List of top Mathematics Questions

A die is rolled once. What is the probability of rolling a number greater than 4?
If the roots of the quadratic equation \( x^2 - 5x + 6 = 0 \) are \( p \) and \( q \), then what is the value of \( p + q \)?
Given that: \[ x = a \sin(2t) (1 + \cos(2t)), \quad y = a \cos(2t) (1 - \cos(2t)) \] Find \(\frac{dy}{dx}\).

The remainder when \( 64^{64} \) is divided by 7 is equal to:

Find the length of the diagonal of a rectangle with length 6 cm and breadth 8 cm.
In a dataset of 50 values, the mean is 40 and the variance is 25. What is the probability that a randomly selected value from this dataset is between 35 and 45?
In the word "UNIVERSITY", find the probability that the two "I"s do not come together.
General solution of the differential equation \[ \frac{dy}{dx} + y \tan x = \sec x \quad \text{is:} \]
Find the roots of the quadratic equation \( 2x^2 - 4x - 6 = 0 \).
Find the value of the determinant \( \begin{vmatrix} 2 & 3 \\ 4 & 5 \end{vmatrix} \).
Find the derivative of the function \( f(x) = 3x^2 - 5x + 7 \).
Solve the system of equations: \[ x + y = 5 \] \[ 2x - y = 4 \]
Solve the system of equations: \[ x + y = 10 \] \[ 3x - y = 5 \]
You are given a sequence of numbers: 2, 5, 10, 17, ... Identify the pattern and find the next three terms in the sequence. Can you express the nth term of this sequence in a general formula?
Explain the concept of a limit. Why is it important in calculus?
Number of solutions in the interval \( [-2\pi, 2\pi] \) for the equation: \[ 2\sqrt{2} \cos^2 \theta + (2 - \sqrt{6}) \cos \theta - \sqrt{3} = 0 \]
Find the value of $ \log_2 32 $.
If $ f(x) = 3x^2 + 5x - 7 $, find $ f(2) $.
If $ x = 2 $, what is the value of $ 3x^2 - 5x + 7 $?
Find the sum of the roots of the quadratic equation $ 2x^2 - 5x + 3 = 0 $.
Find the area of a triangle with base 8 cm and height 6 cm.
Find the area of a circle with radius 7 cm.
In a class of 60 students, mathematics examination was conducted. All the students obtained 20 marks each. What would be the mean and standard deviation of marks in mathematics?
If \( \vec{A} = 2\hat{i} + 3\hat{j} \) and \( \vec{B} = 4\hat{i} - \hat{j} \), then the dot product \( \vec{A} \cdot \vec{B} \) is:
If $ \tan \theta = \frac{3}{4} $, find the value of $ \sin \theta $.