List of top Questions asked in KEAM

If \( p \) is the length of the perpendicular from the origin to the line whose intercepts with the coordinate axes are \( \frac{1}{3} \) and \( \frac{1}{4} \), then the value of \( p \) is:

The value of \( \tan(1^\circ) + \tan(89^\circ) \) is equal to:

If \( \sin \theta + \csc \theta = 2 \), then the value of \( \sin^6 \theta + \csc^6 \theta \) is equal to:

The value of \( \sec^2(\tan^{-1} 3) + \csc^2(\cot^{-1} 2) \) is equal to:

\( \cos^{-1}\left(\cos\left(\frac{7\pi}{5}\right)\right) = \)

Let \( s_n = \cos\left(\frac{n\pi}{10}\right) \), \( n=1,2,3, \ldots \). Then the value of \( \frac{s_1s_2\cdots s_{10}}{s_1+s_2+\cdots+s_{10}} \) is equal to:

If \( ab < 1 \) and \( \cos^{-1}\left(\frac{1-a^2}{1+a^2}\right) + \cos^{-1\left(\frac{1-b^2}{1+b^2}\right) = 2 \tan^{-1} x \), then \( x \) is equal to:}

Let \( p, q \) and \( r \) be any three logical statements. Which one of the following is true?

The value of \( \sin^{-1} \left( \frac{2\sqrt{2}}{3} \right) + \sin^{-1 \left( \frac{1}{3} \right) \) is equal to:}

Let \( \theta \in [0, \frac{\pi}{2}] \). Which one of the following is true?

The truth values of \( p, q \) and \( r \) for which \( (p \wedge q) \vee (\sim r) \) has truth value F are respectively:

\( \sim [(\sim p) \wedge q] \) is logically equivalent to:

The number of solutions for the system of equations \( 2x + y = 4 \), \( 3x + 2y = 2 \), and \( x + y = -2 \) is:

The shaded region shown in the figure is given by the inequations: [height=5cm]{Screenshot 2026-05-01 102102.png}

The number of solutions of the inequation \( |x - 2| + |x + 2| < 4 \) is:

The salt of an alkali metal gives violet colour in the flame test. Its aqueous solution gives a white precipitate with barium chloride in hydrochloric acid medium. The salt is

In which one of the following the central atom is sp\textsuperscript{3 hybridized?}

Which of the following are isoelectronic species?
(i) NH\textsubscript{3 (ii) CH\textsubscript{3}\textsuperscript{+} (iii) NH\textsubscript{2}\textsuperscript{--} (iv) NH\textsubscript{4}\textsuperscript{+}
Choose the correct answer from the codes given below}

At 273 K, the density of a certain gaseous oxide at 2 atmosphere is same as that of dioxygen at 5 atmosphere. The molecular mass of the oxide (in g mol\textsuperscript{--1}) is

If two moles of an ideal gas at 500 K occupies a volume of 41 litres, the pressure of the gas is (R = 0.082 L atm K\textsuperscript{--1} mol\textsuperscript{--1})

Potassium dichromate belongs to which crystal system?

The reaction of H\textsubscript{2 is given below
H\textsubscript{2} + CO + R--CH=CH\textsubscript{2} \(\rightarrow\) R--CH\textsubscript{2}--CH\textsubscript{2}--CHO
is specifically called as}

Arrange the following species in the correct order of their stability:
$C_2$, $Li_2$, $O_2^+$, $He_2^+$

Molecular formulae and shapes of some molecules are given below. Choose the incorrect match

Green chemistry deals with