List of top Questions asked in AP EAPCET

There are 8 boys and 7 girls in a class room. If the names of all those children are written on paper slips and 3 slips are drawn at random from them, then the probability of getting the names of one boy and two girls or one girl and two boys is
Let \(x_1, x_2, \ldots, x_{11}\) be the observations satisfying \(\sum_{i=1}^{11} (x_i - 4) = 22\) and \(\sum_{i=1}^{11} (x_i - 4)^2 = 154\). If the mean and variance of the observations are \(\alpha\) and \(\beta\), then the quadratic equation having the roots \(\frac{\alpha}{\beta}\) and \(\frac{\beta}{\alpha}\) is:
If \( \overline{a} = 2\overline{i} - 3\overline{j} + 5\overline{k} \) and \( \overline{b} = -\overline{i} + 3\overline{j} + 3\overline{k} \) are two vectors, then the vector of magnitude 28 units in the direction of the vector \( \overline{a} - \overline{b} \) is:
In \( \triangle ABC \), if \( a = 8 \), \( b = 10 \), \( c = 12 \), then \( \frac{r}{R} = \)
The general solution satisfying both the equations \(\sin x = -\frac{3}{5}\) and \(\cos x = -\frac{4}{5}\) is:
If \( \sqrt{3} \cos \theta + \sin \theta > 0 \), then the range of \( \theta \) is:
\( \csc 48^\circ + \csc 96^\circ + \csc 192^\circ + \csc 384^\circ = \)
\( 1 + \frac{4}{15} + \frac{4 \cdot 10}{15 \cdot 30} + \frac{4 \cdot 10 \cdot 16}{15 \cdot 30 \cdot 45} + \cdots \infty \)
If \(C_0, C_1, C_2, \dots, C_n\) are the binomial coefficients in the expansion of \((1 + x)^n\), then \((C_0 + C_1) - (C_2 + C_3) + (C_4 + C_5) - (C_6 + C_7) + \dots = \)
The number of ways in which a committee of 7 members can be formed from 6 teachers, 5 fathers and 4 students in such a way that at least one from each group is included and teachers form the majority among them, is:
The cubic equation whose roots are the squares of the roots of the equation \( x^3 - 2x^2 + 3x - 4 = 0 \) is
Let \((a-3)x^2 + 12x + (a+6) > 0, \forall x \in \mathbb{R} \text{ and } a \in (t, \infty)\). If \(\alpha\) is the least positive integral value of \(a\), then the roots of \((\alpha-3)x^2 + 12x + (\alpha+2) = 0\) are:
The sum of the squares of the imaginary roots of the equation $ z^8 - 20z^4 + 64 = 0 $ is:
The rank of the matrix \( \begin{bmatrix} 2 & -3 & 4 & 0 \\ 5 & -4 & 2 & 1 \\ 1 & -3 & 5 & -4 \end{bmatrix} \) is
If \( P = \begin{bmatrix} 1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4 \end{bmatrix} \) is the adjoint of a matrix \( A \) and \( \det(A) = 4 \), then the value of \( \alpha \) is:
If \( 11^{12} - 11^2 = k(5 \times 10^9 + 6 \times 10^9 + 33 \times 10^8 + 110 \times 10^7 + \ldots + 33) \), then find the value of \( k \).
If \( f(x) = (x+1)^2 - 1, x \ge -1 \), then \( \{x \mid f(x) = f^{-1}(x)\} \) is:
Let \( [t] \) denote the greatest integer function and \( [t - m] = [t] - m \) when \( m \in \mathbb{Z} \). If \( k = 2[2x - 1] - 1 \) and \( 3[2x - 2] + 1 = 2[2x - 1] - 1 \), then the range of \( f(x) = [k + 5x] \) is:
In a Carnot engine, if the absolute temperature of the source is \( 25% \) more than the absolute temperature of the sink, then the efficiency of the engine is
A force \( F \) is applied on a body of mass \( m \) so that the body starts moving from rest. The power delivered by the force at time \( t \) is proportional to:
Evaluate \( \int \frac{\sec^2 x}{\sin^7 x} \, dx - \int \frac{7}{\sin^7 x} \, dx \):
In triangle $ ABC $, if $ a = 13 $, $ b = 8 $, $ c = 7 $, then $ \cos(B+C) = $
In a triangle ABC, if \((r_1 - r_3)(r_1 - r_2) - 2r_2r_3 = 0\), then \(a^2 - b^2 =\)
If $ \alpha, \beta, \gamma $ are the roots of the equation $ x^3 + px^2 + qx + r = 0 $, then $ \alpha^3 + \beta^3 + \gamma^3 = $
In an LCR series circuit, if the potential differences across inductor, capacitor, and resistor are $60~\text{V}$, $30~\text{V}$, and $40~\text{V}$ respectively, then the net voltage applied to the circuit is