28278 + Interview Questions in Maths in Class 12

1.	Giventhe graph of the function y = f(x) (Fig. 62), find the shape of the graph of the antiderivative I = int_(0)^(x) f (t) dt
Answer» ANSWER :`X = (a)/(2)`

Discussion

2.	Let a_(1), a_(2), a_(3), a_(4) be in A.P. If a_(1) + a_(4) = 10 and a_(2)a_(3) = 24, them the least term of them is
Answer» 1 2 3 4 Answer :B

Discussion

3.	Definite integration as the limit of a sum : lim_(ntooo)[(1)/(n^(2))sec^(2)""(1)/(n^(2))+(2)/(n^(2))sec^(2)""(4)/(n^(2))+.......+(1)/(n)sec^(2)1]a. 'tan1b. 1/2tan1c. 1/2sec1d. 1/2cosec 1
Answer» `tan1` `(1)/(2)tan1` `(1)/(2)SEC1` `(1)/(2)cosec 1` ANSWER :B

Discussion

4.	On which of the following intervals is the function f given by f(x) = x^(100) + sin x –1 decreasing ?
Answer» (0,1) `(PI)/(2),pi` `0,(pi)/(2)` NONE of these ANSWER :D

Discussion

5.	Equation of the plane passing through points (1,-1,3) and (2,3,-4) and parallel to X-axis is
Answer» 7y+4z+5=0 7y+4z-5=0 7y-4z-5=0 7y-4z+5=0 Answer :B

Discussion

6.	Which of the following maximize the objective function P=x/2+y/2 is ?
Answer» (3,0) (2,0) (3,2) (2,3) ANSWER :D

Discussion

7.	Let Abe the image of (2,-1) wr.to y-axis. Without transforming the origin, the axes are turned through an angle of 45^(@) in the clockwise direction. Then A in new system is
Answer» `(1//sqrt(2),3//sqrt(2))` `(-1//sqrt(2), -3//sqrt(2))` `(-3//sqrt(2),1//sqrt(2))` NONE ANSWER :B

Discussion

8.	Solve (dy)/(dx) + y = tan x (0 le x lt (pi)/(2))
Answer»

Discussion

9.	If A, B, C are the centres of three circles touching mutually externally then the radical centre of the circles for triangleABC is
Answer» centroid orthocentre circum centre incentre Answer :D

Discussion

10.	Find the 13^(th) term in the expansion of (9x - 1/(3sqrt(x)))^(18),x != 0.
Answer» ANSWER :` = 18564`

Discussion

11.	The number of ways in which 12 books can be put in 3 shelves, 4 on each is
Answer» `(12!)/((4!)^(3))` `(12!)/((3!)^(3))` `(12!)/((4!)^(3))xx(1)/(3!)` `(12!)/((4!)^(3))xx(1)/(3)` ANSWER :C

Discussion

12.	A point on the ellipse 4x^(2) +9y^(2) = 36 where the normal is parallel to the line 4x- 2y -5=0 is
Answer» ` ((9)/( 5), ( 8)/(5)) ` ` ((8)/(5) , ( -9)/(5))` ` (-( 9)/( 5),( 8)/(5))` ` ( (8)/(5) ,(9)/(5))` ANSWER :A

Discussion

13.	int_(0)^(pi) cos^(3)x . Sin^(4) x dx = …... .
Answer» `-PI` `0` `pi` `2PI` ANSWER :B

Discussion

14.	Match the following . {:("Parabola","" "Focus"),("I".y^(2)-x-3y+2=0,""(a)(1,2)),("II".y^(2)-8x-4y-4=0,""(b)(-2,5)),("III".x^(2)+4x-8y+28=0,""(c)(1,-1)),("IV".x^(2)-2x-8y-23=0,""(d)(5//4,1)):}
Answer» a,B,C,d b,c,a,d d,a,b,c b,d,a,c Answer :C

Discussion

15.	Let A= R- (3), B= R-{1}. Let f: A to B be defined by f(x)= ((x-2)/(x-3)) AA x in A. Then show that f is bijective. Hence find f^(-1) (x).
Answer» ANSWER :`F^(-1) (X) = (3x-2)/( x-1) = G(x)`.

Discussion

16.	If 't_(1)' , 't_(2)' and 't_(3)' are the lengths of the tangents draen from centre of x-circle to the circumcircle of the DeltaABC, then (1)/(t _(1)^(2))+(1)/(t _(2)^(2))+(1)/(t_(3)^(2)) is equal to
Answer» `(ABC)/(a+B+c)` `(a+b+c)/(abc)` `(a+b+c)/(2ABC)` `(2 abc)/(a+b+c)` ANSWER :B

Discussion

17.	The perpendicular distance from A (1,4, -2) to the line BC, where B =(2, 1, -2) and C = (0, -5, 1) is
Answer» `(sqrt(26))/(7)` `sqrt((26)/(7))` `(2 sqrt(26))/(7)` `(3 sqrt(26))/(7)` Answer :D

Discussion

18.	{:("List-I","List-II"),(p."The area enclosed between the curves" \|x\| + \|y\| = 2 "and" x^(2) = y "in sq. units is", 1. (24)/(5)),(Q. "The maximum value of the function" f(x) - 3 sin x - 4 cos x - (7)/(3) "will be given by",2. (7)/(3)),(R. "The length of common chord of two circle of radii 3 and 4 units which intersect orthogonally is",3. (16)/(3)),(S. "The length of chord intercepted by the parabola" y^(2) = 4(x + 1) "passing through its focus and inclined at" 60^(@) "with positive x-axis is",4. (8)/(3)):}
Answer» 2,4,1,3 1,2,3,4 3,4,1,2 4,3,2,1 Answer :A

Discussion

19.	Find the values of each of the following : cot(tan^(-1)a+cot^(-1)a)
Answer» ANSWER :`0`

Discussion

20.	Let C be a circle with centreP_(0) and AB be a diameter of C . suppose P_(1)is the midpoint of line segmentP_(0) B, P_(2) the midpoint of line segment P_(1) B and so on Let C_(1),C_(2) ,C_(3)be circles with diameters P_(0)P_(1), P_(1)P_(2),P_(2)P_(3) ,... respectively Suppose the circles C_(1),C_(2),C_(2),... are all shaded The ratio of the area of the unshaded portion of C to that of the original circle is
Answer» `8:9` `9:10` `10:11` `11:12` ANSWER :4

Discussion

21.	What is the equation of the plane through z-axis and parallel to the line (x-1)/costheta=(y+2)/sintheta=(z-3)/0?
Answer» `x COT THETA +y=0` `x tan theta-y=0` `x+y cot theta=0` `x-y tan theta=0` Solution :Let equation of plane through z-axis is `ac+by=0` It is given that this plane is PARELLEL to the line `(x-1)/costheta=(y+2)/SINTHETA=(z-3)/0` Since the plane parallel to the line `:. Acostheta=-bb sin theta=0` `rArr a cos theta =-b sin thetarArr a = -b tan theta` `:.-b tan thetax +by =0` `rArr x tan theta-y=0 (`:' b ne 0`) Which is REQUIRED equation of plane.

Discussion

22.	Given that matrixB = [{:( a,b),(c,d) :}] find lambda so that B^(2) - ( a+d) B =lambda l. where I is a unit matrix of order 2.
Answer» ANSWER :`LAMBDA =(BC -AD) `

Discussion

23.	int (x-1)/((x+1)^(2))dx=....
Answer» `LOG(x+1)+(2)/(x+1)+C` `log(x+1)-(2)/(x+1)+c` `(2)/(x+1)-log(x+1)+c` NONE of these Answer :A

Discussion

24.	Find the range of x for which the binomial expansions of the following are valid .(x + 5)^(3//2)
Answer» ANSWER :`(-5,5)`

Discussion

25.	If z = x + iy and if the point P in the Argand plane represents z , then the locus of P satisfying the equation \|z- 3i\| + \|z + 3i\| = 10 is
Answer» Circle with centre `(-3,3)` Hyperbola with ECCENTRICITY `(5)/(3)` Ellipse with eccentricity `(3)/(5)` Ellipse with eccentricity `(5)/(4)` ANSWER :D

Discussion

26.	An oil company has two depots A and B with capacities of 7000 L and 4000 L respectively. The company is to supply oil to three petrol pumps, D, E and F whose requirements are 4500L, 3000L and 3500L respectively. The distances (in km) between the depots and the petrol pumps is given in the following table : Assuming that the transportation cost of 10 litres of oil is Rs. 1 per km, how should the delivery be scheduled in orderthat the transportation cost is minimum ? What is the minimum cost ?
Answer» ANSWER :The MINIMUM COST of TRANSPORTATION is RS. 4400

Discussion

27.	Let p, q be integers and let alpha , betabe the roots of the equations x^(2) - x - 1 = 0" where " alpha ne beta. For n = 0,1,2, . . .let a_(n) = palpha ^(n) +q beta^(n) . If a_(4) = 28 , then p+(1)/(8) q is equal to ______
Answer» ANSWER :`4 . 50`

Discussion

28.	If A is the set of the divisors of the number 15, B is the set of prime numbers smaller than 10 and C is the set of even numbers smaller than 9, then (A uu C)nnB is the set
Answer» `{1,3,5}` `{1,2,3}` `{2,3,5}` `{2,5}` ANSWER :C

Discussion

29.	1/2 - 3/4 =
Answer» `-5//4` `-2//3` `-1//4` `-1//2` ANSWER :C

Discussion

30.	Evaluate int( x^2)/( 1-x^6)
Answer» ANSWER :`= (1)/(6) LOG \| (1+x^3)/( 1-x^3) \|`

Discussion

31.	Method of integration by parts : If int(xe^(x))/(sqrt(1+e^(x)))dx=f(x)sqrt(1+e^(x))-2logg(x)+c then .........
Answer» `f(X)=x-1,g(x)=(SQRT(1+e^(x))+1)/(sqrt(1+e^(x))-1)` `f(x)=2x-4,g(x)=(sqrt(1+e^(x))-1)/(sqrt(1+e^(x)+1))` `f(x)=x-1,g(x)=(sqrt(1+e^(x))-1)/(sqrt(1+e^(x))+1)` None of these Answer :B

Discussion

32.	overset(pi)underset(0)int xlog (sinx)dx
Answer» ANSWER :`:. I=(PI^(2))/(2)LOG((1)/(2))`

Discussion

33.	Integers a, b, c satisfy a + b - c = 1 and a^2 + b^2 - c^2 = -1. What is the sum of all possible values of a^(2) + b^(2) + c^(2) ?
Answer» ANSWER :18

Discussion

34.	Consider f: {1,2,3} to {a,b,c}given by f (1) =a , f (2) =b and f (3)=c. Find f ^(-1) and show that (f ^(-1)) ^(-1) =f.
Answer» Answer :`F ^(-1) `given by `f ^(-1) (a) = 1, f ^(-1) (b) =2 and f ^(-1) (c ) =3.`

Discussion

35.	Consider the following statements : (i) Mean of 100 observations is 50 and standard deviation is 10. If 5 is added to each observation the new mean and standard deviation are 55, 10. (ii) Mean of 100 observations is 50 and standard deviation is 10. If each observation is multiplied by 3 then the new mean and standard deviation are 50, 10/3. The true statements are :
Answer» only (i) only (II) both (i), (ii) NEITHER (i) nor (ii) ANSWER :A

Discussion

36.	int_(0)^(3)(3x+1)/(x^(2)+9) dx is equal to
Answer» `LOG(2sqrt(2))+(pi)/12` `log(2sqrt(2))+(pi)/2` `log(2sqrt(2))+(pi)/6` `log(2sqrt(2))+(pi)/3` Solution :`int_(0)^(3)(3x+1)/(x^(2)+9)dx=3/2 int_(0)^(3)(2x)/(x^(2)+9)dx` `+int_(0)^(3)(dx)/(x^(2)+9)` `[3/2 log(x^(2)+9)+1/3tan^(-1)(x/3)]_(0)^(3)` `=3/2[log(3^(2)+9)-log(0+9)]` `+1/3[TAN^(-1)(3/3)-tan^(-1)0]` `=3/2(log18-log9)+1/3((pi)/4)` `=3/2 log2+(pi)/12=log(2sqrt(2))+(pi)/12`

Discussion

37.	Integrate the functions (sinx)/(sin(x-a))
Answer» ANSWER :`sinalogabs(SIN(x-a))+xcosa+C`

Discussion

38.	sin(tan^(-1)x),\|x\| lt1 is equal to
Answer» `x/sqrt(1-x^2)` `1/sqrt(1-x^2)` `x/sqrt(1+x^2)` `1/sqrt(1+x^2)` ANSWER :D

Discussion

39.	A rectangle is 5 times as wide as it is long. The area of the rectangle is 320 square feet. What is the perimeter of the rectangle , in feet ?
Answer» 8 40 48 96 Answer :D

Discussion

40.	Evaluate the integral underset(0)overset(5)int x^(2) (sqrt(5-x))^(7) dx
Answer» ANSWER :`(16xx5^(13//2))/(1287)`

Discussion

41.	For the circles x^(2)+y^(2)+4x+3y+2y=4=0, x^(2)+y^(2)+4x-2y+4=0" the line "3x+4y+5=0 is a
Answer» COMMON chord direct common tangent transverse common tangent common tangent Answer :B

Discussion

42.	The relationship between temperature expressed in degrees fahrenheit (F) and degrees Celsius (C) is given by the formula F = 9/5 C + 32 If the temperature is 14 degrees Fahrenheit, what is it in degrees Celsius?
Answer» `-10^(@)` `-12^(@)` `-14^(@)` `-16^(@)` ANSWER :A

Discussion

43.	Integrate the functions in exercise. (1)/(sqrt((x-a)(x-b)))
Answer» Answer :`LOG\|(x-(a+b)/(2))+SQRT((x-a)(x-b))\|+c`

Discussion

44.	If (x^(3)+x^(2)+1)/((x^(2)+2)(x^(2)+3))=(Ax+B)/(x^(2)+2)+(Cx+D)/(x^(2)+3), then A+B+C+D=
Answer» 1 4 3 2 Answer :D

Discussion

45.	If the general solution of the differentialequation y'=(y)/(x)+Phi ((x)/(y)), for some function Phi is givenby y ln\|cx\|=x, where c is an arbitrary constant, then Phi (2) is equal to:
Answer» 4 `(1)/(4)` `-4` `-(1)/(4)` ANSWER :4

Discussion

46.	Given q^2-prlt0,p gt 0, the value of : \|(p,q,px+qy),(q,r,qx+ry),(px+qy,qx+ry,0)\| is :
Answer» 0 `GT0` `LT0` `q^2+pr` ANSWER :C

Discussion

47.	The point to which the origin should be shifted in orderto eliminate x and y terms in the equation 4x^(2) + 9y^(2) - 8x + 36y +4=0 is
Answer» only 1 is TRUE only II is true both I and II are true NEITHER I nor II are true Answer :B

Discussion

48.	If (1)/((ax+b)(cx+d))+(A)/(ax+b)+ (B)/(cx+d) then show that (1)/((ax+b)^(2)(cx+d))=(A)/((ax+b)^(2))+(AB)/(ax+b)+(B^(2))/(cx+d).
Answer» ANSWER :`(A)/((ax+B)^(2))+(AB)/(ax+b)+(B^(2))/(cx+d)`

Discussion

49.	A box contains 2 red, 3 blue and 4 black balls. Three balls are drawn at random. What is the probability that two balls are of the same colour and the third of a different colour.
Answer» ANSWER :`(55)/(84)`

Discussion

50.	Expand in ascending powers of x. cos x,
Answer» SOLUTION :`cosx=1/2(E^(is)+e^(-is))=1/2[(1+ix+(i^2x^2)/(2!)+(i^3x^3)/(3!)+...)+(1-ix+(e^2x^2)/(2!)-(i^3x^3)/(3!)+...)]=1/2[2(1-x^2/(2!)+x^4/(4!)-...)]=1-x^2/(2!)+x^4/(4!)-...`

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Giventhe graph of the function y = f(x) (Fig. 62), find the shape of the graph of the antiderivative I = int_(0)^(x) f (t) dt

Let a_(1), a_(2), a_(3), a_(4) be in A.P. If a_(1) + a_(4) = 10 and a_(2)a_(3) = 24, them the least term of them is

Definite integration as the limit of a sum : lim_(ntooo)[(1)/(n^(2))sec^(2)""(1)/(n^(2))+(2)/(n^(2))sec^(2)""(4)/(n^(2))+.......+(1)/(n)sec^(2)1]a. 'tan1b. 1/2tan1c. 1/2sec1d. 1/2cosec 1

On which of the following intervals is the function f given by f(x) = x^(100) + sin x –1 decreasing ?

Equation of the plane passing through points (1,-1,3) and (2,3,-4) and parallel to X-axis is

Which of the following maximize the objective function P=x/2+y/2 is ?

Let Abe the image of (2,-1) wr.to y-axis. Without transforming the origin, the axes are turned through an angle of 45^(@) in the clockwise direction. Then A in new system is

Solve (dy)/(dx) + y = tan x (0 le x lt (pi)/(2))

If A, B, C are the centres of three circles touching mutually externally then the radical centre of the circles for triangleABC is

Find the 13^(th) term in the expansion of (9x - 1/(3sqrt(x)))^(18),x != 0.

The number of ways in which 12 books can be put in 3 shelves, 4 on each is

A point on the ellipse 4x^(2) +9y^(2) = 36 where the normal is parallel to the line 4x- 2y -5=0 is

int_(0)^(pi) cos^(3)x . Sin^(4) x dx = …... .

