43030 + Interview Questions in Mathematics

1.	Find the solution of dydx=2y−x
Answer» Find the solution of $\frac{d y}{d x} = 2^{y - x}$

Discussion

2.	The sum of all values of x in [0,2π], for which sinx+sin2x+sin3x+sin4x=0, is equal to
Answer» The sum of all values of $x$ in $[0, 2 π]$ , for which $sin x + sin 2 x + sin 3 x + sin 4 x = 0$ , is equal to

Discussion

3.	The Cartesian equation of a line is . Write its vector form.
Answer» The Cartesian equation of a line is . Write its vector form.

Discussion

4.	Let P be (5,3) and a point R on y=x and Q on the X - axis be such PQ+QR+RP is minimum. Then the coordinates of Q are
Answer» Let $P$ be $(5, 3)$ and a point $R$ on $y = x$ and $Q$ on the $X$ - axis be such $P Q + Q R + R P$ is minimum. Then the coordinates of $Q$ are

Discussion

5.	if alpha, beta, gamma are thevroots of x^3+8=0 then the equation whose root are aplha^2, beta^2, gamma^2
Answer» if alpha, beta, gamma are thevroots of x^3+8=0 then the equation whose root are aplha^2, beta^2, gamma^2

Discussion

6.	The angles of a quadrilateral are in A.P. and the greatest angle is 120∘. Express the angles in radians.
Answer» The angles of a quadrilateral are in A.P. and the greatest angle is $120^{\circ}$ . Express the angles in radians.

6.

The angles of a quadrilateral are in A.P. and the greatest angle is 120∘. Express the angles in radians.

Answer»

The angles of a quadrilateral are in A.P. and the greatest angle is

$120^{\circ}$ . Express the angles in radians.

Discussion

7.	Let ∗ be a binary operation on the set Q of rational number as follows: (i) a∗b=a+ab Find which of the binary operation are commutative and which are associative?
Answer» Let $$ be a binary operation on the set Q of rational number as follows: $(i) a b = a + a b$ Find which of the binary operation are commutative and which are associative?

Discussion

8.	The range of t such that 2sint=1−2x+5x23x2−2x−1 has a solution, where t∈[−π2,π2]is
Answer» The range of $t$ such that $2 sin t = \frac{1 - 2 x + 5 x^{2}}{3 x^{2} - 2 x - 1}$ has a solution, where $t \in [- \frac{π}{2}, \frac{π}{2}]$ is

Discussion

9.	Find the particular solution of the differential equation(1 – y2) (1 + log x) dx + 2xy dy = 0, given that y = 0 when x = 1.
Answer» Find the particular solution of the differential equation (1 – y²) (1 + log x) dx + 2xy dy = 0, given that y = 0 when x = 1.

Discussion

10.	If a2−aC2=a2−aC4 , then a is:
Answer» If $^{a^{2} - a} C_{2} =^{a^{2} - a} C_{4}$ , then $a$ is:

Discussion

11.	For the equation 2x2+(a+1)x+(a−1)=0, the difference between the roots is equal to their product. Then the value of a is
Answer» For the equation $2 x^{2} + (a + 1) x + (a - 1) = 0$ , the difference between the roots is equal to their product. Then the value of $a$ is

Discussion

12.	limx→42−√x4−x
Answer» ${lim}_{x \to 4} \frac{2 - \sqrt{x}}{4 - x}$

Discussion

13.	Question 19For what valuel of m is x3–2mx2+16 is divisible by x +2?
Answer» Question 19 For what valuel of m is $x^{3} - 2 m x^{2} + 16$ is divisible by x +2?

Discussion

14.	A line passes through (2, 2) is perpendicular to the line 3x + y = 3, It's y intercept is (A) 1 3 (B) 2 3 (C) 1 (D) 4 3
Answer» A line passes through (2, 2) is perpendicular to the line 3x + y = 3, It's y intercept is (A) 1 3 (B) 2 3 (C) 1 (D) 4 3

Discussion

15.	Determine whether each of the following relations are reflexive, symmetric and transitive: (iii) Relation R in the set A = {1, 2, 3, 4, 5, 6} as R = {(x, y): y is divisible by x}
Answer» Determine whether each of the following relations are reflexive, symmetric and transitive: (iii) Relation R in the set A = {1, 2, 3, 4, 5, 6} as R = {(x, y): y is divisible by x}

Discussion

16.	Find themaximum and minimum values of x + sin 2x on [0, 2π].
Answer» Find the maximum and minimum values of x + sin 2x on [0, 2π].

Discussion

17.	10. If acose + bsine = 3 and asine - bcos0 = 4, then a^2 b^2 has the value
Answer» 10. If acose + bsine = 3 and asine - bcos0 = 4, then a^2 b^2 has the value

Discussion

18.	The value of {3200328}, where {.} denotes the fractional part function, is
Answer» The value of ${\frac{3^{2003}}{28}},$ where ${.}$ denotes the fractional part function, is

Discussion

19.	If cos θ=−12 and 0<θ < 360∘ ,then the solutions are
Answer» If $cos θ = - \frac{1}{2}$ and $0 < θ < 360^{\circ}$ ,then the solutions are

Discussion

20.	If nC4, nC5, nC6 are in A.P., then the value(s) of n is/are
Answer» If $^{n} C_{4},^{n} C_{5},^{n} C_{6}$ are in A.P., then the value(s) of $n$ is/are

Discussion

21.	The product of three consecutive numbers is always divisible by 6. Verify this statement with the help of some examples.
Answer» The product of three consecutive numbers is always divisible by 6. Verify this statement with the help of some examples.

Discussion

22.	35. If 49x - b =(7x+1/2)(7x-1/2), then find the value of X.
Answer» 35. If 49x - b =(7x+1/2)(7x-1/2), then find the value of X.

Discussion

23.	The value of a for which the function f(x)=asinx+13sin3x has an extremum at x=π3 is
Answer» The value of $a$ for which the function $f (x) = a sin x + \frac{1}{3} sin 3 x$ has an extremum at $x = \frac{π}{3}$ is

Discussion

24.	∫1ln(xx)(1+lnx)dx is equal to(where C is constant of integration)
Answer» $\int \frac{1}{ln (x^{x}) (1 + ln x)} d x$ is equal to (where $C$ is constant of integration)

Discussion

25.	The number of solution(s) of \|y\|=(x−1) and \|y\|=ex−2 is
Answer» The number of solution(s) of $\| y \| = (x - 1)$ and $\| y \| = e^{x - 2}$ is

Discussion

26.	Let the lines y−k1x−β=0 and y−k2x−β=0,(k1≠k2),k1,k2∈R intersect at P and the lines x−p1y−α=0 and x−p2y−α=0,(p1≠p2),p1,p2∈R intersect at Q. If the points P and Q always lies on or inside the triangle formed by the lines 2x−3y−6=0, 3x−y+3=0 and 3x+4y−12=0, then
Answer» Let the lines $y - k_{1} x - β = 0$ and $y - k_{2} x - β = 0, (k_{1} \neq k_{2}), k_{1}, k_{2} \in R$ intersect at $P$ and the lines $x - p_{1} y - α = 0$ and $x - p_{2} y - α = 0, (p_{1} \neq p_{2}), p_{1}, p_{2} \in R$ intersect at $Q$ . If the points $P$ and $Q$ always lies on or inside the triangle formed by the lines $2 x - 3 y - 6 = 0, 3 x - y + 3 = 0$ and $3 x + 4 y - 12 = 0$ , then

Discussion

27.	Prove That:- 2sec^2 A-sec^4 A-2cosec^2 A+cosec^4 A = cot^4 A-tan^4 A
Answer» Prove That:- 2sec^2 A-sec^4 A-2cosec^2 A+cosec^4 A = cot^4 A-tan^4 A

Discussion

28.	A given convex pentagon ABCDE has the property that the area of each of the five triangles ABC, BCD, CDE, DEA, and EAB is unity. Show that all pentagons with the above property have same area, and calculate the area. Show, further that there are infinitely many non-congruent pentagons having the above property.
Answer» A given convex pentagon ABCDE has the property that the area of each of the five triangles ABC, BCD, CDE, DEA, and EAB is unity. Show that all pentagons with the above property have same area, and calculate the area. Show, further that there are infinitely many non-congruent pentagons having the above property.

Discussion

29.	Let x(t) be signal with its Laplace transform X(s). If x(t) is defined as x(t)=e−tcostu(t). Another function y(t) is defined as y(t)=∫τ−∞x(τ)dτ.Then the Laplace transform of y(t) is
Answer» $Let x(t) be signal with its Laplace transform X(s). If x(t) is defined as x(t) = e^{- t} cos t u (t) . Another function y(t) is defined as y (t) = \int_{- \infty}^{τ} x (τ) d τ$ . $Then the Laplace transform of y(t) is$

Discussion

30.	explain henry law
Answer» explain henry law

Discussion

31.	The base of an equilateral triangle with side 2a lies along the y−axis such that the mid-point of the base is at the origin. Find vertices of the triangle.
Answer» The base of an equilateral triangle with side $2 a$ lies along the $y -$ axis such that the mid-point of the base is at the origin. Find vertices of the triangle.

Discussion

32.	how to solve integral of sin^2 dx
Answer» how to solve integral of sin^2 dx

Discussion

33.	Find the value of n such that(i) nP5=42 nP3, n>4(ii) nP4n−1P4=53, n>4
Answer» Find the value of $n$ such that $(i)^{n} P_{5} = 42^{n} P_{3}, n > 4$ $(i i) \frac{^{n} P_{4}}{^{n - 1} P_{4}} = \frac{5}{3}, n > 4$

Discussion

34.	For a given 2×2 matrix A, it is observed thatA∣∣∣1−1∣∣∣=−1∣∣∣1−1∣∣∣ and A∣∣∣1−2∣∣∣=−2∣∣∣1−2∣∣∣ then the matrix A is
Answer» For a given $2 \times 2$ matrix $A$ , it is observed that $A ∣ ∣ ∣ \begin{matrix} 1 - 1 \end{matrix} ∣ ∣ ∣ = - 1 ∣ ∣ ∣ \begin{matrix} 1 - 1 \end{matrix} ∣ ∣ ∣$ and $A ∣ ∣ ∣ \begin{matrix} 1 - 2 \end{matrix} ∣ ∣ ∣ = - 2 ∣ ∣ ∣ \begin{matrix} 1 - 2 \end{matrix} ∣ ∣ ∣$ then the matrix $A$ is

Discussion

35.	44.x=4, y =
Answer» 44.x=4, y =

Discussion

36.	Let f be a positive function Let I1=∫k1−kx f{x(1−x)}dx I2=∫k1−kf{x(1−x)}dx where 2k−1>0,. If I2=pI1 then the value of p is
Answer» Let $f$ be a positive function Let $I_{1} = \int_{1 - k}^{k} x f {x (1 - x)} d x$ $I_{2} = \int_{1 - k}^{k} f {x (1 - x)} d x$ where $2 k - 1 > 0,$ . If $I_{2} = p I_{1}$ then the value of $p$ is

Discussion

37.	The maximum value of sin22π3+x+sin22π3-x is(a) 1/2(b) 3/2(c) 1/4(d) 3/4
Answer» The maximum value of $\sin^{2} (\frac{2 π}{3} + x) + \sin^{2} (\frac{2 π}{3} - x)$ is (a) 1/2 (b) 3/2 (c) 1/4 (d) 3/4

Discussion

38.	All the functions with straight line graphs are either strictly increasing functions or strictly decreasing functions.F
Answer» All the functions with straight line graphs are either strictly increasing functions or strictly decreasing functions. F

Discussion

39.	Complete the pattern.3140624, 3140724, 3140824, _________
Answer» Complete the pattern. 3140624, 3140724, 3140824, _________

39.

Complete the pattern.3140624, 3140724, 3140824, _________

Answer»

Complete the pattern.

3140624, 3140724, 3140824, _________

Discussion

40.	If R is the set of real numbers and Q is the set of rational numbers, then what isR - Q?11.
Answer» If R is the set of real numbers and Q is the set of rational numbers, then what isR - Q?11.

