List of top Mathematics Questions

The transformed equation of \( x^2 - y^2 + 2x + 4y = 0 \) when the origin is shifted to the point \( (-1,2) \) is:
If \( |x| < 1 \), the coefficient of \( x^2 \) in the power series expansion of \( \frac{x^4}{(x+1)(x-2)} \) is:
If \( |x| < 1 \), then the number of terms in the expansion of \( \left[ \frac{1}{2} (1.2 + 2.3x + 3.4x^2 + \dots) \right]^{-25} \) is:
If \( \alpha, \beta \) are the roots of the equation \( x^2 - 6x - 2 = 0 \), \( \alpha > \beta \), and \( a_n = \alpha^n - \beta^n, n \geq 1 \), then the value of \( \frac{a_{10} - 2 a_8}{2 a_9} \) is:
If both the roots of the equation \( x^2 - 6ax + 2 - 2a + 9a^2 = 0 \) exceed 3, then:
The general solution of the differential equation: \[ (1 + \tan y) (dx - dy) + 2x \, dy = 0. \]
The general solution of the differential equation: $$ x \, dy - y \, dx = \sqrt{x^2 + y^2} \, dx. $$ 
The sum of the order and degree of the differential equation: \[ x \left( \frac{d^2 y}{dx^2} \right)^{1/2} = \left( 1 + \frac{dy}{dx} \right)^{4/3} \] is:
Evaluate the integral: \[ \int \frac{x^2 - 1}{x^3\sqrt{2x^4 - 2x^2 + 1}} \,dx. \]
The general solution of the equation \( \tan x + \tan 2x - \tan 3x = 0 \) is:
If set A has 5 elements, and set B has 7 elements, then the number of one-one functions that can be defined from A to B is
Evaluate: \[ \lim_{x \to 0} \left[ \frac{1}{x} - \frac{1}{e^x - 1} \right] \]
If \( A = \begin{bmatrix} a & 1 & 2 \\ 1 & b & 3 \\ c & 1 & 3 \end{bmatrix} \) and \( \text{Adj } A = \begin{bmatrix} 7 & -1 & -5 \\ -3 & 9 & 5 \\ 1 & -3 & 5 \end{bmatrix} \), then \( a^2 + b^2 + c^2 = \) ?
The rank of the word "TABLE" counted from the rank of the word "BLATE" in dictionary order 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:
8 teachers and 4 students are sitting around a circular table at random. The probability that no two students sit together is:
Evaluate the limit: \[ \lim_{n \to \infty} \left( \frac{1}{\sqrt{n^2}} + \frac{1}{\sqrt{n^2 - 1}} + \dots + \frac{1}{\sqrt{n^2 - (n-1)^2}} \right). \]
The distance of a point \( (2,3,-5) \) from the plane \( \vec{r} \cdot (4i - 3j + 2k) = 4 \) is:
In \( \triangle ABC \), if \( b + c : c + a : a + b = 7:8:9 \), then the smallest angle (in radians) of that triangle is:
Let \( f(x) \) be defined as: \[ f(x) = \begin{cases} 0, & x = 0 \\ 2 - x, & 0 < x < 1 \\ 2, & x = 1 \\ 1 - x, & 1 < x < 2 \\ -\frac{3}{2}, & x \geq 2 \end{cases} \] Then which of the following is true?
If the slope of one of the pair of lines represented by \( 2x^2 + 3xy + Ky^2 = 0 \) is 2, then the angle between the pair of lines is:
The length of x-intercept made by the pair of lines \( 2x^2 + xy - 6y^2 - 2x + 17y - 12 = 0 \) is:
If the ellipse \(4x^2 + 9y^2 = 36\) is confocal with a hyperbola whose length of the transverse axis is 2, then the points of intersection of the ellipse and hyperbola lie on the circle:
Evaluate the integral: \[ I = \int_{-\pi}^{\pi} \frac{x \sin x}{1 + \cos^2 x} \,dx. \]
The domain of the real-valued function \( f(x) = \sqrt{9 - \sqrt{x^2 - 144}} \) is