List of top Mathematics Questions

Find the area of a triangle with base 12 cm and height 5 cm.
Find the value of $ x $ that satisfies the equation $ 2x + 3 = 11 $.
Find the roots of the quadratic equation $ x^2 - 5x + 6 = 0 $.
Evaluate the expression: \[ f\left(f(f(x))\right) + \left(f(f(x))\right)^2 \quad \text{if} \quad x = 1 \]
Evaluate the determinant of the matrix: \[ \left| \begin{array}{cc} 1 & \tan x
-\tan x & 1 \end{array} \right| \]
Evaluate the integral: \( \int \sin^5 x \, dx \)
Find the value of \( \frac{d}{dx} (3x^2 + 4x + 5) \).
Find the value of \( \tan 45^\circ \).
The sum of the ages of a father and his son is 60 years. The father is three times as old as the son. What is the son's age?
If the sum of the first \( n \) terms of an arithmetic progression (AP) is given by \( S_n = 3n^2 + 2n \), find the 4th term of the AP.
Find the area of a circle whose radius is 7 cm.
If \( \sin \theta = \frac{3}{5} \), find the value of \( \cos \theta \).
Find the value of \( \log_2 32 \).
Find the value of \( \sin 30^\circ + \cos 60^\circ \).
The area of a triangle with base 12 cm and height 5 cm is?
If \( y = x^x + x^x \), then find \( \frac{dy}{dx} \):
If ∫ (2x + 3)/((x - 1)(x^2 + 1)) dx = log_x {(x - 1)^(5/2)(x^2 + 1)^a} - (1/2) tan^(-1)x + C, then the value of a is:
Find the value of the integral: ∫ (2x + 3)/((xy)(x^2 + 1)) dx
If the system of equations \[ x + 2y - 3z = 2 \] \[ 2x + \lambda y + 5z = 5 \] \[ 4x + 3y + \mu z = 33 \] has infinite solutions, then \( \lambda + \mu \) is equal to
If the sum, \( \sum_{r=1}^9 \frac{r+3}{2r} \cdot \binom{9}{r} \) is equal to \( \alpha \cdot \left( \frac{3}{2} \right)^9 - \beta \), then the value of \( (\alpha + \beta)^2 \) is equal to:
Consider the following statements:
Statement-I: The set of all solutions of the linear inequalities 3x + 8 < 17 and 2x + 8 ≥ 12 are x < 3 and x ≥ 2 respectively.
Statement-II: The common set of solutions of the linear inequalities 3x + 8 < 17 and 2x + 8 ≥ 12 is (2,3).
Which of the following is true?
Which of the following statements is not correct?

A coin has a true probability \( \mu \) of turning up Heads. This coin is tossed 100 times and shows up Heads 60 times. The following hypothesis is tested: 
\[ H_0: \mu = 0.5 \quad ({Null Hypothesis}), \quad H_1: \mu>0.5 \quad ({Alternative Hypothesis}) \] 
Using the Central Limit Theorem, the \( p \)-value of the above test is ________ (round off to three decimal places). 
Hint: If Z is a random variable that follows a standard normal distribution, then P (Z ≤ 2) = 0.977.

If \( X \) is a continuous random variable whose probability density function is given by

\[ f_X(x) = \begin{cases} cx^3 + 0.25, & \text{for } 0 \leq x \leq 1, \ c \in \mathbb{R} \\ 0, & \text{elsewhere} \end{cases} \]

Then the value of \( c \) is ________________ (in integer).
If \( X \) is a continuous random variable whose probability density function is given by

\[ f_X(x) = \begin{cases} \frac{1}{x^2}, & \text{for } 1 < x < \infty \\ 0, & \text{elsewhere} \end{cases} \]

Then the median of \( X \) is ________________ (in integer).