List of top Questions asked in UP Board XII

A coil has a resistance of 10 Ω and inductance of 0.4 Henry. It is connected to an AC source of 6.5 V, 30 Hz. Find the average power consumed in the circuit.

What is the value of resistance of ideal ammeter and ideal voltmeter? Why are an ammeter and a voltmeter respectively connected in series and parallel in a circuit? 
 

Define Mutual Inductance. Show that Henry = Newton Meter / Ampere².

In the given circuit, find the potential difference between \( A \) and \( B \). 
 

What is total internal reflection and critical angle? What is the working principle of Optical Fibre. 
 

The intensity of the magnetic field \( B \) due to a current-carrying circular coil of radius 12 cm at its center is \( 0.5 \times 10^{-4} \, \text{Tesla} \) perpendicular to the plane of the coil upward. Calculate the magnitude and direction of current flowing in the coil. 
 

Deduce the formula of torque on an electric dipole placed in a uniform electric field. 
 

Calculate the energy equivalence of unified atomic mass unit. 
 

Define the 'wavefront' of a wave. 
 

Ionisation energy of Hydrogen atom is 13.6 eV. In a state where \( n = 2 \), what will be ionisation energy of its electron? 
 

Deduce the dimensional equation of self-inductance. 
 

State Ampere's Circuital Law. 
 

Write the equation for the relationship between specific conductivity (\( \sigma \)) and drift velocity (\( v_d \)). 
 

Diffusion current in a p-n junction is greater than the drift current in magnitude: 
 

The equation \( E = pc \), (where \( E \) and \( p \) are energy and momentum respectively) is valid: 
 

An electromagnetic wave propagating through vacuum, described by \( E = E_0 \sin(kx - \omega t) \), \( B = B_0 \sin(kx - \omega t) \), then: 
 

Differentiate \( y = x^x + (\cos x)^{\tan x} \) with respect to \( x \).

The probabilities of solving a question by \( A \) and \( B \) independently are \( \frac{1}{2} \) and \( \frac{1}{3} \) respectively. If both of them try to solve it independently, find the probability that:

 

 

Suppose that \( A = \{ 1, 2, 3 \} \), \( B = \{ 4, 5, 6, 7 \} \), and \( f = \{ (1, 4), (2, 5), (3, 6) \} \) be a function from \( A \) to \( B \). Then \( f \) is:

(e) The angle between the vectors \( 3\hat{i} - 2\hat{j} + \hat{k} \) and \( 2\hat{i} + \hat{j} + 3\hat{k} \) will be:
Find the shortest distance between the lines: \[ \vec{r} = 3\hat{i} + 3\hat{j} - 5\hat{k} + \lambda(2\hat{i} + 3\hat{j} + 6\hat{k}), \] \[ \vec{r} = \hat{i} + 2\hat{j} - 4\hat{k} + \mu(2\hat{i} + 3\hat{j} + 6\hat{k}). \]
If \( A \) and \( B \) are independent events, where \( P(A) = \frac{3}{10} \), \( P(B) = \frac{6}{10} \), then find \( P(A \cup B) \) and \( P(A \cap B) \).
Find the shortest distance between two lines \( l_1 \) and \( l_2 \) whose vector equations are: \[ \mathbf{r} = \hat{i} + \hat{j} + \lambda (2\hat{i} - \hat{j} + \hat{k}) \] and \[ \mathbf{r} = 2\hat{i} + \hat{j} - \hat{k} + \mu (3\hat{i} - 5\hat{j} + 2\hat{k}). \]
Prove that a relation \( R = \{(a, b) : (a-b) \) is a multiple of \( 5 \} \) is an equivalence relation in the set of integers \( \mathbb{Z} \).
(c) Prove that \[ \begin{vmatrix} 1 \omega & \omega^2 \\ \omega & \omega^2 1 \\ \omega^2 1 \omega \end{vmatrix} = 0 \], where \( \omega \) is a cube root of unity.