List of top Questions asked in AP EAPCET

A box of mass 2 kg is placed on a inclined plane that makes 30\(^\circ\) with the horizontal. The coefficient of friction between the box and inclined plane is 0.2. A force F is applied on the box perpendicular to the incline to prevent the box from sliding down. The minimum value of F is (acceleration due to gravity = 10 m s\(^{-2}\))
box of mass 2 kg is placed on a inclined plane that makes 30◦
A car is moving along a straight line is brought to a stop within a distance of 200 m and in time 10 s. The initial speed of the car is
A ball is thrown upward from the top of a building at an angle of 30\(^\circ\) to the horizontal and with an initial speed of 20 m s\(^{-1}\). If the ball strikes the ground after 3 s, then the height of the building is (acceleration due to gravity = 10 ms\(^{-2}\))
A particle is moving on a circular path with a constant speed v. It's change of velocity as it moves from A to B in the figure is
moving on a circular path with a constant speed
\( \int_{-\pi/4}^{\pi/4} \cos^8 x \ dx = \)
If \( f(x) = \sin(\tan^{-1} x) \), then \( \int_0^1 xf''(x)dx = \)
If an open cylinder of given surface area has maximum volume then its radius is
If \(x+y=k, x>0, y>0\) then \(x^2+y^2\) is minimum if
If \( \int \frac{x^8+4}{x^4-2x^2+2} dx = Ax^5+Bx^3+Cx+K \), then \(5A+3B+C = \)
If \( f(x) = \begin{cases 4 & -\infty<x<-\sqrt{5}
x^2-1 & -\sqrt{5} \le x \le \sqrt{5}
4 & \sqrt{5}<x<\infty \end{cases} \). If k is the number of points where f(x) is not differentiable then k -- 2 =}
Assertion (A) : \( f(x)=|x| \) is differentiable at \( x=a \neq 0 \) and continuous but not differentiable at \( x=0 \) Reason (R) : If a function is differentiable at a point then it is continuous at that point. But converse is not true. .
The minimum distance of a point on the curve \( y = x^2 - 4 \) from the origin is
A ray makes angles \( \frac{\pi}{3} \) and \( \frac{\pi}{4} \) with Y and Z-axes respectively. Then the value of the sine of the angle made by the ray with X-axis is
A plane meets the X, Y, Z -- axes in A, B, C respectively. If the centroid of the triangle ABC is \((2, -3, 5)\) then the perpendicular distance from origin to the given plane is
If the centroid of a triangle with vertices \((4, p, -3), (-1, -1, 2)\) and \((3, 5, -8)\) is given by mid point of \((1, 4, -2)\) and \((q, 2, -4)\), then \(p^2+q^2 = \)
\( \lim_{x \to a} \frac{x^3+a^3}{x+a} = 7 \implies a = \)
\( \lim_{x \to \frac{\pi}{2}} \frac{1-\tan\frac{x}{2}}{1+\tan\frac{x}{2}} \cdot \frac{1-\sin x}{(\pi-2x)^3 = \)}
The length of the latus rectum of the parabola \( y^2-4x-4y+8=0 \) is
The eccentricity of the ellipse \( 9x^2+16y^2=144 \) is
If \( ax^2 - 34xy - 5y^2 + 2x + 26y - 5 = 0 \) represents a pair of straight lines, then the value of a is
The equations of the lines perpendicular to \(x^2 - 5xy + 4y^2 = 0\) and passing through (2, 1) is
Suppose the hypotenuse and its opposite vertex of an isosceles right angled triangle are \(3x+4y-4=0\) and \((2,2)\) respectively. Then, which of the following is another side of the triangle?
A point P on a line is at a distance of 4 units from the origin (0, 0). If the line makes 60\(^\circ\) with the negative direction of the x-axis, then P is
A bag contains 3 white, 2 blue and 5 red balls. One ball is drawn at random from this bag. Then, the probability that the ball drawn is not red is
A person P speaks truth in 75% cases and another person R in 80% cases. Then the probability that they likely to contradict each other in narrating the same event is