List of top Questions asked in AP EAPCET

A body starts from rest with uniform acceleration and its velocity at a time of \( n \) seconds is \( v \). The total displacement of the body in the \( n \)-th and \( (n - 1) \)-th seconds of its motion is
Tangents are drawn at three points P($t_1$), Q($t_2$), R($t_3$) on the parabola $y^2 = x$. Let these tangents intersect each other at the points L, M, N. If $t_1 = 2$, $t_2 = -4$, $t_3 = 6$, then the area of the triangle LMN is
If \( 3\sqrt{2}x - 4y = 12 \) is a tangent to the hyperbola \(\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\) and \(\frac{5}{4}\) is its eccentricity, then \( a^2 - b^2 = \)
The number of ways in which a cricket team of 11 members can be formed out of 6 batsmen, 6 bowlers, 4 all-rounders, and 4 wicket-keepers by selecting at least 4 batsmen, at least 3 bowlers, at least 2 all-rounders, and only one wicket-keeper is
The co-ordination number of chromium in K[Cr(H$_2$O)$_2$(C$_2$O$_4$)$_2$] is
If $y = \frac{x^4\sqrt{3x-5}}{\sqrt{(x^2-3)(2x-3)}}$, then $\frac{dy}{dx}|_{x=2} =$
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 $g + f + c =$
Observe the following reactions (g = gas):
I. N$_2$(g) + 3H$_2$(g) $\xrightarrow[\text{200 atm}]{\text{773K, X}}$ 2NH$_3$(g)
II. CO(g) + H$_2$O(g) $\xrightarrow[\text{673 K}]{\text{Y}}$ CO$_2$(g) + H$_2$(g)
III. CH$_4$(g) + H$_2$O(g) $\xrightarrow[\text{1270 K}]{\text{Z}}$ CO(g) + 3H$_2$(g)
Catalysts X, Y, Z respectively are
If a travelling wave is given by \( y(x, t) = 0.5 \sin(70.1x - 10\pi t) \), where \( x \) and \( y \) are in metres, the time \( t \) is in seconds, then the frequency of the wave is
The path difference between two waves given by the equations \( y_1 = a_1 \sin\left(\omega t - \frac{2\pi x}{\lambda}\right) \) and \( y_2 = a_2 \sin\left(\omega t - \frac{2\pi x}{\lambda} + \phi\right) \) is
For a first-order reaction, the ratio between the time taken to complete $\frac{3}{4}$th of the reaction and time taken to complete half of the reaction is
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
If a solid sphere is rolling without slipping on a horizontal plane, then the ratio of its rotational and total kinetic energies is
A wire of length 0.5 m and area of cross-section $4 \times 10^{-6}$ m$^2$ at a temperature of 100°C is suspended vertically by fixing its upper end to the ceiling. The wire is then cooled to 0°C, but is prevented from contracting, by attaching a mass at the lower end. If the mass of the wire is negligible, then the value of the mass attached to the wire is [Young's modulus of material of the wire = $10^{11}$ N/m$^2$; coefficient of linear expansion of the material of the wire = $10^{-5}$ K$^{-1}$ and acceleration due to gravity = 10 m/s$^2$]
A refrigerator of coefficient of performance 5 that extracts heat from the cooling compartment at the rate of 250 J per cycle is placed in a room. The heat released per cycle to the room by the refrigerator is
The area (in sq. units) of the region bounded by the curves \( y = x^2 \) and \( y = 8 - x^2 \) is
$L_1 = ax - 3y + 5 = 0$ and $L_2 = 4x - 6y + 8 = 0$ are two parallel lines. If $p, q$ are the intercepts made by $L_1 = 0$ and $m, n$ are the intercepts made by $L_2 = 0$ on the X and Y coordinate axes, respectively, then the equation of the line passing through the points $(p, q)$ and $(m, n)$ is
If $x^2 + y^2 + \sin y = 4$, then the value of $\frac{d^2y}{dx^2}$ at $x=-2$ is
If $y = \tan^{-1}(\frac{3x - x^3}{1-3x^2}) + \tan^{-1}(\frac{7x}{1-12x^2})$, then at $x=0$, $\frac{dy}{dx} =$
If \( x \log_{10} x \frac{dy}{dx} + y = 2 \log_{10} x \) and \( y(e) = 0 \), then \( y(e^2) = \)
The number of integers between 10 and 10,000 such that in every integer every digit is greater than its immediate preceding digit, is
In a water tank, an air bubble rises from the bottom to the top surface of the water. If the depth of the water in the tank is 7.28 m and atmospheric pressure is 10 m of water, then the ratio of the radii of the bubble at the bottom of the tank and at the top surface of the water is (Temperature of the water in the tank is constant)
$3x+4y-43=0$ is a tangent to the circle $S = x^2+y^2-6x+8y+k=0$ at a point P. If C is the center of the circle and Q is a point which divides CP in the ratio -1:2, then the power of the point Q with respect to the circle S=0 is
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
A wire is stretched 1 mm by a force F. If a second wire of same material, same length and 4 times the diameter of the first wire is stretched by the same force F, then the elongation of the second wire is