List of top Questions asked in KEAM

Find the vertex of the parabola \( 4y = x^2 - 6x + 17 \).
Evaluate the integral: $ \int \frac{1}{x(x^4 + 1)} \, dx $
Evaluate the integral: \[ \int e^x \sec(x) \left( \tan(x) + 1 \right) \, dx \]
Given the set $ S = \{ a, b, c, d, e, f \} $, find the total number of subsets with an odd number of elements.
The cubic polynomial \( 2x^3 - 3x^2 - 36x + 28 \) is increasing in the range of \( x \). Find the interval where the function is increasing.

If $ | \vec{a} | = 3 $, $ | \vec{b} | = 2 $, then find $ (3\vec{a} - 2\vec{b}) \cdot (3\vec{a} + 2\vec{b}) $.

If $ \sum_{k=0}^{n+1} C_k^n = 512 $, find $ \sum_{k=0}^{n} C_k^n $.
For smaller deformations, stress is directly proportional to the strain for any material. Then the constant of proportionality is called as its
A hockey player hits a ball with an impulse of 15 Ns. If time of hit is 0.2 s, the average force exerted by the player on the ball is
The most common oxidation states of chromium are
What is the magnetic moment of a divalent ion with three unpaired electrons?
If the position of the particle as a function of time \( t \) is \( \vec{r} = 8t \hat{i} + 3t^2 \hat{j} + 3 \hat{k} \, \text{m} \), then the acceleration of the particle is (in \( \text{m/s}^2 \))
The bond angle of Cr-O-Cr bond in dichromate ion is
The percentage of Cr(III) in Ruby is
An ideal Carnot engine has an efficiency of 40 %. The ratio of the temperature of the sink to that of the source is
The magnetic moment of an electron revolving in an orbit of 0.5 m radius with a velocity of \( 8 \times 10^7 \, \text{m/s} \) is (in \( \text{Am}^2 \))

Benzene diazonium chloride on treatment with reagent 'X' gives iodobenzene. The reagent ‘X’ is

The number of moles of alkyl halides required to convert primary amine into quaternary ammonium salt is
The order of boiling point of the following amines is (i) Butan-1-amine
(ii) N-Ethylethanamine
(iii) N,N-Dimethylethanamine
An aromatic compound (X) of molecular formula, C7H7Cl, on ammonolysis gives Y (Molecular formula, C7H9N). The compound Y reacts with two moles of CH3Cl gives N, N-Dimethylphenylmethanamine. The compounds 'X' and 'Y' are
Three particles of equal mass lie at distances of 1 cm, 2 cm, and 3 cm from the origin. The distance of their center of mass from the origin is
Which of the following compounds is used to cover the surface of a metallic object to prevent corrosion?
Which of the following gases has the lowest solubility in water at 298 K?
The temperature and pressure required for reforming benzene from n-hexane is
When C6H5CHO reacts with the mixture of HNO3 and H2SO4 at 273-283K, it gives