Discussion

41.	∫tan6xdx is equal to(where C is integration constant)
Answer» $\int {tan}^{6} x d x$ is equal to (where $C$ is integration constant)

Discussion

42.	The equation of the normal to the curve y = tan x at (0, 0) is ______________.
Answer» The equation of the normal to the curve y = tan x at (0, 0) is ______________.

Discussion

43.	Some statements are given, followed by some conclusions. Consider the statements to be true even if they seem to be at variance from commonly known facts. Decide which of the given conclusions follow from the given statements. Statements: All players are spectators. Some spectators are theatres. Some theatres are dramas. Conclusions: I. Some dramas are spectators. II. Some players are dramas. III. Some theatres are players. IV. All spectators are players.
Answer» Some statements are given, followed by some conclusions. Consider the statements to be true even if they seem to be at variance from commonly known facts. Decide which of the given conclusions follow from the given statements. Statements: All players are spectators. Some spectators are theatres. Some theatres are dramas. Conclusions: I. Some dramas are spectators. II. Some players are dramas. III. Some theatres are players. IV. All spectators are players.

Discussion

44.	If for some real number a, limx→0sin 2x+a sin xx3 exists then the limit is equal to
Answer» If for some real number $a$ , $lim x \to 0 \frac{sin 2 x + a sin x}{x^{3}}$ exists then the limit is equal to

Discussion

45.	If the angles made by a straight line with the coordinate axes are α,π/2−α,β then β=
Answer» If the angles made by a straight line with the coordinate axes are $α, π / 2 - α, β t h e n β =$

Discussion

46.	If the Booloean expression Y(A,B,C,D)=∑m(1,3,7,11,15)+d(0,2,5)then its simplified form of the expression 'Y' is
Answer» If the Booloean expression $Y (A, B, C, D) = \sum m (1, 3, 7, 11, 15) + d (0, 2, 5)$ then its simplified form of the expression 'Y' is

Discussion

47.	There are 8 events that can be scheduled in a week. Then total number of ways that these 8 events are scheduled on exactly 6 days of a week is given by 266×k! , where k∈N. The value of k is
Answer» There are $8$ events that can be scheduled in a week. Then total number of ways that these $8$ events are scheduled on exactly $6$ days of a week is given by $266 \times k!,$ where $k \in N .$ The value of $k$ is

Discussion

48.	Evaluate the following integrals:∫033x-1 dx
Answer» Evaluate the following integrals: $\int_{0}^{3} \|3 x - 1\| d x$

Discussion

49.	limx→2x−2√x−√2
Answer» ${lim}_{x \to 2} \frac{x - 2}{\sqrt{x} - \sqrt{2}}$

Discussion

50.	If 4 sin−1x+cos−1x=π then x is equal to
Answer» If $4 s i n^{- 1} x + c o s^{- 1} x = π$ then x is equal to

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Find the solution of dydx=2y−x

The sum of all values of x in [0,2π], for which sinx+sin2x+sin3x+sin4x=0, is equal to

The Cartesian equation of a line is . Write its vector form.

Let P be (5,3) and a point R on y=x and Q on the X - axis be such PQ+QR+RP is minimum. Then the coordinates of Q are

if alpha, beta, gamma are thevroots of x^3+8=0 then the equation whose root are aplha^2, beta^2, gamma^2

The angles of a quadrilateral are in A.P. and the greatest angle is 120∘. Express the angles in radians.

Let ∗ be a binary operation on the set Q of rational number as follows: (i) a∗b=a+ab Find which of the binary operation are commutative and which are associative?

The range of t such that 2sint=1−2x+5x23x2−2x−1 has a solution, where t∈[−π2,π2]is

Find the particular solution of the differential equation(1 – y2) (1 + log x) dx + 2xy dy = 0, given that y = 0 when x = 1.

If a2−aC2=a2−aC4 , then a is:

For the equation 2x2+(a+1)x+(a−1)=0, the difference between the roots is equal to their product. Then the value of a is

limx→42−√x4−x

Question 19For what valuel of m is x3–2mx2+16 is divisible by x +2?

