List of top Questions asked in AP EAPCET

Which of the following do not exist?
A diatomic gas has an initial internal energy of 80 cal. A work of 18 cal is done on the gas, and the gas releases heat energy of 42 J. The final internal energy of the gas is:
Three moles of a gas at a temperature \( T \) are heated to thrice its volume by keeping the pressure constant. If \( \gamma \) is the ratio of specific heats, then the increase in internal energy of the gas is:
Among the following, the charge that does not exist on any type of charged body is:
The vector form of the universal law of gravitation:
A 20 g copper block is suspended by a vertical spring causing 1 cm elongation over the natural length of the spring. If a beaker of water is placed below the block so that the copper block is completely immersed in the liquid, the elongation of the spring is (Density of copper 9000 kg m\(^{-3}\), Density of water 1000 kg m\(^{-3}\), \( g = 10 \) ms\(^{-2}\)):
The relation between volume (V) and absolute temperature (T) of a gas in an adiabatic process is:
The force required to stop a body of mass 10 kg moving along a straight line path with a velocity of 10 ms\(^{-1}\) in a time of 10 s is:
A truck of mass 2000 kg is moving along a circular path having a radius of curvature of 10 m. If the banking angle is 39°, then the maximum permissible speed of the truck is (Acceleration due to gravity = 10 ms\(^{-2}\), take tan 39° = 0.81):
\(\int \frac{8^{1+x} + 4^{1+x}}{2^{2x}} dx =\):
Let \( n \in (0, \infty) \). If for all the curves \( y = x^n \log x \) for distinct values of \( n \), we have \( y = x - 1 \) as the tangent at a fixed point \((\alpha, \beta)\), then \(\alpha + \beta = \):
If \(\int \frac{dx}{1 + \sin x} = \tan \left( \frac{x}{2} - \theta \right) + C\), then \(\theta =\):
Let \( S_n = 1 + 3x + 9x^2 + 27x^3 + \ldots + n \text{ terms} -\frac{1}{3}<x<\frac{1}{3} \). If \( f(x) = S_n \), then \( f(x) \) is discontinuous at the point \( x = \):
The locus of the point on the curve \( y = \sin x \) where the tangent drawn at that point always passes through the point \( (0, \pi) \) is:
\( f(x) \) and \( g(x) \) are differentiable functions such that \( \frac{f(x)}{g(x)} = \) a non-zero constant. If \( \frac{f'(x)}{g'(x)} = \alpha(x) \) and \( \left( \frac{f(x)}{g(x)} \right)' = \beta(x) \), then \( \frac{\alpha(x) - \beta(x)}{\alpha(x) + \beta(x)} = \):
If all the normals drawn to the curve \( y = \frac{1 + 3x^2}{3 + x^2} \) at the points of intersection of \( y = \frac{1 + 3x^2}{3 + x^2} \) and \( y = 1 \) pass through the point \( (\alpha, \beta) \), then \( 3\alpha + 2\beta = \):
If A and B are the points of intersection of the circles \( x^2 + y^2 - 4x + 6y - 3 = 0 \) and \( x^2 + y^2 + 2x - 2y - 2 = 0 \), then the distance between A and B is:
A parabola having its axis parallel to the Y-axis passes through the points \(\left(0, \frac{2}{5}\right)\), \((4, -2)\), and \(\left(1, \frac{8}{5}\right)\). Then the point that lies on this parabola is:
Let the eccentricity of the ellipse \(2x^2 + ay^2 - 8x - 2ay + (8 - a) = 0\) be \(\frac{1}{\sqrt{3}}\). If the major axis of this ellipse is parallel to the Y-axis, then the equation of the tangent to this ellipse with slope 1 is:
The equation of the pair of asymptotes of the hyperbola \(\frac{(x - 3)^2}{3} - \frac{(y - 2)^2}{2} = 1\) is:
Let \( S = 0 \) be the circle passing through the points \((2, 0)\), \((1, -2)\), and \((-1, 1)\). Then the point \((1, 2)\):
If a cubical die is thrown, then the mean and variance of the random variable \( X \), giving the number on the face that shows up, are respectively:
If the image of the point \( (3, 8) \) in the line \( x + 3y = 7 \) is \( (\alpha, \beta) \), then \( \alpha + \beta = \)
The square of the distance from the origin to the point of intersection of the pair of lines \( ax^2 + 2hxy - ay^2 + 2gx + 2fy + c = 0 \) is:
If the vectors \( \vec{a} = 2\vec{i} + 3\vec{j} - \vec{k} \), \( \vec{b} = 4\vec{i} - \vec{j} + 3\vec{k} \), and \( \vec{c} = p\vec{i} + \vec{j} - \vec{k} \) are coplanar, then: \[ |\vec{a} \times \vec{c}| = ? \]