List of top Questions asked in AP EAPCET

\( \csc 48^\circ + \csc 96^\circ + \csc 192^\circ + \csc 384^\circ = \)
\( 1 + \frac{4}{15} + \frac{4 \cdot 10}{15 \cdot 30} + \frac{4 \cdot 10 \cdot 16}{15 \cdot 30 \cdot 45} + \cdots \infty \)
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
When a sphere is taken to the bottom of a sea of depth $1~\text{km}$, it contracts in volume by $0.01%$. Then the bulk modulus of the material of the sphere is (Acceleration due to gravity = $10~\text{m/s}^2$)
The increasing order of number of lone pair electrons on the central atom of the following molecules is which of the following?
I) ${ClF3}$
II) ${XeF2}$
III) ${SF4}$
IV) ${SiH4}$
The number of primary (1$^\circ$), secondary (2$^\circ$), and tertiary (3$^\circ$) alcohols possible for the formula C$_5$H$_{12}$O respectively are:

Match the following:

List-I (Atomic number, Z)List-II (Block)
A) 112I) \(s\)
B) 116II) \(p\)
C) 88III) \(d\)
D) 100IV) \(f\)
Observe the following reactions
I) Sucrose (aq) + H2O →[x] glucose + fructose
II) Glucose (aq) →[y] ethanol + CO2
What are $x$ and $y$ respectively? Identify the correct option from the following:
The set of all real values of $x$ such that \[ f(x) = \frac{[x] - 1}{\sqrt{[x]^2 - [x] - 6}} \] is a real valued function is