List of top Mathematics Questions

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 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 \( \frac{1}{x} + \frac{1}{x+2} = \frac{5}{6} \).
What is the area of a triangle with base 8 cm and height 6 cm?
The sum of the first 10 terms of an arithmetic progression is 150. If the first term is 10, what is the common difference?
Find the value of \( x \) in the equation \( 2x + 3 = 7x - 8 \).
What is the area of a triangle with base \( 12 \, \text{cm} \) and height \( 8 \, \text{cm} \)?
Find the derivative of \( f(x) = 4x^3 - 6x^2 + 2x - 5 \).
Find the value of \( \log_2 32 \).
Find the derivative of \( f(x) = 3x^2 - 4x + 7 \).
Find the value of λ, if the points A(−1,−1,2), B(2,8,λ), C(3,11,6) are collinear.
How many numbers are divisible by 3 between 50 and 500?

Let $ y(x) $ be the solution of the differential equation $$ x^2 \frac{dy}{dx} + xy = x^2 + y^2, \quad x > \frac{1}{e}, $$ satisfying $ y(1) = 0 $. Then the value of $ 2 \cdot \frac{(y(e))^2}{y(e^2)} $ is ________.

Prime factorisation of 156 will be:
Ram kumar, a trader mixes two varieties of Moong dal, totally weighing 90kg worth Rs7443. The price of the first variety that he mixes is Rs57.50 per kg and that of the second variety is Rs111.50 per kg. How much quantity of the second variety of moong dal does he mix?
Out of the following which is a Pythagorean triplet ?

The following table shows the ages of the patients admitted in a hospital during a year. Find the mode and the median of these data.
\[\begin{array}{|c|c|c|c|c|c|c|} \hline Age (in years) & 5-15 & 15-25 & 25-35 & 35-45 & 45-55 & 55-65 \\ \hline \text{Number of patients} & \text{6} & \text{11} & \text{21} & \text{23} & \text{14} & \text{5} \\ \hline \end{array}\]

If \( f: \mathbb{R} \to \mathbb{R} \) and \( g: \mathbb{R} \to \mathbb{R} \) be functions defined by \( f(x) = \cos x \) and \( g(x) = 3x^2 \) respectively, then prove that \( gof \neq fog \).