List of top Mathematics Questions

If \( \mathbf{a} \) and \( \mathbf{b} \) are position vectors of two points \( P \) and \( Q \) respectively, then find the position vector of a point \( R \) in \( QP \) produced such that \[ QR = \frac{3}{2} QP. \]
The derivative of \( \sin x \) with respect to \( \log x \) is:
If assumed mean of a data is 47.5, \( \sum f_i d_i = 435 \) and \( \sum f_i = 30 \), then mean of that data is:
Area of a sector of a circle with radius 4 cm and angle 30° is (use \( \pi = 3.14 \)):
Given the equation: \[ 81 \sin^2 x + 81 \cos^2 x = 30 \] Find the value of \( x \).

What is the angle between the hour and minute hands at 4:30?

If $ f(x) = 2x^2 - 3x + 5 $, find $ f(3) $.
What is the sum of the first 10 terms of the arithmetic progression with first term 3 and common difference 2?
If the roots of the quadratic equation \( x^2 - 6x + k = 0 \) are real and distinct, what is the range of values for \( k\)?
If \( \sin \theta + \cos \theta = \sqrt{2} \), what is the value of \( \sin \theta \cos \theta \)?
What is the value of \( \int_0^{\pi/2} \sin x \cos x \, dx\)?
Prove that \(\dfrac{\sin \theta}{1 + \cos \theta} + \dfrac{1 + \cos \theta}{\sin \theta} = 2\csc \theta\)
If \( \sin \theta + \cos \theta = 1 \), what is the value of \( \sin^2 \theta + \cos^2 \theta \)?
If log$_{10}$(x + 1) = 2, what is the value of x?
The sum of the first 30 terms of an arithmetic progression is 930. If the first term is 2, what is the common difference of the progression?
If the roots of the quadratic equation \( 2x^2 - 5x + k = 0 \) are real and distinct, what is the range of values for \( k \)?
If \(x^2 + y^2 = 25\) and \(xy = 12\), then what is the value of \(x^4 + y^4\)?
Evaluate the integral: $$ \int_0^{\pi/4} \frac{\ln(1 + \tan x)}{\cos x \sin x} \, dx $$
Find the derivative of \( y = \sin(x^2) \) with respect to \( x \).
Let \( P_n = \alpha^n + \beta^n \), \( P_{10} = 123 \), \( P_9 = 76 \), \( P_8 = 47 \), and \( P_1 = 1 \). The quadratic equation whose roots are \( \frac{1}{\alpha} \) and \( \frac{1}{\beta} \) is:
What is the value of \( \sin 30^\circ \)?
The roots of the equation \( x^2 + 5x + 6 = 0 \) are:
The equation of a straight line is given by \( y = 3x + 4 \). What is the slope of the line?
A bag contains 5 red, 3 blue, and 2 green balls. If two balls are drawn at random without replacement, what is the probability that both are red?
Using integration, find the area of the region bounded by the line \[ y = 5x + 2, \] the \( x \)-axis, and the ordinates \( x = -2 \) and \( x = 2 \).