List of top Questions asked in TS EAMCET- 2025

If \(y = (\sin^{-1}x)^2\), then \((1-x^2)\frac{d^2y}{dx^2} - x\frac{dy}{dx} =\)

The area of the region bounded by the curves \(y=x^3\), \(y=x^2\) and the lines \(x=0\) and \(x=2\) is

\( \int \frac{2\sin x - 3\cos x}{4\cos x - 3\sin x} dx = \)

If \( y = x^{\log x} + (\log x)^x, x>1 \) then \( (\frac{dy}{dx})_{x=e} = \)

If \( \int(x+2) \sqrt{x^{2}-x+2} d x=\frac{1}{3} f(x)+\frac{5}{8} g(x)+\frac{35}{16} h(x)+c \) then \( f(-1)+g(-1)+h\left(\frac{1}{2}\right)= \)

If \( (x^2-3x+2)e^{\frac{y}{x-1}} = x+2 \) then \( \left(\frac{dy}{dx}\right)_{x=0} = \)

There is a possible error of 0.02 cm in measuring the base diameter of a right circular cone as 14 cm. If the semi-vertical angle of the cone is 45°, then the approximate error in its volume is (in cu. cm)

The equation which represents the system of parabolas whose axis is parallel to y-axis satisfies the differential equation

The acute angle between the curves \( y = 3x^2 - 2x - 1 \) and \( y = x^3 - 1 \) at their point of intersection which lies in the first quadrant is

If \( \lim_{x \to 0} \frac{3x^3 - (1-x^2)^{3/2}}{x^2\sin x} = p + \log q \) then pq =

If \( x = 2\sqrt{2}\sqrt{\cos 2\theta} \) and \( y = 2\sqrt{2}\sqrt{\sin 2\theta} \), \( 0<\theta<\frac{\pi}{4} \) then the value of \( \frac{dy}{dx} \) at \( \theta = 22\frac{1}{2}^\circ \) is

Let 'a' be a positive real number. If a real valued function \( f(x) = \begin{cases}\frac{6^x - 3^x - 2^x + 1}{1 - \cos\left(\frac{x}{a}\right)} & \text{if } x \neq 0 \\ \log 3 \log 4 & \text{if } x = 0 \end{cases} \) is continuous at \( x=0 \), then \( a = \)

If \( (h,k) \) is the new origin to be chosen to eliminate first degree terms from the equation \( S = 2x^2 - xy - y^2 - 3x + 3y = 0 \) by translation and if \( \theta \) is the angle with which the axes are to be rotated about the origin in anticlockwise direction to eliminate xy-term from \( S = 0 \), then \( \tan 2\theta = \)

If a line L passing through a point A(2,3) intersects another line \( 4x-3y-19=0 \) at the point B such that \( AB=4 \), then the angle made by the line L with positive X-axis in anti-clockwise direction is

If the equation of the circle passing through the points (-1,0), (-1,1), (1,1) is \( ax^2+ay^2+2gx+2fy-2=0 \) then \( a = \)

For the circle \( x-2=5\cos\theta \), \( y+1=5\sin\theta \) where \( \theta \) is the parameter, the line \( x=1+\frac{\sqrt{3}}{2}r \), \( y=-2+\frac{r}{2} \) where \( r \) is the parameter, is a

If the line passing through the point \((4, -3)\) and having negative slope makes an angle of \(45^\circ\) with the line joining the points \((1,1), (2,3)\) then the sum of intercepts of that line is

If the length of the chord 2x+3y+k=0 of the circle \(x^2+y^2-2x+4y-11=0\) is \(2\sqrt{3}\), then the sum of all possible values of k is

By shifting the origin to the point (-1,2) through translation of axes, if $ax^2+2hxy+by^2+2gx+2fy+c=0$ is the transformed equation of $2x'^2-x'y'+y'^2-3x'+4y'-5=0$, then $2(f+g+h) =$

If the perpendicular drawn from the point (2,-3) to the straight line $4x-3y+8=0$ meets it at M(a,b) and $a^3-b^3=k^3$, then $k =$

If the slopes of the lines represented by the equation $6x^2+2hxy+4y^2 = 0$ are in the ratio 2:3, then the value of h such that both the lines make acute angles with the positive X-axis measured in positive direction is

The line $4x-3y+2 = 0$ intersects the circle $x^2+y^2-2x+6y+c=0$ at two points A, B and AB=8. If (1,k) is a point on the given circle and $k>0$, then $k =$

If the product of the perpendicular distances from any point on the hyperbola \( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \) to its asymptotes is \( \frac{36}{13} \) and its eccentricity is \( \frac{\sqrt{13}}{3} \), then \( a - b = \)

The equation of the circle whose radius is 3 and which touches the circle \(x^2 + y^2 - 4x - 6y - 12 = 0\) internally at \((-1, -1)\) is

The lines x+y+4=0, x-2y-4=0 and 3x+4y-2=0