List of top Questions asked in AP EAPCET

The square of the slope of a common tangent to the circle \(4x^2 + 4y^2 = 25\) and ellipse \(4x^2 + 9y^2 = 36\) is
If five logic gates are connected as shown in the figure, then the values of $y_1$, $y_2$, and $y_3$ are respectively
logic gates
Which of the following is the common monomer for the polymers Bakelite and Melamine?
If \(O(0,0,0), A(1,2,1), B(2,1,3)\), and \(C(-1,1,2)\) are the vertices of a tetrahedron, then the acute angle between its face \(OAB\) and edge \(BC\) is
If \( \int x^2 \cos^3 x\, dx = \frac{1}{6}f(x) + g(x) \sin 2x + h(x) \cos 2x + c \), then \( f(1) + g(2) + h\left(\frac{1}{2}\right) = \)
A transistor works as an amplifier when
A horizontal telegraph wire of length $30~\text{m}$ fell from a height of $20~\text{m}$. If resistance is $40~\Omega$ and horizontal component of Earth’s magnetic field is $2 \times 10^{-5}~\text{T}$, the induced current is
Three dice are thrown simultaneously and the sum of the numbers is noted. If A = getting sum greater than 14 and B = getting sum divisible by 3, then \(P(A \cap B) + P(A \cup B) =\)
Given \(f(x) = x^2 - 5x + 4\). Out of first 20 natural numbers, if a number \(x\) is chosen at random, then the probability that the chosen \(x\) satisfies the inequality \(f(x)>10\) is
If the points A, B, C, D with position vectors \(\vec{i} + \vec{j} - \vec{k}, -\vec{i} + 2\vec{k}, \vec{i} - 2\vec{j} + \vec{k}, 2\vec{i} + \vec{j} + \vec{k}\) form a tetrahedron, then angle between faces ABC and ABD is
The specific conductance of 0.05 M NaOH solution is 0.0115 S cm$^{-1}$. What is its molar conductance ($\Lambda_m$) in S cm$^2$ mol$^{-1}$?
For the reaction: A + 2B $\rightarrow$ 3C + 2D, if rate of disappearance of B is $x \times 10^{-2}$ mol L$^{-1}$ s$^{-1}$, the ratio of rate of reaction to rate of appearance of C is:

Match the following:

List-I (Aquated ion)List-II (Colour)
A) Ni\(^{2+}\)V) Green
B) Fe\(^{3+}\)III) Yellow
C) Mn\(^{3+}\)I) Violet
D) V\(^{4+}\)II) Blue
Evaluate the integral \[ \int_{\frac{1}{2}}^{\frac{\sqrt{3}}{2}} \frac{1}{\left(x + \sqrt{1 - x^2}\right) \cdot \left(1 - x^2\right)} \, dx = \]
Which of the following orders is not correct about the property shown against it?
Consider the following changes I and II
Change I: ${O2 → O2^{2-}}$
Change II: ${O2 → O2^{-}}$
The correct statements about these changes (I) and (II) in accordance with MO theory are
Which of the following orders are correct against the stated property?
I) NaO$_2 < KO$_2 < RbO$_2 < CsO$_2$ — stability
II) Mg(OH)$_2 < Ca(OH)$_2 < Sr(OH)$_2$ — basic strength
III) MgCO$_3 < CaCO$_3 < SrCO$_3$ — thermal stability
Identify the air pollutant which in high concentration leads to stiffness of flower buds?
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 = $10~\text{m/s}^2$)
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
The point of intersection of the lines represented by \(\vec{r} = (\hat{i} - 6\hat{j} + 2\hat{k}) + t(\hat{i} + 2\hat{j} + \hat{k})\) and \(\vec{r} = (4\hat{j} + \hat{k}) + s(2\hat{i} + \hat{j} + 2\hat{k})\) is
If the four points (6,2,4), (1,3,5), (1,-2,3), and (6,k,2) are coplanar, then \(k =\)
If the variance of the first \(n\) natural numbers is 10 and the variance of the first \(m\) even natural numbers is 16, then \(n : m =\)
If the polynomial \( f(x) = x^4 + ax^3 + bx^2 + cx + d \) is divided by \( x - 1 \) and \( x + 1 \), the remainders are 5 and 3 respectively. If \( f(x) \) is divided by \( x^2 - 1 \), then the remainder is