List of top Questions asked in UP Board XII

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.
Find \( x \) and \( y \) if \[ 2 \left[ \begin{array}{cc} 1 & 3 \\ 0 & x \end{array} \right] + \left[ \begin{array}{cc} y & 0 \\ 1 & 2 \end{array} \right] = \left[ \begin{array}{cc} 5 & 6 \\ 1 & 8 \end{array} \right]. \]