List of top Mathematics Questions

The equation of a common tangent to the parabolas \( y = x^2 \) and \( y = -(x - 2)^2 \) is:

If the coordinates of the points A and B are (3, 3)  and  (7, 6),  then the length of the portion of the line AB intercepted between the axes is:

The derivative of \( e^{x^3} \) with respect to \( \log x \) is:
If \( y = \sqrt{\frac{1 + \cos 2\theta}{1 - \cos 2\theta}} \), then \( \frac{dy}{d\theta} \) at \( \theta = \frac{3\pi}{4} \) is:
Bag P contains 6 red and 4 blue balls, and bag Q contains 5 red and 6 blue balls. A ball is transferred from bag P to bag Q and then a ball is drawn from bag Q. What is the probability that the ball drawn is blue?
The probability that a card drawn from a pack of 52 cards will be a diamond or a king is:
What is the angle between the two straight lines \( y = (2 - \sqrt{3})x + 5 \) and \( y = (2 + \sqrt{3})x - 7 \)?
The shortest distance between the lines \[ \frac{x - 3}{2} = \frac{y - 2}{3} = \frac{z - 1}{-1} \] and \[ \frac{x + 3}{2} = \frac{y - 6}{1} = \frac{z - 5}{3} \] is:
A circle touches both the y-axis and the line \( x + y = 0 \). Then the locus of its center is:
If \( f(x) = \frac{x}{\sqrt{1 + x^2}} \), then \( (f \circ f)(x) \) is:

The range of the function \( f(x) = \sqrt{3x^2 - 4x + 5} \) is: 
 

A set A has 3 elements and another set B has 6 elements. Then:
The probability of getting a sum greater than 7 when a pair of dice are thrown is:
The maximum value of \( z = 5x + 2y \) subject to the constraints: \[ x + y \leq 7, \quad x + 2y \leq 10, \quad x, y \geq 0 \]
For all \( n \in \mathbb{N} \), the sum of \( \frac{n^5}{5} + \frac{n^3}{3} + \frac{7n}{15} \) is:
If the sum of an infinite GP \( a, ar, ar^2, ar^3, \dots \) is 15 and the sum of the squares of each term is 150, then the sum of the series \( ar^2, a r^4, ar^6, \dots \) is:
The area enclosed between the curve \( y = \log_e(x + e) \) and the coordinate axes is:
If \( P(B) = \frac{3}{5} \), \( P(A \mid B) = \frac{1}{2} \), and \( P(A \cup B) = \frac{4}{5} \), then the value of \( P(A \cup B)' + P(A' \cup B) \) is:
The middle term in the expansion of \( \left(\frac{10}{x} + \frac{x}{10}\right)^{10} \) is:
If \( \sec^2 \theta = \frac{4}{3} \), then the general value of \( \theta \) is:
Negation of the Boolean expression \( p \Leftrightarrow (q \Rightarrow p) \) is:
Number of words from the letters of the word BHARAT in which B and H will never come together is:
If \( \vec{a} = \hat{i} + \hat{j} + \hat{k} \), \( \vec{a} \cdot \vec{b} = 1 \) and \( \vec{a} \times \vec{b} = \hat{j} - \hat{k} \), then \( \vec{b} \) is:
The function \( f(x) = \tan^{-1}(\sin x + \cos x) \) is an increasing function in:
The interval in which the function \( f(x) = 4x^2 + x \) is decreasing is: