28278 + Interview Questions in Maths in Class 12 Page 1 InterviewSolution

1.	P (-2,-1) and (0,-3) are the limiting points of a coaxial system of whichC -= x^(2) + y^(2)+ 5x + y + 4 = 0is a member. The circleS -= x^(2) + y^(2) - 4x - 2y - 15 = 0is orthogonal to the circle C . The point where the polar of P cuts the circle S is
Answer» (3,6) (-3,6) (-6,3) (6,3) ANSWER :D

Discussion

2.	Which of the following is/are discontinous at x = 1 ?
Answer» `F(X)=(1)/(1+2^(TANX))` `g(x)=lim_(nrarroo)(1)/(1+n SIN^(-2)(PIX))` `h(x)=2^(-2^((1)^((1)/(1-x)))), x ne 1 and h(1)=1` `phi(x)=(x-1)/(\|x1\|+2(x-1)^(2)), x ne 1 and phi(1) =1` Answer :B::C::D

Discussion

3.	Write Minors and Cofactors of the elments of following determinants : \|{:(1,0,4),(3,5,-1),(0,1,2):}\|
Answer» ANSWER :`M_(11)=11,M_(12)=-6,M_(13)=3,M_(21)=-4,M_(22)=2,M_(23)=-1,M_(31)=-20,M_(32)=-13,M_(33)=5` `A_(11)=11,A_(12)=-6,A_(13)=3,A_(21)=4,A_(22)=2,A_(23)=-1,A_(31)=20,A_(32)=-13,A_(33)=5`

Discussion

4.	The vertex of the parabola (y-1)^2 =8 (x-1) is at the centre of a circle and the parabola cuts that circle atthe ends of its latusrectum. Then the equation of that circle is
Answer» ANSWER :`X^(2)+y^(2)=20`

Discussion

5.	{{:(5x-3y=10),(6y=kx-42):} In the system of linear equations above, k represents a constant. If the system of equations has no solution, what is the value of 2k?
Answer» `5/2` 5 10 20 Solution :Start by recognizing that for two lines to be parallel, the coefficients for x must be identical in the two equations, dutto for the coefficients for y. Manipulate the second EQUATION so that it is in the same format as the first one: `kx - 6y=42` The y-coefficient in the first equation, `5x-3y=10, is 3.` Divide the second equation by 2 in ORDER to make the y-coefficients in both equatinos equal: `k/2x -3y=21` Now set the x-coefficient equal to the x-coefficient in the first equation: ` k /2=5` `k=10` Note that the question asks for the value of 2K, so the correct answer is (D), 20.

Discussion

6.	f(x) ={{:(1-sqrt(1-x^(2)),if -1lexle1),(1+ log ""(1)/(x), if xgt1):}
Answer» continuousanddifferentibable at x=1 continuousbut not differentiableat x=1 neither continuousnor differentiableat =1 NONEOF these Answer :B

Discussion

7.	Given that alpha, beta, gamma, delta are in a geometric progression. If alpha, beta are the roots of x^(2)-x+p=0 " and "gamma, delta are the roots of x^(2)-4x+q=0, where p and q are integers, then the ordered pair (p, q) =
Answer» (2, 32) (2, -32) (-2, 32) (-2, -32) ANSWER :D

Discussion

8.	A poor , frustrated artist named Fresco created a plan to make money. He collected trash, repurposed it into sculptures, then asked various celebrities to write and paint on these trash objects, which he then sold on his own as modern high art. The chart below separately showsthe cost and revenue of his plan. The linear cost function, C(x) , represents the total money spent to make and market the art , while the linear revenue function, R(x) , shows the amount of money he has made in sculpture sales. Fresco initially spent money promoting the project in the media . He also had to pay the celebrities to participate . After 6 months , Fresco had created and sold x number of trash sculptures and finally broke even : he hadn't made or lost any money . How many sculptures did Fresco sell in his first 6 months of the project ?
Answer» 3 5 7 10 Answer :B

Discussion

9.	A poor , frustrated artist named Fresco created a plan to make money. He collected trash, repurposed it into sculptures, then asked various celebrities to write and paint on these trash objects, which he then sold on his own as modern high art. The chart below separately showsthe cost and revenue of his plan. The linear cost function, C(x) , represents the total money spent to make and market the art , while the linear revenue function, R(x) , shows the amount of money he has made in sculpture sales. The cost function in the chart is determined by a constant production cost per sculpture - in this case, the amount Fresco pays each celebrity to participate - as well as a fixed cost , or the initial cost of promoting the project . What is the fixed cost of Fresco's trash sculpture project ?
Answer» `$1,000` `$5,000` `$10,000` `$15,000` ANSWER :C

Discussion

10.	An ellipse is incribed in a rectangle and if the angle between the diagonals is tan ^(-1)2sqrt2then e=
Answer» `( 1)/(sqrt3) ` ` (1)/(3) ` ` (1)/(sqrt2) ` ` (1)/(2) ` ANSWER :C

Discussion

11.	A poor , frustrated artist named Fresco created a plan to make money. He collected trash, repurposed it into sculptures, then asked various celebrities to write and paint on these trash objects, which he then sold on his own as modern high art. The chart below separately showsthe cost and revenue of his plan. The linear cost function, C(x) , represents the total money spent to make and market the art , while the linear revenue function, R(x) , shows the amount of money he has made in sculpture sales. The selling price of each trash sculptureis an integer number of dollars . According to the revenuefunction , what is the selling price of one trash sculpture ?
Answer» `$1,000` `$1,667` `$2,000` `$3,000` ANSWER :D

Discussion

12.	Determine whether or not each of the defination of given below gives a binary opertion. In the even that is not a binary opertion, give justification for this. (i) On Z ^(+), define by a b =a -b (ii) On Z ^(+), define by a b b =ab (iii) On R, define by a b =ab ^(2) (iv) On Z ^(+), define by a b = \|a-b\| (v) On Z ^(+), define by a b =a
Answer» ANSWER :(i) NO (II) Yes (iii) ES (iv) Yes (v) Yes

Discussion

13.	The unit vector perpendicular to both the vectors (3, -1, 0) and (-2, 1, 3) is …………..
Answer» `+-(-3,-9,1)` `+-(-3,9,-1)` `+-(1)/(SQRT(91))(-3,-9,1)` `+-(1)/(sqrt(91))(-3,9,-1)` Answer :C

Discussion

14.	The product of the perpendiculars from (-1,2) to the pair of lines 2x^(2) – 5xy + 2y^(2) + 3x – 3y + 1 = 0 is
Answer» `(5)/(12)` `(12)/(5)` `(6)/(5)` `(5)/(6)` ANSWER :B

Discussion

15.	Write the first three terms of the expansion of (2+x)^(-1//2)
Answer» SOLUTION :N/A

Discussion

16.	If for sequence lt a_n gtsum of n terms S_n= 2n^2+3n then find the sum {:(""Sigma Sigma),(1lei lt j le 10):}a_ia_j
Answer» Solution :We have `S_(N)=2n^(2)+3N` `thereforea_(n)=S_(n)-S_(n-1)` `=2n^(2)+3n-2(n-1)^(2)-3(n-1)` =4n+1 Therefore, the sequence is 5,9,13… `thereforeunderset(1leiltjle10)(SigmaSigma)a_(i)a_(J)=(sum_(i=1)^(10)sum_(j=1)^(10)(4i+1)cdot(4j+1)-sum_(i=1)^(10)(4i+1)^(2))/2` `=((sum_(i=1)^(10)(4i+1))^(2)-sum_(i=1)^(10)(4i+1)^(2))/2` =23145

Discussion

17.	Differentiate (x^2-x+2)^2
Answer» SOLUTION :`y=(x^2-x+2)^2` `dy/dx=2(x^2-x+2)xxd/dx(x^2-x+2)` `=2(x^2-x+2)(2x-1)`

Discussion

18.	Solve the following differential equations sec x (dy)/(dx) - y = sin x
Answer» ANSWER :`y = -(SIN X + 1) + CE^(sin x)`

