List of top Questions asked in KEAM

Square planar compound is:
Order of acidity CH=CH, CH₃-C=CH, CH₃-C=C-CH₃?
Which one of the series of hydrogen spectrum is in the visible region?
Which shows +6 oxidation state in fluorides?
Which of the following is an extensive property?
Young's modulus and shear modulus are applicable for:
Energy of H atom in ground state is 13.6 eV. No of spectral lines emitted by 'H' atom when a photon of energy 12.75 eV is received?
Axis of parabola is \( x = 0 \). If the vertex is at a distance of 3 from the origin above the x-axis, find the vertex.
The acceleration of a particle varies with time as \( a = 6t \). What is the displacement and velocity of the particle at \( t = 4s \)?
Friedel Craft's reaction is an example of:
Benzene when treated with Br\(_2\) in the presence of FeBr\(_3\), gives 1,4-dibromobenzene and 1,2-dibromobenzene. Which type of reaction is this?
Evaluate the following sum: \[ \sum_{n=1}^{2025} i^n (1+i) \]
Coefficient of friction is the ratio of?
If force is 500 N and instantaneous velocity is 20 m/s, what is the instantaneous power?
A block is tied to a string of length 98 cm and is rotated in a horizontal circle. Find the angular velocity if the centripetal acceleration \( a = g \).
Evaluate the following statement: \[ f(x) = \sin(|x|) - |x| \text{ is not differentiable at } x = \underline{\hspace{2cm}} \]
Find the range of \( f(x) = \log_e(4x^2 - 4x + 1) \)
Find the probability of getting at most 2 heads when 4 coins are tossed.
Evaluate the following integral: \[ \int e^x \left[\frac{1}{1+x(1+x)^2}\right] dx \]
Evaluate the derivative of the function: \[ f(x) = x |x|, \quad \text{find} \quad f'(-10) \]
Given that \( \mathbf{a} \times (2\hat{i} + 3\hat{j} + 4\hat{k}) = (2\hat{i} + 3\hat{j} + 4\hat{k}) \times \mathbf{b} \), \( |\mathbf{a} + \mathbf{b}| = \sqrt{29} \), \( \mathbf{a} \cdot \mathbf{b} = ? \)
Given the following probabilities: \[ P(A) = 0.7, P(B) = 0.5, P(A \cup B) = 0.9, \quad \text{find} \quad P(A/B) \]
Evaluate the following integral: \[ \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \left( x^4 + x^3 + x \right) \cos x \, dx \]
Evaluate the integral: \[ \int \frac{\sin(2x)}{\sin(x)} \, dx \]
Find the center of the ellipse given by the equation \[ 4x^2 + 24x + 9y^2 - 18y + 9 = 0 \]