List of top Mathematics Questions asked in AP EAPCET

OABCD is a pentagon in which \(OA\) and \(CB\) are parallel and \(OD\) and \(AB\) are parallel. If \[ \overrightarrow{OA}=\overrightarrow{a}, \qquad \overrightarrow{OD}=\overrightarrow{d}, \] and \[ \frac{OA}{CB}=2, \qquad \frac{OD}{AB}=\frac13, \] then \[ \overrightarrow{AD}+\overrightarrow{OC}+\overrightarrow{DC} \] is equal to:

Let $\overline{a}=x\overline{i}-2\overline{j}+3\overline{k}$, $\overline{b}=-2\overline{i}+x\overline{j}-\overline{k}$ and $\overline{c}=7\overline{i}-2\overline{j}+x\overline{k}$. If $x=x_0$ is the point of the local maxima of $f(x)=\overline{a}\cdot(\overline{b}\times\overline{c})$, then at $x=x_0$, $\overline{a}\cdot\overline{b}+\overline{b}\cdot\overline{c}+\overline{c}\cdot\overline{a}=$

If the angles of triangle ABC are in arithmetic progression and the sides a, b and c satisfy \( \frac{\sqrt{3}}{2} < \frac{b}{a} < 1 \) and \( c < b \), then the possible values of the side c are:

If \( \sinh^{-1}(2) + \sinh^{-1}(3) = \alpha \), then \( \cosh \alpha = \)

All the values of \(\alpha\) satisfying the equations \( 2\cos^2 \alpha - 3\cos \alpha = 32\tan^8 \theta \) and \( 3\cos 2\theta = 1 \) are:

The domain of \( f(x) = \cos^{-1}[\log_2(x^2+5x+8)] \) is:

If \( A+B+C=\pi \) and \( \cos A = \cos B \cos C \), then \( \tan A - \tan B - \tan C = \)

Calculate \[ \sin\frac{8\pi}{9}\, \sin\frac{7\pi}{9}\, \sin\frac{2\pi}{3}\, \sin\frac{5\pi}{9}. \]

If \[ \frac{3x^2+x+2} {(3x^2+x+4)(3x^2+x+1)} = \frac{Ax+B}{3x^2+x+4} + \frac{Cx+D}{3x^2+x+1}, \] then \((A+B)+(C+D)\) is:

If \( 7\sin x + 15\sin y = 17 \), then the maximum value of \( 7\cos x + 15\cos y \) is:

The number of skew symmetric matrices of order \( 3 \times 3 \) that can be formed by using all the elements 0, \( \pm a, \pm b, \pm c \) is:

Evaluate \[ \sum_{r=1}^{\infty} \frac{1\cdot3\cdot5\cdots(2r-1)} {2^{2r}r!} (\sqrt{3})^r : \]

Let the numerical values of the coefficients of a polynomial belong to the set \( \{0, 1, 2, \dots, 9\} \). Then the number of reciprocal polynomials of third degree with the leading coefficient 1 that can be formed is:

All the solutions \((n,r)\) of the equation \( \frac{{}^nC_r}{{}^{n+1}C_r} = \frac{1}{3} \) can be obtained from one of the following equations given in the options for \( k=1,2,3, \dots \):

If the expansion of \[ \left(\frac{1+15x}{1-3x}\right) \] is valid and the coefficient of \(x^3\) in its expansion is \(k(3^3)\), then \(k=\)

If \( \alpha, \beta, \gamma \) are the roots of the equation \( x^3 - 3x + 1 = 0 \), then \( \frac{\alpha}{1-\alpha} + \frac{\beta}{1-\beta} + \frac{\gamma}{1-\gamma} = \)

If \( x^5 + ax^4 + bx^3 + cx^2 + 5x + d = 0 \) is an odd order reciprocal equation of second type and \( \frac{1+\sqrt{3}i}{2} \) is a root, then \( b-c = \)

The quadratic expression having zero's equal to the non-integral roots of \( ||3x-4|-6|=5 \) is:

Consider the quadratic expression \( f(x) = x^2 + (10-a)x - 10a \). The sum of all values of 'a', such that the roots of \( f(x)=3 \) are integers is:

The modulus of the product of all the values of \( (2+3i)^{3/5} \) is:

On a matrix A when three elementary operations namely interchange of \( R_1 \) and \( R_2 \), \( R_2 \rightarrow R_2 - 2R_1 \), \( R_3 \rightarrow R_3 - 3R_1 \) are applied successively, A is transformed to \( \begin{bmatrix} 1 & 3 & 4 \\ 2 & 1 & 5 \\ 6 & 1 & 2 \end{bmatrix} \). Then \( \text{Tr}(A) = \)

Among the solutions of the equation \( x^6 = 64 \), the sum of all those solutions whose real part is negative is:

For a \( 3 \times 3 \) non singular matrix A, if \( \text{Adj}(\text{Adj}(\text{Adj}(\text{Adj}(A)))) = |A|^n A \), then \( n = \)

If \( \text{Arg}(\frac{z-1}{z+5}) = \pi/3 \) and \( |z-1|=|z+5| \), then \( |z|^2 = \)

If the two systems of equations \( x+y-2z=0, 4x+4y-8z=0, 3x+3y-6z=0 \) and \( x+y+z=3, 2x+2y-z=\lambda, x+y-\mu z=1 \) have the same set of solutions, then \( \lambda+\mu = \)