List of top Mathematics Questions

Let \( A(2, 3), B(1, -1) \) be two points. If \( P \) is a variable point such that \( \angle APB = 90^\circ \), then the locus of \( P \) is
The length of the subnormal at any point on the curve \( y = \left(\frac{x}{2024}\right)^k \) is constant if the value of \( k \) is:
If the roots of the equation \[ Z^3 + iZ^2 + 2i = 0 \] are the vertices of a triangle ABC, then that triangle ABC is:
The solution of the differential equation \[ \frac{dy}{dx} = \frac{y + x \tan \left( \frac{y}{x} \right)}{x}. \] \[ \sin\frac{y}{x} = \]
Find the sum of the sequence: \( 2 + 3 + 5 + 6 + 8 + 9 + \dots + 2n \) terms.

If \( T = 2\pi \sqrt{\frac{L}{g}} \), \( g \) is a constant and the relative error in \( T \) is \( k \) times to the percentage error in \( L \), then \( \frac{1}{k} = \) ? 

The differential equation formed by eliminating arbitrary constants \( A \) and \( B \) from the equation \[ y = A \cos 3x + B \sin 3x \] is:
When an unfair dice is thrown, the probability of getting a number \( k \) on it is \( P(X = k) = k^2 P \), where \( k = 1, 2, 3, 4, 5, 6 \) and \( X \) is the random variable denoting a number on the dice. Then, the mean of \( X \) is:
If all the letters of the word ‘SENSELESSNESS’ are arranged in all possible ways and an arrangement among them is chosen at random, then, the probability that all the E’s come together in that arrangement is:
The value of \( c \) such that the straight line joining the points \[ (0,3) \quad {and} \quad (5,-2) \] is tangent to the curve \[ y = \frac{c}{x+1} \] is:

If \( y = x - x^2 \), then the rate of change of \( y^2 \) with respect to \( x^2 \) at \( x = 2 \) is: 

If \( (r, \theta) \) denotes \( r (\cos \theta + i \sin \theta) \). If \[ x = (1, \alpha), \quad y = (1, \beta), \quad z = (1, \gamma) \] and \( x + y + z = 0 \), then \[ \sum \cos (2\alpha - \beta - \gamma) = \]
Parametric equations of the circle \( 2x^2 + 2y^2 = 9 \) are:
The equation of the circle touching the circle \[ x^2 + y^2 - 6x + 6y + 17 = 0 \] externally and to which the lines \[ x^2 - 3xy - 3x + 9y = 0 \] are normal is:
The locus of the midpoint of the system of parallel chords parallel to the line \( y = 2x \) to the hyperbola \( 9x^2 - 4y^2 = 36 \) is:
All values of \( (8i)^{\frac{1}{3}} \) are:
In \(\triangle ABC\), \(r r_1 \cot^ \frac{A}{2} + r r_2 \cot^ \frac{B}{2} + r r_3 \cot^ \frac{C}{2} = \)
If \( \overrightarrow{a}, \overrightarrow{b} \) are two non-collinear vectors, then \( |\overrightarrow{b}| \overrightarrow{a} + |\overrightarrow{a}| \overrightarrow{b} \) represents
In a Binomial distribution, the difference between the mean and standard deviation is 3, and the difference between their squares is 21. Then, the ratio \( P(x = 1) : P(x = 2) \) is:
Let \( \overline{X} \) and \( \overline{Y} \) be the arithmetic means of the runs of two batsmen A and B in 10 innings respectively, and \( \sigma_A, \sigma_B \) are the standard deviations of their runs in them. If batsman A is more consistent than B, then he is also a higher run scorer only when
In \(\triangle ABC\), if \(4r_1 = 5r_2 = 6r_3\), then \(\sin^2 \frac{A}{2} + \sin^2 \frac{B}{2} + \sin^2 \frac{C}{2} =\)
A student writes an exam with 8 true/false questions. He passes if he answers at least 6 correctly. Find the probability that he fails.

For the probability distribution of a discrete random variable \( X \) as given below, the mean of \( X \) is:

When the origin is shifted to \( (h, k) \) by translation of axes, the transformed equation of \( x^2 + 2x + 2y - 7 = 0 \) does not contain \( x \) and constant terms. Then \( (2h + k) = \):
Assertion (A): If \( A = 10^\circ, B = 16^\circ, C = 19^\circ \), then: \[ \tan(2A) \tan(2B) + \tan(2B) \tan(2C) + \tan(2C) \tan(2A) = 1. \] Reason (R): If \( A + B + C = 180^\circ \), then: \[ \cot\left(\frac{A}{2}\right) + \cot\left(\frac{B}{2}\right) + \cot\left(\frac{C}{2}\right) = \cot\left(\frac{A}{2}\right) \cot\left(\frac{B}{2}\right) \cot\left(\frac{C}{2}\right). \]