List of top Questions asked in TS EAMCET

The number of normals that can be drawn through the point $(9,6)$ to the parabola $y^2 = 4x$ is:

If $ T_4 $ represents the 4th term in the expansion of $ \left( 5x + \frac{7}{x} \right)^{-\frac{3}{2}} $ and $ x \not\in \left[ \frac{\sqrt{7}}{5}, \frac{\sqrt{7}}{5} \right] $, then $ \left( x^3 \cdot \sqrt{5x} \right) T_4 = $:}

If the normal drawn at the point $ P(9, 9) $ on the parabola $ y^2 = 9x $ meets the parabola again at $ Q(a, b) $, then $ 2a + b = \text{?} $

S' is the focus of the ellipse $ \frac{x^2}{25} + \frac{y^2}{b^2} = 1, (b<5) $ lying on the negative X-axis and $ P(\theta) $ is a point on this ellipse. If the distance between the foci of this ellipse is 8 and $ S'P = 7 $, then $ \theta $ is:

If the function $ f(x) $ is given by \[ f(x) = \begin{cases} \frac{\tan(a(x-1))}{\frac{x-1}{x}}, & tif0<x<1
\frac{x^3-125}{x^2 - 25} , & \text{if } 1 \leq x \leq 4
\frac{b^x - 1}{x}, & \text{if } x>4 \end{cases} \] is continuous in its domain, then find $ 6a + 9b^4 $.

The position vectors of the vertices $ A, B, C $ of a triangle are given as: \[ \vec{A} = \hat{i} - 2\hat{j} + k, \quad \vec{B} = 2\hat{i} + \hat{j} - k, \quad \vec{C} = \hat{i} - \hat{j} - 2k \] If $ D $ and $ E $ are the midpoints of $ BC $ and $ CA $ respectively, then the unit vector along $ \overrightarrow{DE} $ is:

If $ Z_1, Z_2, Z_3 $ are three complex numbers with unit modulus such that \[ |Z_1 - Z_2|^2 + |Z_1 - Z_3|^2 = 4 \] then \[ Z_1 Z_2 + \overline{Z_1} Z_2 + Z_1 Z_3 + \overline{Z_1} Z_3 = \]

The trigonometric equation $ \sin^{-1}x = 2\sin^{-1}a $ has a solution. Find the valid range for $ a $.

If Rolle's Theorem is applicable for the function:

\[ f(x) = \begin{cases} x^p \log x, & x \neq 0 \\ 0, & x = 0 \end{cases} \]

on the interval $[0,1]$, then a possible value of $ p $ is:

The sum of the maximum and minimum values of the function \[ f(x) = \frac{x^2 - x + 1}{x^2 + x + 1} \] is:

If $ f(x) = ax^2 + bx + c $ is an even function and $ g(x) = px^3 + qx^2 + rx $ is an odd function, and if $ h(x) = f(x) + g(x) $ and $ h(-2) = 0 $, then $ 8p + 4q + 2r = $?

If $\frac{x^2}{2x^2 + 7x + 6} = \frac{Ax + B}{x^2 + a} + \frac{Cx + D}{ax^2 + 3}$, then $A + B + C - 2D =$

Given $(\sin \theta - \csc \theta)^2 + (\cos \theta + \sec \theta)^2 = 5$ and $\theta$ lies in the third quadrant, find $(\sin \theta + \cos \theta)^3$.

In the reaction: \[ NH_2CONH_2 + 2H_2O \rightarrow [X] \rightleftharpoons 2NH_3 + H_2O + [Y] \] The hybridization of carbon in $ X $ and $ Y $ respectively are:

The efficiency of a reversible heat engine working between two temperatures is 50\%. The coefficient of performance of a refrigerator working between the same two temperatures but in reverse direction is: