List of top Questions asked in KEAM- 2018

An oscillator circuit contains an inductor 0.05 H and a capacitor of capacity 80 $\mu$F. When the maximum voltage across the capacitor is 200 V, the maximum current (in amperes) in the circuit is

A cylindrical tube, open at both the ends has fundamental frequency $n$. If one of the ends is closed, the fundamental frequency will become

The dimensions of $\varepsilon_0$ (permittivity in free space) is

A particle of rest mass $m_0$ is travelling so that its total energy is twice its rest mass energy. It collides with another stationary particle of rest mass $m_0$ to form a new particle. What is the rest mass of the new particle?

A uniform bar of mass $m$ is supported by a pivot at its top about which the bar can swing like a pendulum. If a force $F$ is applied perpendicular to the lower end of the bar as shown in figure, what is the value of $F$ in order to hold the bar in equilibrium at an angle $\theta$ from the vertical

Two particles A and B of same mass have their de Broglie wavelengths in the ratio $\lambda_A : \lambda_B = k : 1$. Their potential energies $U_A : U_B = 1 : k^2$. The ratio of their total energies $E_A : E_B$ is

Consider a wire with density $\rho$ and stress $\sigma$. For the same density, if the stress increases 2 times, the speed of the transverse waves along the wire changes by

A particle is moving along the x-axis such that its acceleration is proportional to the displacement from the equilibrium position and they are in the same direction. The displacement $x(t)$ is given by

A block of mass 1 kg is free to move along the x-axis. It is at rest and from time $t=0$ onwards it is subjected to a time-dependent force $F(t)$ in the x-direction. The force $F(t)$ varies with $t$ as shown in figure. The kinetic energy of the block at $t=4$ s is

Two soap bubbles of radii 3 mm and 4 mm confined in vacuum coalesce isothermally to form a new bubble. The radius of the bubble formed (in mm) is

A pipe of 1 m length is closed at one end. Taking the speed of sound in air as 320 $\text{ms}^{-1}$, the air column in the pipe cannot resonate for the frequency (in Hz)

A wave pulse in a string is described by the equation $y_1=\frac{5}{(3x-4t)^2+2}$ and another wave pulse in the same string is described by $y_2=\frac{-5}{(3x+4t-6)^2+2}$. The values of $y_1, y_2$ and $x$ are in meters and $t$ in seconds. Which of the following statement is correct?

A body P floats in water with half its volume immersed. Another body Q floats in a liquid of density $\frac{3}{4}$ of the density of water with two-third of the volume immersed. The ratio of density of P to that of Q is

The maximum transverse velocity and maximum transverse acceleration of a harmonic wave in a one-dimensional string are 1 $\text{ms}^{-1}$ and 1 $\text{ms}^{-2}$ respectively. The phase velocity of the wave is 1 $\text{ms}^{-1}$. The waveform is

If $x$, $v$ and $a$ denote the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period T, then which of the following do not change with time?

The position vector of the particle is $\vec{r}(t)=a\cos\omega t\,\hat{i}+a\sin\omega t\,\hat{j}$, where $a$ and $\omega$ are real constants of suitable dimensions. The acceleration is

Some of the following equations are kinematic equations, where the symbols have their usual meaning. The work-energy theorem is represented by

A rubber cord of density $d$, Young's modulus $Y$ and length $L$ is suspended vertically. If the cord extends by a length $0.5 \, L$ under its own weight, then $L$ is

Which of the following graphs represents the speed $v$ of a projectile as a function of time $t$

A body of mass $m=1$ kg is moving in a medium and experiences a frictional force $F=-kv$, where $v$ is the speed of the body. The initial speed is $v_0=10\,\text{ms}^{-1}$ and after $10$ s, its energy becomes half of initial energy. Then, the value of $k$ is

Find current, i.

Sum of last $30$ coefficients in the binomial expansion of $(1 + x)^{59}$ is

The sum of odd integers from $1$ to $2001$ is

The focus of the parabola $y^2 - 4y - x+3=0$ is

Let $f : \bullet \to \bullet $ satisfy $f (x) f ( y) = f (xy) $ for all real numbers $x$ and $y$. If $f (2)= 4$, then $f \left( \frac{1}{2} \right) = $