List of top Questions asked in KEAM

Which of the following has square planar structure?
Which of the following compound has the lowest boiling point?
An organic compound contains 37.5% C, 12.5% H and the rest oxygen. What is the empirical formula of the compound?

The value of \[ \left(\frac{10i}{(2-i)(3-i)}\right)^{2024} \] is equal to:

The modulus of the complex number \[ \frac{(1 + i)^{10} (2 - i)^6}{(2i - 4)^4} \] is equal to:
If \[ \frac{1}{1 - \tan x} = \frac{3 + \sqrt{3}}{2}, \quad 0 \leq x \leq \frac{\pi}{2}, \] then the value of \( x \) is equal to:
Evaluate the integral: \[ \int_{\frac{\pi}{5}}^{\frac{3\pi}{10}} \frac{\sqrt{\tan x}}{1 + \sqrt{\tan x}} \, dx \]
Given that: \[ \frac{1}{\tan A - \tan B} = \]

The general solution of the differential equation \( \frac{dy}{dx} = xy - 2x - 2y + 4 \) is:

If \( f'(x) = 4x\cos^2(x) \sin\left(\frac{x}{4}\right) \), then \( \lim_{x \to 0} \frac{f(\pi + x) - f(\pi)}{x} \) is equal to:

11\( (10P_7) \) =
The value of \[ \frac{\cos^{-1}(0) + \sin^{-1}\left( \frac{\sqrt{3}}{2} \right) + \cos^{-1}\left( \frac{1}{2} \right)}{\sin^{-1}(1) + \cos^{-1}\left( \frac{\sqrt{3}}{2} \right) + \sin^{-1}\left( \frac{1}{\sqrt{2}} \right)} \] is equal to:
The angle between the lines \[ \frac{x-1}{6} = \frac{y-5}{8} = \frac{z-3}{10} \quad {and} \quad \frac{x+1}{2} = \frac{2y+3}{2} = \frac{z+3}{2} \] is:

The focus of the parabola \(y^2 + 4y - 8x + 20 = 0\) is at the point:

An assignment of probabilities for outcomes of the sample space \( S = \{1, 2, 3, 4, 5, 6\} \) is as follows:

\[ \begin{array}{c|c c c c c c} 1 & 2 & 3 & 4 & 5 & 6 \\ \hline k & 3k & 5k & 7k & 9k & 11k \end{array} \]

If this assignment is valid, then the value of \( k \) is:

A flywheel ensures a smooth ride on the vehicle because of its:
The resistance of a wire at 0 °C is 4 \(\Omega\). If the temperature coefficient of resistance of the material of the wire is \(5 \times 10^{-3} / ^\circ C\), then the resistance of a wire at 50 °C is:

The centre of the hyperbola \(16x^2 - 4y^2 + 64x - 24y - 36 = 0\) is at the point:

Let \[ A = \begin{pmatrix} 3 & -2 & 1 \\ -1 & 3 & -1 \end{pmatrix} \] and \[ B = \begin{pmatrix} 1 \\ \alpha \\ -1 \end{pmatrix}. \] If \[ AB = \begin{pmatrix} -2 \\ 6 \end{pmatrix}, \] then the value of \( \alpha \) is equal to:

Evaluate the integral: \[ \int \frac{x^2 - 1}{x^4 + 3x^2 + 1} \, dx \]
If the power of a lens is +4 D, then the lens is a

The integral \(\int e^x \sqrt{e^x} \, dx\) equals:

If a line makes angles \(\alpha\), \(\beta\), and \(\gamma\) with the positive directions of the x, y, and z-axis respectively, then \(\cos 2\alpha + \cos 2\beta + \cos 2\gamma\) equals:

The period of the function \( f(x) = \sin\left( \frac{3x}{2} \right) \) is equal to:

The foci of the ellipse \(\frac{x^2}{49} + \frac{y^2}{24} = 1\) are: