussion

40.	Integrate the following functions with respect to x. (cos2x-cos2alpha)/(cosx-cosalpha)
Answer» ANSWER :`2(sinx+xcosalpha)+C`

Discussion

41.	int (cos^(2)x)/(1-sinx)dx=
Answer» ANSWER :`x-cosx+c`

Discussion

42.	If the radius of the circle touching the pair of lines 7x^(2) - 18 xy +7y^(2) = 0 and the circle x^(2) +y^(2) - 8x - 8y = 0, and contained in the given circle is equal to k, then k^(2) is equal to
Answer» 10 9 8 7 Solution : `tan theta = \|(2sqrt(h^(2)-AB))/(a+b)\| =(4sqrt(2))/(7)` `:. tan. (theta)/(2) = (1)/(2sqrt(2))` `:. sin .(theta)/(2) = (1)/(3) = (SQRT(2)(8-alpha))/(sqrt(2)alpha)` `:. alpha = 6` Hence, EQUATION of CIRCLE is `(x-6)^(2) +(y-6)^(2) = 8`.

Discussion

43.	Applying a suitable change of the variable, find the followingdefiniteintegrals : (a)int_(0)^(2) (dx)/((sqrtx - 1) + sqrt((x + 1)^(3))) (b)int_(0)^(a) (dx)/(x + sqrt(a^(2) - x^(2))) (c)int_(1)^(2) (dx)/(x (1 + x^(4)))(d)int_(sqrt((3a^(2)+ b^(2) )//2))^(sqrt((a^(2) + b^(2))//2)) (xdx)/(sqrt((x^(2) -a^(2))(b^(2) - x^(2))))
Answer» Answer :(a)`(pi)/(6)` (b) `(pi)/(4) ` (c)`(1)/(4) In "" (32)/(17)` (substitution`X^(4) = t`) (d)`(pi)/(4) ` (substitution`x^(2) = a^(2) cos^(2) t + b^(2) SIN^(2) t`)

Discussion

44.	Evaluate the following integrals intcossqrt(x) dx
Answer» ANSWER :`2[SQRT(X)sinsqrt(x)+cossqrt(x)]+C`

Discussion

45.	LetP(x)be apolynomialwithintegralcoefficients . Ifthereexiststwointefersa andbsuchthatp(a) - p(b)=1then
Answer» botha andb MUSTBE even botha and b mustbe ODD a andb aretwoconsecutiveintergers none of these ANSWER :C

Discussion

46.	Equation of one of the tangents passing through (2, 8) to the hyperbola 5x^(2)-y^(2)=5 is
Answer» ` 3X+y-14=0` `3x- y+2=0` `x+y+3=0` `x-y+6=0` ANSWER :B

Discussion

47.	Compute P for n=10,r=3
Answer» SOLUTION :`N=10,r=3` `:.""^nP_r=(n!)/((n-r)!)=(10!)/(7!)` `=1098=720`

Discussion

48.	Find the volume of the solid formed by revolving the region bounded by the parabola y=x^(2), x-axis, ordinates x=0 and x=1 about the x-axis.
Answer» ANSWER :`(838)/(15)PI`

Discussion

49.	Find the domain of definition of the following functions : f(x)=sqrt(((x-1)(x+2))/((x-3)(x-4)))
Answer» ANSWER :`x in (-OO,-2]UU[1,3)uu(4,oo)`.

Discussion

50.	Dancers and sports person are able to maintain their proper body position by using their internal sense of balance. Sensing of this sort of body's internal condition and position is performed by :-
Answer» ORGAN of corti Crista MACULA Otolithic organ Answer :A

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

If alpha_(1), alpha_(2), alpha_(3), alpha_(4) are the roots of the equation x^(4)+(2-sqrt(3))x^(2)+2+sqrt(3)=0, then the value of (1-alpha_(1))(1-alpha_(2))(1-alpha_(3))(1-alpha_(4)) is

Find the maximum and minimum values of x+sin(2x) on [0, 2pi].

Examine the following functions for continuity : f(x)=(x^(2)-25)/(x+5),xne-5

{:(" "Lt),(n rarr oo):} 1/n [Sin^(2). (pi)/(2n)+Sin^(2). (2pi)/(2n)+...+Sin^(2). (npi)/(2n)]=

Find the area of the region enclosed by the parabola x^(2) = y and the line y = x + 2 and the x-axis.

An aeroplane flying at a height of 3000 m above the ground passes vertically another place at an instant when the angle of elevation of the two planes from the same point on the ground are 60^(@) and 45^(@)respectively. The height of the lower plane from the ground is :

If bar(x) and bar(y) are non zero, non collinear vector then the number of unit vectors which are perpendicular to both bar(x) and bar(y) is ……………

Solve system of linear equations ,using matrix methodx-y +z= 4 2x+y-3z =0x+y+z=2

In the given figure AB, BC, BD cannot be in

If A= [(alpha,2),(2,alpha)] and |A^(3)|= 27, then alpha= _______

Bag 4 contains 3 red and 2 white balls, and Bag B contains 2 red and 5 white balls. A bag is selected at random, a ball is drawn and put into the other bag, then a ball is drawn from the second bag. Find the probability that both balls drawn are of the same colour.

{:(" "Lt),(n rarr oo):}(((2n)!)/(n!n^(n)))^(1/n)=

Integrate the followingint2xcot(x^2+3)dx

Which of the followingis/are correct .

Find theequation of the tangent and normal at (1, 1) to the circle 2x^(2) + 2 y^(2) - 2x - 5y + 3 = 0

Using elementary row transformations , find the inverse of[{:(2,1),(1,1):}]

Findavalueof "x"forwhichx(hati+ hatj+ hatk)isaunitvector .

N is the set of natural numbers and R is a relation on N xx N defined by (a, b)R(c, d) if an only if a+d=b+c then R is

Find the term independent of x in (1+3x)^(n)(1+(1)/(3x))^(n).

Find the maximum profit that a company can make, if the profit function is given by p(x) = 41 – 72x – 18x^(2)

There are 8 pairs of shoes in a cupboard. Find the number of ways of selecting 4 shoes so that there is no pair ?

Chords AB and CD of parabola y^(2)=8x intersect at E(2,0). Tangents at A and B intersect at P(x_(1),y_(1)) and those at C and D intersect at Q (x_(2),y_(2)).Then |x_(1)-x_(2)|=

Prove that : Find the 9^("th")" term of "(2+(x)/(3))^(-5)

If p=4sqrt(3q), what is 3q, in terms of p?

If S and S^(1) are the foci BB^(1) is the minor axis such that Ang(SBS^(1)) = sin^(-1) (3/5)then e =

Evaluation of definite integrals by subsitiution and properties of its : I_(1)=int_(a)^(pi-a)xf(sinx)dx,I_(2)=int_(a)^(pi-a)f(sinx)dx then I_(2)=……..

int_(-1)^(1)(sqrt(1+x+x^(2))-sqrt(1-x+x^(2)))/(sqrt(1+x+x^(2))+sqrt(1-x+x^(2)))dx=

If (1+x)^(n)=C_(0)+C_(1)+x+C_(2)x^(2)+...+C_(n) x^(n) Show that C_(1)-(1)/(2)*C_(2)+(1)/(3)*C_(3)-...+(-1)^(n-1)*(1)/(n)C_(n)=1+(1)/(2)+(1)/(3)+...+ (1)/(n)

A line makesan angle (pi)/(4) with each y-axis and z-axis. The angle that it makes with the x - axis is

Find all the values of following . (-32)^(1//5)

Solve : (x+y)^(2//3)+2(x-y)^(2//3)=3(x^2-y^2)^(1//3) and 3x-2y=13.

|z-4|lt|z-2| represents the region given by

If the straight line mx-y=1+2x intersects the circle x^2+y^2=1at least at one point , thenthe set of values of m is

Evaluate:int ( dx)/( sqrt(x+1) +""^(3) sqrt(x+1))

Fill int the blanks choosing correct answer from the bracket. In a Delta ABC if b sinC + c sinB = 2 then b sinC = _____.

Find the vector equation of the plane which is at a distance of (6)/(sqrt(29)) the from the origin and its normal vector from the origin is 2hati-3hatj+4hatk. Also find its cartesian form.

int (overset(oo)underset(r=o)sum(x^(r)2^(r))/(r!))dx=

Integrate the following functions with respect to x. (cos2x-cos2alpha)/(cosx-cosalpha)

int (cos^(2)x)/(1-sinx)dx=

If the radius of the circle touching the pair of lines 7x^(2) - 18 xy +7y^(2) = 0 and the circle x^(2) +y^(2) - 8x - 8y = 0, and contained in the given circle is equal to k, then k^(2) is equal to

Evaluate the following integrals intcossqrt(x) dx

LetP(x)be apolynomialwithintegralcoefficients . Ifthereexiststwointefersa andbsuchthatp(a) - p(b)=1then

Equation of one of the tangents passing through (2, 8) to the hyperbola 5x^(2)-y^(2)=5 is

Compute P for n=10,r=3

Find the volume of the solid formed by revolving the region bounded by the parabola y=x^(2), x-axis, ordinates x=0 and x=1 about the x-axis.

Find the domain of definition of the following functions : f(x)=sqrt(((x-1)(x+2))/((x-3)(x-4)))

Dancers and sports person are able to maintain their proper body position by using their internal sense of balance. Sensing of this sort of body's internal condition and position is performed by :-

If (1+x)^(n)=C_(0)+C_(1)+x+C_(2)x^(2)+...+C_(n) x^(n) Show that C_(1)-(1)/(2)C_(2)+(1)/(3)C_(3)-...+(-1)^(n-1)*(1)/(n)C_(n)=1+(1)/(2)+(1)/(3)+...+ (1)/(n)