List of top Mathematics Questions asked in AP EAPCET

In \( \triangle ABC \), if \( r_1 : r_2 = 7:8 \) and \( r_1 : r_3 = 3:4 \), then \( a : b : c = \)
The coefficient of \( x^3 \) in the expansion of \( (1 - x)^{\frac{3}{2}} \), where \( |x|<1 \), is:
If \( \cos\alpha + \cos\beta = \frac{1}{3} \) and \( \sin\alpha + \sin\beta = \frac{1}{4} \), then \( \cos(\alpha + \beta) = \)
A question paper has two sections A and B. Section A has 8 questions and Section B has 6 questions. A student has to answer 10 questions, choosing at least 4 from section A and at least 3 from section B. The number of ways the student can answer the paper is:
The number of positive even divisors of 6300 is:
If 5 dice are rolled simultaneously, then the number of ways of getting a total of 7 from the numbers on their faces is:
If \( P(x) = 0 \) is a polynomial of least degree with integer coefficients and \( \sqrt{2} + \sqrt{3}i \) is one of its roots, then that equation is:
If the sum of the coefficients of even powers of \( x \) in the expansion of \( (1 - x + x^2)^{2n} \) is 3281, then \( n \) is:
If the roots of the equation \( 3x^2 + 4kx + 3 = 0 \) are non-real, then \( k \) lies in the interval:
The sum of the fourth powers of the roots of the equation \( 16x^2 - 10x + 1 = 0 \) is:
If \( \csc\theta \) and \( \cot\theta \) are the roots of \( cx^2 + bx + a = 0 \) where \( bc \neq 0 \), then evaluate \( b^2(b^2 - 4ac) \):
If \( -3 + ix^2y \) and \( x^2 + y + 4i \) are complex conjugates, then \( x = \):
If \( z = 1 + \cos\theta - i\sin\theta \) and \( 0<\theta<\pi \), then \[ \left[ |z - 1|^2 \cdot \frac{|z|^2}{4} \right]^{1/2} = \]
In the Argand plane, the values of \( z \) satisfying the equation \( |z - 1| = |i(z + 1)| \) lie on:
If \( 1, \omega, \omega^2 \) are the cube roots of unity and \( f(x, y) = (x + y)(x\omega + y\omega^2)(x\omega^2 + y\omega) \), then \( f(2, 3) \) is:
If \( f : \mathbb{R} \setminus \{0\} \to \mathbb{R} \) is defined by \( f(x) = x + \frac{1}{x} \), then the value of \( \left(f(x)\right)^2 \) is:
If \( A = \begin{bmatrix} 2 & 0 & -3 \\ 4 & 3 & 1 \\ -5 & 7 & 2 \end{bmatrix} \) is expressed as a sum of a symmetric matrix \( P \) and a skew-symmetric matrix \( Q \), then \( P^T - Q^T \) equals:
The sum of the distinct values of \( x \) for which the matrix \( A = \begin{bmatrix} 1 & 1 & x \\ 1 & x & 1 \\ x & 1 & 1 \end{bmatrix} \) has no inverse, is:
If \( A + 2B = \begin{bmatrix} 1 & 2 & 0 \\ 6 & -3 & 3 \\ -5 & 3 & 1 \end{bmatrix} \) and \( 2A - B = \begin{bmatrix} 2 & -1 & 5 \\ 2 & -1 & 6 \\ 0 & 1 & 2 \end{bmatrix} \), then \( \text{Tr}[A] - \text{Tr}[B] \) equals:
The range of the real valued function \( f(x) = \sqrt{9 - x^2} \) is:
If \( y = y(x) \) is the solution of the differential equation \[ x \frac{dy}{dx} = y + xe^{-\frac{y}{x}}, \quad y(1) = \log e \] , then \( y(e) = \)
The order and degree of the differential equation \[ 3x^2 \frac{d^2 y}{dx^2} - \sin\left( \frac{d^3 y}{dx^3} \right) + \cos(xy) = 0 \] are:
Let \( c_1, c_2, c_3, c_4 \) be arbitrary constants. The order of the differential equation corresponding to \[ y = c_1 e^x + c_2 e^{\log_e x} + c_3 \sin^2 x - c_4 (\cos^5 x - 1) \] is:
If \( 5f(x) + 3f\left( \frac{1}{x} \right) = 2 - \frac{1}{x}, x \ne 0 \), then \( \int_1^2 f\left( \frac{1}{x} \right) dx = \)
If \[ f(x) = \lim_{n \to \infty} n^2 \left( \frac{1}{x^n} - \frac{1}{x^{n+1}} \right), x>0, \] then \[ \int x f(x) \, dx = ? \]