List of top Mathematics Questions

Find the measure of \( \angle VDA \).

Find a unit vector in the direction of \( \overrightarrow{DA} \).

Find a unit vector in the direction of \( \overrightarrow{DA} \).

How far is the star \( V \) from star \( A \)?

What rebate in price of the calculator should the store give to maximise the revenue?

Determine the number of units (\( x \)) that should be sold to maximise the revenue \( R(x) = x \cdot p(x) \). Also verify the result.

If the lines \[ \frac{x - 1}{-3} = \frac{y - 2}{2k} = \frac{z - 3}{2} \] and \[ \frac{x - 1}{3k} = \frac{y - 1}{1} = \frac{z - 6}{-7} \] are perpendicular to each other, find the value of \( k \) and hence write the vector equation of a line perpendicular to these two lines passing through the point \( (3, -4, 7) \).

Find the distance between the line \[ \frac{x}{2} = \frac{2}{y - 6} = \frac{1}{-z - 1} \] and another line parallel to it passing through the point \( (4, 0, -5) \).

Given matrix:
Let \[ A = \begin{bmatrix} 2 & 1 & -3 \\ 3 & 2 & 1 \\ 1 & 2 & -1 \end{bmatrix} \] Find \( A^{-1} \) and hence solve the following system of equations:

System of equations:
\[ 2x + y - 3z = 13, \quad 3x + 2y + z = 4, \quad x + 2y - z = 8 \]

Check whether the relation \( S \) in the set of real numbers \( \mathbb{R} \), defined by:

\[ S = \{(a, b) \mid a - b + \sqrt{2} \text{ is an irrational number} \} \] is reflexive, symmetric, or transitive.

Let \( A = \mathbb{R} - \{5\} \) and \( B = \mathbb{R} - \{1\} \). Consider the function \( f : A \to B \), defined by: \[ f(x) = \frac{x - 3}{x - 5} \] Show that \( f \) is one-one and onto.

Using integration, find the area bounded by the ellipse \( 9x^2 + 25y^2 = 225 \), the lines \( x = -2, x = 2 \), and the X-axis.

Sketch the graph of \( y = x|x| \) and hence find the area bounded by this curve, the X-axis, and the ordinates \( x = -2 \) and \( x = 2 \), using integration.

A biased die is twice as likely to show an even number as an odd number. If such a die is thrown twice, find the probability distribution of the number of sixes. Also, find the mean of the distribution.

A card from a well-shuffled deck of 52 playing cards is lost. From the remaining cards of the pack, a card is drawn at random and is found to be a King. Find the probability of the lost card being a King.

Solve the following linear programming problem graphically: Maximise \( Z = 2x + 3y \), subject to the constraints: \( x + y \leq 6, \, x \geq 2, \, y \geq 3, \, x \geq 0, \, y \geq 0. \)

Find the particular solution of the differential equation \( \left( x (e)^y/^x + y \right) dx = x \, dy \), given that \( y = 1 \) when \( x = 1 \).

Find the particular solution of the differential equation: \[ \frac{dy}{dx} = y \cot 2x, \] given that \( y\left(\frac{\pi}{4}\right) = 2 \).

Find: \[ \int \frac{3x+5}{\sqrt{x^2+2x+4}} \,dx. \]

Find: \[ \int e^x \left[ \frac{1}{(1+x^2)^{3/2}} + \frac{x}{\sqrt{1+x^2}} \right] dx. \]

Evaluate \( \int_0^{\pi/4} \frac{x}{1+\cos 2x + \sin 2x} \, dx \).

Given that \( y = (\sin x)^x \cdot x^{\sin x} + a^x \), find \( \frac{dy}{dx} \).

Evaluate \( \int \frac{dx}{x(x^2-1)} \).

The volume of a cube is increasing at the rate of \( 6 \, \text{cm}^3/\text{s} \). How fast is the surface area of the cube increasing, when the length of an edge is \( 8 \, \text{cm} \)?