List of top Questions asked in TS EAMCET- 2024

If \(4+3x-7x^2\) attains its maximum value \(M\) at \(x=\alpha\) and \(5x^2-2x+1\) attains its minimum value at \(x=\beta\), then \[ \frac{28\,(M - \alpha)}{5\,(m + \beta)} =\,? \] \textit{(Assume \(m\) is that minimum value of \(5x^2 -2x +1\) at \(x=\beta\))}
f is a real valued function satisfying the relation \(f\bigl(3x + \tfrac{1}{2x}\bigr) \;=\; 9x^2 + \tfrac{1}{4x^2}\). If \(f\bigl(x + \tfrac{1}{x}\bigr) = 1\) then \(x =\) ?
If \(\vec{a},\,\vec{b},\,\vec{c}\) are non-coplanar vectors. If the three points \[ \lambda \vec{a} - 2\vec{b} + \vec{c},\quad 2 \vec{a} + \lambda\vec{b} - 2\vec{c},\quad 4\vec{a} + 7\vec{b} - 8\vec{c} \] are collinear, then \(\lambda = \,?\)
\(\vec{r}\) is a vector perpendicular to the plane determined by \(\vec{r_1}=2\mathbf{i}-\mathbf{j}\) and \(\vec{r_2}=\mathbf{j}+2\mathbf{k}\). If the magnitude of the projection of \(\vec{r}\) on the vector \(2\mathbf{i}+\mathbf{j}+2\mathbf{k}\) is 1, then \(\lvert \vec{r}\rvert =\,?\)

The number of common roots among the 12th and 30th roots of unity is ?

∫ √(2x2 - 5x + 2) dx = ∫ (41/60) dx,

and

-1/2 > α > 0, then α = ?

A convex lens of focal length 10 cm is placed coaxially at a distance of 4 cm to the right of another convex lens of focal length 16 cm. If an object is placed at a distance of 8 cm to the left of the convex lens of focal length 16 cm, then the distance of the final image from the object is:
A copper wire of cross-sectional area 0.01 cm\(^2\) is subjected to a tension of 22 N. If Young’s modulus and Poisson’s ratio of copper are \(1.1 \times 10^{11}\) Nm\(^2\) and 0.32 respectively, then the change in the cross-sectional area of the wire is:
The electron gain enthalpy (in kJ/mol) of oxygen, sulphur, selenium respectively are
If two electromagnetic waves with electric fields given by $$ \vec{E_1} = E_0 \sin (kx - \omega t) \hat{j} $$ and $$ \vec{E_2} = E_0 \sin (kx - \omega t + \pi) \hat{j} $$ - interfere, then the peak value of the electric field of the resultant wave is
When an alternating voltage given by \(E = 100 \sin(10^2 t)\), where \(E\) is in volts and \(t\) is in seconds, is applied across a capacitor of capacitance \(20 \, \mu F\), the peak current flowing in the circuit is
An alkene \( X \) (\( C_5H_{10} \)) on reaction with \( HBr \) gave \( Y \) (\( C_5H_{11}Br \)). \( Y \) undergoes hydrolysis via an \( S_N1 \) mechanism. What is \( X \)?
From the following, identify the set that contains all meta directing groups:
Assertion (A): In Arachis, fruits are geocarpic.
Reason (R): Seeds are non-endospermic in Arachis.
Identify the enzyme of the following reaction: \[ \text{Phosphoglyceric acid + ATP} \xrightarrow{\text{Enzyme}} \text{Bisphosphoglyceric acid + ADP} \]
During the process of aerobic respiration, O\(_2\) utilisation occurs in the following stage only:
Evaluate the expression: \[ \cos^{-1} \frac{3}{5} + \sin^{-1} \frac{5}{13} + \tan^{-1} \frac{16}{63} \]
If \(2 \tan^2 \theta - 4 \sec \theta + 3 = 0\), then \(2 \sec \theta\) is:
If \( \alpha \) is a root of the equation \( x^2 - x + 1 = 0 \), then \(\left(\alpha + \frac{1}{\alpha}\right)^3 + \left(\alpha^2 + \frac{1}{\alpha^2}\right)^3 + \left(\alpha^3 + \frac{1}{\alpha^3}\right)^3 + \left(\alpha^4 + \frac{1}{\alpha^4}\right)^3 =\)
If the focus of an ellipse is \((-1,-1)\), equation of its directrix corresponding to this focus is \(x + y + 1 = 0\) and its eccentricity is \(\frac{1}{\sqrt{2}}\), then the length of its major axis is:
The sum of all the 4-digit numbers formed by taking all the digits from \(2, 3, 5, 7\) without repetition is

\( \vec{a}, \vec{b}, \vec{c} \) are three vectors such that \(|\vec{a}| = 3\), \(|\vec{b}| = 2\sqrt{2}\), \(|\vec{c}| = 5\), and \( \vec{c} \) is perpendicular to the plane of \( \vec{a} \) and \( \vec{b} \).

If the angle between the vectors \( \vec{a} \) and \( \vec{b} \) is \( \frac{\pi}{4} \), then

\[ |\vec{a} + \vec{b} + \vec{c}| = \ ? \]

Given two planes with equations \( \mathbf{r} \cdot (\mathbf{i} - \mathbf{j} + \mathbf{k}) = 5 \) and \( \mathbf{r} \cdot (2\mathbf{i} + \mathbf{j} - \mathbf{k}) = 3 \). A plane \( \pi \) passing through the line of intersection of these two planes also passes through the point (0,1,2). If the equation of \( \pi \) is \( \mathbf{r} \cdot (a\mathbf{i} + b\mathbf{j} + c\mathbf{k}) = m \), determine the value of \( \frac{bc}{a^2} \):

Find \( \frac{dy}{dx} \) for the given function:

\[ y = \tan^{-1} \left( \frac{\sin^3(2x) - 3x^2 \sin(2x)}{3x \sin(2x) - x^3} \right). \]

The function \( y = 2x^3 - 8x^2 + 10x - 4 \) is defined on \([1,2]\). If the tangent drawn at a point \( (a,b) \) on the graph of this function is parallel to the X-axis and \( a \in (1,2) \), then \( a = \) ?