A line passes through (2, 2) is perpendicular to the line 3x + y = 3, It's y intercept is (A) 1 3 (B) 2 3 (C) 1 (D) 4 3

Determine whether each of the following relations are reflexive, symmetric and transitive: (iii) Relation R in the set A = {1, 2, 3, 4, 5, 6} as R = {(x, y): y is divisible by x}

Find themaximum and minimum values of x + sin 2x on [0, 2π].

10. If acose + bsine = 3 and asine - bcos0 = 4, then a^2 b^2 has the value

The value of {3200328}, where {.} denotes the fractional part function, is

If cos θ=−12 and 0&lt;θ &lt; 360∘ ,then the solutions are

If nC4, nC5, nC6 are in A.P., then the value(s) of n is/are

The product of three consecutive numbers is always divisible by 6. Verify this statement with the help of some examples.

35. If 49x - b =(7x+1/2)(7x-1/2), then find the value of X.

The value of a for which the function f(x)=asinx+13sin3x has an extremum at x=π3 is

∫1ln(xx)(1+lnx)dx is equal to(where C is constant of integration)

The number of solution(s) of |y|=(x−1) and |y|=ex−2 is

Let the lines y−k1x−β=0 and y−k2x−β=0,(k1≠k2),k1,k2∈R intersect at P and the lines x−p1y−α=0 and x−p2y−α=0,(p1≠p2),p1,p2∈R intersect at Q. If the points P and Q always lies on or inside the triangle formed by the lines 2x−3y−6=0, 3x−y+3=0 and 3x+4y−12=0, then

Prove That:- 2sec^2 A-sec^4 A-2cosec^2 A+cosec^4 A = cot^4 A-tan^4 A

Let x(t) be signal with its Laplace transform X(s). If x(t) is defined as x(t)=e−tcostu(t). Another function y(t) is defined as y(t)=∫τ−∞x(τ)dτ.Then the Laplace transform of y(t) is

explain henry law

The base of an equilateral triangle with side 2a lies along the y−axis such that the mid-point of the base is at the origin. Find vertices of the triangle.

how to solve integral of sin^2 dx

Find the value of n such that(i) nP5=42 nP3, n&gt;4(ii) nP4n−1P4=53, n&gt;4

For a given 2×2 matrix A, it is observed thatA∣∣∣1−1∣∣∣=−1∣∣∣1−1∣∣∣ and A∣∣∣1−2∣∣∣=−2∣∣∣1−2∣∣∣ then the matrix A is

44.x=4, y =

Let f be a positive function Let I1=∫k1−kx f{x(1−x)}dx I2=∫k1−kf{x(1−x)}dx where 2k−1&gt;0,. If I2=pI1 then the value of p is

The maximum value of sin22π3+x+sin22π3-x is(a) 1/2(b) 3/2(c) 1/4(d) 3/4

All the functions with straight line graphs are either strictly increasing functions or strictly decreasing functions.F

Complete the pattern.3140624, 3140724, 3140824, _________

If R is the set of real numbers and Q is the set of rational numbers, then what isR - Q?11.

∫tan6xdx is equal to(where C is integration constant)

The equation of the normal to the curve y = tan x at (0, 0) is ______________.

If for some real number a, limx→0sin 2x+a sin xx3 exists then the limit is equal to

If the angles made by a straight line with the coordinate axes are α,π/2−α,β then β=

If the Booloean expression Y(A,B,C,D)=∑m(1,3,7,11,15)+d(0,2,5)then its simplified form of the expression 'Y' is

There are 8 events that can be scheduled in a week. Then total number of ways that these 8 events are scheduled on exactly 6 days of a week is given by 266×k! , where k∈N. The value of k is

Evaluate the following integrals:∫033x-1 dx

limx→2x−2√x−√2

If 4 sin−1x+cos−1x=π then x is equal to

If cos θ=−12 and 0<θ < 360∘ ,then the solutions are

Find the value of n such that(i) nP5=42 nP3, n>4(ii) nP4n−1P4=53, n>4

Let f be a positive function Let I1=∫k1−kx f{x(1−x)}dx I2=∫k1−kf{x(1−x)}dx where 2k−1>0,. If I2=pI1 then the value of p is