List of top Mathematics Questions asked in AP EAPCET

If \[ \int \frac{4e^x + 6e^{-x}}{9e^x - 4e^{-x}} \, dx = Ax + B \log \left( 9e^{2x} - 4 \right) + C, \text{ then } (A, B) = \]
If \( f(x) = \int \frac{dx}{x^2 + 2} \) and \( f(\sqrt{2}) = 0 \), then \( f(0) = \)
Evaluate the integral: \[ \int \frac{e^x \left( 2 + \sin(2x) \right)}{1 + \cos(2x)} \, dx \]
If \( I = \int_{-a}^{a} \left( x^4 - 2x^2 \right) \, dx \), then \( I \) is minimum at \( a = \):

Assertion (A): \[ \int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{(\sin x)^{\sqrt{2}}}{(\sin x)^{\sqrt{2}} + (\cos x)^{\sqrt{2}}} \, dx = \frac{\pi}{12} \]

Reason (R): \[ \int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{f(x)}{f(x) + f\left(\frac{\pi}{2}-x\right)} \, dx = \frac{\pi}{12} \]

If \( [x] \) is the greatest integer not exceeding \( x \), then \[ \int_{-0.5}^{1.5} x^2 [x] \, dx = \]
Evaluate the integral: \[ \int_0^{50\pi} \sqrt{1 - \cos 2x} \, dx \]
The area (in square units) bounded by the curves \( x^2 = 9y \), \( (x - 6)^2 = 9y \), and the X-axis is:
If \( \frac{dy}{dx} = f(x,y) \) is a homogeneous differential equation, then the general form of \( f(x,y) \) is:
The order and degree of the differential equation \[ \frac{d^3 y}{dx^3} + 2 \left( \frac{d^2 y}{dx^2} \right) + xy = 0 \] are respectively:
If \( f(a) = \log \left| \frac{1 - a}{1 + a} \right| \) for \( a \neq \{-1, 1\} \), then the set of values of all \( a \), for which \( f\left( \frac{2a}{1 + a^2} \right)>0 \) is:
If \( \det(AB) = \det(A)\det(B) \) and \( A \) is a non-singular matrix of order \( 3 \times 3 \), then \( \det(\text{adj}(A)) \) is:
One of the 15th roots of \( -1 \) is:
The product of the four values of \( \left( 1 + i\sqrt{3} \right)^{3/4} \) is:
If one root of the equation \( ax^2 + bx + c = 0 \) is twice another root, then the equation \( ax^2 + bx + c = 0 \) is:
If \( -1 \) is a twice repeated root of the equation \( ax^3 + bx^2 + cx + 1 = 0 \), then \( ax^3 + bx^2 + cx + 1 = 0 \) represents:
If \( C_j = \binom{n}{j} \), then \( C_0 C_t + C_1 C_{t+1} + C_2 C_{t+2} + \dots + C_n = \)
The coefficient of the highest power of \( x \) in the expansion of \[ \left( x + \sqrt{x^2 - 1} \right)^3 + \left( x - \sqrt{x^2 - 1} \right)^8 \text{ is:} \]
The number of non-negative integral solutions of \( x_1 + x_2 + x_3 + x_4 = 10 \) is:
If \( A = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \), where \( a, b, c, d \in \{-1, 1\} \), then the number of singular matrices in \( A \) is:
If \( \cot x \cot y = a \) and \( x + y = \frac{\pi}{6} \), then the quadratic equation satisfying \( \cot x \) and \( \cot y \) is:
If \( \tan A + \tan B = x \) and \( \cot A + \cot B = y \), then \( \tan(A + B) = \)
If \( \triangle ABC \) is a right-angled isosceles triangle and \( \angle C = 90^\circ \), then \( r = \frac{1}{5} \) is:
If \( 7i - 4j - 5k \) is the position vector of vertex A of a tetrahedron ABCD and \( -i + 4j - 3k \) is the position vector of the centroid of the triangle BCD, then the position vector of the centroid of the tetrahedron ABCD is:
Let \( \mathbf{OA = i + 2j - 2k} \) and \( \mathbf{OB = -2i - 3j + 6k} \) be the position vectors of two points A and B. If C is a point on the bisector of \( \angle AOB \) and \( OC = \frac{\sqrt{42}}{2} \), then \( OC = \)