List of top Questions asked in KEAM

If $ f(x) = \frac{\sqrt{x^4}}{\sqrt{x^2}} $, find $ f'(27) $.
Solve the following differential equation and integrate: $ \frac{dy}{dx} + \frac{2x}{1 + x^2} \cdot y = x $
Equation of parabola having focii (-3, 1) and (3, 1)
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 \( |Z| \).
Given the function \( h(x) = f(g(x)) \), where \( f(x) = f'(x) = 3 \), and \( g(x) = 9 \), find \( g'(3) \), \( f'(3) \), and \( h'(3) \).
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?
If \( A \) is a \( 3 \times 3 \) matrix and \( |B| = 3|A| \) and \( |A| = 5 \), then find \( \left| \frac{\text{adj} B}{|A|} \right| \).
Given the function \( F(x) = |\sin(3x)| - \cos(3x) \), for \( \frac{\pi}{6} \leq x \leq \frac{\pi}{3} \), find \( f' \left( \frac{\pi}{4} \right) \).
The amount of NaOH required to neutralize 9.8g H\(_2\)SO\(_4\) is:
If \( -5<x \leq -1 \), then \( -21 \leq 5x + 4 \leq b \). Find \( b \).
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?
An unbiased die is tossed until a sum \( S \) is obtained. If \( X \) denotes the number of times tossed, find the ratio \( \frac{P(X = 2)}{P(X = 5)} \).
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?
A planet revolves around the sun with a time period 27 times that of planet B. Planet A is at \( x \) times the distance of planet B from the sun. Find the value of \( x \).
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
Which has intramolecular hydrogen bonding?
Ortho nitrophenol, Para nitrophenol

Identify the product of the reaction: