List of top Mathematics Questions asked in AP EAMCET

P, Q, and R try to hit the same target one after another. Their probabilities of hitting are $ \frac{2}{3}, \frac{3}{5}, \frac{5}{7} $ respectively. Find the probability that the target is hit by P or Q but not by R.

Let $ A(2, 3), B(1, -1) $ be two points. If $ P $ is a variable point such that $ \angle APB = 90^\circ $, then the locus of $ P $ is

If $ \alpha, \beta, \gamma $ are the roots of the determinant equation: \[ \begin{vmatrix} 1-x & -2 & 1
-2 & 4-x & -2
1 & -2 & 1-x \end{vmatrix} = 0 \] then $ \alpha \beta + \beta \gamma + \gamma \alpha $ is:

If $ L, M, N $ are the midpoints of the sides PQ, QR, and RP of triangle $ \Delta PQR $, then $ \overline{QM} + \overline{LN} + \overline{ML} + \overline{RN} - \overline{MN} - \overline{QL} = $:

If the coefficients of $x^5$ and $x^6$ are equal in the expansion of $ \left( a + \frac{x}{5} \right)^{65} $, then the coefficient of $x^2$ in the expansion of $ \left( a + \frac{x}{5} \right)^4 $ is:

Given \[ A = \begin{bmatrix} 0 & 1 & 2 \\ 4 & 0 & 3 \\ 2 & 4 & 0 \end{bmatrix} \] $\quad B \text{ is a matrix such that }$ $AB = BA. \text{ If } AB \text{ is not an identity matrix, then the matrix that can be taken as } B \text{ is:} $

Given the equation: \[ y = (\tan^{-1} 2x)^2 + (\cot^{-1} 2x)^2, \] find the expression: \[ (1+4x^2)^2 y'' - 16. \]

If the line through the point $ P(5,3) $ meets the circle $ x^2 + y^2 - 2x - 4y + \alpha = 0 $ at $ A(4, 2) $ and $ B(x_1, y_1) $, then $ PA \times PB = $:

The range of the real valued function $ f(x) = \frac{x^2 + 2x - 15}{2x^2 + 13x + 15} $ is:

If the points with position vectors \[ (\mathbf{a}i + 10j + 13k), \quad (6i + 11j + 11k), \quad \left(\frac{9}{2}i + \beta j - 8k\right) \] are collinear, then evaluate $ (19a - 6\beta)^2 $.

Evaluate the sum: \[ \sin^2 18^\circ + \sin^2 24^\circ + \sin^2 36^\circ + \sin^2 42^\circ + \sin^2 78^\circ + \sin^2 90^\circ + \sin^2 96^\circ + \sin^2 102^\circ + \sin^2 138^\circ + \sin^2 162^\circ. \]

If $ H $ is the orthocenter of $ \triangle ABC $ and $ AH = x $, $ BH = y $, $ CH = z $, then evaluate: \[ \frac{abc}{xyz} \]

Evaluate the expression: \[ \sin^2 76^\circ + \sin^2 16^\circ - \sin 76^\circ \sin 16^\circ \]

Evaluate the expression: \[ \tan 6^\circ \tan 42^\circ \tan 66^\circ \tan 78^\circ \]

The absolute value of the difference of the coefficients of $x^4$ and $x^6$ in the expansion of
$\frac{2x^2}{(x^2+1)(x^2+2)}$
is:

While solving a system of linear equations $ AX = B $ using Cramer’s rule, if \includegraphics[]{6.png}

If $ M_1 $ and $ M_2 $ are the maximum values of $ \frac{1}{11 \cos 2x + 60 \sin 2x + 69} $ and $ 3 \cos^2 5x + 4\sin^2 5x $ respectively, then $ \frac{M_1}{M_2} = $:

5 boys and 6 girls are arranged in all possible ways. Let $X$ denote the number of linear arrangements in which no two boys sit together, and $Y$ denote the number of linear arrangements in which no two girls sit together. If $Z$ denotes the number of ways of arranging all of them around a circular table such that no two boys sit together, then $X:Y:Z$ = ?

If the number of real roots of $ x^9 - x^5 + x^4 - 1 = 0 $ is $ n $, the number of complex roots having argument on imaginary axis is $ m $, and the number of complex roots having argument in the second quadrant is $ k $, then $ m.n.k $ is:

If $ \alpha $ and $ \beta $ are two distinct negative roots of the equation $ x^5 - 5x^3 + 5x^2 - 1 = 0 $, then the equation of least degree with integer coefficients having $ \sqrt{-\alpha} $ and $ \sqrt{-\beta} $ as its roots 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 $ (\alpha, \beta, \gamma) $ are the direction cosines of an angular bisector of two lines whose direction ratios are (2,2,1) and (2,-1,-2), then $ (\alpha + \beta + \gamma)^2 $ is:

If $ f(x + h) = 0 $ represents the transformed equation of $$ f(x) = x^4 + 2x^3 - 19x^2 - 8x + 60 = 0 $$ and this transformation removes the term containing $ x^3 $, then $ h $ is:

Find the general solution of the differential equation $ ( \sin y \cos^2 y - x \sec^2 y ) dy = (\tan y) dx $.

The set of all real values of $x$ satisfying the inequality $\frac{7x^2 - 5x - 18}{2x^2 + x - 6}<2$ is