List of top Questions asked in AP EAPCET

A Carnot engine having efficiency $60%$ receives heat from a source at temperature $600~\text{K$. For the same sink temperature, to increase its efficiency to $80%$, the temperature of the source is}
A gaseous mixture consists of $2$ moles of oxygen and $4$ moles of argon at temperature $T$. Neglecting all vibrational modes, the total internal energy of the mixture is
If \( x^2 - 5x + 6 \) is a factor of \( f(x) = x^4 - 17x^3 + kx^2 - 247x + 210 \), find the other quadratic factor of \( f(x) \).
Evaluate the integral $\displaystyle \int_0^{\frac{\pi{2}} \log(\tan x + \cot x)\, dx$}
If \(|\vec{a}| = 2, |\vec{b}| = 3, |\vec{c}| = 5, |\vec{a} + \vec{b} + \vec{c}| = \sqrt{69}\) and angle between \((\vec{a}, \vec{b}) = \dfrac{\pi}{3}\), then angle between \((\vec{c}, \vec{a}) =\)
\( \int \frac{x}{(1-x^2)\sqrt{2 - x^2} dx = \)}
If \(P\) is a variable point which is at a distance of 2 units from the line \(2x - 3y + 1 = 0\) and \(\sqrt{13}\) units from the point (5, 6), then the equation of the locus of \(P\) is
\( \int \frac{1 + x + \sqrt{x + x^2}}{\sqrt{x + \sqrt{1 + x}}} dx = \)
If $a = \ln \left( \frac{1}{z^2} \right)$ and $z$ is any non-zero complex number such that $|z| = 1$, then which of the following is the correct expression for $a$?
Evaluate \(\lim\limits_{x \to \infty} \dfrac{5x^3 - x^2 \sin 5x}{x^3 \cos 4x + 7|x|^3 - 4|x| + 3}\)
The bob of a simple pendulum of length $200~\text{cm}$ is released from horizontal position.
If $10%$ of its initial energy is lost to air resistance, then the speed of bob at the mean position is
(Acceleration due to gravity $= 10~\text{m/s}^2$)
If \( ax^2 + bx + e>0 \) for all \( x \in \mathbb{R} \) and the expressions \( cx^2 + ax + b \) and \( ax^2 + bx + c \) have their extreme values at the same point \( x \), then for the expression \( cx^2 + ax + b \), find the correct statement regarding its extreme value.
If $P_n$ denotes the product of the binomial coefficients in the expansion of $(1 + x)^n$, then find \[ \frac{P_{n+1}}{P_n}. \]
If a straight current-carrying wire of linear density $0.12~\text{kg/m$ is suspended in mid-air by a uniform horizontal magnetic field of $0.5~\text{T}$ normal to the length of the wire, then the current through the wire is (Neglect earth’s magnetic field)}
Two concentric loops $A$ and $B$ of same radius $2\pi~\text{cm$ are placed at right angles to each other. If the currents flowing through $A$ and $B$ are $3~\text{A}$ and $4~\text{A}$ respectively, then the net magnetic field at their common center is}
A short bar magnet is placed in a uniform magnetic field of $2~\text{T}$ such that the axis of the magnet makes an angle of $45^\circ$ with the field. If the torque acting is $0.36~\text{Nm}$, the magnetic moment of the magnet is
In a triangle ABC, if \(r_1 = 3, r_2 = 4, r_3 = 6\), then \(b =\)

Which of the following is the correct statement for an ideal gas (constant =\( \textit{energy}\) )?
 

If \[ A = \begin{bmatrix} a & b & c \\ d & e & f \\ l & m & n \end{bmatrix} \] is a matrix such that $|A|>0$ and \[ Adj(A) = \begin{bmatrix} 0 & 4 & -6 \\ 10 & 8 & 0 \\ 2 & 4 & -4 \end{bmatrix}, \] then find the value of \[ \frac{cd}{fb} + \frac{ln}{em}. \]
If \[ \binom{p}{q} = \binom{p}{q} \quad \text{and} \quad \sum_{i=0}^m \binom{10}{i} \binom{20}{m-i} \text{ is maximum, then find } m. \]
The equation \((2p - 3)x^2 + 2pxy - y^2 = 0\) represents a pair of distinct lines
A steel sphere of radius $1.2~\text{cm}$ collides with another steel sphere at rest.
If the collision is elastic and the first sphere moves with $\dfrac{7}{9}$ of its initial velocity after collision,
then the radius of the second sphere is
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:
The catalyst used for the isomerisation of n-alkanes to branched chain alkanes is:
What are X and Y respectively, in the given set of reactions?
CH3CH2CH2Cl