Match the following . {:("Parabola","" "Focus"),("I".y^(2)-x-3y+2=0,""(a)(1,2)),("II".y^(2)-8x-4y-4=0,""(b)(-2,5)),("III".x^(2)+4x-8y+28=0,""(c)(1,-1)),("IV".x^(2)-2x-8y-23=0,""(d)(5//4,1)):}

Let A= R- (3), B= R-{1}. Let f: A to B be defined by f(x)= ((x-2)/(x-3)) AA x in A. Then show that f is bijective. Hence find f^(-1) (x).

If 't_(1)' , 't_(2)' and 't_(3)' are the lengths of the tangents draen from centre of x-circle to the circumcircle of the DeltaABC, then (1)/(t _(1)^(2))+(1)/(t _(2)^(2))+(1)/(t_(3)^(2)) is equal to

The perpendicular distance from A (1,4, -2) to the line BC, where B =(2, 1, -2) and C = (0, -5, 1) is

Find the values of each of the following : cot(tan^(-1)a+cot^(-1)a)

What is the equation of the plane through z-axis and parallel to the line (x-1)/costheta=(y+2)/sintheta=(z-3)/0?

Given that matrixB = [{:( a,b),(c,d) :}] find lambda so that B^(2) - ( a+d) B =lambda l. where I is a unit matrix of order 2.

int (x-1)/((x+1)^(2))dx=....

Find the range of x for which the binomial expansions of the following are valid .(x + 5)^(3//2)

If z = x + iy and if the point P in the Argand plane represents z , then the locus of P satisfying the equation |z- 3i| + |z + 3i| = 10 is

Let p, q be integers and let alpha , betabe the roots of the equations x^(2) - x - 1 = 0" where " alpha ne beta. For n = 0,1,2, . . .let a_(n) = palpha ^(n) +q beta^(n) . If a_(4) = 28 , then p+(1)/(8) q is equal to ______

If A is the set of the divisors of the number 15, B is the set of prime numbers smaller than 10 and C is the set of even numbers smaller than 9, then (A uu C)nnB is the set

1/2 - 3/4 =

Evaluate int( x^2)/( 1-x^6)

Method of integration by parts : If int(xe^(x))/(sqrt(1+e^(x)))dx=f(x)sqrt(1+e^(x))-2logg(x)+c then .........

overset(pi)underset(0)int xlog (sinx)dx

Integers a, b, c satisfy a + b - c = 1 and a^2 + b^2 - c^2 = -1. What is the sum of all possible values of a^(2) + b^(2) + c^(2) ?

Consider f: {1,2,3} to {a,b,c}given by f (1) =a , f (2) =b and f (3)=c. Find f ^(-1) and show that (f ^(-1)) ^(-1) =f.

int_(0)^(3)(3x+1)/(x^(2)+9) dx is equal to

Integrate the functions (sinx)/(sin(x-a))

sin(tan^(-1)x),|x| lt1 is equal to

A rectangle is 5 times as wide as it is long. The area of the rectangle is 320 square feet. What is the perimeter of the rectangle , in feet ?

Evaluate the integral underset(0)overset(5)int x^(2) (sqrt(5-x))^(7) dx

For the circles x^(2)+y^(2)+4x+3y+2y=4=0, x^(2)+y^(2)+4x-2y+4=0" the line "3x+4y+5=0 is a

The relationship between temperature expressed in degrees fahrenheit (F) and degrees Celsius (C) is given by the formula F = 9/5 C + 32 If the temperature is 14 degrees Fahrenheit, what is it in degrees Celsius?

Integrate the functions in exercise. (1)/(sqrt((x-a)(x-b)))

If (x^(3)+x^(2)+1)/((x^(2)+2)(x^(2)+3))=(Ax+B)/(x^(2)+2)+(Cx+D)/(x^(2)+3), then A+B+C+D=

If the general solution of the differentialequation y'=(y)/(x)+Phi ((x)/(y)), for some function Phi is givenby y ln|cx|=x, where c is an arbitrary constant, then Phi (2) is equal to:

Given q^2-prlt0,p gt 0, the value of : |(p,q,px+qy),(q,r,qx+ry),(px+qy,qx+ry,0)| is :

The point to which the origin should be shifted in orderto eliminate x and y terms in the equation 4x^(2) + 9y^(2) - 8x + 36y +4=0 is

If (1)/((ax+b)(cx+d))+(A)/(ax+b)+ (B)/(cx+d) then show that (1)/((ax+b)^(2)(cx+d))=(A)/((ax+b)^(2))+(AB)/(ax+b)+(B^(2))/(cx+d).

A box contains 2 red, 3 blue and 4 black balls. Three balls are drawn at random. What is the probability that two balls are of the same colour and the third of a different colour.

Expand in ascending powers of x. cos x,