List of top Questions asked in TS EAMCET- 2026

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

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.

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.

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 \[ (a-2)|\tan\alpha| = ? \]

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

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:

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 \(2\lambda=\) ?

\(f(x)\) 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.}

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:

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

If the area of the triangle formed by the points \((0,0,0)\), \((1,1,1)\) and \((t,2t,3t)\) is \(\sqrt6\), then the sum of squares of all possible values of \(t\) 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:

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:

If a circle inscribed in the parabola \(y^{2}=4ax\) passes through its focus, then the equation of the circle is:

If \(3x+4y-24=0\) and \(3x-4y-32=0\) are tangents to a circle and \(4x+3y-1=0\) is a normal, then \(r+h+k=\):

If two vertices of a quadrilateral are the centres of the circles \[ S\equiv x^{2}+y^{2}-2x-2y-2=0 \] and \[ S^{\prime}\equiv x^{2}+y^{2}-6x-6y+14=0 \] and the other two vertices of that quadrilateral are the points of intersection of these two circles, then the area of the quadrilateral is:

If line \(4x-3y+c=0\) makes a chord of length 10 on circle \(x^2+y^2-2x+4y-23=0\), then \(c=\):

The tangent drawn at a point \(P\) on the circle \(x^{2}+y^{2}+6x+6y-2=0\) cuts the line \(5x-2y+6=0\) at a point \(Q\). If \(PQ=5\), then a point \(Q\) having integral coordinates is:

Let P be any point on circle \(x^2+y^2=16\) and \(A=(1,2)\). If the locus of point dividing AP in ratio 3:2 is a circle, its radius is:

In triangle ABC, B lies on positive x-axis, A=(-1,0), \(a=4\sqrt{3}\), \(\angle A=120^\circ\). If C has integer coordinate condition, distance of C from origin is:

The line \((3a+1)x+(7a+2)y=17a+5\) represents concurrent lines. If \(d\) is distance from \((3,1)\) to line of slope 1 in this family, find \(2d^2\):

One of the pair of lines \(x^{2}-3y^{2}-4x-6\sqrt{3}y-5=0\) is \(x+by+c=0\) \((b<0)\). If the other line intersects the curve \(x^{2}-5y^{2}-4x=0\) at two points A and B, then \(\angle AOB=\):