List of top Questions asked in KEAM

Find the limit: $ \lim_{x \to 0^+} 2 \left\lfloor x \right\rfloor - \frac{x}{|x|} $
Find the limit: $ \lim_{x \to 0^+} 2 \left\lfloor x \right\rfloor - \frac{x}{|x|} $
Equation of parabola having focii (-3, 1) and (3, 1)
Solve the following differential equation and integrate: $ \frac{dy}{dx} + \frac{2x}{1 + x^2} \cdot y = x $
Find the value of $ \sin 60^\circ - \sin 80^\circ + \sin 100^\circ - \sin 120^\circ $
If $ f(x) = \frac{\sqrt{x^4}}{\sqrt{x^2}} $, find $ f'(27) $.
If $ f(x) = \frac{1}{x^2} $, $ u = f(x) $, and $ f'(x) $, then find $ \frac{du}{dx} $.
Given the system of equations: \[ Z + \bar{Z} = 4 \quad \text{and} \quad Z - \bar{Z} = 6 \] Find \( |Z| \).
A cylindrical vessel contains 16 kg at 1 atm. A certain amount of substance is taken out so that pressure becomes 0.7 atm. Find the amount taken out (in kg).
Express the final answer to the proper number of significant figures: \[ 18.0 + 11.515 + 13.2 = \ldots \]
The product of the first five terms of a GP is 32. What is the 3rd term?
Given the function \( F(x) = |\sin(3x)| - \cos(3x) \), for \( \frac{\pi}{6} \leq x \leq \frac{\pi}{3} \), find \( f' \left( \frac{\pi}{4} \right) \).
3 capacitors of capacitance \( 12 \mu \text{F} \) each is connected in series. If the voltage is 12V, what charge is drawn from the cell?
N\(_2\) exerts partial pressure of 7.698 bar in 1L water at 298K. What is the mole fraction of N\(_2\) in the solution? Given that N\(_2\) = 76.48K bar.
Solve the system of equations: \[ \begin{bmatrix} 4 & 9 \\ 12 & -3 \\ 8 & -2 \end{bmatrix} \begin{bmatrix} 7 \\ 9 \end{bmatrix} = \begin{bmatrix} \alpha \\ \beta \end{bmatrix} \]
Evaluate the integral: \[ \int e^x \sec(x) \left( \tan(x) + 1 \right) \, dx \]
Which is a heterocyclic compound?
If \( B = 400\sqrt{2} \sin(\omega t - kx) \), find the peak value of the magnetic field of the electromagnetic wave.
Find pH of the solution if \([H^+] = 2 \times 10^{-4} \, \text{mol/L}\)
Matrix match: Match the items in the list with the appropriate compounds.

Matrix match
  • i) Non-reducing disaccharide → c) Sucrose
  • ii) Reducing disaccharide → e) Maltose
  • iii) Aldohexose → b) Glucose
  • iv) Ketohexose → a) Fructose
  • v) Polysaccharide → d) Lactose

Identify the product of the reaction:

What is the Reimer Tieman reaction?
What is Layer's test?
The power dissipated by a particle with constant force and constant acceleration is proportional to the:
The dimension of \( \lambda \times t \) (decay constant \(\lambda\) multiplied by time \(t\)) is: