28278 + Interview Questions in Maths in Class 12

1.	A variable plane passes through a fixed point (1,-2,3) and meets the co-ordinate axes in A, B and C . The locus of the point of intersection of the plane through A,B and C parallel to the co-ordinate planes is the surface.......
Answer» `xy- (1)/(2)yz + (1)/(3) ZN = 6` `yz - 2zx + 3XY = XYZ` `xy-2yz + 3zx = 3xyz` NONE of these Answer :B

Discussion

2.	Evaluate the following definite integrals as limit of sums : int_(1)^(4)(3x^(2)+2x+5)dx
Answer» ANSWER :93

Discussion

3.	Assertion (A) : If the roots of (b-c) x^(2) + (c-a) x+(a-b) = 0 are equal then a, b, c are in A.P. Reason (R): If in ax^(2) + bx + c = 0, sum of the coefficients is equal to zero then c = a
Answer» Both A, R are true and R explain Assertion Both A, R are true but R does't explain A A is true R is FALSE A is false R is true Answer :C

Discussion

4.	Find the probability of getting one king and one queen when two cards are drawn from pack of 52 cards.
Answer» ANSWER :`(8)/(663)`

Discussion

5.	Which point maximise the objective function P=x/4+(9y)/(20)?
Answer» (0,0) (0,150) -90150 (160,0) ANSWER :C

Discussion

6.	If Delta is defined on P(X) (X ne phi)by , A deltaB = (A cupB) - (A cap B) , then ..........
Answer» identity for `DELTA` is `PHI` and INVERSE of A is A. identity for `Delta` is A and inverse of A is `phi` . identity for `Delta` is A'and inverse of A is A. identity for `Delta` is X and inverse of A is `phi` . Solution :N/A

Discussion

7.	Consider the binary opertions : R xx R to R and o : R xx R to R defined as a b = \|a -b\| and a o b =a, AA a, b in R. Show that is commutative but not associative, o is associative but not commutative. Further, show that AA a,b,c in R, a (b o c) = (ab) o (a c).[If it is so, we say that the opertion distributes over the opertion 0]. Does o distribute over ? Justify your answer.
Answer» ANSWER :NO

Discussion

8.	The transformed equation with integer coeficients whoseroots are multiplied by some constant of those of x^(3) - 4x^(2) - (1)/(4) x - (1)/(9) = 0 is
Answer» `y^(4) - y^(3) + 3Y^(2) - 10y+ 1 = 0` `y^(3) - 24y^(2) - 9Y - 24 = 0` `y^(4) - 2y^(3) + 6Y - 6 = 0` `y^(4) - 5Y^(3) + 3y^(2) - 9y + 27 = 0` Answer :2

Discussion

9.	Let f(x) = sin(x/3) + cos((3x)/10) for all real x. Find the least natural number n such that f(npi + x) = f(x) for all real x.
Answer» ANSWER :6

Discussion

10.	Let f(x) denote the sum of the infinite trigonometric series f(x)=underset(n=1)overset(infty)Sigma sin (2x)/(3^(n)) sin (x)/(3^(n)) then the sum of the solution of the equation f(x)=0 lyingin the interval (0,629) is
Answer» 10100 `PI` 5050 `pi` 4950 `pi` NONE of these ANSWER :A

Discussion

11.	The mean deviation about the mean for the following data
Answer» `9.33` `5.6` `8.33` `9.6` ANSWER :D

Discussion

12.	Find the asymptotes of the following curves : y=1/x+4x^(2)
Answer» ANSWER :x=0

Discussion

13.	If cos alpha+cosbeta+cosgamma = 0 = sinalpha + sinbeta + singamma then sin^2alpha+sin^2beta+sin^2gamma=
Answer» 0 `1/2` `3/2` 2 Answer :C

Discussion

14.	If alpha, beta, gamma are roots of x^(3) = 5x + 4 = 0 then {alpha^(3) + beta^(3) + gamma^(3))^(2) is equal to
Answer» 12 13 169 144 Answer :d

Discussion

15.	If log_(8)3=x*log_(2)3, then x=
Answer» `(1)/(3)` 3 4 `log_(4)3` Solution :`x=(log_(8)3)/(log_(2)3)=((LOG3)/(log8))/((log3)/(LOG2))=(log2)/(3log2)=(1)/(3)`

Discussion

16.	A bag contains 6 white balls and 4 balck balls. A ball is drawn and is put back in the bag with 5 balls of the same colours as that of the ball drawn . A ball is drawn again at random. What is the probability that the ball drawn now is white.
Answer» ANSWER :`(3)/(5)`

Discussion

17.	If veca = hati+2hatj+hatk, vecb = 2hati- 2hatj + 2hatk and vecc = hati + 2hatj + hatk then
Answer» `veca` and `vecb` have the same DIRECTION `veca` and `VECC` have opposite DIRECTIONS. `vecb` and `vecc` have opposite directions Answer :D

Discussion

18.	Integration of some particular functions : int(dx)/(sqrt(x^(2)-6x+9))=......+c where x in (-oo, 3)
Answer» `-LOG\|x-3\|` `log\|x-3\|` `log(x-3)` `log(3-x)` ANSWER :A

Discussion

19.	If P(n): 2^(n)ltn! Then the smallest positive integer for which P(n) is true, is
Answer» 4 2 5 3 Answer :A

Discussion

20.	Find the angle between the lines (5-x)/(-2)=(y+3)/(1)=(1-z)/(3) and x/3=(1-y)/(-2)=(z+5)/(-1).
Answer» ANSWER :`COS^(-1)((11)/(14))`

Discussion

21.	Find (dy)/(dx) given 2x + 3y = sin x.
Answer» ANSWER :`(cosx-2)/(3)`

Discussion

22.	On 1 sub R - {-1, 1}, int tan^(-1) ((2x)/(1-x^(2))) dx=
Answer» `2X tan^(-1) ((2x)/(1-x^(2))) + log (1 + x^(2)) + C` `x tan^(-1) ((2x)/(1-x^(2))) - log (1-x^(2)) + c` `x tan^(-1) ((2x)/(1-x^(2))) - log (1 -x^(2)) + c` `x^(2) tan^(-1) ((x)/(1-x^(2))) + log (1-x^(2)) + c` ANSWER :C

Discussion

23.	Which of the following set are finite and which are infinite ?The set R of real number.
Answer» Solution :"The SET R of REAL NUMBERS" is an infinite set.

Discussion

24.	Solve system of linear equations ,using matrix method2x+ 3y + 3z=5 x-2y +z=-4 3x-y-2z=3
Answer» ANSWER :`x=1 ""x=2""z=-1`

Discussion

25.	The area enclosed by the ellipse x^2/a^2+y^2/b^2=1 is :
Answer» ANSWER :`piab`

Discussion

26.	The Principle value ofcot ^(-1)(-sqrt3)is
Answer» `(5PI)/(6)` ` (pi)/(3)` ` (pi)/(2)` `(pi)/(4)` Answer :A

Discussion

27.	Evalute the following integrals int (1)/(5 +4x - 2x^(2))dx
Answer» Answer :`(1)/(2sqrt(14))log\|(x-1+sqrt((7)/(2)))/(x-1-sqrt((7)/(2)))\|+C`

Discussion

28.	An unbiased dice is tossed. The random variable X is defined on the sample space with this experiment is as follows X(w)= {("1, If even number comes up"),("0, If odd number comes up"):} Find probability distribution of X.
Answer» ANSWER :`(##KPK_AIO_MAT_XII_P2_C13_E01_051_A01##)`

Discussion

29.	int (cos 2 x. sin 4x)/(cos ^(4) x(1+ cos ^(2) 2x))dx =
Answer» `LOG [(1+ cos ^(2) X)/(1+cos 2X)]-TAN ^(2) x + c ` `log ((1+ cos ^(2) x)/(1+cos 2x))-tan ^(2) x + c ` `log ((1+ cos ^(2) x)/(1+cos 2x))-sec ^(2) x + c ` `log (((1+ cos ^(2) x)^(2))/(1+cos 2x))-sec ^(2) x + c ` Answer :D

Discussion

30.	Consider the following statements : (i) Mode can be computed from histogram. (ii) Median is not independent of change of scale. (iii) Variance is independence of change of origin and scale. Which of these is/are correct :
Answer» only (i) only (II) only (i) and (ii) (i), (ii) and (III) ANSWER :C

Discussion

31.	Write the value of int(sec^2x)/(cosec^2x)dx.
Answer» SOLUTION :`INT(sec^2x)/(cosec^2x)dx=inttan^2xdx=int(sec^2x-1)dx=tanx-x+c`

Discussion

32.	s is the midpoint of bar(qr) r=-2q {:("Quantity A","Quantity B"),(5,0):}
Answer» ANSWER :QUANTITY A is GREATER.

Discussion

33.	Using elementary transformations, find the inverseof the matrices [(3,1),(5,2)]
Answer» ANSWER :`[(2,-1),(-5,3)]`

Discussion

34.	f: R rarr R, f(x) is a differentiable function such that all its successive derivatives exist. f'(x) can be zero at discrete points only and f(x)f''(x) le 0 AA x in R If f(a)=0, then which of the following is correct
Answer» `f(a+h) f''(a-h) LT 0` `f(a+h) f''(a-h) GT 0` `f(a+h) f''(a-h) lt 0` `f(a+h) f''(a-h) lt 0` ANSWER :B

Discussion

35.	If a four digit number is formed by using the digits 1,2,3 and 5 with no repetition, then the probability that the number is divisible by 5 is :
Answer» (1/2) (1/3) (3/4) (1/4) ANSWER :D

Discussion

36.	The roots x_(1),x_(2), x_(3) of the equatiion x^(3) + ax + a=0, where a is a non-zero real, satisfy x_(1)^(2)/x_(2) + (x_(1)+1)/(x_(1)x_(2)x_(3)) +............ + ((x_(1)+1)(x_(2)+1)....(x_(n+1)+1))/(x_(1)x_(2)......x_(n))=0
Answer» ANSWER :`{x_(1), x_(2)) = (-2,1 - SQRT(5),1+sqrt(5))` all its PERMUTATION.

Discussion

37.	a : If 1/((x-2)(x^(2)+1))=A/(x-2)+(Bx+C)/(x^(2)+1) " then "A=1/5, B=-1/5, C=-2/5. R : 1/((x-a)(x^(2)+b))=1/(a^(2)+b)[1/(x-a)-(x+a)/(x^(2)+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 :D

Discussion

38.	Integration of some particular functions : int(1)/(sqrt(2-3x-x^(2)))dx=....+c
Answer» `SIN^(-1)((2-3x)/(SQRT(3)))` `sin^(-1)((2x-1)/(sqrt(15)))` `sin^(-1)((2x+3)/(sqrt(17)))` `sin^(-1)((3+2x)/(3sqrt(2)))` Answer :C

Discussion

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

Discussion

40.	If n(A) = 3, then number of equivalence relations is
Answer» 5 4 2 6 Answer :A

Discussion

41.	A coin is tossed 19 times random variable X denotes the numbers of heads on it Then for ……….. value of r for P(X = r)is maximum.
Answer» 12 9 15 19 Answer :B

Discussion

42.	If the progression 3, 10, 17, …… and 63, 65, 67, …… are such that their n^(th) terms are equal, that n is equal to
Answer» 13 15 9 8 Answer :A

Discussion

43.	A block slides down an inclined plane of angle 53^(@) with constant velocity .It is then projected up the same plane with an initial velocity of 8m//s . How far up(in m) the inclione will it move before coming to rest?
Answer» ANSWER :`2.00`

Discussion

44.	Solve the following differential equations. y^(2)dx+(x^(2)-xy+y^(2))dy=0
Answer» ANSWER :`:. Log\|y\| = TAN^(-1)y+c`

Discussion

45.	Given that a,b and c are real numbers such that b^(2) =4ac and a gt 0. The maximal possible set D sub R on which the function f: D rarr R given by f(x) =log (ax^(3)+ (a+b)x^(2)+(b+c)x+c) is defined, is
Answer» `R-{-(B)/(2a)}` `R-({-(b)/(2a)}CUP(-oo -1))` `R-({-(b)/(2a)}cup (X , x ge 1))` `R-({-b l2a} cup (-oo-1))` ANSWER :D

Discussion

46.	Choose the correct opion The expression x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y-1-y_2), when written in the form of a determinant of 3rdorder ,it will be
Answer» `\|{:(x_1,-y_1,1),(x_2,-y_2,-1),(x_3,-y_3,1):}\|` `\|{:(x_1,y_1,1),(x_2,y_2,1),(x_3,y_3,1):}\|` `\|{:(x_1,-y_1,1),(x_2,y_2,1),(-x_3,y_3,1):}\|` ANSWER :B

Discussion

47.	How many positive integers appear in the list[(2006)/(1)][(2006)/2].......[(2006)/(2006)] where [x] represents the greatest integer that does not exceed x?
Answer» ANSWER :88

Discussion

48.	If1 , omega , omega^(2)are the cube roots of unity prove that (1 - omega + omega^(2))^(6) + ( 1 - omega ^(2) + omega)^(6) = 128 = (1 - omega + omega^(2))^(7) + ( 1 + omega - omega^(2))^(7)
Answer»

Discussion

49.	It is known that 10% of certain articles manufactured are defective. What is the probability that in a random sample of 12 such articles, 9 are defective?
Answer» ANSWER :`(22 XX 9^(3))/(10^(11))`

Discussion

50.	In the redox .............
Answer» Solution :VALENCY FACTOR of `KmnO_(4) =5` Vancy factor of oxalate `=2` `5M, V_(1)=2M_(2) V_(2)`

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

A variable plane passes through a fixed point (1,-2,3) and meets the co-ordinate axes in A, B and C . The locus of the point of intersection of the plane through A,B and C parallel to the co-ordinate planes is the surface.......

Evaluate the following definite integrals as limit of sums : int_(1)^(4)(3x^(2)+2x+5)dx

Assertion (A) : If the roots of (b-c) x^(2) + (c-a) x+(a-b) = 0 are equal then a, b, c are in A.P. Reason (R): If in ax^(2) + bx + c = 0, sum of the coefficients is equal to zero then c = a

Find the probability of getting one king and one queen when two cards are drawn from pack of 52 cards.

Which point maximise the objective function P=x/4+(9y)/(20)?

If Delta is defined on P(X) (X ne phi)by , A deltaB = (A cupB) - (A cap B) , then ..........

The transformed equation with integer coeficients whoseroots are multiplied by some constant of those of x^(3) - 4x^(2) - (1)/(4) x - (1)/(9) = 0 is

Let f(x) = sin(x/3) + cos((3x)/10) for all real x. Find the least natural number n such that f(npi + x) = f(x) for all real x.

Let f(x) denote the sum of the infinite trigonometric series f(x)=underset(n=1)overset(infty)Sigma sin (2x)/(3^(n)) sin (x)/(3^(n)) then the sum of the solution of the equation f(x)=0 lyingin the interval (0,629) is

The mean deviation about the mean for the following data

Find the asymptotes of the following curves : y=1/x+4x^(2)

If cos alpha+cosbeta+cosgamma = 0 = sinalpha + sinbeta + singamma then sin^2alpha+sin^2beta+sin^2gamma=

If alpha, beta, gamma are roots of x^(3) = 5x + 4 = 0 then {alpha^(3) + beta^(3) + gamma^(3))^(2) is equal to

If log_(8)3=x*log_(2)3, then x=

A bag contains 6 white balls and 4 balck balls. A ball is drawn and is put back in the bag with 5 balls of the same colours as that of the ball drawn . A ball is drawn again at random. What is the probability that the ball drawn now is white.

If veca = hati+2hatj+hatk, vecb = 2hati- 2hatj + 2hatk and vecc = hati + 2hatj + hatk then

Integration of some particular functions : int(dx)/(sqrt(x^(2)-6x+9))=......+c where x in (-oo, 3)

If P(n): 2^(n)ltn! Then the smallest positive integer for which P(n) is true, is

Find the angle between the lines (5-x)/(-2)=(y+3)/(1)=(1-z)/(3) and x/3=(1-y)/(-2)=(z+5)/(-1).

