List of top Questions asked in KEAM

A balloon of mass 60 g is moving up with an acceleration of 4 m/s\(^2\). The mass to be added to the balloon to descend it down with the same acceleration is (g = 10 m/s\(^2\)):
If a planet orbits the Sun in an elliptical orbit, the quantities associated with the planet that remain constant are:
The quantity of heat conducted through a metal rod kept at its ends at 100°C and 120°C is 5 J/s. If the ends are kept at 200°C and 220°C, then the quantity of heat conducted in 10 seconds is:
Let \[ A = \begin{pmatrix} 0 & 1 \\ -1 & 2 \end{pmatrix} \quad \text{and} \quad B = \begin{pmatrix} 1 & 1 \\ -1 & -1 \end{pmatrix}. \] If \( XA = B \), then \( X \) is:
cos \( A \cos 2A \) is equal to:
Find the value of \[ \sin \left( 2 \sin^{-1} \left( \frac{1}{2} \right) \right). \] The answer is:
Two gases under the same thermal conditions have the same number of molecules per unit volume. If the respective molecular diameters of the gases are in the ratio 1 : 3, then their respective mean free paths are in the ratio:
If \( \overrightarrow{a} = \alpha \hat{i} + \beta \hat{j} \) and \( \overrightarrow{b} = \alpha \hat{i} - \beta \hat{j} \) are perpendicular, where \( \alpha \neq \beta \), then \( \alpha + \beta \) is equal to:
Let \( \mathbb{N} \) be the set of all natural numbers. Let \( R \) be a relation defined on \( \mathbb{N} \) given by \( aRb \) if and only if \( a + 2b = 11 \). Then the relation \( R \) is:
If \( |x| \leq 1 \), then \( \sin \left( 2 \sin^{-1} x + \cos^{-1} x \right) \) is equal to:
In an Young double slit experiment without varying the distance of the screen and the slit separation, if the wavelength of monochromatic source is changed one by one in the ratio 2:3:4, then the corresponding fringe widths measured will be in the ratio:
Let \( A \) be a symmetric matrix and \( B \) be a skew symmetric matrix. If

\[ A + B = \begin{pmatrix} 1 & 3 \\ -2 & 5 \end{pmatrix}, \] then \( A - B \) is equal to:
The expression
\[ \frac{1 + \cos\left(\frac{\pi}{5}\right) + i \sin\left(\frac{\pi}{5}\right)}{1 + \cos\left(\frac{\pi}{5}\right) - i \sin\left(\frac{\pi}{5}\right)} \] is equal to:
The shortest distance between the parallel straight lines \[ \overrightarrow{r_1} = \hat{k} + s(\hat{i} + \hat{j}), \quad t, s \in \mathbb{R} \quad {and} \quad \overrightarrow{r_2} = \hat{j} + t(\hat{i} + \hat{j}), \] is:
The centre of the circle \( (x-3)(x+1)+(y-1)(y+3)=0 \) is:
Real part of \[ \left( \frac{1+i}{1-i} \right) \left( \frac{2+i}{2-i} \right) \] is:
Let \( z \) be a non-zero complex number such that \[ z = \frac{16}{\bar{z}}. \] Then the locus of \( z \) is:
The integrating factor of

\[ (1 + 2e^{-x}) \frac{dy}{dx} - 2e^{-x} y = 1 + e^{-x} \] is:
If \[ \lim_{x \to 1} \frac{x^2 - ax - b}{x - 1} = 5, { then } a + b = ? \]
Out of the following pair of elements, identify isotones:
Number of integers greater than 7000 can be formed using the digits 2, 4, 5, 7, 8 is (Repetition of digits is not allowed):
The integral

\[ \int \frac{\sec x}{(\sec x + \tan x)^2} \, dx \] is:
Evaluate the integral \[ \int_{-500}^{500} \ln \left( \frac{1000 + x}{1000 - x} \right) dx \]
The length of the latus rectum of the parabola \( y^2 = x \) is:
A body of mass \( M \) is at equilibrium under the action of four forces \( F_1, F_2, F_3 \), and \( F_4 \). If \( F_1 \) is removed from the body, then the body moves with an acceleration of: