List of top Questions asked in KEAM- 2024

If $ A = \begin{bmatrix} 4 & -1 \\ 12 & x \end{bmatrix} $ and $ A^2 = A $, then the value of $ x $ is:

The solution of the inequality $ |3x - 4| \leq 5 $ is

The value of $ x $ that satisfies the equation:

\[ \begin{vmatrix} x & 1 & 1 \\ 2 & 2 & 0 \\ 1 & 0 & -2 \end{vmatrix} = 6 \]

If $ \alpha = \tan^2 x + \cot^2 x $, where $ x \in \left( 0, \frac{\pi}{2} \right) $, then $ \alpha $ lies in the interval:

The integral $ \int e^x \sec x (1 + \tan x) \, dx $ is equal to:

The value of $ \sin^2 \left( \frac{3\pi}{8} \right) + \sin^2 \left( \frac{7\pi}{8} \right) $ is:

Let \[ A = \begin{pmatrix} 2 & -1 & 1 \\ -1 & 0 & 2 \\ 1 & -2 & -1 \end{pmatrix} \] and let $ B = \frac{1}{|A|} A $. Then the value of $ |B| $ is equal to:

If $ a_1 = 3 $ and $ a_n = n \cdot a_{n-1} $, for $ n \geq 2 $, then $ a_6 $ is equal to

The solution of $ \frac{e^y}{dx} = x + 2 $ is:

If

\[ R = \{(x, y) : x, y \in \mathbb{Z}, \, x^2 + 3y^2 \leq 7 \} \] is a relation on the set of integers $ \mathbb{Z} $, then the range of the relation $ R $ is:

Evaluate $ \int \frac{e^{6 \log x} - e^{5 \log x}}{e^{4 \log x} - e^{3 \log x}} \, dx $:

The sum of the first 20 terms of the G.P. $ \sqrt{3} + \frac{-1}{\sqrt{3}} + \frac{1}{3\sqrt{3}} + \cdots $ is equal to

The area bounded by the curves $ y = x^2 $ and $ y = 2x $ in the first quadrant, is equal to:

The value of $ \lim_{x \to 0} \frac{\sin(5x)}{\sin(3x)} $ is:

The point of intersection of the lines $\frac{x-3}{2} = \frac{y-2}{2} = \frac{z-6}{1}$ and $\frac{x-2}{3} = \frac{y-4}{2} = \frac{z-1}{3}$ is:

The period of the function $ \sin\left( \frac{\pi x}{4} \right) $ is

If $ f(x) = x + 8 $, and $ g(x) = 2x^2 $, then $ (g \circ f)(x) $ is equal to

If $ 2 $ is a solution of the inequality $ \frac{x-a}{a-2x}<-3 $, then $ a $ must lie in the interval:

The value of $ \tan \left( \cos^{-1} \left( \frac{-24}{25} \right) \right) $ is equal to

Let $ f(x) = x \sin(x^4) $. Then $ f'(x) $ at $ x = \sqrt[4]{\pi} $ is equal to:

The coefficient of $ x^3 $ in the expansion of \[ \frac{1}{(1 + 2x)^{-10}} \] is:

Let $ f(x) = \sqrt{4 - x^2} $, $ g(x) = \sqrt{x^2 - 1} $. Then the domain of the function $ h(x) = f(x) + g(x) $ is equal to:

If the function \[ f(x) = \begin{cases} x^2, & \text{for } x < 4 \\ 5x - k, & \text{for } x \geq 4 \end{cases} \] is continuous at $ x = 4 $, then the value of $ k $ is equal to

For the reaction:

$3Fe_{(s)} + 2O_2{(g)} \rightarrow Fe_3O_4{(s)}$

$\Delta H = -1650\,\text{kJ mol}^{-1}$, $\Delta S = -600\,\text{J K}^{-1} \text{mol}^{-1}$ at $300\,\text{K}$. What is the value of free energy change for the reaction at $300\,\text{K}$?

Gatterman reaction is used to convert benzene diazonium chloride to