List of top Questions asked in AP EAPCET

\[ \text{If } \lim_{x \to 0} \frac{\cos 2x - \cos 4x}{1 - \cos 2x} = k, \text{ then evaluate } \lim_{x \to k} \frac{x^k - 27}{x^{k+1} - 81} \]
Evaluate the limit: \[ \lim_{n \to \infty} \left( \frac{1}{1^2 + n^2} + \frac{2}{2^2 + n^2} + \frac{3}{3^2 + n^2} + \cdots + \frac{n}{n^2 + n^2} \right) \]
If a tangent to the hyperbola \( xy = -1 \) is also a tangent to the parabola \( y^2 = 8x \), then the equation of that tangent is:
A is the set of all matrices of order 3 with entries 0 or 1 only. Let \( B \subset A \) be the subset consisting of all matrices with determinant value 1. Let \( C \subset A \) be the subset consisting of all matrices with determinant value -1. Then, which of the following is true?
At 25$^\circ$C, the percentage of ionization of x M acetic acid is 4.242. What is the pH of the acetic acid solution?
Given: $\log 4.242 = 0.6275$, $\log 0.04242 = -1.372$, $K_a = 1.8 \times 10^{-5}$
If $P_n$ denotes the product of the binomial coefficients in the expansion of $(1 + x)^n$, then find \[ \frac{P_{n+1}}{P_n}. \]
A liquid drop of diameter $D$ splits into $3375$ small identical drops. If $S$ is the surface tension of the liquid, then the change in the surface energy in the process is
If all letters of the word COMBINATION are arranged to form 11-letter words with \( C \) and \( N \) at the ends and no vowel in the middle position, find the number of such words.
Consider the following
Statement-I: During isothermal expansion of an ideal gas its enthalpy decreases.
Statement-II: When 2.0 L of an ideal gas expands isothermally into vacuum, $\Delta U = 0$.
209 g of an element reacts with chlorine to form 315.5 g of its chloride. What is the weight of oxygen that reacts with 418 g of the same element? (Cl = 35.5, O = 16)
A student has probability \(\dfrac{2}{3}\) of getting distinction in a test. Out of 5 tests, the probability that he gets distinction in at least 3 tests is
If \(y = (ax + b)\cos x\), then \(y_2 + y_1 \sin 2x + y(1 + \sin^2 x) = \)
Consider the following statements:
Statement-I: CH$_3$NH$_2$ is more basic than NH$_3$, but C$_6$H$_5$NH$_2$ is less basic than NH$_3$.
Statement-II: The order of basic strength of amines in aqueous phase follows
(C$_2$H$_5$)$_2$NH > C$_2$H$_5$NH$_2$ > C$_6$H$_5$NH$_2$
Evaluate the integral $\displaystyle \int_0^{\frac{\pi{2}} \log(\tan x + \cot x)\, dx$}
If \( A + B + C = \frac{\pi}{4} \), then evaluate the expression:
\[ \sin 4A + \sin 4B + \sin 4C \]
The general solution of the differential equation \((x+2y)^3\frac{dy}{dx} = y = 0, y>0\) is
Two thin convex lenses are kept in contact coaxially. If the focal length of the combination is $4~\text{cm$ and the sum of the focal lengths of the two lenses is $18~\text{cm}$, then the focal length of the lens of low power is}
In the structure of diborane, the number of 2-centre-2-electron bonds is X and 3-centre-2-electron bonds is Y. The value of (X + Y) is:
Which of the following sets are correctly matched?
I) Hg — distillation
II) Cu — poling
III) B — zone refining
IV) Ti — liquation
If a ball projected vertically upwards with certain initial velocity from the ground crosses a point at a height of 25 m twice in a time interval of 4 s, then the initial velocity of the ball is
(Acceleration due to gravity $= 10~\text{m/s}^2$)
A body of mass $1~\text{kg$ is attached to the lower end of a vertically suspended spring of force constant $600~\text{N/m}$. If another body of mass $0.5~\text{kg}$ moving vertically upward hits the suspended body with a velocity $3~\text{m/s}$ and is embedded in it, then the frequency of the oscillation is}
If the variance of the first \(n\) natural numbers is 10 and the variance of the first \(m\) even natural numbers is 16, then \(n : m =\)
$H_2O_2$ with $KMnO_4$ in acidic medium gives a manganese compound 'X' and in basic medium gives another manganese compound 'Y'. The oxidation states of manganese in X and Y respectively are:
If \[ A = \begin{bmatrix} 1 & 2 & -2 \\ 2 & -1 & 2\\ -1 & 1 & -2 \end{bmatrix}, \] then find $A + 2A^{-1}$.
At 298 K, the value of $K_c$ for the reaction A$_2$O$_4$(g) $\rightleftharpoons$ 2AO$_2$(g) is $x$ mol L$^{-1}$. What is the approximate $K_p$ value for this reaction?
Given: $R = 0.082$ L atm mol$^{-1}$ K$^{-1}$