28278 + Interview Questions in Maths in Class 12

1.	Find the equation of the parabola whose axis is parallel to Y-axis and which passes through the points (4,5),(-2,11) and (-4,21).
Answer» ANSWER :`X^(2)-2x-y+5=0`

Discussion

2.	The negative of a matrix is obtained by multiplying it by …….
Answer» ANSWER :`-1`.

Discussion

3.	Let P represent the point (3, 6) on the parabola y^(2)=12 x. For the parabola y^(2)=12 x, if l_(1) is the length of the normal chord drawn at P and l_(2) is the length of the focal chord drawn through P, then l_(1)/l_(2)=
Answer» `2sqrt(2)` `3` `4sqrt(2)` 5 Answer :A

Discussion

4.	1,2,4,6,8,9 transformed into another series whose mean is 12. Two middle terms of the transformed series are
Answer» `7,8` ` 10,14` ` 9, 15` ` 11, 13` ANSWER :D

Discussion

5.	A = {(x,y) : y = 1//x,0 ne x in R} , B = {(x, y) : y = - x, x in R} then
Answer» `A NN B=A` `A nn B=B` `A nn B=phi` `A nn B=A UU B` ANSWER :C

Discussion

6.	If length of three sides of a trapezium other than base are equal to 10 cm, then find the area of the trapezium when it is maximum.
Answer» ANSWER :`75sqrt(3)CM^(2)`

Discussion

7.	IFsin^(-1) x sin ^(-1) y =(2pi )/(3) thencos ^(-1)y=(pi)/(lamda ). Findthevalueoflamda
Answer» ANSWER :2

Discussion

8.	IF12 x^2- mxy+ 3y^2- 5y^2 -2canberesolvarbleintotwo linearfactorsthenm=
Answer» `+-6` `+-3` `+-5` `+-7` ANSWER :D

Discussion

9.	Evaluate int(1 - x) (4 - 3x) (2x + 3)dx
Answer» Answer :`(3)/(2)X^(4) - (5)/(3) x^(3) - (13)/(2)x^(2) + 12x + c`

Discussion

10.	Let p: Kiran passed the examination q: Kiran is sad The symbolic from of a statement "it is not ture Kiran passed therefore she is sad" is
Answer» <P>(~p`rarr`Q) (p`rarr`q) ~(p`rarr`~q) ~(p`HARR`q) Answer :B

Discussion

11.	If the two lines, whose d.C.s l,m,n are given by the equation al+bm+cn=0 and fmn + gnl + hlm=0, are mutually perpendicular, then
Answer» `f/a + G/B + h/C=0` `a/f + b/g +c/h=0` `f/a^(2) + g/b^(2) + h/c^(2)=0` `a^(2)/f + b^(2)/g +c^(2)/h=0` ANSWER :A

Discussion

12.	Seven digits from the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 are written in random order. Find the probability that the seven digited number is divisible by 9.
Answer» ANSWER :`(1)/(9)`

Discussion

13.	2500 single men and 2500 single women were asked about whether they owned any dogs or cats. The table below displays a summery of the results. Of the people who said they had neigher dogs nor cats, 200 were selected at random, and they were asked if they had any pets at all. 43 people said they did have pets,and the remaining 157 said that they did not. Based on both the initial data given in the table, together with the new data stated in this paragraph, which of the following is most likely to be accurate?
Answer» Approximately 482 of the ORIGINAL PEOPLE SURVEYED WOULD SAY that they have no pets. Approximately 1758 of the original people surveyed would say that they have no pets. Approximately 1963 of the original people surveyed would say that they have no pets. Approximately 3925 of the original people surveyed would say that they have no pets. Answer :B

Discussion

14.	The solution of (dy)/(dx) = ((y)/(x))^(1//3) is
Answer» `X^(2//3) + y^(2//3) = C` `y^(2//3) - x^(2//3) = c` `x^(1//3) + y^(1//3) = c` `y^(1//3) - x^(1//3) = c` ANSWER :B

Discussion

15.	If A = [(1,2,3),(3,-2,1),(4,2,1)]
Answer» ANSWER :`A^(2) = A^(-1)`

Discussion

16.	Find the power of the point P with respect to the circle S = 0 when P = (5,-6), and S-= x^(2) + y^(2) + 8x + 12y + 15
Answer» ANSWER :` 4X- 3Y +7 =0`

Discussion

17.	{:(I."If" a = 2i - 3j -k. b = i + 4j - 2k"then" (a + b) xx (a - b), a. 42 i + 14 j - 21 k),(II. "If" a = 3i - j - 2k. b - 2i + 3j + k "then" (a + 2b) xx (2a - b), b. -5i + 5j + 5k),(III. "If" a = i + 2j - 3k. b = 2i + j + k "then" a xx b, c. -25i + 35j - 55 k),(IV. "If" a = 2i + 3j + 6k. b = 3i - 6j + 2k "then" a xx b, d. -20i - 6j - 22k):}
Answer» a,c,d,b b,a,d,c a,d,c,b d,c,b,a Answer :D

Discussion

18.	If the period of the function f(x) = sin 5x cos 3x is alpha, then cos alpha=
Answer» `1` `(1)/(SQRT2)` `-(1)/(2)` `-1` ANSWER :D

Discussion

19.	int_(0)^(5) [x] dx=
Answer» 0 5 10 15 Answer :C

Discussion

20.	If1 , omega , omega^(2) are the cube roots of unity , then find the values of the following . (1 - omega) ( 1 - omega ^(2)) ( 1 - omega^(4)) ( 1 - omega^(8))
Answer» ANSWER :9

Discussion

21.	An urn contains 5 black 6 red and 4 white balls.Five balls are drawn at random from the urn. Find the probability that all graduates? What is the probability of at least one graduate?
Answer» ANSWER :`(400)/(1001)`

Discussion

22.	Let f (n) = sum _(r =2)^(n) (r )/(""^r C_(2) ""^(r+1) C_(2)) , a = lim _(x to oo) f (n) and x ^(2) -(2n -(1)/(2)) x +t =0 has two positive roots alpha and beta. minimum value of (4)/(alpha ) + (1)/(beta) is :
Answer» 2 6 3 4 Answer :B

Discussion

23.	If f(x) is strictly increasing function then h(x) is non monotonic function given
Answer» ` a in (0,3)` `a in (-2,2)` `(3,OO)` `a in (-oo,0)cup (3,oo)` Solution :h(x)is non MONOTONIC function if `3af(x)^(2)-2af(x)+1` changes sign for which `DGT0 or 4a^(2)-12agt0` `a in(-oo,0)cup(3,oo)`

Discussion

24.	If the antiderivative of (1)/(x^(2)sqrt(1+x^(2))) is -sqrt(f(x))/(x)+C then f(x) is equal to
Answer» `1 + 1//x^(2)` `TAN^(-1)x` `1+x^(2)` `2sqrt(1+x^(2))` Answer :C

Discussion

25.	An unbiased die of six faces, market with the integers 1,2,3,4,5,6, one on each face, is thrown thrice in succession. What is the total number of outcomes ?
Answer» Solution :An UNBIASED DIE of six FACES, marked with the integers 1,2,3,4,5,6, one on each face is thrown thrice in succession. `:.` The total NUMBER of OUTCOMES `=6^3=216.`

Discussion

26.	For real valued functions f and g, f(x) = 2sin (pi/x) and g(x) = sqrtx. Then fog(4) - gof (6) = ..............
Answer» 0 `1/2` 1 `sqrt3/2` SOLUTION :N/A

Discussion

27.	Find the domain and range of those relations in a which are functions. {(a,2),(b,3),(c,4)}
Answer» SOLUTION :RANGE of the FUNCTION is {2,3,4}

Discussion

28.	The sum of 100 observations and sum of their squares are 400 and 2,475 respectively . Later on three observatons 3,4 and 5 were found to be incorrect.If the incorrect observations are omitted, then variance of the remaining observations is:
Answer» `8.25` `8.50` `8.00` `9.00` ANSWER :D

Discussion

29.	There are 12 different books in a shelf. In how many ways we can select atleast one of them?
Answer» ANSWER :4095

Discussion

30.	int (x^(2)-1)/((x^(2)+1)(x^(2)+2)(x^(2)+3))dx=
Answer» `Tan^(-1)x+(3)/(sqrt(2))Tan^(-1)((x)/(sqrt(2)))-(2)/(sqrt(3))Tan^(-1)((x)/(sqrt(3)))+C` `-Tan^(-1)x+(3)/(sqrt(2))Tan^(-1)((x)/(sqrt(2)))-(2)/(sqrt(3))Tan^(-1)((x)/(sqrt(3)))+c` `Tan^(-1)x-(3)/(sqrt(2))Tan^(-1)((x)/(sqrt(2)))-(2)/(sqrt(3))Tan^(-1)((x)/(sqrt(3)))+c` none Answer :A

Discussion

31.	If a straight line passes through the points ((-1)/(2), 1)and (1, 2), then its x-intercept is
Answer» -2 -1 2 1 Answer :A

Discussion

32.	The sum of the solutions in (0,2pi)for the equation cosx cos (pi/3-x)cos (pi/3+x)=1/4 is
Answer» `4PI` `PI` `2PI` `3pi` ANSWER :C

Discussion

33.	Find the slope of the tangent to curve y=x^3-x+1 at the point whose x-coordinate is 2.
Answer» SOLUTION :`y=x^3-x+1(DY)/DX=3x^2-1` SLOPE of the TANGENT `=(dy)/dx]_(x=2)=3xx2^2-1=11`

Discussion

34.	Mean and variance of random variable X are 2 and 1 respectively. Then ……….. is the probability that X takes more than one value.
Answer» `(11)/(16)` `(5)/(16)` `(7)/(16)` `(13)/(16)` ANSWER :A

Discussion

35.	Lt_(x rarr 0) ((1+x)^(n)-nx-1)/(x^(2)) n gt 1is euqal to
Answer» N n(n-1) `(n(n-1))/(2)` does not EXIST ANSWER :C

Discussion

36.	If f(x) = x^(3) + bx^(2) + ax satisfies the conditionsof Rolle's theorem in [1, 3] with c = 2 + (1)/sqrt(3)then (a, b) is equal to
Answer» `(11,6)` `(11,-6)` `(-6,11)` `(6,11)` ANSWER :B

Discussion

37.	Are fand g both necessarily onto, if gof is onto?
Answer» SOLUTION :N/A

Discussion

38.	ABC is an isosceles triangle and B=90. If B and the midpoint P of AC are represented by 3+2i and 1-I then other vertices are
Answer» 4+ I,-2-3i 4-3i,-2+i 4-I,-2-i none Answer :B

Discussion

39.	If z_(1) and z_(2) be two non zero complex numbers such that (z_(1))/(z_(2))+(z_(2))/(z_(1))=1, then the origin and the points represented by z_(1) and z_(2)
Answer» LIE on a straight L!ne form a right ANGLED triangle form an equilaleral triangle form an ISOSCELES triangle Answer :C

Discussion

40.	Find the sum of the infinite series 1+(1)/(3)+(1.3)/(3.6)+(1.3.5)/(3.6.9)+…..
Answer» SOLUTION :N/A

Discussion

41.	Three vectors vec(a),vec(b)andvec(c) are of the same length and the angle between any two of them is the same. If vec(a)=hat(i)+hat(j)andvec(b)=hat(j)+hat(k)," then "vec(c) is
Answer» `-(1)/(3)(hat(i)-4hat(j)+hat(k))` `hat(i)+hat(k)` `-(1)/(3)(-hat(i)+4hat(j)+hat(k))` `(1)/(7)(hat(i)+2HAT(j)+3hat(k))` ANSWER :A::B

Discussion

42.	A, B and C are three non-zero vectors, no two of them are parallel. If A + B is collinear to C and B + C is collinear to A, then A + B + C is equal to
Answer» A B C 0 Solution :Since, A + B is collinear to C and B + C is collinear to A. `therefore A + B = lambda C` and `B + C = MU A` where, `lambda` and `mu` are SCALARS. `implies A+B+C=(lambda+1)C` and `A+B+C=(mu+1)A` `implies (lambda+1)C=(mu+1)A` If `lambda ne-1`, then `C=(mu+1)/(lambda+1)A` implies C and A are collinear. This is a contradiction to the given CONDITION. `therefore lambda = - 1` `therefore A + B + C = 0`

Discussion

43.	The substitution required to change (3y-7x+7) dx + (7y-3x+3)dy = 0 into a homogeneous equation is
Answer» X = X+1 y = Y x = X, y = Y+1 x = X + 1 y = Y+1 x = X +2, y = Y+2 Answer :A

Discussion

44.	The probability function of the binomial distribution is P(x)= ((6), (x))p^(x)q^(6-x), x= 0, 1, 2, ....., 6.If 2P(2) = 3P(3) then value of q is ……….
Answer» `(9)/(17)` `(3)/(2)` `(1)/(3)` `(2)/(3)` Answer :D

Discussion

45.	Let I be the purchase value of an equipment and v (t) be the value after it has been used for t years. The value V (t) depreciates at a rate given by differential equation (dV(t))/(dt)= -k(T-t), where k gt 0 is a constant and T is the total life in years of the equipment. Then the scrap value v(T) of the equipment is _______
Answer» `I-(K(T-t)^(2))/(2)` `e^(-KT)` `T^(2)-(1)/(k)` `I-(kT^(2))/(2)` ANSWER :4

Discussion

46.	If g(x) = int_(0)^(x) cos 4(t) dt , then g(x+pi) equals
Answer» `(G(X))/(g(PI))` `g(x)+g(pi)` `g(x)-g(pi)` `g(x).g(pi)` ANSWER :2,3

Discussion

47.	int (secx)/((sec x+ tan x)^(2))dx=
Answer» ANSWER :`-(1)/(2(secx+tanx)^(2))+C`

Discussion

48.	Radius of an air bubble increases at the rate of (1)/(2) cm/sec. At what rate volume at bubble increases when radius is 1 cm.
Answer» ANSWER :`2PI(CM)^(3)//SEC`.

Discussion

49.	If A+B+C=180^(@) then cos A+cos B-cosC=
Answer» `-1+4sinA//2sin B//2 SIN C//2` `-1+4cosA//2cosB//2sinC//2` `-1+4cosA//2cosB//2cosC//2` `-1+4cosA//2sinB//2cosC//2` ANSWER :B

Discussion

50.	If alpha, beta ar the roots of the quadratic equation x ^(2) -(3+ 2 ^(sqrt(log _(2)3))-3 ^(sqrt(log _(3)2)))x-2 (3 ^(log _(3)2)-2^(log _(z)3))=0,then the value of alpha ^(2) + alpha betais equal to :
Answer» 3 5 7 11 Answer :C

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Find the equation of the parabola whose axis is parallel to Y-axis and which passes through the points (4,5),(-2,11) and (-4,21).

The negative of a matrix is obtained by multiplying it by …….

Let P represent the point (3, 6) on the parabola y^(2)=12 x. For the parabola y^(2)=12 x, if l_(1) is the length of the normal chord drawn at P and l_(2) is the length of the focal chord drawn through P, then l_(1)/l_(2)=

1,2,4,6,8,9 transformed into another series whose mean is 12. Two middle terms of the transformed series are

A = {(x,y) : y = 1//x,0 ne x in R} , B = {(x, y) : y = - x, x in R} then

If length of three sides of a trapezium other than base are equal to 10 cm, then find the area of the trapezium when it is maximum.

IFsin^(-1) x sin ^(-1) y =(2pi )/(3) thencos ^(-1)y=(pi)/(lamda ). Findthevalueoflamda

IF12 x^2- mxy+ 3y^2- 5y^2 -2canberesolvarbleintotwo linearfactorsthenm=

Evaluate int(1 - x) (4 - 3x) (2x + 3)dx

Let p: Kiran passed the examination q: Kiran is sad The symbolic from of a statement "it is not ture Kiran passed therefore she is sad" is

If the two lines, whose d.C.s l,m,n are given by the equation al+bm+cn=0 and fmn + gnl + hlm=0, are mutually perpendicular, then

Seven digits from the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 are written in random order. Find the probability that the seven digited number is divisible by 9.

The solution of (dy)/(dx) = ((y)/(x))^(1//3) is

If A = [(1,2,3),(3,-2,1),(4,2,1)]

Find the power of the point P with respect to the circle S = 0 when P = (5,-6), and S-= x^(2) + y^(2) + 8x + 12y + 15

If the period of the function f(x) = sin 5x cos 3x is alpha, then cos alpha=

int_(0)^(5) [x] dx=

If1 , omega , omega^(2) are the cube roots of unity , then find the values of the following . (1 - omega) ( 1 - omega ^(2)) ( 1 - omega^(4)) ( 1 - omega^(8))

An urn contains 5 black 6 red and 4 white balls.Five balls are drawn at random from the urn. Find the probability that all graduates? What is the probability of at least one graduate?

Let f (n) = sum _(r =2)^(n) (r )/(""^r C_(2) ""^(r+1) C_(2)) , a = lim _(x to oo) f (n) and x ^(2) -(2n -(1)/(2)) x +t =0 has two positive roots alpha and beta. minimum value of (4)/(alpha ) + (1)/(beta) is :

If f(x) is strictly increasing function then h(x) is non monotonic function given

If the antiderivative of (1)/(x^(2)sqrt(1+x^(2))) is -sqrt(f(x))/(x)+C then f(x) is equal to

An unbiased die of six faces, market with the integers 1,2,3,4,5,6, one on each face, is thrown thrice in succession. What is the total number of outcomes ?

For real valued functions f and g, f(x) = 2sin (pi/x) and g(x) = sqrtx. Then fog(4) - gof (6) = ..............

Find the domain and range of those relations in a which are functions. {(a,2),(b,3),(c,4)}

The sum of 100 observations and sum of their squares are 400 and 2,475 respectively . Later on three observatons 3,4 and 5 were found to be incorrect.If the incorrect observations are omitted, then variance of the remaining observations is:

There are 12 different books in a shelf. In how many ways we can select atleast one of them?

int (x^(2)-1)/((x^(2)+1)(x^(2)+2)(x^(2)+3))dx=

If a straight line passes through the points﻿ ((-1)/(2), 1)and (1, 2), then its x-intercept is﻿

The sum of the solutions in (0,2pi)for the equation cosx cos (pi/3-x)cos (pi/3+x)=1/4 is

Find the slope of the tangent to curve y=x^3-x+1 at the point whose x-coordinate is 2.

Mean and variance of random variable X are 2 and 1 respectively. Then ……….. is the probability that X takes more than one value.

Lt_(x rarr 0) ((1+x)^(n)-nx-1)/(x^(2)) n gt 1is euqal to

If f(x) = x^(3) + bx^(2) + ax satisfies the conditionsof Rolle's theorem in [1, 3] with c = 2 + (1)/sqrt(3)then (a, b) is equal to

Are fand g both necessarily onto, if gof is onto?

ABC is an isosceles triangle and B=90. If B and the midpoint P of AC are represented by 3+2i and 1-I then other vertices are

If z_(1) and z_(2) be two non zero complex numbers such that (z_(1))/(z_(2))+(z_(2))/(z_(1))=1, then the origin and the points represented by z_(1) and z_(2)

Find the sum of the infinite series 1+(1)/(3)+(1.3)/(3.6)+(1.3.5)/(3.6.9)+…..

Three vectors vec(a),vec(b)andvec(c) are of the same length and the angle between any two of them is the same. If vec(a)=hat(i)+hat(j)andvec(b)=hat(j)+hat(k)," then "vec(c) is

A, B and C are three non-zero vectors, no two of them are parallel. If A + B is collinear to C and B + C is collinear to A, then A + B + C is equal to

The substitution required to change (3y-7x+7) dx + (7y-3x+3)dy = 0 into a homogeneous equation is

The probability function of the binomial distribution is P(x)= ((6), (x))p^(x)q^(6-x), x= 0, 1, 2, ....., 6.If 2P(2) = 3P(3) then value of q is ……….

If g(x) = int_(0)^(x) cos 4(t) dt , then g(x+pi) equals

int (secx)/((sec x+ tan x)^(2))dx=

Radius of an air bubble increases at the rate of (1)/(2) cm/sec. At what rate volume at bubble increases when radius is 1 cm.

If A+B+C=180^(@) then cos A+cos B-cosC=

If alpha, beta ar the roots of the quadratic equation x ^(2) -(3+ 2 ^(sqrt(log _(2)3))-3 ^(sqrt(log _(3)2)))x-2 (3 ^(log _(3)2)-2^(log _(z)3))=0,then the value of alpha ^(2) + alpha betais equal to :

If a straight line passes through the points ((-1)/(2), 1)and (1, 2), then its x-intercept is