List of top Questions asked in KEAM- 2024

If \[ A = \begin{bmatrix} -7 & 3 \\ 3 & -1 \end{bmatrix} \] then \( \det(A^5) \) is equal to:
The lowest frequency of the air column in an open pipe of length \( L \) is \( v \) (velocity of sound in air)
The principle involved in the performance of a circus acrobat is the conservation of
The melting point of \( \beta \)-form of crystalline glucose is
In an LCR series resonance circuit driven by the alternating voltage \( V = V_0 \sin \omega t \), inductance \( L = 1 \, \mu H \), capacitance \( C = 1 \, \mu F \) and resistance \( R = 1 \, k\Omega \). The resonant angular frequency (in rad/s) is:
Let \( A \) be a \( 3 \times 3 \) matrix with \( |A| = 7 \). If \( B = 3A \), then the value of \[ \left| \frac{{adj } A}{B} \right| \] is equal to
Kjeldahl method can be used to estimate nitrogen in
The number of de Broglie waves associated with Bohr electron when it completes one revolution in its third orbit is
Which of the following vitamin deficiency causes increased fragility of RBCs and muscular weakness?
Electromagnetic waves of frequency \( 5 \times 10^{14} \, {Hz} \) lie in the
The range of the function \( f(x) = 8 + \sqrt{x - 5} \) is:
Let \( z = x + iy \), where \( y>0 \). If \( z + \overline{z} = 6 \) and \( |z| + | \overline{z} | = 10 \), then \( z = \)
Which of the following statement is true with regard to Daniell cell?
Speed of a transverse wave on a stretched string under tension \(T\) and linear density \(\mu\) is
The general solution of the differential equation \[ 2y \tan x + \frac{dy}{dx} = 5 \sin x \] is:
If \[ f(x) = \sqrt[3]{x^2} + \sqrt{x}, \] then the value of \( f'(64) \) is equal to
Let \( A = \{ 1, 3, 5, 7, \dots, 21 \} \). The number of ways 4 numbers, containing always 11, can be selected from the set A is equal to
Find the integrating factor of the differential equation: \[ (3 \sin x \cos x) \, dy = (1 + 3y \sin^2 x) \, dx, \quad {where} \quad 0<x<\frac{\pi}{2} \] is
Which of the following molecule is paramagnetic?
The angle between the vectors \( \vec{a} \) and \( \vec{b} \) is \( \frac{\pi}{3} \). If \( | \vec{a} \cdot \vec{b} |^2 = 15 \), then \( | \vec{a} \times \vec{b} |^2 \) is equal to
Which of the following has square planar structure?
If \( \vec{a} = 5\hat{i} - 7\hat{j} + 9\hat{k} \) and \( \vec{b} = -5\hat{i} + 7\hat{j} - 9\hat{k} \), then \( \vec{a} \cdot (\vec{a} \times \vec{b}) + (\vec{a} + \vec{b}) \cdot \hat{b} \) is equal to

The vapour pressure of H\(_2\)O at 323K is 95 mm of Hg. 176g of sucrose (Molar mass = 342 gmol\(^{-1}\)) is added to 900g of H\(_2\)O at 323K. 
The vapour pressure of solution is about

Ice is coated uniformly around a sphere of radius 15 cm. If ice is melting at the rate of \( 80 { cm}^3/{min} \) when the thickness is 5 cm, then the rate of change of thickness of ice is

When a diode is reverse biased