List of top Questions asked in AP EAPCET

If $X$ is a binomial variate with mean $\frac{16}{5}$ and variance $\frac{48}{25}$, then $P(X \leq 2) =$
Two acids A and B are titrated separately. 25 mL of 0.5 M Na$_2$CO$_3$ solution requires 10 mL of A and 40 mL of B for complete neutralisation. The volume (in L) of A and B required to produce 1 L of 1 N acid solution respectively are
The ratio of the focal lengths of a convex lens when kept in air and when it is immersed in a liquid is 1:2. If the refractive index of the material of the lens is 1.5, then the refractive index of the liquid is
As shown in the figure, two thin coplanar circular discs A and B each of mass 'M' and radius 'r' are attached to form a rigid body. The moment of inertia of this system about an axis perpendicular to the plane of disc B and passing through its centre is
A coil of resistance 200 $\Omega$ is placed in a magnetic field. If the magnetic flux $\phi$ (in weber) linked with the coil varies with time 't' (in second) as per the equation $\phi = 50t^2 + 4$, then the current induced in the coil at a time t = 2 s is
For all $n \in \mathbb{N}$, if $n(n^2+3)$ is divisible by $k$, then the maximum value of $k$ is
The time period of a simple pendulum on the surface of the earth is T. If the pendulum is taken to a height equal to half of the radius of the earth, then its time period is
If the surface area of a spherical bubble is increasing at the rate of 4 sq.cm/sec, then the rate of change in its volume (in cubic cm/sec) when its radius is 8 cms is
Consider the following cell reaction: 2Fe$^{3+}$(aq) + 2I$^-$ (aq) $\rightarrow$ 2Fe$^{2+}$(aq) + I$_2$(s). At 298 K, the cell emf is 0.237 V. The equilibrium constant for the reaction is 10$^x$. The value of x is (F = 96500 C mol$^{-1}$; R = 8.3 J K$^{-1}$ mol$^{-1}$)
If $\cot(\cos^{-1} x) = \sec\left(\tan^{-1}\left(\frac{a}{\sqrt{b^2 - a^2}}\right)\right)$, $b>a$, then $x =$
If \( f(x) = \begin{cases} \frac{(e^x - 1) \log(1 + x)}{x^2} & \text{if } x>0 \\ 1 & \text{if } x = 0 \\ \frac{\cos 4x - \cos bx}{\tan^2 x} & \text{if } x<0 \end{cases} \) is continuous at \( x = 0 \), then \(\sqrt{b^2 - a^2} =\)
A sample of paramagnetic salt contains $2 \times 10^{24}$ atomic dipoles each of dipole moment $1.5 \times 10^{-23}$ JT$^{-1}$. The sample is placed under homogeneous magnetic field of 0.6 T and cooled to a temperature 4.2 K. The degree of magnetic saturation achieved is 20%. Then total dipole moment of the sample for a magnetic field of 0.9 T and a temperature of 2.8 K is
$f(x)$ is an $n^{th}$ degree polynomial satisfying $f(x) = \frac{1}{2}\left[f(x)f\left(\frac{1}{x}\right) + f\left(\frac{f(x)}{x}\right)\right]$. If $f(2) = 33$, then the value of $f(3)$ is
If $\alpha$, $\beta$, and $\gamma$ are the roots of the equation $2x^3 + 3x^2 - 5x - 7 = 0$, then $\frac{1}{\alpha^2} + \frac{1}{\beta^2} + \frac{1}{\gamma^2} =$
If the range of a body projected with a velocity of 60 m/s is \( 180\sqrt{3} \) m, then the angle of projection of the body is (Acceleration due to gravity = 10 m/s\(^2\))
Let $\mathbf{a} = 4\mathbf{i} + 3\mathbf{j}$ and $\mathbf{b}$ be two perpendicular vectors in the XOY-plane. A vector $\mathbf{c}$ in the same plane and having projections 1 and 2 respectively on $\mathbf{a}$ and $\mathbf{b}$ is
In compound (X), hyperconjugation is present and in (Y), resonance effect is present. What are X and Y, respectively?
An alcohol X(C$_4$H$_{10}$O) on dehydration gave alkene (C$_4$H$_8$) as major product, which on bromination followed by treatment with Y gave alkyne C$_4$H$_6$. Alkyne C$_4$H$_6$ does not react with sodium metal. What are X and Y?

p-Chlorotoluene is the major product in which of the following reactions?

If the equation of the circle passing through the point $(8, 8)$ and having the lines $x + 2y - 2 = 0$ and $2x + 3y - 1 = 0$ as its diameters is $x^2 + y^2 + px + qy + r = 0$, then $p^2 + q^2 + r =$
\(\int_{-2\pi}^{2\pi} \sin^2(2x) \cos^4(2x) \, dx =\)
If \(\int \left( \frac{x^{49} \tan^{-1}(x^{50})}{1 + x^{100}} + \frac{x^{50}}{1 + x^{100}} \right) dx = k f(x) + c\) where \(k\) is a constant, then \(f(x) - f\left( \frac{1}{x^{49}} \right) =\)

$\left( 1 + \sqrt{5} + i \sqrt{10 - 2\sqrt{5}} \right)^5$

If a unit circle $S = x^2 + y^2 + 2gx + 2fy + c = 0$ touches the circle $S' = x^2 + y^2 - 6x + 6y + 2 = 0$ externally at the point $(-1, -3)$, then $g + f + c =$
An aqueous solution containing 0.2 g of a non-volatile solute 'A' in 21.5 g of water freezes at 272.814 K. If the freezing point of water is 273.16 K, the molar mass (in g mol$^{-1}$) of solute A is [K$_f$(H$_2$O) = 1.86 K kg mol$^{-1}$]