List of top Questions asked in AP EAPCET

If the distance travelled by a freely falling body in the last but one second of its motion is 5 m, then the last second is:

The angle of projection of a projectile whose path is shown in the given figure is:

If the equation of motion of a projectile is \( Y = AX - B X^2 \), then the ratio of the maximum height reached and the range of the projectile is:

If a particle is moving along a circle of radius \( r \) with constant speed \( v \), then the magnitude of the change in velocity when the particle moves from \( P \) to \( Q \), where \( PQ \) makes an angle \( \theta \) at the center of the circle is:

If the tension in the horizontal wire shown in the figure is 30 N, then the weight \( W \) and tension in the wire \( OA \) are respectively:

A car of mass \( 2000 \) kg is accelerating from rest. If its engine is supplying constant power of \( 10 \) kW, then the velocity of the car at a time of \( 10 \) s is:

A body of mass \( M \) is moving with a uniform speed \( v \) on a frictionless horizontal surface under the influence of two forces \( F_1 \) and \( F_2 \) as shown in the figure. The net power of the system is:

Find the area (in square units) of the region bounded by the lines \( x=0 \), \( x=\frac{\pi}{2} \), and the curves \( f(x) = \sin x \), \( g(x) = \cos x \):

Evaluate the integral: \[ I = \int_{\pi/6}^{\pi/3} \cos^{-4} x \, dx \]

Evaluate the integral: \[ I = \int_0^{3\pi/2} \frac{\cos^5 x}{\cos^3 x+\sin^3 x}dx \]

The general solution of the differential equation \( \sec(x - y + 1) dy = dx \) is:

The differential equation for which \( y^2 = 4a(x + a) \) (where \( a \) is a parameter) is the general solution is:

The general solution of the differential equation \[ \frac{dy}{dx} = \frac{2xy-4x+y-2}{2xy+x-4y-2} \] is:

Of the following, the pair of physical quantities not having the same dimensional formula is:

If the lengths of the tangent, subtangent, normal, and subnormal for the curve \( y = x^2 + x - 1 \) at the point \( (1,1) \) are \( a, b, c, \) and \( d \) respectively, then their increasing order is:

Evaluate the integral: \[ \int \frac{x+1}{x^3 - 1}dx \]

Evaluate the integral: \[ \int \frac{x^4-16x^2+2x+8}{x^3-4x^2+2}dx \]

Evaluate the integral: \[ \int \frac{\sec^2 x}{(\sec x+\tan x)^{5/2}}dx \]

Evaluate the integral: \[ \int \left[\frac{1}{\cos x} - \frac{1}{\sin x} - \frac{1}{\sin x + 3\cos x}\right] dx \]

Evaluate the integral: \[ \int \operatorname{Cos}^{-1} \left( \frac{1-x^2}{1+x^2} \right) dx \]

Evaluate the integral: \[ I = \int_0^x \frac{t^2}{\sqrt{a^2 + t^2}} dt \]

If a function \( f(x) \) is given as: \[ f(x) = \begin{cases} \frac{\sqrt{1+ax^2+bx^3}-\sqrt{1-ax^2-bx^3}}{x^2}, & x<0
5, & x = 0
\frac{\tan3x-\sin3x}{bx^3}, & x>0 \end{cases} \] and is continuous at \( x = 0 \), then the geometric mean of \( a \) and \( b \) is:

If \( y = \log(\sec(\tan^{-1}x)) \) for \( x>0 \), then \( \frac{dy}{dx} \) at \( x = 1 \) is:

If \( y = \operatorname{Sin}^{-1} \frac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}} \) and \( -\frac{3\pi}{2}<x<-\frac{\pi}{2} \), then \( \frac{dy}{dx} \) is:

If \( x = \sqrt{2}e^t(\sin t - \cos t) \) and \( y = \sqrt{2}e^t(\sin t + \cos t) \), then \( \left[ \frac{d^2y}{dx^2} \right]_{t=\frac{\pi}{4}} \) is: