List of top Questions asked in KEAM

A particle of mass m and charge q with an initial velocity v is subjected to a uniform magnetic field B along the vertical direction. The particle will

Consider a convex lens made of material of refractive index \( n = \frac{3}{2} \) and radius of curvature \( R \). What is the relation between focal length and radius?

A pure inductor of inductance \( 0.1 \, \text{H} \) is connected to an AC source (of rms voltage 220 V and angular frequency 300 Hz). The rms current is

Solve the equation: \[ \frac{(3x - 4)^2}{9} - \frac{(4x - 3)^2}{8} = 1 \quad \text{(length of the latus rectum)} \]

In YDSE, when light of wavelength 700nm is used, a fringe width of 0.5mm is obtained. What happens when light of wavelength 500nm is used?

The products obtained by the ozonolysis of 2-methylbut-1-ene are:

Given: \( P(B) = 0.8 \) and \( P(A \cup B) = 0.8 \), find \( P(A' \cup B') \).

The equation of perpendicular bisector of the line segment joining the points (10, 0) and (0, -4) is

A 3-digit number greater than 500 is to be made with the numbers 3, 4, 5, and 7. Find the number of possible ways.

The end-points of a diameter of a circle are \( (-1, 4) \) and \( (5, 4) \). Then the equation of the circle is

The 1st and 20th term of a GP are 512 and \( \frac{1}{1024} \), respectively. Find the common ratio.

Evaluate the integral: \[ \int 16x^3 \log_e x \, dx \]

Evaluate the integral: \[ \int_0^1 \frac{t}{(t + 1)^3} \, dt \]

Find the number of combinations of 3-lettered numbers that can be created by 3, 4, 5, and 7 with repeating. The three digits cannot be equal to zero.

If \( ay = x + b \) is the equation of the line passing through the points (-5, -2) and (4, 7), then the value of \( 2a + b \) is equal to:

Given that \( |AB| = 21 \) and \( |A^{-1}| = 7 \), find \( |B| \).

Evaluate the integral: \[ \int \left( 27x^3 (1 - x^3)^{\frac{1}{3}} \right) dx \]

2-methyl propene is obtained as product when sodium methoxide reacts with

Find the alkene which gives 2 mol of acetone by ozonolysis.

Benzene diazonium salt in the presence of Cu/HBr will give bromobenzene (C\(_6\)H\(_5\)Br) and release nitrogen gas (N\(_2\)). This reaction is known as:

Which aldehyde does not give Fehling test?

What is the name of the element which is known as Eka-Aluminium?

Which of the following is used to convert sodium chromate to sodium dichromate in the preparation of potassium dichromate?

Which of the following series in hydrogen spectrum corresponds to UV radiation?

When CO is reacted with \( H_2 \) at 573 K, methanol is formed. Which is the catalyst used in this process?