List of top Questions asked in AP EAPCET- 2023

Let the points $P_1(\frac{\pi}{4}), P_2(\frac{3\pi}{4}), P_3(\frac{5\pi}{4}), P_4(\frac{7\pi}{4})$ lie on the hyperbola $\frac{x^2}{9} - \frac{y^2}{16} = 1$. Then they form:
If $f(g(x+y)) = f(g(x)) + f(g(y))$, $g(1)=2$, $f(2)=1$, then $g(f(x))$ is discontinuous on:
The number of metalloids in the following elements are: Si, Mn, B, F, Cu, Ag, K, Sb, As, Na, Ge
The polar of a point with respect to the circle \( x^2 + y^2 - 10x + 12y - 3 = 0 \), which is not a tangent and not a chord of contact, is:
If the tangent to the curve $x^3y^2 + \dfrac{x^2}{y} = 5$ is parallel to X-axis, then a point on its locus is:

Given \( f(x) = \begin{cases} \frac{1}{2}(b^2 - a^2), & 0 \le x \le a \\[6pt] \frac{1}{2}b^2 - \frac{x^2}{6} - \frac{a^3}{3x}, & a<x \le b \\[6pt] \frac{1}{3} \cdot \frac{b^3 - a^3}{x}, & x>b \end{cases} \). Then:

The area (in sq units) of the triangle formed by the normal at point $(1,0)$ on the curve $x = e^{\sin y}$ with coordinate axes is:
The slope of the tangent at any point $(x,y)$ on the curve is equal to the product of the coordinates of that point. If the equation of the normal to the curve at the point $(\sqrt{2},e)$ is $ax+by=1$, then $\dfrac{b}{a}=$

$\displaystyle \int \frac{dx}{\sin(x-a)\cos(x-b)} =$

$\int_0^\pi x \sin^3 x \cos^2 x\ dx =$

$\displaystyle \int_{\frac{1}{25}}^{1} x^{-2} e^{x^{-1/2}} dx =$

The area (in sq. units) bounded by the curves $y=\frac{8}{x}$, $y=2x$ and $x=4$ is

Which one of the following is a linear differential equation?
A rtain physical quantity is calculated from the formula $\frac{\pi}{3}(a^2-b^2)hd$, where a, b and h are all lengths and d is density. The physical quantity being calculated is
A swimmer wants to cross a river which is flowing at a speed 'v'. If the swimmer can swim in still water at speed 'V', the direction he should swim to cross the river in least time is
The resultant magnitude of two vectors of same magnitude is equal to magnitude of either. The angle between the two vectors is
A body of mass 10 kg is kept on a rough horizontal surfa of coefficient of friction 0.3. If a horizontal for of 50 N is applied on the body, then the acleration of the body is (Acleration due to gravity $= 10 \text{ ms}^{-2}$)
The heat energy released by water of mass 2 kg when it is cooled by $10~^\circ\text{C}$ is (Specific heat capacity of water $= 4200 \text{ J kg}^{-1} \text{K}^{-1}$)
Which of the following statements regarding ntre of mass is NOT true?
A particle of mass 10 g is moving towards east with a velocity of $10 \text{ ms}^{-1}$ and another particle of mass 15 g is moving towards north with a velocity of $5 \text{ ms}^{-1}$. The magnitude of the velocity of the ntre of mass of the system of the two particles is
The sag developed in a bar of length $l$, breadth $b$, and thickness $d$ when subjected to a load $w$ at the nter is (Y -- Young's modulus of the material of the bar)
When an iron rod is heated, the variation of colour from dull red to white can be explained by
A gas is expanded from an initial state to a final state along a path that consists of (a) an isothermal expansion doing 40 J work, (b) an adiabatic expansion doing W work, (c) an isothermal expansion doing 30 J work. If the total change in the internal energy of the gas is -20 J, the work done by the gas during the adiabatic expansion W =
The critical angle for diamond with respect to air is nearly
In order to quadruple the resistan of a uniform wire, a part of it is uniformly stretched so that the final length of the wire becomes $1.5$ times the original length. The fractional length of the stretched part is