Find (dy)/(dx) given 2x + 3y = sin x.

On 1 sub R - {-1, 1}, int tan^(-1) ((2x)/(1-x^(2))) dx=

Which of the following set are finite and which are infinite ?The set R of real number.

Solve system of linear equations ,using matrix method2x+ 3y + 3z=5 x-2y +z=-4 3x-y-2z=3

The area enclosed by the ellipse x^2/a^2+y^2/b^2=1 is :

The Principle value ofcot ^(-1)(-sqrt3)is

Evalute the following integrals int (1)/(5 +4x - 2x^(2))dx

An unbiased dice is tossed. The random variable X is defined on the sample space with this experiment is as follows X(w)= {("1, If even number comes up"),("0, If odd number comes up"):} Find probability distribution of X.

int (cos 2 x. sin 4x)/(cos ^(4) x(1+ cos ^(2) 2x))dx =

Consider the following statements : (i) Mode can be computed from histogram. (ii) Median is not independent of change of scale. (iii) Variance is independence of change of origin and scale. Which of these is/are correct :

Write the value of int(sec^2x)/(cosec^2x)dx.

s is the midpoint of bar(qr) r=-2q {:("Quantity A","Quantity B"),(5,0):}

Using elementary transformations, find the inverseof the matrices [(3,1),(5,2)]

f: R rarr R, f(x) is a differentiable function such that all its successive derivatives exist. f'(x) can be zero at discrete points only and f(x)f''(x) le 0 AA x in R If f(a)=0, then which of the following is correct

If a four digit number is formed by using the digits 1,2,3 and 5 with no repetition, then the probability that the number is divisible by 5 is :

The roots x_(1),x_(2), x_(3) of the equatiion x^(3) + ax + a=0, where a is a non-zero real, satisfy x_(1)^(2)/x_(2) + (x_(1)+1)/(x_(1)x_(2)x_(3)) +............ + ((x_(1)+1)(x_(2)+1)....(x_(n+1)+1))/(x_(1)x_(2)......x_(n))=0

a : If 1/((x-2)(x^(2)+1))=A/(x-2)+(Bx+C)/(x^(2)+1) " then "A=1/5, B=-1/5, C=-2/5. R : 1/((x-a)(x^(2)+b))=1/(a^(2)+b)[1/(x-a)-(x+a)/(x^(2)+b)]

Integration of some particular functions : int(1)/(sqrt(2-3x-x^(2)))dx=....+c

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

If n(A) = 3, then number of equivalence relations is

A coin is tossed 19 times random variable X denotes the numbers of heads on it Then for ……….. value of r for P(X = r)is maximum.

If the progression 3, 10, 17, …… and 63, 65, 67, …… are such that their n^(th) terms are equal, that n is equal to

A block slides down an inclined plane of angle 53^(@) with constant velocity .It is then projected up the same plane with an initial velocity of 8m//s . How far up(in m) the inclione will it move before coming to rest?

Solve the following differential equations. y^(2)dx+(x^(2)-xy+y^(2))dy=0

Given that a,b and c are real numbers such that b^(2) =4ac and a gt 0. The maximal possible set D sub R on which the function f: D rarr R given by f(x) =log (ax^(3)+ (a+b)x^(2)+(b+c)x+c) is defined, is

Choose the correct opion The expression x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y-1-y_2), when written in the form of a determinant of 3rdorder ,it will be

How many positive integers appear in the list[(2006)/(1)][(2006)/2].......[(2006)/(2006)] where [x] represents the greatest integer that does not exceed x?

If1 , omega , omega^(2)are the cube roots of unity prove that (1 - omega + omega^(2))^(6) + ( 1 - omega ^(2) + omega)^(6) = 128 = (1 - omega + omega^(2))^(7) + ( 1 + omega - omega^(2))^(7)

It is known that 10% of certain articles manufactured are defective. What is the﻿ probability that in a random sample of 12 such articles, 9 are defective?

In the redox .............

It is known that 10% of certain articles manufactured are defective. What is the probability that in a random sample of 12 such articles, 9 are defective?