28278 + Interview Questions in Maths in Class 12

1.	Let R be the relation in the set N given by R={(a,b), a=b -2, b gt 6}. Choose the correct answer.
Answer» `(2,4) in R` `(3,8) in R ` `(6,8) in R` `((8,7) in R` ANSWER :B

Discussion

2.	The value of sum_(k=0)^(7) [ (({:(k),(k):}))/(({:(14),(k)):})sum_(r=k)^(14) ({:(r),(k):})({:(14),(r):})], where ({:(n),(r):}) denotes ""^(n) C_(r) , is
Answer» `6^(7)` GREATER than `7^(6)` `8^(7)` greater than `7^(8)` ANSWER :A::B

Discussion

3.	If the solution of (dy)/(dx) = (x-y)/(x+y) " is " ax^(2) + bxy + cy^(2) = k, k gt 0 then the ascending order of a, b, c is
Answer» a, B ,C b, c,a c, a,b b, a, c Answer :B

Discussion

4.	A is a set containing n elements. A subset P of A is chosen at random. The set A is reconstructed by replacing the elements of P. A subset Q of A is again chosen at random. Find the probability that P nn Q contains exactly two elements
Answer» ANSWER :`.^(n) C_(2) (3^(n-2))/(4^(n))`

Discussion

5.	One vertex of the equilateral triangle with centroid at the origin and one side as x + y - 2 = 0 is
Answer» (-1,-1) (2, 2) (-2,-2) (4, 5) Answer :C

Discussion

6.	A is a set containing n elements. A subset P of A is chosen at random. The set A is reconstructed by replacing the elements of P. A subset Q of A is again chosen at random. Find the probability that P uu Q contains exactly r elements
Answer» Answer :`.^(n) C_(R) (3^(r))/(4^(n))`

Discussion

7.	int(dx)/(sqrt(e^(2x)-1)) =……+c
Answer» `SIN^(-1)(e^x)` `SEC^(-1) (e^x)` `tan^(-1) (e^x)` `COT^(-1) (e^x)` Answer :B

Discussion

8.	A is a set containing n elements. A subset P of A is chosen at random. The set A is reconstructed by replacing the elements of P. A subset Q of A is again chosen at random. Find the probability that P uu Q = A
Answer» ANSWER :`((3)/(4))^(N)`

Discussion

9.	intdx/(9+x^2) =
Answer» `tan^-1(x/3) + C` `1/3tan^-1(x/3) + C` `1/3tan^-1x + C` `tan^-1x + C` ANSWER :B

Discussion

10.	Statewhichof the followingstatemetn is false
Answer» an unbounded solution of a linear PROGRAMMING PROBLEMIS a solution whose objective FUNCTIN is finite any linear programming problem is EITHER a problem of maiximization or a problem of minizmization a problem of maximaization of the objective function z is nothing but a problem of minimization of the function z an lpp MAY have a unboiunded solution Answer :A

Discussion

11.	Let f be a continuous function satisfying f(x) f(y)=f(x)+f(y)+f(xy)-2 for all x,y in R and f(2)=5 then lim_(x to 4) f(x) is
Answer»

Discussion

12.	A is a set containing n elements. A subset P of A is chosen at random. The set A is reconstructed by replacing the elements of P. A subset Q of A is again chosen at random. Find the probability that (i) Q is subset of P(ii) the number of elements in P is more than the number of elements in Q.
Answer» Answer :`(1)/(2) - (.^(2N) C_(n))/(2^(2n+1))`

Discussion

13.	General solution of differential equation (dy)/(dx)+ y=1 (y ne 1)
Answer» ANSWER :`y = 1 + AE^(-X)`

Discussion

14.	If equation x^2+y^2+2hxy+2gx+2fy+c=0represents a circle , then the condition for the circle to pass through three quadrants but not passing through the originis
Answer» `g^2 GT c` `t^2 gt c` c gt 0 c LT 0 ANSWER :A::B::C

Discussion

15.	In 2000, if an equal percentage of passenger cars and demand - reponse vehicles experienced mechanical problems, and the number of passenger cars that experienced such problems was 13,436, approximately how many demadn - response vehicles experienced mechanical problems?
Answer» 1352 2928 4099 7263 Answer :B

Discussion

16.	Find the area of the region enclosed by the curves y=x^(2) and y= sqrtx
Answer» ANSWER :`((1)/(3))`

Discussion

17.	Differentiate ((x-1)/(x+1))^2
Answer» SOLUTION :`y=((x-1)/(x+1))^2` `dy/dx=2((x-1)/(x+1)) cdotd/dx((x-1)/(x+1))` `2 CDOT(x-1)/(x+1)cdot(d/dx(x-1)cdot(x+1)-(x-1)cdot d/dx(x+1))/(x+1)^2` `=2(x-1)/(x+1) cdot ((x+1)-(x-1))/(x+1)^2`=(4(x-1))/(x+1)^3`

Discussion

18.	x^(2)dy+(xy + y^(2))dx = 0, y = 1 when x = 1
Answer» ANSWER :`y + 2X = 3X^(2) y`

Discussion

19.	Ifalpha, beta, gammaare therootsofx^3 +px^2 +qx +r=0then findsumalpha^2beta + sumalpha beta ^2
Answer» ANSWER :`3r-pq`

Discussion

20.	Integrate the following functions 1/ sqrt((x-1) (x-2))
Answer» Solution :`(X-1)(x-2) = x^2-3x+2` =`x^2-3x+9/4 -9/4 +2` =`(x-3/2)^2 -1/4` therefore` INT 1/sqrt((x-1)(x-2)) dx` `int 1/sqrt((x-(3/2))^2-(1/2)^2) dx` =`log\|x-3/2 + sqrt((x-(3/2))^2-(1/2)^2)\|+c` =`log\|x-3/2 + sqrt(x^2-3x+2)\|+c`

Discussion

21.	Differentiatesec^(-1) ((1)/(4x^(3)-3x)), 0 lt x lt (1)/(sqrt2)
Answer» ANSWER :`=(-3)/(SQRT(1-x^(2)))`

Discussion

22.	If f(x) = cos x, then
Answer» f(X) is strictly DECREASING in `(0, pi)` f(x) is strictly increasing in `(0, 2pi)` f(x) is neither increasing nor decreasing in `(pi, 2pi)` All the above are correct Answer :A

Discussion

23.	Which of the followingis/are correct?
Answer» If `A` is a `nxxn` matrix such that `a_(ij)=(i^(2)+j^(2)-5ij).(j-i)Aai` and `j` then trace `(A)=0` If `A` is a `nxxn` matrix such that `a_(ij)=(i^(2)+j^(2)-5ij).(j-i)Aai` and `j` then trace `(A)!=0` If `P` is a `3xx3` ORTHOGONAL matrix, `alpha, beta, gamma` are the ANGLES made by a straight line with `OX, OY, OZ` and `A=[(sin^(2)alpha, sinalpha.sinbeta, sinalpha.singamma), (sinalpha.sinbeta, sin^(2)beta, sinbeta.singamma), (sinalpha.singamma, sinbeta.singamma, sin^(2)gamma)]` and `Q=P^(T)AP`, then `PQ^(6)P^(T)=32A` If matrix `A=[a_(ij)]_(3xx3)` and matrix `B=[b_(ij)]_(3xx3)` where `a_(ij)+a_(ji)=0` and `b_(ij)-b_(ji)=0 AA i` and `j` then `A^(6)B^(7)` is a singular matrix Solution :(A) `a_(ij)=-a_(ji)impliesa_(ij)+a_(ji)=0impliesA` is skew symmetric matrix (C) `A^(2)=2AimpliesA^(3)=2^(2)impliesA^(6)=2^(5)A` (D) `A^(6)B^(7)` is a skew symmetric matrix of odd order

Discussion

24.	The statement pto(q to p) is equivalent to
Answer» `qtop` `~qvv~p` `p^^~q` `~qtop` ANSWER :B

Discussion

25.	D(f+g)=
Answer» `RR -[-2,0)` `RR-[-1,0)` `[-2,(1)/(2)]` none of these ANSWER :B

Discussion

26.	Integrate the function 1/(sqrt((x-a)(x-b)))
Answer» ANSWER :`logabs(X-(a+b)/2+sqrt((x-a)(x-b)))+C`

Discussion

27.	the value of int(dx)/(x^2-a^2) is:
Answer» `Logabs(x^2 - a^2) + c` `1/(2A) Logabs((x-a)-(x+a))+c` `2X/(x^2-a^2)^3` `Logabs((x-a)/(x+a)) + c` Answer :B

Discussion

28.	[x sin^(2)((y)/(x)) - y] dx + x dy = 0, y = (pi)/(4) when x = 1
Answer» ANSWER :`COT((y)/(X)) = LOG \|EX\|`

Discussion

29.	Given that (1-x) (1+x+x^(2) +x^(3) +x^(4)) = 31/32 and x is a rational number. Then 1+x+x^(2) + x^(3) + x^(4)+ x^(5) is:
Answer» ANSWER :`63/32`

Discussion

30.	If, \|z+4\| le 3, then the maximum value of \|z+1\| is
Answer» `5` `4` `6` `3` ANSWER :C

Discussion

31.	int(x^(3)+4x-3)/(x^(2)+4)dx=Ax^(2)+B "tan"^(-1)(x)/(2)+c then A+B=... where A, B in R
Answer» `-(1)/(2)` `-1` 2 `(1)/(2)` ANSWER :B

Discussion

32.	Which of the given values of x and y make the following pair of matrices equal [{:(3x+7,5),(y+1,2-3x):}],[{:(0,y-2),(8,4):}].
Answer» `x=-(1)/(3),y=7` Not POSSIBLE to FIND `y=7,x=-(2)/(3)` `x=-(1)/(3),y=-(2)/(3)` Answer :B

Discussion

33.	intdx/sqrt(x^2-6x+5)
Answer» SOLUTION :`INTDX/sqrt(x^2-6x+5)=intdx/((x-3)^2-2^2)` =`In[x-3+sqrt(x^2-6x+5)]+C` `[becauseintdx/sqrt(x^2-a^2)=In(x+sqrt(x^2-a^2))]`

Discussion

34.	Let the point P pepresent z = x + iy , x , y in Rin the argand plane . Let thecurvesC_(1) and C_(2)be the loci of Psatisfying the conditions(i)(2z+i)/(z - 2)is purely imaginary and(ii) Arg ((z+i)/(z+1)) = (pi)/(2)respectively .Then the point of intersection of the curves C_(1) andC_(2), other thanthe origin, is
Answer» (1,2) `((2)/(7),-(5)/(7))` `(-3,4)` `((5)/(37),-(30)/(37))` ANSWER :D

Discussion

35.	Let (alpha,beta) be the focus of x^(2) + 2xy +1 -y^(2) then 12beta + 4alpha is equal to
Answer» <P> Solution :LET parabola be `(X+y-k)^(2)=LAMBDA(y-x+p)` comparing the above EQUATION with parabola`x^(2)+2xy=2x+1-y^(2)`, we get lambda, k and p`

Discussion

36.	A Bohr hydrogen atom undergoes a transition n=5rarrn=4 and emits a photon of frequency v. Frequency of circular motion of electron in n = 4 orbit is V_(4). Find the ratio v//v_(4).(54)/(25N), where N is an integer find N
Answer» Solution :`0003` `E_(n)=-(MZ^(2)e^(4))/(8 epsilon_(0)^(2)n^(2)h^(2))` so , `hv=+(mz^(2)e^(4))/(8 epsilon_(0)^(2)h^(2))[(1)/(16)-(1)/(25)]` `:. V=(mz^(2)e^(4))/(8 epsilon_(0)^(2)h^(3))[(9)/(16xx25)] " " ...(1)` and frequency `v_(4)=(1)/(T)=(v)/(2pir)=((ZE^(2))/(2 epsilon_(0)nh))(1)/(2pi)((pi m z e^(2))/(epsilon_(0)h^(2)n^(2)))=(z^(2)e^(4)m)/(4 epsilon_(0)^(2)n^(3)h^(3)) "" ....(2)` `:. v//v_(4)=18//25`

Discussion

37.	India plays two hockey matches each with Pakistan and England. In any match, the probabilities of India getting points 0,1,2 are 0.4,0.1,0.5 respectively. Assuming that the outcomes are independent the probability of India getting 7 points is
Answer» `0.0125` `0.05` `0.250` `0.005` ANSWER :B

Discussion

38.	Choose the correct answer: If P(A\|B) gt P(A), then which of the following is correct :
Answer» <P>`P(B\|A) lt P(B)` `P(A cap B) lt P(A).P(B)` `P(B\|A) GT P(B)` P(B\|A)=P(B) ANSWER :C

Discussion

39.	For x to 0 determine the order of smallness, relative to the infinitesimal beta(x)=x, of the following infinitesimals (a) sqrt(sin^(2) x+x^(4)) (b) (x^(2)(1+x))/(1+root3(x))
Answer» ANSWER :`(a) 1; (B) 2`

Discussion

40.	If two events A and B are such that P(A')= 0.3, P(B)=0.5 and P(A cap B) = 0.3, then P(B \| A cup B')is …………
Answer» 0.375 0.32 0.31 0.28 Answer :A

Discussion

41.	If P(A)= 0.4, P(B)= 0.8 and P(B//A)= 0.6 then P(A cup B) is equal to ……..
Answer» 0.24 0.3 0.48 0.96 Answer :D

Discussion

42.	If alpha+ beta + gamma = 1, alpha^(2) + beta^(2) + gamma^(2) = 2and alpha^(3) + beta^(3) + gamma^(3) = 3,then alpha^(5) + beta^(5) + gamma^(5) =
Answer» 6 18 36 45 Answer :1

Discussion

43.	(1 +x)^15 = a_0 + a_1x +…..+a_15 x^15 rArr sum_(r = 1)^15 r (a_r)/(a_(r - 1)) =
Answer» 110 115 120 135 Answer :C

Discussion

44.	If f(x)=overset(x)underset(0)t sin t dt, then f(x)=.....
Answer» `COS X+x SINX` `x sin x` `x cos x` `sinx x+x cos x` Answer :B

Discussion

45.	Let O be the origin and A be the point (64,0). If P, Q divide OA in the ratio 1:2:3, then the point P is
Answer» `((32)/(3), 0)` (32, 0) `((64)/(3), 0)` `(16, 0)` ANSWER :A

Discussion

46.	cosh (2i theta) =
Answer» `I sin 2 THETA` `(0, 1)` `[1, OO)` `(1, oo)` Answer :B

Discussion

47.	For each of thefollowing graphs, comment whether f(x) is increasing or decreasing or neither increasing nor decreasing at x = a. (##CEN_GRA_C01_S01_018_Q01.png" width="80%">
Answer» SOLUTION :(i) Neither monotonically increasing nor monotonically decreasing as `f(a- H) ltf(a) and f(a+h) LT f(a)` (ii) Monotonically decreasing as ` f(a-h) gt f(a) gt f(a+h)` (III) Monotonically increasing as ` f(a-h) lt f(a) lt f(a+h)` (iv) Neithermonotonically increasing nor monotonically decreasing as ` f(a-h) lt f (a)" but " f(a+h) = f(a)`

Discussion

48.	If [[2,3],[4,5]]=[[x,3],[2x,5]], then x =
Answer» 3 4 2 None of these Answer :C

Discussion

49.	Let functions are defined from set A to set B where B={alpha,beta} and alpha & beta are the roots of the equation t^(2)-sqrt(2)t-pi=0 then the number of functions which are
Answer» discontinuous only at each EVEN INEGERS if `A=[0,11]` is 682 discontinuous only at each ODD integer if `A=[0,11]` is 243 discontinous only at PRIME numbers if `A=[0,11]` is 81 discontinuous only at `x=5k(kepsilon I^(+))` if `A=0,11]` is 27 Solution :(A) `2C_(1)(2xx2-1)^(5)` (B) `(2xx2-1)^(5)xx1` (C) `(2xx2-1)^(4)xx1` (D) `(2xx2-1)^(2)=9`

Discussion

50.	Find all real numbers V which there is atleast one triplet (x, y,z) of nonzero real numbers such that x^(2)y + y^(2)z +z^(2)x = xy^(2) + yz^(2) + zx^(2)=rxyz
Answer» ANSWER :`R in (-INFTY,-) CUP [3, infty)`

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Let R be the relation in the set N given by R={(a,b), a=b -2, b gt 6}. Choose the correct answer.

The value of sum_(k=0)^(7) [ (({:(k),(k):}))/(({:(14),(k)):})sum_(r=k)^(14) ({:(r),(k):})({:(14),(r):})], where ({:(n),(r):}) denotes ""^(n) C_(r) , is

If the solution of (dy)/(dx) = (x-y)/(x+y) " is " ax^(2) + bxy + cy^(2) = k, k gt 0 then the ascending order of a, b, c is

A is a set containing n elements. A subset P of A is chosen at random. The set A is reconstructed by replacing the elements of P. A subset Q of A is again chosen at random. Find the probability that P nn Q contains exactly two elements

One vertex of the equilateral triangle with﻿ centroid at the origin and one side as x + y - 2 = 0 is﻿

A is a set containing n elements. A subset P of A is chosen at random. The set A is reconstructed by replacing the elements of P. A subset Q of A is again chosen at random. Find the probability that P uu Q contains exactly r elements

int(dx)/(sqrt(e^(2x)-1)) =……+c

A is a set containing n elements. A subset P of A is chosen at random. The set A is reconstructed by replacing the elements of P. A subset Q of A is again chosen at random. Find the probability that P uu Q = A

intdx/(9+x^2) =

Statewhichof the followingstatemetn is false

Let f be a continuous function satisfying f(x) f(y)=f(x)+f(y)+f(xy)-2 for all x,y in R and f(2)=5 then lim_(x to 4) f(x) is

A is a set containing n elements. A subset P of A is chosen at random. The set A is reconstructed by replacing the elements of P. A subset Q of A is again chosen at random. Find the probability that (i) Q is subset of P(ii) the number of elements in P is more than the number of elements in Q.

General solution of differential equation (dy)/(dx)+ y=1 (y ne 1)

If equation x^2+y^2+2hxy+2gx+2fy+c=0represents a circle , then the condition for the circle to pass through three quadrants but not passing through the originis

In 2000, if an equal percentage of passenger cars and demand - reponse vehicles experienced mechanical problems, and the number of passenger cars that experienced such problems was 13,436, approximately how many demadn - response vehicles experienced mechanical problems?

Find the area of the region enclosed by the curves y=x^(2) and y= sqrtx

Differentiate ((x-1)/(x+1))^2

x^(2)dy+(xy + y^(2))dx = 0, y = 1 when x = 1

Ifalpha, beta, gammaare therootsofx^3 +px^2 +qx +r=0then findsumalpha^2beta + sumalpha beta ^2

Integrate the following functions 1/ sqrt((x-1) (x-2))

Differentiatesec^(-1) ((1)/(4x^(3)-3x)), 0 lt x lt (1)/(sqrt2)

If f(x) = cos x, then

Which of the followingis/are correct?

The statement pto(q to p) is equivalent to

D(f+g)=

Integrate the function 1/(sqrt((x-a)(x-b)))

the value of int(dx)/(x^2-a^2) is:

[x sin^(2)((y)/(x)) - y] dx + x dy = 0, y = (pi)/(4) when x = 1

Given that (1-x) (1+x+x^(2) +x^(3) +x^(4)) = 31/32 and x is a rational number. Then 1+x+x^(2) + x^(3) + x^(4)+ x^(5) is:

If, |z+4| le 3, then the maximum value of |z+1| is

int(x^(3)+4x-3)/(x^(2)+4)dx=Ax^(2)+B "tan"^(-1)(x)/(2)+c then A+B=... where A, B in R

Which of the given values of x and y make the following pair of matrices equal [{:(3x+7,5),(y+1,2-3x):}],[{:(0,y-2),(8,4):}].

intdx/sqrt(x^2-6x+5)

Let (alpha,beta) be the focus of x^(2) + 2xy +1 -y^(2) then 12beta + 4alpha is equal to

A Bohr hydrogen atom undergoes a transition n=5rarrn=4 and emits a photon of frequency v. Frequency of circular motion of electron in n = 4 orbit is V_(4). Find the ratio v//v_(4).(54)/(25N), where N is an integer find N

India plays two hockey matches each with Pakistan and England. In any match, the probabilities of India getting points 0,1,2 are 0.4,0.1,0.5 respectively. Assuming that the outcomes are independent the probability of India getting 7 points is

Choose the correct answer: If P(A|B) gt P(A), then which of the following is correct :

For x to 0 determine the order of smallness, relative to the infinitesimal beta(x)=x, of the following infinitesimals (a) sqrt(sin^(2) x+x^(4)) (b) (x^(2)(1+x))/(1+root3(x))

If two events A and B are such that P(A')= 0.3, P(B)=0.5 and P(A cap B) = 0.3, then P(B | A cup B')is …………

If P(A)= 0.4, P(B)= 0.8 and P(B//A)= 0.6 then P(A cup B) is equal to ……..

If alpha+ beta + gamma = 1, alpha^(2) + beta^(2) + gamma^(2) = 2and alpha^(3) + beta^(3) + gamma^(3) = 3,then alpha^(5) + beta^(5) + gamma^(5) =

(1 +x)^15 = a_0 + a_1x +…..+a_15 x^15 rArr sum_(r = 1)^15 r (a_r)/(a_(r - 1)) =

If f(x)=overset(x)underset(0)t sin t dt, then f(x)=.....

Let O be the origin and A be the point﻿ (64,0). If P, Q divide OA in the ratio 1:2:3,﻿ then the point P is

cosh (2i theta) =

For each of thefollowing graphs, comment whether f(x) is increasing or decreasing or neither increasing nor decreasing at x = a. (##CEN_GRA_C01_S01_018_Q01.png" width="80%">

If [[2,3],[4,5]]=[[x,3],[2x,5]], then x =

Let functions are defined from set A to set B where B={alpha,beta} and alpha & beta are the roots of the equation t^(2)-sqrt(2)t-pi=0 then the number of functions which are

Find all real numbers V which there is atleast one triplet (x, y,z) of nonzero real numbers such that x^(2)y + y^(2)z +z^(2)x = xy^(2) + yz^(2) + zx^(2)=rxyz

One vertex of the equilateral triangle with centroid at the origin and one side as x + y - 2 = 0 is

Let O be the origin and A be the point (64,0). If P, Q divide OA in the ratio 1:2:3, then the point P is