List of practice Questions

Two charges +7 mC and -4 mC at coordinates (-7, 0, 0) and (7, 0, 0), respectively, find the electrostatic potential energy. \[ \epsilon_0 = 8.85 \times 10^{-12} \, \text{C}^2 \, \text{N}^{-1} \, \text{m}^{-2}. \]
The value of \( E_0 \) is 9.3 V/m and \( c \) is \( 3 \times 10^8 \, \text{m/s} \). Find the value of \( B_0 \).
The system of equations: \[ x + y + z = 6, \quad x + 2y + 5z = 9, \quad x + 5y + \lambda z = \mu, \] has no solution if:
Given the matrix \[ A = (a_{ij}), \] where \[ A_{11} = \begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix}, \quad A_{14} = \begin{bmatrix} 4 & 1 \\ 3 & 0 \end{bmatrix}, \quad A_{21} = \begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix}, \quad A_{23} = \begin{bmatrix} 2 & 1 \\ 1 & 2 \end{bmatrix}, \quad \text{find} \, a_{23}. \]
If the square of the shortest distance between the lines $$ \frac{x-2}{1} = \frac{y-1}{2} = \frac{z+3}{-3} \quad \text{and} \quad \frac{x+1}{2} = \frac{y+3}{4} = \frac{z+5}{-5}, $$ is $ \frac{m}{n} $, where $m, n$ are coprime numbers, then $m+n$ is equal to:
If pH of water is 7 at 25°C, then the pH of water at 180°C will:
The atomic number of the element with the least melting point in group 14 is:
Alpha-helix and beta-sheet protein structures belong to which category of structure?
Find the charge on the capacitor in the steady state. \vspace{1cm} \includegraphics[width=0.7\textwidth]{a.png}
If the angle of prism equals the angle of minimum deviation, and given that the refractive index \( \mu = \sqrt{3} \), then the angle of the prism is:
Number of terms in an arithmetic progression is \(2n\). Sum of terms occurring at even places is 40 and sum of terms occurring at odd places is 55. If the first term exceeds the last term by 27, then \( n \) equals to:
A proton is moving with a uniform velocity of \( 2 \times 10^8 \, \text{m/s} \) in uniform magnetic and electric fields which are perpendicular to each other. If the electric field is switched off, then the proton moves in a circular path of radius \( 1.6 \times 10^{-5} \, \text{m} \). Then the magnetic field \( B \) is:
Find the area bounded between two curves: \[ x^2 + y^2 = 25 \quad \text{and} \quad y = |x - 1|. \]
If \[ (7 + e^{2x}) dy - (1 + 2e^{2x})(y + 3) dx = 0, \quad y(0) = 5, \] then \( y(n2) = \)?
The system of equations is given as: \[ (\lambda + 1)x + (\lambda + 2)y + (\lambda - 1)z = 0 \] \[ \lambda x + (\lambda - 1)y + (\lambda + 1)z = 0 \] \[ (\lambda - 1)x + (\lambda + 1)y + (\lambda + 2)z = 0 \] If the above system of equations has infinite solutions, then \( \lambda^2 + \lambda \) is:
Find the value of \[ \sin 70^\circ \left( \cot 10^\circ \cot 70^\circ - 1 \right). \]
If 2 g phenol is allowed to react with \( \text{Br}_2/\text{H}_2\text{O} \), how much \( \text{Br}_2 \) will be required to produce 2,4,6-tribromophenol (rounded to the nearest integer)?
Calculate the percentage by weight of S if 160 grams of organic compound produce 466 grams of BaSO₄.
The value of \( a = 3 \), the sum of first 4 terms is equal to the one fifth of the sum of next 4 terms in A.P., then find the sum of the first 20 terms.
The total number of ways the word 'DAUGHTER' can be arranged so that all vowels don't occur together:
Two biased dice are rolled. Out of which one die contains 1, 1, 2, 2, 3, 3, and another die contains 1, 2, 2, 3, 3, 4. Then the probability of getting a sum of 4 or 5 is:
Which of the following does not belong to the same group?
Electric flux \( \varphi \) is related with linear charge density \( \lambda \) and surface charge density \( \sigma \) as \( \varphi = \alpha \lambda + \beta \sigma \). Where \( \alpha \) and \( \beta \) are of appropriate dimension. The dimension of \( \frac{\beta}{\alpha} \) is:
Statement 1: Hotter water moves faster than cold water.
Statement 2: Soap water has a higher surface tension than fresh water.
Which of the following react with Hinsberg reagent?