Discussion

19.	Match the following :
Answer» <P> Answer :(A)- r ,(B)- p , (C)-s (D) Q

Discussion

20.	Solve the equation : 6x^4 -35x^(3) + 62x^(2) -35x + 6=0
Answer» ANSWER :`3+-2sqrt(2), 2+-sqrt(3)`

Discussion

21.	Probability of an event that one male person lives 10 years more is (1)/(4) . His wife lives 10 years more is (1)/(3) . Then of least one person lives has ......... probability.
Answer» `(5)/(12)` `(1)/(2)` `(7)/(12)` `(11)/(12)` ANSWER :B

Discussion

22.	Evaluate int_(0)^(pi) sin^(3) theta(1+2 cos theta)(1+ cos theta)^(2) d theta
Answer» ANSWER :`(8)/(3)`

Discussion

23.	If A=[{:(0,1),(1,1):}]andB=[{:(0,-1),(1,0):}]show that (A+B)*(A-B)neA^(2)-B^(2).
Answer» ANSWER :`=[{:(2,1),(1,3):}]`

Discussion

24.	Ifa,bare any twooddpositiveintegers suchthata gt b .Then thelargestpositiveintegerwhichdividesallthenumbersof thenumbers of theforma^1 -b^2 Is
Answer» 6 5 8 9 Answer :C

Discussion

25.	Evaluate int_(0)^(pi//2) cos^(5) x dx.
Answer» ANSWER :`8/15`

Discussion

26.	A coplanar beam of light emerging from a point surce have the equation lambda x-y+2(1+lambda)-0, AA lambda in R : the rays of beam strike an elliptical surface and get reflected inside the ellipse. The reflected rays form another convergent beam having the equation mu x-y+2(1-mu)=0, AA mu in R. Further it is found that the foot of the perpendicular from the point (2, 2) upon any tangent to the ellipse lies on the circlex^(2)+y^(2)-4y-5=0 Q. The area of the largest that an incident ray and corresponding reflected ray can enclose with the major axis of the ellipse is equal to :
Answer» `4sqrt(5)` `SQRT(5)` `3sqrt(5)` `2sqrt(5)` ANSWER :D

Discussion

27.	A coplanar beam of light emerging from a point surce have the equation lambda x-y+2(1+lambda)-0, AA lambda in R : the rays of beam strike an elliptical surface and get reflected inside the ellipse. The reflected rays form another convergent beam having the equation mu x-y+2(1-mu)=0, AA mu in R. Further it is found that the foot of the perpendicular from the point (2, 2) upon any tangent to the ellipse lies on the circlex^(2)+y^(2)-4y-5=0 Q. The least value of total distance travelled by an incident ray and the corresponding reflectedray is equal to :
Answer» 6 3 `SQRT(5)` `2sqrt(5)` ANSWER :A

Discussion

28.	Match the following :
Answer» <P> ANSWER :(A) - s (B)- p (C) - Q (D) - s

Discussion

29.	Match the following :
Answer» <P>`{:(P,Q,R,S),(4,1,3,2):}` `{:(P,Q,R,S),(3,2,1,4):}` `{:(P,Q,R,S),(1,4,2,3):}` `{:(P,Q,R,S),(2,3,4,1):}` ANSWER :D

Discussion

30.	A variable line passing through the fixed point (alpha, beta) intersects the co-ordinate axes at A and B. If O is the origin, the the locus of the centroid of the triangle OAB is
Answer» `betax+alphay=3xy` `alphax+betay=3xy` `alphax-betay=3xy` `betax-alphay=3xy` ANSWER :A

Discussion

31.	I : The function log (log x) increases in (1,oo). II : The function x^x is decreasing in (0,1/e).
Answer» only I is TRUE only II is true both I and II are true NEITHER I nor II true Answer :C

