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KEAM
List of top Questions asked in KEAM
If $ f(x) = \frac{\sqrt{x^4}}{\sqrt{x^2}} $, find $ f'(27) $.
KEAM - 2025
KEAM
Mathematics
Derivatives
Solve the following differential equation and integrate:
$ \frac{dy}{dx} + \frac{2x}{1 + x^2} \cdot y = x $
KEAM - 2025
KEAM
Mathematics
Differential equations
Equation of parabola having focii (-3, 1) and (3, 1)
KEAM - 2025
KEAM
Mathematics
Conic sections
If $ f(x) = \frac{1}{x^2} $, $ u = f(x) $, and $ f'(x) $, then find $ \frac{du}{dx} $.
KEAM - 2025
KEAM
Mathematics
Derivatives
Given the system of equations:
\[ Z + \bar{Z} = 4 \quad \text{and} \quad Z - \bar{Z} = 6 \] Find \( |Z| \).
KEAM - 2025
KEAM
Mathematics
Complex numbers
Given the function \( h(x) = f(g(x)) \), where \( f(x) = f'(x) = 3 \), and \( g(x) = 9 \), find \( g'(3) \), \( f'(3) \), and \( h'(3) \).
KEAM - 2025
KEAM
Mathematics
Functions
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).
KEAM - 2025
KEAM
Physics
Gas laws
Express the final answer to the proper number of significant figures:
\[ 18.0 + 11.515 + 13.2 = \ldots \]
KEAM - 2025
KEAM
Physics
Significant figures
The product of the first five terms of a GP is 32. What is the 3rd term?
KEAM - 2025
KEAM
Mathematics
Geometric Progression
If \( A \) is a \( 3 \times 3 \) matrix and \( |B| = 3|A| \) and \( |A| = 5 \), then find \( \left| \frac{\text{adj} B}{|A|} \right| \).
KEAM - 2025
KEAM
Mathematics
Matrix Operations
Given the function \( F(x) = |\sin(3x)| - \cos(3x) \), for \( \frac{\pi}{6} \leq x \leq \frac{\pi}{3} \), find \( f' \left( \frac{\pi}{4} \right) \).
KEAM - 2025
KEAM
Mathematics
Functions
The amount of NaOH required to neutralize 9.8g H\(_2\)SO\(_4\) is:
KEAM - 2025
KEAM
Chemistry
Thermodynamics
If \( -5<x \leq -1 \), then \( -21 \leq 5x + 4 \leq b \). Find \( b \).
KEAM - 2025
KEAM
Mathematics
Algebra
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?
KEAM - 2025
KEAM
Physics
Electromagnetic waves
An unbiased die is tossed until a sum \( S \) is obtained. If \( X \) denotes the number of times tossed, find the ratio \( \frac{P(X = 2)}{P(X = 5)} \).
KEAM - 2025
KEAM
Mathematics
Probability
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.
KEAM - 2025
KEAM
Chemistry
Expressing Concentration of Solutions
Solve the system of equations:
\[ \begin{bmatrix} 4 & 9 \\ 12 & -3 \\ 8 & -2 \end{bmatrix} \begin{bmatrix} 7 \\ 9 \end{bmatrix} = \begin{bmatrix} \alpha \\ \beta \end{bmatrix} \]
KEAM - 2025
KEAM
Mathematics
Linear Algebra
Evaluate the integral:
\[ \int e^x \sec(x) \left( \tan(x) + 1 \right) \, dx \]
KEAM - 2025
KEAM
Mathematics
Integration
Which is a heterocyclic compound?
KEAM - 2025
KEAM
Chemistry
Classification Of Organic Compounds
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 \( x \).
KEAM - 2025
KEAM
Physics
Astronomy
If \( B = 400\sqrt{2} \sin(\omega t - kx) \), find the peak value of the magnetic field of the electromagnetic wave.
KEAM - 2025
KEAM
Physics
Structure of atom
Find pH of the solution if \([H^+] = 2 \times 10^{-4} \, \text{mol/L}\)
KEAM - 2025
KEAM
Chemistry
Conductance
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
KEAM - 2025
KEAM
Chemistry
Amines
Which has intramolecular hydrogen bonding?
Ortho nitrophenol, Para nitrophenol
KEAM - 2025
KEAM
Chemistry
Aldehydes, Ketones and Carboxylic Acids
Identify the product of the reaction:
KEAM - 2025
KEAM
Chemistry
Expressing Concentration of Solutions
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