43030 + Interview Questions in Mathematics

1.	If xy−yx=ab, find dydx.
Answer» $If x^{y} - y^{x} = a^{b},$ find $\frac{d y}{d x} .$

Discussion

2.	Maximise Z=2x+ySubject to constraints:x+3y
Answer» Maximise Z=2x+y Subject to constraints: x+3y<=15 3x-4y<=12 x,y>=0

Discussion

3.	If n(A) = 20, n(B) = 10, and if a ≤ n(A △ B) ≤ b where a, b ∈ I +, then a + b is equal to
Answer» If n(A) = 20, n(B) = 10, and if a ≤ n(A △ B) ≤ b where a, b ∈ I +, then a + b is equal to

Discussion

4.	The sum of first n terms of two APs are in the ratio (3n + 8) : (7n + 15). Find the ratio of their 12th terms.
Answer» The sum of first n terms of two APs are in the ratio (3n + 8) : (7n + 15). Find the ratio of their 12th terms.

Discussion

5.	41. The area bounded by the circles x-square+y-square=1 and x-square+y-square=2, and the pair of lines 2x-square-3xy-2y-square=0 (y>0), is
Answer» 41. The area bounded by the circles x-square+y-square=1 and x-square+y-square=2, and the pair of lines 2x-square-3xy-2y-square=0 (y>0), is

Discussion

6.	If z1,z2,z3 are any three roots of the equation z6=(z+1)6, then arg(z1−z3z2−z3) can be equal to
Answer» If $z_{1}, z_{2}, z_{3}$ are any three roots of the equation $z^{6} = (z + 1)^{6},$ then $arg (\frac{z_{1} - z_{3}}{z_{2} - z_{3}})$ can be equal to

Discussion

7.	In a single-channel queueing model, the customer arrival rate is 12 per hour and the serving rate is 24 per hour. The expected time that a customer is in queue is ____ minutes.2.5
Answer» In a single-channel queueing model, the customer arrival rate is 12 per hour and the serving rate is 24 per hour. The expected time that a customer is in queue is ____ minutes. 2.5

Discussion

8.	The set of real values of x, for which h(x)=1+2x2+4x4+6x6+⋯+100x100 is concave downward is
Answer» The set of real values of $x$ , for which $h (x) = 1 + 2 x^{2} + 4 x^{4} + 6 x^{6} + \dots + 100 x^{100}$ is concave downward is

Discussion

9.	The magnitude of the position vector of the point (3, 4) will be ___
Answer» The magnitude of the position vector of the point (3, 4) will be ___

Discussion

10.	The probability that randomly selected positive integer is relatively prime to 6
Answer» The probability that randomly selected positive integer is relatively prime to 6

Discussion

11.	Integrate eaxsinbx with respect to x.
Answer» Integrate $e^{a x} sin b x$ with respect to $x$ .

Discussion

12.	Let there are 10 cards of numbered 1 to 10, one card is selected at random. Consider the following events:A: The number on selected card is divisible by 2B: The number on selected card is odd.If S is the sample space, then which of the following is/are correct ?
Answer» Let there are $10$ cards of numbered $1$ to $10,$ one card is selected at random. Consider the following events: $A :$ The number on selected card is divisible by $2$ $B :$ The number on selected card is odd. If $S$ is the sample space, then which of the following is/are correct ?

Discussion

13.	1x+y,12y,1y+zareinA.P.. Prove that x, y, z are the consecutive terms of G.P, then we have to prove that y2=xz
Answer» $\frac{1}{x + y}, \frac{1}{2 y}, \frac{1}{y + z} a r e i n A . P .$ . Prove that x, y, z are the consecutive terms of G.P, then we have to prove that $y^{2} = x z$

Discussion

14.	Let O be the centre of the circle x2+y2=r2, where r>√52. Suppose PQ is a chord of this circle and the equation of the line passing through P and Q is 2x+4y=5. If the centre of the circumcircle of the triangle OPQ lies on the line x+2y=4, then the value of r is
Answer» Let $O$ be the centre of the circle $x^{2} + y^{2} = r^{2},$ where $r > \frac{\sqrt{5}}{2} .$ Suppose $P Q$ is a chord of this circle and the equation of the line passing through $P$ and $Q$ is $2 x + 4 y = 5.$ If the centre of the circumcircle of the triangle $O P Q$ lies on the line $x + 2 y = 4,$ then the value of $r$ is

Discussion

15.	The angle between the curves x2=8y and y2=8x at (8, 8) is
Answer» The angle between the curves $x^{2} = 8 y$ and $y^{2} = 8 x$ at $(8, 8)$ is

Discussion

16.	Find the solution of sin x=−√32
Answer» Find the solution of $sin x = - \frac{\sqrt{3}}{2}$

Discussion

17.	The order of a differential equation representing a family of curves is same as:
Answer» The order of a differential equation representing a family of curves is same as:

Discussion

18.	Prove that the Greatest Integer Function f: R → R given by f(x) = [x], is neither one-once nor onto, where [x] denotes the greatest integer less than or equal to x.
Answer» Prove that the Greatest Integer Function f: R → R given by f(x) = [x], is neither one-once nor onto, where [x] denotes the greatest integer less than or equal to x.

Discussion

19.	Show that each of the relation R in the set A={x∈Z:0≤x≤12}, given by (ii) R = {(a, b) : a = b} is an equivalence relation. Find the set of all elements related to 1 in each case.
Answer» Show that each of the relation R in the set $A = {x \in Z : 0 \leq x \leq 12}$ , given by (ii) R = {(a, b) : a = b} is an equivalence relation. Find the set of all elements related to 1 in each case.

Discussion

20.	If the tangents are drawn to the circle x2+y2=12 at the point where it meets the circle x2+y2−5x+3y−2=0, then the point of intersection of these tangents is
Answer» If the tangents are drawn to the circle $x^{2} + y^{2} = 12$ at the point where it meets the circle $x^{2} + y^{2} - 5 x + 3 y - 2 = 0$ , then the point of intersection of these tangents is

Discussion

21.	The planes 3x-6y-2z=7 and 2x+y-λz=5 are perpendicular. Then the value of λ is __________.
Answer» The planes $3 x - 6 y - 2 z = 7 and 2 x + y - λ z = 5$ are perpendicular. Then the value of $λ$ is __________.

Discussion

22.	Let 2(1+x3)100=100∑i=0{aixi−cos(π2(x+i))}. If 50∑i=0a2i=2k, then the value of k is
Answer» Let $2 {(1 + x^{3})}^{100} = 100 \sum i = 0 {a_{i} x^{i} - cos (\frac{π}{2} (x + i))} .$ If $50 \sum i = 0 a_{2 i} = 2^{k},$ then the value of $k$ is

Discussion

23.	Prove that- sin 5x - 2 sin 3x + sin x/ cos 5x - cos x = tan x
Answer» Prove that- sin 5x - 2 sin 3x + sin x/ cos 5x - cos x = tan x

Discussion

24.	400th root of 20²⁰^20
Answer» 400th root of 20²⁰^20

Discussion

25.	∫sin2x√9−sin4xdx is equal to
Answer» $\int \frac{sin 2 x}{\sqrt{9 - {sin}^{4} x}} d x$ is equal to

Discussion

26.	4. 3(7 i7) (7+ i7)
Answer» 4. 3(7 i7) (7+ i7)

Discussion

27.	3. Find the equation of a line on which length of perpendicular from the origin is 5 units, also the perpersdicular makes angle 30 with the positive direction of x-asis. an
Answer» 3. Find the equation of a line on which length of perpendicular from the origin is 5 units, also the perpersdicular makes angle 30 with the positive direction of x-asis. an

Discussion

28.	If a variable takes the discrete values α+4,α−72,α−52,α−3,α−2α+12,α−12,α+5(α>0),then the median is
Answer» If a variable takes the discrete values $α + 4, α - \frac{7}{2}, α - \frac{5}{2}, α - 3, α - 2 α + \frac{1}{2}, α - \frac{1}{2}, α + 5 (α > 0),$ then the median is

Discussion

29.	f((x+y)/2) =( f(x)+f(y)) /2 for every x, y belongs to R. f(0)=1, f'(0)=-1 find f(x).
Answer» f((x+y)/2) =( f(x)+f(y)) /2 for every x, y belongs to R. f(0)=1, f'(0)=-1 find f(x).

Discussion

30.	∫3sin x-2cos x13-cos2 x-7sin xdx
Answer» $\int \frac{(3 \sin x - 2) \cos x}{13 - \cos^{2} x - 7 \sin x} d x$

Discussion

31.	Quadratic equation x2+(a−1)ix+5=0 (a∈R) will have a pair of conjugate complex roots, if
Answer» Quadratic equation $x^{2} + (a - 1) i x + 5 = 0 (a \in R)$ will have a pair of conjugate complex roots, if

Discussion

32.	For the function y = f(x) the formal definition of derivative is f′(x)=limΔx→0f(X+ΔX)−f(X).
Answer» For the function y = f(x) the formal definition of derivative is $f^{'} (x) = {lim}_{Δ x \to 0} f (X + Δ X) - f (X) .$

Discussion

33.	When 10 is subtracted from all the observations, the mean is reduced to 60% of its value. If 5 is added to all the observations, then the mean will be
Answer» When $10$ is subtracted from all the observations, the mean is reduced to $60 %$ of its value. If $5$ is added to all the observations, then the mean will be

Discussion

34.	The real value of λ for which the system of equations λx + y + z = 0, -x + λy + z = 0, - x - y + λz = 0 has a non-zero solution, is _____________.
Answer» The real value of λ for which the system of equations λx + y + z = 0, -x + λy + z = 0, - x - y + λz = 0 has a non-zero solution, is _____________.

Discussion

35.	If 1ab′+1ba′ = 0, then lines xb′+ya′ and xa+yb = 1 are ___________________
Answer» If $\frac{1}{a b^{'}} + \frac{1}{b a^{'}}$ = 0, then lines $\frac{x}{b^{'}} + \frac{y}{a^{'}}$ and $\frac{x}{a} + \frac{y}{b}$ = 1 are ___________________

Discussion

36.	1. sin 2x
Answer» 1. sin 2x

Discussion

37.	Mean of numbers 50C01, 50C23, 50C45,⋯, 50C5051 is
Answer» Mean of numbers $\frac{^{50} C_{0}}{1}, \frac{^{50} C_{2}}{3}, \frac{^{50} C_{4}}{5}, \dots, \frac{^{50} C_{50}}{51}$ is

Discussion

38.	The point(s) on Y-axis which is/are at a distance of 4 units from the line x3+y4=1 will be
Answer» The point(s) on Y-axis which is/are at a distance of 4 units from the line $\frac{x}{3} + \frac{y}{4} = 1$ will be

Discussion

39.	A train consists of n carriages and there are P passengers. Each one of the P passengers randomly selects the carriage in which he will ride. On the basis of above information, answer nC11p−nC22p+nC33p....+(−1)n−1 nCnnp is equal to,
Answer» A train consists of n carriages and there are P passengers. Each one of the P passengers randomly selects the carriage in which he will ride. On the basis of above information, answer $^{n} C_{1} 1^{p} -^{n} C_{2} 2^{p} +^{n} C_{3} 3^{p} . . . . + (- 1)^{n - 1 n} C_{n} n^{p}$ is equal to,

39.

A train consists of n carriages and there are P passengers. Each one of the P passengers randomly selects the carriage in which he will ride. On the basis of above information, answer nC11p−nC22p+nC33p....+(−1)n−1 nCnnp is equal to,

Answer»

A train consists of n carriages and there are P passengers. Each one of the P passengers randomly selects the carriage in which he will ride. On the basis of above information, answer

$^{n} C_{1} 1^{p} -^{n} C_{2} 2^{p} +^{n} C_{3} 3^{p} . . . . + (- 1)^{n - 1 n} C_{n} n^{p}$ is equal to,

Discussion

40.	The integral ∫sec23x cosec43x dx is equal to
Answer» The integral $\int {sec}^{\frac{2}{3}} x c o s e c^{\frac{4}{3}} x d x$ is equal to

Discussion

41.	If X and Y are two sets such that n(X)=20,n(Y)=25andn(XUY)=40, thenn(X−Y)=
Answer» If $X$ and $Y$ are two sets such that $n (X) = 20, n (Y) = 25 and n (X U Y) = 40$ , $t h e n n (X - Y) =$

Discussion

42.	The value of ∫∣∣x2+2∣∣dx is
Answer» The value of $\int ∣ ∣ x^{2} + 2 ∣ ∣ d x$ is

Discussion

43.	Find the projection of the vector ^i−^j on the vector ^i+^j
Answer» Find the projection of the vector $^i -^j$ on the vector $^i +^j$

Discussion

44.	14. ABC is a variable triangle such that A is (1,2), and B and c lies on the line y=x+ (so is a variable).Then the locus of the orthocentre of triangle ABC is
Answer» 14. ABC is a variable triangle such that A is (1,2), and B and c lies on the line y=x+ (so is a variable).Then the locus of the orthocentre of triangle ABC is

Discussion

45.	Verify Rolle's theorem for the function y=x2+2,a=−2 and b=2.
Answer» Verify Rolle's theorem for the function $y = x^{2} + 2, a = - 2$ and $b = 2$ .

Discussion

46.	If A and B are independent events, then PA∪B=1-x where x = _______________.
Answer» If A and $B$ are independent events, then $P (A \cup B) = 1 - x$ where x = _______________.

Discussion

47.	The values of λ and μ such that the system of equations x+y+z=6, 3x+5y+5z=26, x+2y+λz=μ has no solution, are:
Answer» The values of $λ$ and $μ$ such that the system of equations $x + y + z = 6, 3 x + 5 y + 5 z = 26, x + 2 y + λ z = μ$ has no solution, are:

Discussion

48.	Question 4 (iv)Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.(iv) -10, - 6, - 2, 2 …
Answer» Question 4 (iv) Which of the following are APs? If they form an A.P. find the common difference d and write three more terms. (iv) -10, - 6, - 2, 2 …

Discussion

49.	1.If xyz +xy +xz+ yz+ x +y z =384,where x, y, z are positive integers, then the value of x +y+ z is
Answer» 1.If xyz +xy +xz+ yz+ x +y z =384,where x, y, z are positive integers, then the value of x +y+ z is

Discussion

50.	If , for some prove that is a constant independent of a and b .
Answer» If , for some prove that is a constant independent of a and b .

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

If xy−yx=ab, find dydx.

Maximise Z=2x+ySubject to constraints:x+3y

If n(A) = 20, n(B) = 10, and if a ≤ n(A △ B) ≤ b where a, b ∈ I +, then a + b is equal to

The sum of first n terms of two APs are in the ratio (3n + 8) : (7n + 15). Find the ratio of their 12th terms.

41. The area bounded by the circles x-square+y-square=1 and x-square+y-square=2, and the pair of lines 2x-square-3xy-2y-square=0 (y>0), is

If z1,z2,z3 are any three roots of the equation z6=(z+1)6, then arg(z1−z3z2−z3) can be equal to

In a single-channel queueing model, the customer arrival rate is 12 per hour and the serving rate is 24 per hour. The expected time that a customer is in queue is ____ minutes.2.5

The set of real values of x, for which h(x)=1+2x2+4x4+6x6+⋯+100x100 is concave downward is

The magnitude of the position vector of the point (3, 4) will be ___

The probability that randomly selected positive integer is relatively prime to 6

Integrate eaxsinbx with respect to x.

Let there are 10 cards of numbered 1 to 10, one card is selected at random. Consider the following events:A: The number on selected card is divisible by 2B: The number on selected card is odd.If S is the sample space, then which of the following is/are correct ?

1x+y,12y,1y+zareinA.P.. Prove that x, y, z are the consecutive terms of G.P, then we have to prove that y2=xz

Let O be the centre of the circle x2+y2=r2, where r&gt;√52. Suppose PQ is a chord of this circle and the equation of the line passing through P and Q is 2x+4y=5. If the centre of the circumcircle of the triangle OPQ lies on the line x+2y=4, then the value of r is

The angle between the curves x2=8y and y2=8x at (8, 8) is

Find the solution of sin x=−√32

The order of a differential equation representing a family of curves is same as:

Prove that the Greatest Integer Function f: R → R given by f(x) = [x], is neither one-once nor onto, where [x] denotes the greatest integer less than or equal to x.

Show that each of the relation R in the set A={x∈Z:0≤x≤12}, given by (ii) R = {(a, b) : a = b} is an equivalence relation. Find the set of all elements related to 1 in each case.

If the tangents are drawn to the circle x2+y2=12 at the point where it meets the circle x2+y2−5x+3y−2=0, then the point of intersection of these tangents is

The planes 3x-6y-2z=7 and 2x+y-λz=5 are perpendicular. Then the value of λ is __________.

Let 2(1+x3)100=100∑i=0{aixi−cos(π2(x+i))}. If 50∑i=0a2i=2k, then the value of k is

Prove that- sin 5x - 2 sin 3x + sin x/ cos 5x - cos x = tan x

400th root of 20²⁰^20

∫sin2x√9−sin4xdx is equal to

4. 3(7 i7) (7+ i7)

3. Find the equation of a line on which length of perpendicular from the origin is 5 units, also the perpersdicular makes angle 30 with the positive direction of x-asis. an

If a variable takes the discrete values α+4,α−72,α−52,α−3,α−2α+12,α−12,α+5(α&gt;0),then the median is

f((x+y)/2) =( f(x)+f(y)) /2 for every x, y belongs to R. f(0)=1, f'(0)=-1 find f(x).

∫3sin x-2cos x13-cos2 x-7sin xdx

Quadratic equation x2+(a−1)ix+5=0 (a∈R) will have a pair of conjugate complex roots, if

For the function y = f(x) the formal definition of derivative is f′(x)=limΔx→0f(X+ΔX)−f(X).

When 10 is subtracted from all the observations, the mean is reduced to 60% of its value. If 5 is added to all the observations, then the mean will be

The real value of λ for which the system of equations λx + y + z = 0, -x + λy + z = 0, - x - y + λz = 0 has a non-zero solution, is _____________.

If 1ab′+1ba′ = 0, then lines xb′+ya′ and xa+yb = 1 are ___________________

1. sin 2x

Mean of numbers 50C01, 50C23, 50C45,⋯, 50C5051 is

The point(s) on Y-axis which is/are at a distance of 4 units from the line x3+y4=1 will be

A train consists of n carriages and there are P passengers. Each one of the P passengers randomly selects the carriage in which he will ride. On the basis of above information, answer nC11p−nC22p+nC33p....+(−1)n−1 nCnnp is equal to,

The integral ∫sec23x cosec43x dx is equal to

If X and Y are two sets such that n(X)=20,n(Y)=25andn(XUY)=40, thenn(X−Y)=

The value of ∫∣∣x2+2∣∣dx is

Find the projection of the vector ^i−^j on the vector ^i+^j

14. ABC is a variable triangle such that A is (1,2), and B and c lies on the line y=x+ (so is a variable).Then the locus of the orthocentre of triangle ABC is

Verify Rolle's theorem for the function y=x2+2,a=−2 and b=2.

If A and B are independent events, then PA∪B=1-x where x = _______________.

The values of λ and μ such that the system of equations x+y+z=6, 3x+5y+5z=26, x+2y+λz=μ has no solution, are:

Question 4 (iv)Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.(iv) -10, - 6, - 2, 2 …

1.If xyz +xy +xz+ yz+ x +y z =384,where x, y, z are positive integers, then the value of x +y+ z is

If , for some prove that is a constant independent of a and b .

Let O be the centre of the circle x2+y2=r2, where r>√52. Suppose PQ is a chord of this circle and the equation of the line passing through P and Q is 2x+4y=5. If the centre of the circumcircle of the triangle OPQ lies on the line x+2y=4, then the value of r is

If a variable takes the discrete values α+4,α−72,α−52,α−3,α−2α+12,α−12,α+5(α>0),then the median is