Class 12th

The lengths of the sides of a triangle are 10 + x², 10 + x² and 20 – 2x². If for x = k, the area of the triangle is maximum, then 3k² is equal to:

Find the value of the angle of emergence from the prism. Refractive index of the glass is √3.

Let a be an integer such that lim (x→a) [18 - [1-x]] / [x-3a] exists, where [t] is greatest integer ≤ t. Then a is equal to:

Let the system of linear equations x + 2y + z = 2, ax + 3y - z = a, -ax + y + 2z = -a be inconsistent. Then α is equal to:

An electromagnetic wave of wavelength ' λ ' is incident on a photosensitive surface of negligible work function. If ' m ' mass is of photoelectron emitted from the surface has de-Broglie wavelength λ_d, then:

A parallel plate capacitor has a uniform electric field ' E ' in the space between the plates.
If the distance between the plates is ' d ' and the area of each plate is ' A ', the energy stored in the capacitor is: (ε₀ = permittivity of free space)

An inductor of inductance L, a capacitor of capacitance C and a resistor of resistance ' R '
are connected in series to an ac source of potential difference ' V volts as shown in figure.
Potential difference across L, C and R is 40 V, 10 V and 40 V, respectively. The amplitude of current flowing through LCR series circuit is 10√2 A. The impedance of the circuit is:

Given below are two statements:

Statement I: Photovoltaic devices can convert optical radiation into electricity.

Statement II: Zener diode is designed to operate under reverse bias in breakdown region.

In the light of the above statements, choose the most appropriate answer from the options given below:

A screw gauge gives the following readings when used to measure the diameter of a wire
Main scale reading: 0 mm
Circular scale reading: 52 divisions
Given that 1 mm on main scale corresponds to 100 divisions on the circular scale. The diameter of the wire from the above data is:

A full wave rectifier circuit consists of two p-n junction diodes, a centre-tapped transformer, capacitor and a load resistance. Which of these components remove the ac ripple from the rectified output