List of top Questions asked in TS EAMCET- 2026

Two balls P and Q are thrown vertically upwards simultaneously from the ground with velocities $20\ \text{m s}^{-1}$ and $35\ \text{m s}^{-1}$ respectively. The distance between the two balls when the velocity of P becomes zero is: (g = $10\ \text{m s}^{-2}$)}

If the errors in the measurements of diameter, length and electrical resistance of a wire are 1%, 0.5% and 2% respectively, then percentage error in the determination of the resistivity of material of the wire is:

The fundamental force that plays a key role in the large scale phenomena of the universe is:

The solution of the differential equation \[ \frac{dy}{dx} = \frac{3^{x+y}-2\cdot3^x} {3^{x+y}-2\cdot3^y} \] when \[ y(1)=2 \] is:

Evaluate: \[ \int \frac{3x\sec^2\!\sqrt{9x^2-12x+1} -\sec^2\!\sqrt{(3x-2)^2-3}} {\sqrt{9x^2-12x+1}} \,dx \]

Evaluate: \[ \int \frac{1}{\sin x \cos 2x}\,dx \]

If \[ \int_{2}^{3} \frac{3\log x} {3\log x+\log(125-75x+15x^2-x^3)} \,dx = k, \] then \[ 4k^2+2k+1= \]

Evaluate: \[ \int \frac{\cos 2x+\sin 4x} {\sqrt{3\sin 2x-2}} \,dx \]

Evaluate: \[ \int_{0}^{\pi} \sqrt{1+4\cos\frac{x}{2}} \left(\cos\frac{x}{2}-1\right)\,dx \]

Evaluate the definite integral: \[ \int_{-\frac{\pi}{3}}^{\frac{\pi}{3}} \frac{x+\frac{\pi}{2}} {2-\sin^2 x} \,dx \]

If a tangent drawn at the point \(P(h,k)\), where \(h,k\in \mathbb{Z}\), on the curve \[ y=2x^3+3x^2-4x-1 \] passes through the point \(Q(2,8)\), then \(PQ=\)

If \(1^\circ \approx 0.01745\) radians, then the approximate value of \[ \sec 29^\circ \] is:

If the base of an isosceles triangle is \(3\sqrt{2}\) feet and the two equal sides are increasing at the rate of \(1\) ft/s, then the rate of increase of its area (in sq.ft/sec) when the angle between the equal sides is a right angle is

If \[ f(x)=x^3-19x+30 \] is a real valued function with domain \([-4,1]\), then the value of \(c\) according to Lagrange's Mean Value Theorem for \(f(x)\) is

The function \[ f(x)=x|x-1|+|x+2| \] is

Evaluate: \[ \int \frac{\sin4x}{\sin x}\,dx \]

If \[ (3y)^{2x}=5\left(2^{3x}\right), \] then \[ \left(\frac{dy}{dx}\right)_{x=1} = \]

If \[ y=\tan^{-1}\left[\left(\frac{1-\cos 2\sqrt{x}}{1+\cos 2\sqrt{x}}\right)^{\frac12}\right], \qquad 0<x<\frac{\pi^2}{4}, \] then \(y(2y'+y)=\)

If \(f:\mathbb{R}-\{0\}\rightarrow\mathbb{R}\) is a differentiable function such that \[ \frac{1}{3}f(x)+3f\!\left(\frac1x\right) = x-\frac{10}{3}, \] then find \[ f'(3)-f'\!\left(\frac13\right). \]

If a function \[ f(x)= \begin{cases} \dfrac{a}{|x|}, & x\le -1 \text{ or } x\ge 1,[6pt] \\ x^2+b, & -1<x<1, \end{cases} \] is differentiable on \(\mathbb{R}\), then \(a+b=\)

Evaluate \[ \lim_{x\to 0}\frac{\log(4+x)^x-\log 4^x}{\sin^2 x}. \]

Let \(A(4,3,-2)\), \(B(0,-4,2)\), and \(C(-4,7,6)\) be the vertices of a triangle \(ABC\). If \(D(p,q,r)\) is the point of intersection of the bisector of angle \(A\) and the side \(BC\), then \(2p+q+r=\)

The area of the quadrilateral formed by the common tangents drawn to the circle \[ x^2+y^2=16 \] and the ellipse \[ 7x^2+25y^2=175 \] is:

If the eccentricity of the ellipse \[ \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 \qquad (a>b) \] is \[ e=\frac{\sqrt3}{2} \] and the equation of one of its directrices is \[ \sqrt3\,x-4=0, \] then \(ab=\):

Let \(OA\), \(OB\), \(OC\) lying along the \(X\)-, \(Y\)- and \(Z\)-axes respectively represent the coterminous edges of a rectangular parallelepiped. If \(OA=1\), \(OB=2\), \(OC=3\), then the angle between a pair of diagonals of the parallelepiped drawn through the vertices \(O\) and \(A\) is