List of top Questions asked in KEAM

Compute \( \int (\cot 2x + \cos 2x) \, dx \)

If \( y = \log_e (x^3 + 24) \), find \( \frac{dy}{dx} \) at \( y = \log_e 2 \).

Find \(\int_{-1}^{1} \frac{\log(1 + |x|)}{1 + |x|} \, dx\)

If \( y = \frac{1 + \tan^2 x}{1 - \tan^2 x} \), find \( y' \left( \frac{\pi}{8} \right) \), where \( 0<x<\frac{\pi}{4} \).

Increasing order of metallic character

If \(y = 4\sqrt{x}\) then \(\frac{d^2y}{dx^2} =\)

Number of words that can be formed starting and ending with the same letter from the word BANANA.

Number of ways 3 boys and 4 girls can be arranged such that there is one girl between any 2 boys and one boy between any 2 girls.

Relationship between \( t_{90} \) and \( t_{99} \) for a first order reaction:

Lactose is composed of:

Which of the following statements regarding the structure of CO\(_2\) is correct?

Which of the following is allylic alcohol?

Enthalpy of formation of \( \text{C}_6\text{H}_6 \), \( \text{CO}_2(g) \) and \( \text{H}_2\text{O}(l) \) are -393.5, -285.8 and +48.5 KJ/mol respectively. Find the enthalpy of combustion of \( \text{C}_6\text{H}_6 \):

Which of the following has a planar structure with two lone pairs?

The \( K_c \) of the reaction \[ \text{NH}_3(g) + \text{O}_2(g) \rightleftharpoons 2\text{NO}(g) \] at 1500 K is 0.1. What is the concentration of NO, when the initial concentration of \( \text{N}_2 \) and \( \text{O}_2 \) is 0.04 mol?

Ratio of between the maximum wavelength of Lyman and Balmer series.

Which reagent gives as major product from phenol

Hinsberg reagent is

If ‘m’ is the molality, ‘M’ is the molarity, ‘d’ is the density in g/cm\(^3\) and ‘M\(_2\)’ is the molarity of solute. What is the relation between them?

Which of the following has highest pKa value?

Which 3d series of element has least enthalpy of atomization?

The isomerism shown by the following compound: \[ [\text{Co}(CN)_6][\text{Cr}(NH_3)_6] \quad [\text{Co}(CN)_6][\text{Cr}(NH_3)_6] \]

Energy of \(2h\nu_0\) fall on a metal of work function \(h\nu_0\) cause velocity of \(v_1\), when \(5h\nu_0\) fall velocity ratio of \(v_1/v_2\)

P\(_4\) \(\rightarrow\) PH\(_3\) + H\(_2\)PO\(_2\)
Oxidation state of phosphorus change from -------- to -------- respectively.

Which of the following have minimum and maximum threshold energy K, Na, Mg, Li?