Discussion

32.	Prove that thefunctions do not have maxima or minima: h(x) = x^(3) +x^(2) +x+1
Answer» ANSWER :no MAXIMA or MINIMA.

Discussion

33.	Ifthe lines(x+1)/(2) =(y-1)/( 1) =(z+1)/(3) and (x+2)/(2) =( y-k)/(3) =(z)/(4)are , coplanar , then the value of k is
Answer» ` 11//2` ` -11//2` `9//2` `-9//2` ANSWER :A

Discussion

34.	If the latusrectum subtends a right angle at the centre of the hyperbola then its eccentricity
Answer» `SQRT3` `sqrt3+1` `(sqrt3+1)/SQRT2` `(sqrt3+1)/sqrt3` ANSWER :B

Discussion

35.	Find the number of positive integers from 1 to 1000. Which are divisible by atleast one of 2, 3 or 5.
Answer» ANSWER :734

Discussion

36.	If a and b are real number between 0 and 1 such that the points z_1=a+I,z_2=1 +bi and z_3=0 form an equilateral triangle then a, b, are
Answer» `2-sqrt(3),2-sqrt(3)` `2-sqrt(3),2+sqrt(3)` `2+sqrt(3),2-sqrt(3)` none Answer :A

Discussion

37.	Ifalpha, beta , gammaare the rootsofx^3 - 6x^2+11 x-6=0thenfindtheequationwhoserootsare alpha^2 + beta^2, beta^2 + gamma^2 , gamma^2 + alpha^2
Answer» ANSWER :`X^3 -28x^2 + 245 x -650 =0`

Discussion

38.	If P(A cap B)= (1)/(12) and P(A' cap B')= (1)/(2) then P(A) + P(B) = .......
Answer» `(7)/(12)` `(1)/(12)` `(5)/(12)` `(11)/(12)` ANSWER :A

Discussion

39.	Match the differential equations in List-I to their integrating factors in List-II {:(,"List - I",,"List-II",),((i), (x^(3)+1)(dy)/(dx)+x^(2)y=0,(a),x^(3),),((ii),x^(2)(dy)/(dx) +3xy = x^(6),(b),(x^(3)+1)^(2),),((iii),(x^(3)+1)(dy)/(dx)+6x^(2)(x^(3)+1)y = x^(2),(c),(x^(2) + 1)^(2),),((iv),(x^(2)+1)(dy)/(dx)+4xy = lnx,(d),x^(2)+1,),(,,(e),(x^(3)+1)^((1)/(3)),),(,,(f),(x^(3)+1)^((1)/(2)),):} The correct matching is
Answer» i-d, ii-a, iii-B, iv-c i-e, ii-a, iii-a, iv-c i-e, ii-b, iii-c, iv-f i-e, ii-a, iii-c, iv-d Answer :B

Discussion

40.	Determine graphically the maximize value of the subjective functionZ = 10x + 25y "…(1)" subject to the constraints : x le 3, y le 3"…(2)" x+y le 5"…(3)" x ge 0, y ge 0".. .(4)"
Answer» Answer :It has no MINIMUM value SUBJECT to the GIVEN CONSTRAINTS.

Discussion

41.	If the normal at P to the rectangular hyperbola x^(2) - y^(2) = 4 meets the axes of x and y in G and g respectively and C is the centre of the hyperbola, then 2PC =
Answer» PG pg Gg none of these ANSWER :C

Discussion

42.	If A =sin ^(3)+ cos ^(4) theta , then for all values of theta,A lies in the interval
Answer» `[1,2]` `[(3)/(4),1]` `[(1)/(2), (3)/(4)]` `[(3)/(4) , (19)/(16)]` ANSWER :B

Discussion

43.	If z_(1), z_(2) are conjugate complex numbers and z_(3), z_(4) are also conjugate, then arg.((z_(3))/(z_(2))) is :
Answer» `AGR.((z_(1))/(z_(4)))` `agr.((z_(4))/(z_(1)))` `agr.((z_(2))/(z_(4)))` `agr.((z_(1))/(z_(3)))` Answer :A

