List of top Mathematics Questions asked in TS EAMCET

P and Q are the extremities of a focal chord of the parabola \( y^2 = 4ax \). If \( P = (9,9) \) and \( Q = (p, q) \), then \( p - q \) is:
The number of normals that can be drawn through the point \((9,6)\) to the parabola \(y^2 = 4x\) is:
The point \((p, q)\) is the point of intersection of a latus rectum and an asymptote of the hyperbola \(9x^2 - 16y^2 = 144\). If \(p>0\) and \(q>0\), then \(q = \ldots\)
Length of the common chord of the circles \(x^2 + y^2 - 6x + 5 = 0\) and \(x^2 + y^2 + 4y - 5 = 0\) is:
The equations of the directrices of the ellipse \(9x^2 + 4y^2 - 18x - 16y - 11 = 0\) are:
The end of a latus rectum of the ellipse \(3x^2 + 4y^2 = 12\) is lying in the third quadrant. If the normal drawn at \(L_1\) to this ellipse intersects the ellipse again at the point \(P(a,b)\), then find the value of \(a\):
A, B, C are the vertices of a triangle ABC. If the bisector of \( \angle BAC \) intersects the side BC at D\((p,q,r)\), then \( \sqrt{2p+q+r} = ? \)
If \( \theta \) is the acute angle between the curves \( y^2 = x \) and \( x^2 + y^2 = 2 \), then \( \tan \theta \) is:

If \( A = \begin{pmatrix} x & y & y \\ y & x & y \\ y & y & x \end{pmatrix} \) and \( 5A^{-1} = \begin{pmatrix} -3 & 2 & 2 \\ 2 & -3 & 2 \\ 2 & 2 & -3 \end{pmatrix} \), then \( A^2 - 4A \) is:

The approximate value of \( \sqrt[3]{730} \) obtained by the application of derivatives is:
The general solution of the differential equation \[ \frac{dy}{dx} = \frac{2y^2 + 1}{2y^3 - 4xy + y}. \]
A right circular cone is inscribed in a sphere of radius 3 units. If the volume of the cone is maximum, then the semi-vertical angle of the cone is:
If \( f(x) = kx^3 - 3x^2 - 12x + 8 \) is strictly decreasing for all \( x \in \mathbb{R} \), then:
Evaluate the integral: \[ \int e^{-2x} \left( \tan 2x - 2\sec^2 2x \tan 2x \right) dx. \]
If \( \int x^3 \sin 3x \,dx = f(x) \cos 3x + g(x) \sin 3x + c \), then evaluate \( 27(f(x) + xg(x)) \):

If the real-valued function

\[ f(x) = \sin^{-1}(x^2 - 1) - 3\log_3(3^x - 2) \]

is not defined for all \( x \in (-\infty, a] \cup (b, \infty) \), then what is \( 3^a + b^2 \)?

Evaluate the integral: \[ \int \frac{dx}{9\cos^2 2x + 16\sin^2 2x} \]
Evaluate the integral: \[ \int \frac{2\cos 3x - 3\sin 3x}{\cos 3x + 2\sin 3x} dx. \]
Evaluate the integral: \[ I = \int_{\frac{-3\pi}{4}}^{\frac{\pi}{6}} \log(\sin(4x+3)) \,dx \]
Evaluate the integral: \[ \int_0^{16} \frac{\sqrt{x}}{1 + \sqrt{x}} dx. \]
Evaluate the integral: \[ I = \int_{0}^{32\pi} \sqrt{1 - \cos 4x} \,dx \]
The vertical angle of a right circular cone is \( 60^\circ \). If water is being poured into the cone at the rate of \( \frac{1}{\sqrt{3}} \) m\(^3\)/min, then the rate (m/min) at which the radius of the water level is increasing when the height of the water level is 3m is:

If \( A = \begin{pmatrix} 9 & 3 & 0 \\ 1 & 5 & 8 \\ 7 & 6 & 2 \end{pmatrix} \) and

\[ A^T A^{-2} = \begin{pmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{pmatrix} \]

then

\[ \sum_{1 \leq i \leq 3} \sum_{1 \leq j \leq 3} a_{ij} \]

is:

If \( f \) is a real valued function from \( A \) onto \( B \) defined by \( f(x) = \frac{1}{\sqrt{|x| - |x|}} \), then \( A \cap B \) is:}

If \( a \neq b \neq c \), then

\[ \Delta_1 = \begin{vmatrix} 1 & a^2 & bc \\ 1 & b^2 & ca \\ 1 & c^2 & ab \end{vmatrix}, \quad \Delta_2 = \begin{vmatrix} 1 & 1 & 1 \\ a^2 & b^2 & c^2 \\ a^3 & b^3 & c^3 \end{vmatrix} \]

and

\[ \frac{\Delta_1}{\Delta_2} = \frac{6}{11} \]

then what is \( 11(a + b + c) \)?