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:
Let \( \alpha, \beta, \gamma \) be the direction cosines of a vector \( \vec{a} = x \hat{i} + y \hat{j} + z \hat{k} \), where \( z<0 \). If \( \alpha = \frac{-4}{\sqrt{105}} \) and \( \beta = \frac{\sqrt{5}}{\sqrt{21}} \), then \( \gamma \) 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
Evaluate the integral: \[ \int_{0}^{3} |x - 2| \,dx \] is equal to
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
Mobility \( \mu \) of an electron is related to average collision time \( \tau \) as: \[ \mu = \frac{e \tau}{m} \] (where \( e \) is the electronic charge, and \( m \) is the mass of the electron)
Which of the following statement is incorrect with Kolbe’s electrolytic method?
Which of the following substitution reaction with methane requires HIO\(_3\) as an oxidising agent?
Whenever light travels from rarer medium into denser medium its
The length of the side of a cube is \( 1.1 \times 10^{-2} \) m. Its volume in \( m^3 \) up to correct significant figures is:
If \(\vec{a} = 0.4\hat{i} + 0.3\hat{j} + b\hat{k}\) is a unit vector, then the value of b is

A ball is projected in still air. With respect to the ball the streamlines appear as shown in the figure. If speed of air passing through the region 1 and 2 are \( v_1 \) and \( v_2 \), respectively and the respective pressures, \( P_1 \) and \( P_2 \), respectively, then 

Which of the following statement is incorrect?
The function \( f(x) = 6x^4 - 3x^2 - 5 \) is increasing in the set:

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

The reagents and conditions (X) required for the following conversion 

Young’s double-slit experiment is carried out by using green, red and blue lights, one at a time. The fringe widths recorded are \( \beta_G \), \( \beta_R \) and \( \beta_B \) respectively. Then
A person travels in a car from p to q with uniform speed u and returns to p with uniform speed v. The average speed for his round trip is
Which of the following is the most reactive in aromatic electrophilic substitution reaction?
The ratio of the maximum kinetic energy to the maximum potential energy of a bob of a simple pendulum executing small oscillations is
A block of mass 3 kg executes simple harmonic motion under the restoring force of a spring. The amplitude and the time period of the motion are 0.1 m and 3.14 s respectively. The maximum force exerted by the spring on the block is
Which of the following has the least atomic radius?
A particle executes a linear SHM with an amplitude \(a\) and angular velocity \(\omega\). The ratio between its acceleration amplitude and displacement amplitude is
Let \( z = x + iy \), where \( y>0 \). If \( z + \overline{z} = 6 \) and \( |z| + | \overline{z} | = 10 \), then \( z = \)
The electronic configuration of Pd (Z = 46) is