List of top Mathematics Questions

How many 4-digit numbers can be formed using the digits 1, 2, 3, 4, 5 without repetition such that the number is divisible by 5?
Find the coordinates of the point which divides the line segment joining \((2, -3)\) and \((7, 9)\) in the ratio \(3:2\).
If \( z = 2(\cos 60^\circ + i \sin 60^\circ) \), find the value of \( z^3 \).
Find the number of integers \(n\) such that \(1 \leq n \leq 100\) and \(n^2 + 3n + 2\) is divisible by 5.
From a group of 10 men and 8 women, a committee of 5 is to be formed such that it contains at least 3 women. How many such committees are possible?
Two circles with centers $O_1$ and $O_2$ touch externally. The radius of the first circle is 4 cm and the second is 9 cm. The distance between their centers is 13 cm. Find the length of the direct common tangent.
Evaluate: \[ \lim_{x \to 0} \frac{\sin 3x - 3 \sin x}{x^3} \]
If $ x + \frac{1}{x} = 2 \cos \theta $, find the value of \[ x^5 + \frac{1}{x^5} \] in terms of $\theta$.
From the top of a 50 m tall building, the angles of depression to two points on the ground are \( 45^\circ \) and \( 30^\circ \). Find the distance between the two points.
Maximize \( z = 5x + 2y \) subject to \( 2x + y \leq 8 \), \( x \geq 0 \), \( y \geq 0 \). What is the maximum value of \( z \)?
If the word "BITS" is coded using \( A=1, B=2, \ldots, Z=26 \), and the code is the sum of the squares of each letter's value, what is the code for the word?
If \( \vec{p} = 3\hat{i} - \hat{j} + 2\hat{k} \), \( \vec{q} = \hat{i} + 4\hat{j} - \hat{k} \), and \( \vec{r} = 2\hat{i} - 3\hat{j} + 5\hat{k} \), find \( \vec{p} \cdot (\vec{q} \times \vec{r}) \).
Find the sum of the series \( 1 + 3 + 5 + \ldots + 99 \).
Maximize \( z = 3x + 4y \) subject to \( x + y \leq 4 \), \( x \geq 0 \), \( y \geq 0 \). What is the maximum value of \( z \)?
From the top of a 60 m high building, the angles of depression to two points on the ground on the same side of the building are \( 30^\circ \) and \( 60^\circ \). What is the distance between the two points?
If the word "GIFT" is coded using A=1, B=2, ..., Z=26, and each letter’s value is squared, what is the sum of the coded values?
If \( \vec{a} = \hat{i} + 2\hat{j} - \hat{k} \), \( \vec{b} = 2\hat{i} - \hat{j} + 3\hat{k} \), and \( \vec{c} = -\hat{i} + 3\hat{j} + 2\hat{k} \), find \( \vec{a} \cdot (\vec{b} \times \vec{c}) \).
Find the value of \( x \) in the equation \( 4x - 2 = 10 \).
Find the value of \( x \) in the equation \( 5x - 7 = 3x + 9 \).
Find the value of \( x \) in the equation \( 2x + 3 = 7x - 8 \).
Find the derivative of the function: \[ f(x) = 3x^3 - 5x^2 + 2x - 4 \]
Solve the quadratic equation: \[ x^2 - 5x + 6 = 0 \]
The ratio of the sum of two numbers to their difference is 5:1. If the sum of the numbers is 18, find the numbers.
Find the solution of the quadratic equation \( 2x^2 - 3x - 5 = 0 \).
Solve for \( x \) in the equation \( \frac{1}{x} + \frac{1}{x+2} = \frac{5}{6} \).