List of top Questions asked in AP EAPCET

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:
If the tangent drawn to the curve $(x^2+1)(y-3)=x$ at a point P, lying in the first quadrant, is a horizontal line, then the equation of the normal at the point P 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 $\dfrac{b}{a}=$
The curve represented by $x = t^5 + 5t^3 + 20t + 7$ and $y = 4t^3 - 3t^2 - 18t + 3$ is decreasing in the interval

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

If $I_n = \int \tan^n x \, dx \quad (n>1)$, then $I_4 + I_6 =$

If $\int \sqrt{x}(1-x^3)^{-1/2} dx = \frac{2}{3}g(f(x))+c$, then

$\int \frac{x^2}{(x^2-1)(x^2+1)} dx =$

Let $f:\mathbb{R} \to \mathbb{R}$ be a differentiable function such that $|f(x)-f(y)| \le 2|x-y|^{3/2} \ \forall x,y \in \mathbb{R}$. If $f(0)=1$, then $\int_0^1 f^2(x)dx=$
$\int_0^\pi x \sin^3 x \cos^2 x\ dx =$
If $\int_0^{2\pi} |x \sin x| dx = k\pi$, then $k=$

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

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?
If $X=x+h, Y=y+k$ transforms $\frac{dy}{dx} = \frac{2x+3y-7}{3x+2y-8}$ to a homogeneous differential equation, then $(h,k)=$
If $\log y$ is an integrating factor of $\frac{dx}{dy}+P(y)x=Q(y)$, then $P(y)=$
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
If the engine of a long train moving with constant acleration crosses a tree with velocity 'u' and the last compartment of the train crosses the same tree with velocity 'v', then the velocity with which the middle compartment crosses the same tree 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 bullet of mass 20 g moving with $500 \text{ ms}^{-1}$ is pierd 1 cm into a wooden block, then the retarding for experiend by the bullet 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 $= 10 \text{ ms}^{-2}$)
A toy car of mass 100 g is moving with velocity of $(\hat{i}+2\hat{j}-3\hat{k})$ m/s, then the kinetic energy of the car is
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?