Discussion

44.	A : If (5x+1)/((x+2)(x-1))=A/(X+2)+B/(x-1) " then "A=3, B=2. R : (px+q)/((x-a)(x-b))=(pa+q)/((x-a)(a-b))+(pb+q)/((b-a)(x-b)).
Answer» Both A & R are TRUE and R is CORRECT explanation of A Both A & R are true and R is not correct explanation of A A is true but R is FALSE A is false but R is true Answer :A

Discussion

45.	overset((pi)/(2))underset(0)int (1)/((a^(2)cos^(2)x+b^(2)sin^(2)x)^(2))dx
Answer» Answer :`:. I=(PI)/(4)[(a^(2)+b^(2))/(a^(3)+b^(3))]`

Discussion

46.	Identify the type of conic and find centre, foci, vertices, and directices of each of the following: ((x+3)^(2))/(225)-((y-4)^(2))/(64)=1
Answer» Answer :(i) `y = ( - 257)/8` (ii) ` X = ( -53)/3` (III) ` 17/15` (IV) ` y = 2 - 25/sqrt(41)` (v) ` -3 sqrt6` (VI) `2 - 1/sqrt10 `

Discussion

47.	Evaluate the following (i) int_(0)^(30)[x]dx
Answer» ANSWER :435

Discussion

48.	A unit vector perpendicular to each of the vector 3i+2j+4k and 2i+j-k is,
Answer» `+- 6i+8j+k/sqrt(101)` `+- 6i-8j+k/sqrt(104)` `+- 6i-8j-k/sqrt(101)` `+- 6i-8j-4k/sqrt(101)` ANSWER :A

Discussion

49.	Evaluate int_(a)^(b) x dx
Answer» ANSWER :`(1)/(2)(B^(2)-a^(2))`

Discussion

50.	Let A={3,6,9,12,15,18,21} B={4,8,12,16,20} C={2,4,6,8,10,12,14,16} and D={5,10,15,20} Which of the following is incorrect? I. A-B={4,8,16,20} II. (C-B)nn(D-B)=phi III. B-CneB-D
Answer» Only I and II Only II & III Only III & I None of these Answer :A

Discussion

Explore topic-wise InterviewSolutions in .

P (-2,-1) and (0,-3) are the limiting points of a coaxial system of whichC -= x^(2) + y^(2)+ 5x + y + 4 = 0is a member. The circleS -= x^(2) + y^(2) - 4x - 2y - 15 = 0is orthogonal to the circle C . The point where the polar of P cuts the circle S is

Which of the following is/are discontinous at x = 1 ?

Write Minors and Cofactors of the elments of following determinants : |{:(1,0,4),(3,5,-1),(0,1,2):}|

The vertex of the parabola (y-1)^2 =8 (x-1) is at the centre of a circle and the parabola cuts that circle atthe ends of its latusrectum. Then the equation of that circle is

{{:(5x-3y=10),(6y=kx-42):} In the system of linear equations above, k represents a constant. If the system of equations has no solution, what is the value of 2k?

f(x) ={{:(1-sqrt(1-x^(2)),if -1lexle1),(1+ log ""(1)/(x), if xgt1):}

Given that alpha, beta, gamma, delta are in a geometric progression. If alpha, beta are the roots of x^(2)-x+p=0 " and "gamma, delta are the roots of x^(2)-4x+q=0, where p and q are integers, then the ordered pair (p, q) =

An ellipse is incribed in a rectangle and if the angle between the diagonals is tan ^(-1)2sqrt2then e=

The unit vector perpendicular to both the vectors (3, -1, 0) and (-2, 1, 3) is …………..

The product of the perpendiculars from﻿ (-1,2) to the pair of lines﻿ 2x^(2) – 5xy + 2y^(2) + 3x – 3y + 1 = 0 is

Write the first three terms of the expansion of (2+x)^(-1//2)

If for sequence lt a_n gtsum of n terms S_n= 2n^2+3n then find the sum {:(""Sigma Sigma),(1lei lt j le 10):}a_ia_j

Differentiate (x^2-x+2)^2

Solve the following differential equations sec x (dy)/(dx) - y = sin x

Match the following :

Solve the equation : 6x^4 -35x^(3) + 62x^(2) -35x + 6=0

Probability of an event that one male person lives 10 years more is (1)/(4) . His wife lives 10 years more is (1)/(3) . Then of least one person lives has ......... probability.

Evaluate int_(0)^(pi) sin^(3) theta(1+2 cos theta)(1+ cos theta)^(2) d theta

If A=[{:(0,1),(1,1):}]andB=[{:(0,-1),(1,0):}]show that (A+B)*(A-B)neA^(2)-B^(2).

Ifa,bare any twooddpositiveintegers suchthata gt b .Then thelargestpositiveintegerwhichdividesallthenumbersof thenumbers of theforma^1 -b^2 Is

Evaluate int_(0)^(pi//2) cos^(5) x dx.

Match the following :

Match the following :

A variable line passing through the fixed point (alpha, beta) intersects the co-ordinate axes at A and B. If O is the origin, the the locus of the centroid of the triangle OAB is

I : The function log (log x) increases in (1,oo). II : The function x^x is decreasing in (0,1/e).

Prove that thefunctions do not have maxima or minima: h(x) = x^(3) +x^(2) +x+1

Ifthe lines(x+1)/(2) =(y-1)/( 1) =(z+1)/(3) and (x+2)/(2) =( y-k)/(3) =(z)/(4)are , coplanar , then the value of k is

If the latusrectum subtends a right angle at the centre of the hyperbola then its eccentricity

Find the number of positive integers from 1 to 1000. Which are divisible by atleast one of 2, 3 or 5.

If a and b are real number between 0 and 1 such that the points z_1=a+I,z_2=1 +bi and z_3=0 form an equilateral triangle then a, b, are

Ifalpha, beta , gammaare the rootsofx^3 - 6x^2+11 x-6=0thenfindtheequationwhoserootsare alpha^2 + beta^2, beta^2 + gamma^2 , gamma^2 + alpha^2

If P(A cap B)= (1)/(12) and P(A' cap B')= (1)/(2) then P(A) + P(B) = .......

Determine graphically the maximize value of the subjective functionZ = 10x + 25y "…(1)" subject to the constraints : x le 3, y le 3"…(2)" x+y le 5"…(3)" x ge 0, y ge 0".. .(4)"

If the normal at P to the rectangular hyperbola x^(2) - y^(2) = 4 meets the axes of x and y in G and g respectively and C is the centre of the hyperbola, then 2PC =

If A =sin ^(3)+ cos ^(4) theta , then for all values of theta,A lies in the interval

If z_(1), z_(2) are conjugate complex numbers and z_(3), z_(4) are also conjugate, then arg.((z_(3))/(z_(2))) is :

A : If (5x+1)/((x+2)(x-1))=A/(X+2)+B/(x-1) " then "A=3, B=2. R : (px+q)/((x-a)(x-b))=(pa+q)/((x-a)(a-b))+(pb+q)/((b-a)(x-b)).

overset((pi)/(2))underset(0)int (1)/((a^(2)cos^(2)x+b^(2)sin^(2)x)^(2))dx

Identify the type of conic and find centre, foci, vertices, and directices of each of the following: ((x+3)^(2))/(225)-((y-4)^(2))/(64)=1

Evaluate the following (i) int_(0)^(30)[x]dx

A unit vector perpendicular to each of the vector 3i+2j+4k and 2i+j-k is,

Evaluate int_(a)^(b) x dx

Let A={3,6,9,12,15,18,21} B={4,8,12,16,20} C={2,4,6,8,10,12,14,16} and D={5,10,15,20} Which of the following is incorrect? I. A-B={4,8,16,20} II. (C-B)nn(D-B)=phi III. B-CneB-D

The product of the perpendiculars from (-1,2) to the pair of lines 2x^(2) – 5xy + 2y^(2) + 3x – 3y + 1 = 0 is