List of top Mathematics Questions asked in AP EAPCET

A radar system can detect an enemy plane in one out of ten consecutive scans. The probability that it can detect an enemy plane at least twice in four consecutive scans is:
Let \( \vec{a} = 2\hat{i} + \hat{j} + 3\hat{k} \), \( \vec{b} = 3\hat{i} + 3\hat{j} + \hat{k} \), and \( \vec{c} = \hat{i} - 2\hat{j} + 3\hat{k} \) be three vectors. If \( \vec{r} \) is a vector such that \( \vec{r} \times \vec{a} = \vec{r} \times \vec{b} \) and \( \vec{r} . \vec{c} = 18 \), then the magnitude of the orthogonal projection of \( 4\hat{i} + 3\hat{j} - \hat{k} \) on \( \vec{r} \) is:
In \( \triangle ABC \), if \( \sin^2 B = \sin A \) and \( 2\cos^2 A = 3\cos^2 B \), then the triangle is:
If the position vectors of A, B, C, D are \( \vec{A} = \hat{i} + 2\hat{j} + 2\hat{k}, \vec{B} = 2\hat{i} - \hat{j}, \vec{C} = \hat{i} + \hat{j} + 3\hat{k}, \vec{D} = 4\hat{j} + 5\hat{k} \), then the quadrilateral ABCD is a:
Two students appeared simultaneously for an entrance exam. If the probability that the first student gets qualified in the exam is \( \frac{1}{4} \) and the probability that the second student gets qualified in the same exam is \( \frac{2}{5} \), then the probability that at least one of them gets qualified in that exam is
If \( \sum\limits_{i=1}^{9} (x_i - 5) = 9 \) and \( \sum\limits_{i=1}^{9} (x_i - 5)^2 = 45 \), then the standard deviation of the nine observations \( x_1, x_2, \ldots, x_9 \) is
The set of all real values of \( c \) so that the angle between the vectors
\( \vec{a} = c\hat{i} - 6\hat{j} + 3\hat{k} \) and \( \vec{b} = x\hat{i} + 2\hat{j} + 2c\hat{k} \) is an obtuse angle for all real \( x \), is:
If in \( \triangle ABC \), \( B = 45^\circ \), \( a = 2(\sqrt{3} + 1) \) and area of \( \triangle ABC \) is \( 6 + 2\sqrt{3} \) sq. units, then the side \( b = \ ? \)
In \( \triangle ABC \), if A, B, C are in arithmetic progression, then \[ \sqrt{a^2 - ac + c^2} . \cos\left(\frac{A - C}{2}\right) =\ ? \]
The equation \[ \cos^{-1}(1 - x) - 2 \cos^{-1} x = \frac{\pi}{2} \] has:
If \( \sinh^{-1}(2) + \sinh^{-1}(3) = \alpha \), then \( \sinh\alpha = \) ?
\[ \sum_{r=1}^{15} r^2 \left( \frac{{}^{15}C_r}{{}^{15}C_{r-1}} \right) =\ ? \]
Evaluate the following expression: \[ \frac{1}{81^n} - \binom{2n}{1} . \frac{10}{81^n} + \binom{2n}{2} . \frac{10^2}{81^n} - .s + \frac{10^{2n}}{81^n} = ? \]
If \( x \) is a positive real number and the first negative term in the expansion of \[ (1 + x)^{27/5} \text{ is } t_k, \text{ then } k =\ ? \]
An eight digit number divisible by 9 is to be formed using digits from 0 to 9 without repeating the digits. The number of ways in which this can be done is
If \[ \frac{x^2}{(x^2 + 2)(x^4 - 1)} = \frac{A}{x^2 - 1} + \frac{B}{x^2 + 1} + \frac{C}{x^2 + 2}, \text{ then } A + B - C =\ ? \]
A string of letters is to be formed by using 4 letters from all the letters of the word “MATHEMATICS”. The number of ways this can be done such that two letters are of same kind and the other two are of different kind is
If \( \alpha \) is the common root of the quadratic equations \( x^2 - 5x + 4a = 0 \) and \( x^2 - 2ax - 8 = 0 \), where \( a \in \mathbb{R} \), then the value of \( \alpha^4 - \alpha^3 + 68 \) is:
If \( \alpha, \beta, \gamma \) are the roots of the equation \[ x^3 + px^2 + qx + r = 0, \] then \[ (\alpha + \beta)(\beta + \gamma)(\gamma + \alpha) =\ ? \]
The equation \[ x^{\frac{3}{4}(\log_{x} x)^2 + \log_{x} x^{-\frac{5}{4}}} = \sqrt{2} \] has
If \( \alpha, \beta \) are the roots of \( x^2 - 5x - 68 = 0 \) and \( \gamma, \delta \) are the roots of \( x^2 - 5\alpha x - 6\beta = 0 \), then \( \alpha + \beta + \gamma + \delta = \) ?
If \( \omega_1 \) and \( \omega_2 \) are two non-zero complex numbers and \( a, b \) are non-zero real numbers such that \[ |a\omega_1 + b\omega_2| = |a\omega_1 - b\omega_2|, \] then \( \dfrac{\omega_1}{\omega_2} \) is:
Let \( g(x) = 1 + x - \lfloor x \rfloor \) and \[ f(x) = \begin{cases} -1, & x<0\\ 0, & x = 0 \\ 1, & x>0 \end{cases} \] where \( \lfloor x \rfloor \) denotes the greatest integer less than or equal to \( x \). Then for all \( x \), \( f(g(x)) = \)
If \( f : \mathbb{R} \to A \), defined by \( f(x) = \cos x + \sqrt{3}\sin x - 1 \), is an onto function, then \( A = \)
A value of \( \theta \) lying between \( 0 \) and \( \dfrac{\pi}{2} \) 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: