List of top Questions asked in TS EAMCET- 2025

Due to the presence of air resistance, if a body dropped from a height of 20 m reaches the ground with a speed of 18ms$^{-1}$, then the time taken by the body to reach the ground is nearly

A balance is made using a uniform metre scale of mass 100 g and two plates each of mass 200 g fixed at the two ends of the scale and the balance is pivoted at 45 cm mark of the scale. The error when 300 g weight is placed in the plate at 0 cm to weigh vegetables placed in the plate at 100 cm is

The ratio of radii of gyration of a thin circular ring and a circular disc of same radius about a tangential axis in their own planes is $\sqrt{12}:\sqrt{K}$. The value of K is

A ball projected at an angle of 45$^\circ$ with the horizontal crosses two points at equal heights separated by a distance at times 2 s and 8 s respectively. The horizontal distance between the two points is (Acceleration due to gravity = 10 ms$^{-2}$)

The general solution of the differential equation $\frac{dy}{dx} + (\sec x \csc x)y = \cos^2 x$ is

The range of weak nuclear force is of the order of

A piece of length 3.532 m is cut from a rod of length 43.4 m. The length of the remaining rod in metre is (up to correct significant figures)

$\int_{-2}^{4} |2-x^2| dx =$

$\int_{-1}^{1} \frac{\log 2 - \log(1+x)}{\sqrt{1-x^2}} dx =$

If $\frac{5\pi}{4}<x<\frac{7\pi}{4}$, then $\int \sqrt{\frac{1-\sin 2x}{1+\sin 2x}} dx =$

$\int \frac{3^x(x\log 3 - 1)}{x^2} dx =$

$\int_{0}^{\pi/4} \frac{\sec x}{3\cos x + 4\sin x} dx =$

A man of 5 feet height is walking away from a light fixed at a height of 15 feet at the rate of K miles/hour. If the rate of increase of his shadow is $\frac{11}{5}$ feet/sec, then K = (Take 1 mile = 5280 feet)

If the point P($x_1, y_1$) lying on the curve $y = x^2-x+1$ is the closest point to the line $y = x-3$ then the perpendicular distance from P to the line $3x+4y-2=0$ is

There is a possible error of 0.03 cm in a scale of length 1 foot with which the height of a closed right circular cylinder and the diameter of a sphere are measured as 3.5 feet each. If the radii of both cylinder and sphere are same, then the approximate error in the sum of the surface areas of both cylinder and sphere is (in square feet)

For a real number 'a', if a real valued function $f(x) = 4x^3 + ax^2 + 3x - 2$ is monotonic in its domain, then the range of 'a' is

If $y = \text{Sec}^{-1}x$, then $\frac{d^2y}{dx^2} =$

If $x = \sqrt{1-\tan y}$, then $\frac{dy}{dx} =$

If $[t]$ represents the greatest integer $\leq t$ then the value of $\lim_{x\to 3} \frac{11-[2-x]}{[x+10]}$ is

If $y = \sqrt{\log(x^2+1)+\sqrt{\log(x^2+1)+\sqrt{\log(x^2+1)+...}}}$, $|x|<1$, then $\frac{dy}{dx} =$

If the foot of the perpendicular drawn from the point (2,0,-3) to the plane $\pi$ is (1,-2,0) and the equation of the plane is $ax+by-3z+d=0$ then $a+b+d=$

The number of values of 'k' for which the points (-4,9,k), (-1,6,k), (0,7,10) form a right-angled isosceles triangle is

A line makes angles 60$^\circ$, 45$^\circ$, $\theta$ with positive X, Y, Z-axes respectively. If $\theta$ is an acute angle, then $\tan\theta =$

The length of the chord of the ellipse $\frac{x^2}{4} + y^2 = 1$ formed on the line $y = x+1$ is

Let P, Q, R, S be the points of intersection of the circle $x^2 + y^2 = 4$ and the hyperbola $xy = \sqrt{3}$. If P = $(\alpha,\beta)$ and $\alpha>\beta>0$, then the equation of the tangent drawn at P to the hyperbola is