List of top Questions asked in KEAM- 2019

A TV transmitting antenna is 81 m tall. It has a half-power beam width of 10 degrees. If the receiving antenna is at the ground level, the service area covered by the transmitter is determined by
The Brewster's angle for air to water interface is
In a single slit diffraction (of width $\alpha$) by a monochromatic source of wavelength $\lambda$ the first minimum of the intensity distribution occurs at an angle
In the amplitude modulation mode of transmission, the normal speech signal is with a maximum frequency of 5 kHz. If the carrier frequency is 200 kHz, the modulated signal will have the frequencies varying between
A monochromatic source of wavelength 600 nm was used in Young's double slit experiment to produce interference pattern. $I_1$ is the intensity of light at a point on the screen where the path difference is 150 nm. The intensity of light at a point where the path difference is 200 nm is given by
An object is placed at 9 cm in front of a concave mirror of radius of curvature 12 cm. The following statement is true:
A monochromatic light of frequency \( \nu = \frac{1}{6.63} \times 10^{16} \) Hz is produced by a laser. The power emitted is \( P = 10^{-2} \) W. The average number of photons per second emitted by the source is
A parallel plate capacitor (of capacitance \( C \)) with circular plates of radius \( r_0 \) located at positions \( \pm \alpha \), is connected in series with a resistor \( R \) and is charged by a battery of voltage \( V \). Consider a circular loop \( L \) of radius \( \frac{r_0}{2} \) parallel to the capacitor plates is located at the center. Which of the following statements is correct?
An optician prescribes a lens of power +2.5 D. The focal length of the lens in water is (Indices: Lens = 1.5, Water = 1.33):
The work function of three photosensitive materials are: Sodium (2.75 eV), copper (4.65 eV) and gold (5.1 eV). Which of the following statements is correct (Visible light range: $4 \times 10^{14}$ Hz to $8 \times 10^{14}$ Hz)?
The radiation produced by a 100 W bulb has the following property
The electric field of an electromagnetic wave in free space is given by \( \vec{E} = 5\sin\left(\tfrac{2\pi}{3}z - \omega t\right)\hat{y} \) V/m. Which of the following statements is correct?
The variation of speed (in m/s) of an object with time (in seconds) is given by the expression $V(t) = V_0 - 5t + 5t^2$
A boat is moving from the east bank to the west bank on a south flowing river. If the speed of the boat is 4 km/h and that of the river is 3 km/h. If the width of the river is 2 km, the distance travelled by the boat is
A bead is tied on one end of a stiff rope of length 1 m. With the other end of the rope as the center, the rope is rotated in such a way that the bead completes 10 revolutions per second. The centripetal acceleration of the bead is
An accurate measurement implies that:
The magnitude of deceleration required for a body, moving at a speed of 10 m/s to come to a complete halt at a distance of 100 m is:
The following plot gives the variation of acceleration (m/s$^2$) with time (s) for an object that started from rest at time $t = 0$ s. The velocity at time $t = 15$ s (V15) and at 25 s (V25), respectively are
An object, moving with velocity 5 m/s, undergoes an acceleration of 1 m/s$^2$ at time $t = 0$. If the object has a mass of 1 kg, the kinetic energy (KE) of the object at time $t = 5$ s is
The dimensions for pressure is:

The distance between the foci of the ellipse 

\[ \frac{(x+2)^2}{9} + \frac{(y-1)^2}{4} = 1 \]

is ______.

If \( \vec{a} = (1,1,-1), \vec{b} = (-1,2,1) \) and \( \vec{c} = (-1,2,-1) \), then 

\[ \left| (\vec{a} + \vec{b}) \times (\vec{b} + \vec{c}) \right| \]

is ______.

The value of 

\[ \lim_{x \to \infty} \frac{x^3 \sin\left(\frac{1}{x}\right) - 2x^2}{1 + 3x^2} \]

is ______.

In an A.P., if the 5th term is \( \frac{1}{7} \) and the 7th term is \( \frac{1}{5} \), then the sum of the first 35 terms is ______. 

Let

\[ f(x) + 2f\left(\frac{1}{x}\right) = \frac{1}{x} - 5 \] 

Then

\[ \int_{1}^{2} 3f(x)\,dx \]

equals ______.