List of top Questions asked in TS EAMCET- 2026

Law of conservation of mass was regarded as another basic conservation law of nature until the advent of:

The area of the region bounded by the curve \[ y=|x-2|+|x-8|, \] the X-axis and the lines \(x=0\) and \(x=10\) is:

Statement-I: When two quantities are multiplied, the relative error in the result is the sum of the relative errors in the quantities.
Statement-II: When two quantities are divided, the relative error in the result is the difference of the relative errors in the quantities.

If \([t]\) denotes the greatest integer function, then \[ \int_{-2}^{2} \left[ \frac{x^2+[x+1]} {1+x^2} \right]dx = \ ? \]

Two trains A and B are moving in the same direction with velocities \(V_A\) and \(V_B\) respectively and a third train C is moving in opposite direction. If velocity of C with respect to B is twice the velocity of A with respect to B, then velocity of A with respect to C is:

If \[ \int\frac1{1+\cos x}\,dx = \frac1{f\!\left(\frac x2\right)}+C_1, \] then \[ \int f(x)\,dx= \ ? \]

If \[ \int\frac{dx}{\sqrt{4x^{2}+11x+6}} = \frac12\cosh^{-1}\!\left(\frac{f(x)}{5}\right)+C \] and \[ f(1)=19, \] then \(f(2)=\) ?

If \[ \int \log x\sqrt{\left(\frac{\log x}{x}\right)^2+\frac1{x^2}}\,dx = \frac{f(x)}{3}\sqrt{1+(\log x)^2}+C \] and \(f(1)=1\), then \(f(e)=\) ?

Evaluate: \[ \int \sin^{-1}x\,dx-\int \cos^{-1}x\,dx. \]

Let \[ f:[0,1]\rightarrow\mathbb R \] be a function defined by \[ f(x)+f(1-x)=1. \] Then \[ \int_0^1 f(x)\,dx= \ ? \]

A rectangle is inscribed in the parabola \[ y=9-x^{2} \] such that two of its vertices are on the X-axis and another two on the parabola. The dimensions of such rectangle lying above the X-axis and having maximum area is:

If \[ \frac{d}{dx} \left( \frac{\sec x+\tan x} {\sec x-\tan x} \right) =k \] at \[ x=\frac{\pi}{4}, \] then \[ \frac{k}{2\sqrt2}-2\sqrt2= \ ?} \]

Statement-I: The equation of the tangent to the curve \[ y=3x^2-5 \] drawn through the point \((1,2)\) is \[ y=6x-4. \] Statement-II: If \(L,M,N\) are respectively the lengths of tangent, normal and subnormal drawn to a curve at a point \((a,b)\), then \[ \frac{(L)(N)}{M}=b^2. \] Choose the correct option.

A function is defined as \[ f(x)= \begin{cases} 3x-1, & 0\le x\le 2,\\ \sqrt{25(x-1)}, & 2\le x<\infty. \end{cases} \] For \(f(x)\) in the interval \(\left[\frac13,3\right]\), choose the correct statement.

In the interval \([-5,5]\), if \[ f(x)=(x+3)^2(x-2)^3 \] is increasing on \[ S=\{x\mid -5\le x<\alpha \text{ and } \beta<x\le5\}, \] then \(f(\alpha)-f(\beta)=\) ?

If the angle between the curves \[ y^2=4x \] and \[ y=ax^2-5 \] at the point \((1,2)\) is \(\alpha\), then \[ (a-2)|\tan\alpha| = ? \]

\(f(x)\) is an \(n^{th}\) degree polynomial and \(\alpha_1,\alpha_2,\ldots,\alpha_n\) are distinct zeros of \(f(x)\). \(g(x)\) is a polynomial having three zeros common with the zeros of \(f(x)\). Assertion (A): \(|f(x)|g(x)\) is continuous and differentiable at all \(\alpha_i\).
Reason (R): \[ \lim_{x\to a}\frac{|x-a|}{x-a} \] does not exist and \[ \lim_{x\to a}|x-a|=0. \] Choose the correct option.}

If the direction cosines of the line common to the planes \[ x+2y-z-1=0 \] and \[ 3x-4y+z-5=0 \] are \((l,m,n)\), then \(|l+m-n|=\)

If \[ f(x)= \frac{\lambda e^{\frac1x}+3e^{-\frac1x}} {(\lambda+2)e^{\frac1x}-e^{-\frac1x}}, \qquad x\neq0 \] and \(f(0)=k\), \(k\in\mathbb R\), is a continuous function at \(x=0\), then \(2\lambda=\) ?

If \(P(1,2,5)\), \(Q(3,0,7)\), \(R(6,-3,10)\) are collinear and \((\alpha,\beta,\gamma)\) is a point at distance 3 from \(P\) on the same line, then the value of \(\alpha+\beta+\gamma\) lying between 6 and 7 is:

\(y=4\) is the directrix of the parabola \[ x^{2}+8x+12y+k=0. \] If \(l\) is the length of its latus rectum, then \(l-k=\) ?

For a hyperbola \[ \frac{x^2}{a^2}-\frac{y^2}{b^2}=1, \] the distance between its vertex and focus lying on the positive X-axis is 2. If the length of its latus rectum is 13, then the eccentricity is:

The area of the rectangle formed by the tangents drawn at the ends of both major and minor axes of an ellipse is 24. If the eccentricity of the ellipse is \(\frac{1}{4}\), then the equation of the ellipse is:

The centre of the ellipse lies on the lines \(2x+3y=5\) and \(x+3y=4\). If the eccentricity of the ellipse is \(\frac23\), length of its major axis is 4 and its minor axis is parallel to Y-axis, then the equation of the ellipse is:

\((1,1)\) is the focus of the parabola \[ y^{2}-4ax-2ay+a^{2}=0. \] If the circles \[ (x-\alpha)^2+(y-\beta)^2=r^2 \] touch the X-axis and the axis of the given parabola, then \[ \{(\alpha,\beta)\} \] is: