List of top Mathematics Questions asked in AP EAPCET

The value of \(c\) of Lagrange's Mean Value Theorem for \[ f(x)=\sqrt{25-x^2} \] on \([1,5]\) is:

The integral \[ \int \frac{1}{\sqrt[4]{(x-1)^3(x+2)^5}} \, dx \] is equal to:

The value of the integral \[ \int_{-\frac{\pi}{8092}}^{\frac{\pi}{8092}} \frac{\sec(2023x)}{1 + (2023)^{2023x}} \, dx \] is equal to:

The value of the integral \[ \int_{-2}^{2} x^4 (4 - x^2)^{\frac{7}{2}} \, dx \] is equal to:

The value of the integral \[ \int_{0}^{2} x^8 \left( \frac{4}{x^2} - 1 \right)^{\frac{5}{2}} \, dx \] is equal to:

The value of the integral \[ \int_{-\frac{\pi}{8}}^{\frac{\pi}{8}} \frac{\sin^4(4x)}{1 + e^{4x}} \, dx \] is equal to:

If \( A = \begin{bmatrix} 1 & 2 3 & 4 \end{bmatrix} \), then \( \text{adj}(\text{adj}(\text{adj } A)) \)

If \( A = \begin{bmatrix} 5 & 5\alpha & \alpha 0 & \alpha & 5\alpha 0 & 0 & 5 \end{bmatrix} \) and \( \det(A^2) = 25 \), then \( |\alpha| = \)

If \( \begin{vmatrix} 9 & 25 & 16 16 & 36 & 25 25 & 49 & 36 \end{vmatrix} = K \), then \( K, K + 1 \) are the roots of the equation:

\( A = \begin{bmatrix} 0 & k & k k & -4 & -6 k & -3 & -5 \end{bmatrix} \) is a singular matrix for:

If \( a \neq b \neq c \), \( \Delta_1 = \begin{vmatrix} 1 & a^2 & bc 1 & b^2 & ca 1 & c^2 & ab \end{vmatrix} \), \( \Delta_2 = \begin{vmatrix} 1 & 1 & 1 a^2 & b^2 & c^2 a^3 & b^3 & c^3 \end{vmatrix} \) and \( \frac{\Delta_1}{\Delta_2} = \frac{6}{11} \), then \( 11(a + b + c) = \)

A value of \( \theta \) lying between \( 0 \) and \( \pi / 2 \) and satisfying \[ \begin{vmatrix} 1 + \sin^2 \theta & \cos^2 \theta & 4 \sin 4\theta \sin^2 \theta & 1 + \cos^2 \theta & 4 \sin 4\theta \sin^2 \theta & \cos^2 \theta & 1 + 4 \sin 4\theta \end{vmatrix} = 0 \] is:

If \( \begin{vmatrix} 1 & 2 & 3 - \lambda 0 & -1 - \lambda & 2 1 - \lambda & 1 & 3 \end{vmatrix} = A\lambda^3 + B\lambda^2 + C\lambda + D \), then \( D + A = \)

If \( A = \begin{bmatrix} x & 2 & 1 -2 & y & 0 2 & 0 & -1 \end{bmatrix} \), \( x \) and \( y \) are non-zero numbers, trace of \( A = 0 \) and determinant of \( A = -6 \), then the minor of the element \( 1 \) of \( A \) is:

The determinant \[ \det \begin{bmatrix} \frac{a^2 + b^2}{c} & c & c a & \frac{b^2 + c^2}{a} & a b & b & \frac{c^2 + a^2}{b} \end{bmatrix} \] is equal to:

If \( A = \begin{bmatrix} x & y & y y & x & y y & y & x \end{bmatrix} \) is a matrix such that \( 5A^{-1} = \begin{bmatrix} -3 & 2 & 2 2 & -3 & 2 2 & 2 & -3 \end{bmatrix} \), then \( A^2 - 4A = \)

If \( A = \begin{bmatrix} a & 1 & 2 1 & 2 & b c & 1 & 3 \end{bmatrix} \) 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 value of the limit \( \lim_{n \to \infty} \left( \frac{1}{1^2 + n^2} + \frac{2}{2^2 + n^2} + \frac{3}{3^2 + n^2} + \cdots + \frac{n}{n^2 + n^2} \right) \) is equal to:

The value of the integral \( \int_{-2\pi}^{2\pi} \sin^4 x \cos^6 x \, dx \) is equal to:

The value of the integral \( \int_{0}^{32\pi} \sqrt{1 - \cos 4x} \, dx \) is equal to:

The value of the integral \( \int_{0}^{\pi/2} \sin^6 x \cos^4 x \, dx \) is equal to:

The value of the integral \( \int_{-\frac{\pi}{15}}^{\frac{\pi}{15}} \frac{\cos 5x}{1 + e^{5x}} \, dx \) is equal to:

The value of the integral \(\int_{0}^{3\pi/2} \frac{\cos^3 x}{\cos^3 x + \sin^3 x} \, dx\) is:

The value of the integral \(\int_{0}^{\pi} \frac{x \sin x}{1 + \cos^2 x} \, dx\) is:

The value of the integral \(\int_{0}^{\pi} \frac{x \sin x}{\sin^2 x + 2 \cos^2 x} \, dx\) is: