GATE 2023

GATE 2025 - Q1

Consider the matrix A below:$$\begin{bmatrix}2&3&4&5\\0&6&7&8\\0&0&\alpha&\beta//0&0&0&\gamma \end{bmatrix}$$

Correct Answer: Option B

Charge of an electron is $-1.602×10^{-19}\;C$

RPSC Lecturer - Q2

🌾The electric flux density is given $$D=(2y^2+z)I_x+4xyI_y+xI_z\;c/m^2$$ The volume charge density at point $(-1,\; 0,\; 3)$ is

a) $0\;c/m^3$

b) $-2\;c/m^3$

c) $-4\;c/m^3$

d) $-8\;c/m^3$ 

Correct Answer: Option C
 
Charge of an electron is $-1.602×10^{-19}\;C$.$$1e^-=-1.602×10^{-19}\;C$$ Then $$-1C=\frac{1}{1.602×10^{-19}} e^-$$ Hence $6.24×10^{18}$ number of electrons constitutes one coulomb of negative charge or electricity.

RPSC Lecturer - Q3

🌾The work done by a force $$F=4I_x-3I_y+2I_z\;m$$ in giving a $1\;nC$ charge a displacement of $10I_x+2I_y-7I_z\;m$ is

a) $103\;nJ$

b) $60\;nJ$

c) $40\;nJ$

d) $20\;nJ$

Correct Answer: Option D

One coulomb of charge equals

$$-1C=6.24×10^{18}\;e^-$$

‘n’ coulombs of charge equals,$$-nC=n×6.24×10^{18}\;e^-$$

Hence, $-3.941\;C$ equals, $$=3.941×6.24×10^{18}\;e^-$$ $$=24.59×10^{18}\;e^-$$ $$=2.459×10^{19}\;e^-$$

RPSC Lecturer - Q4

🌾If a vector field P is solenoidal, which of this is true?

a) $\oint_s P.ds=0$

b) $\oint_l P.dl=0$

c) $\nabla× (P)=0$

d) $\nabla×P\neq0$

Correct Answer: Option A and C

Unit of charge is coloumb.

Since $I=Q/t$ and $Q=It$, the unit of charge is also ampere-seconds

RPSC Lecturer - Q5

🌾The boundary condition valid at the boundary between two dielectrics $1$ and $2$ is

a) $E_{t1}=E_{t2}$

b) $E_1=E_2$

c) $D_{n1}=D_{n2}$

d) both A and C

Correct Answer: Option B

Current flow is nothing but the rate of flow of charge $$I=\frac{Q}{t}$$

RPSC Lecturer - Q6

🌾The magnetic field at any point on the axis of a current carrying circular coil will be

a) perpendicular to the axis

b) parallel to the axis

c) at an angle $45^{\circ}$ with the axis

d) zero

Correct Answer: Option B

Current flow is nothing but the rate of flow of charge $$I=\frac{Q}{t}$$

RPSC Lecturer - Q7

🌾Which of these statements is not characteristic of a static magnetic field?

a) It is conservative

b) It is solenoidal

c) It has no sink or sources

d) Magnetic flux lines are always closed

Correct Answer: Option B

Charge of an electron is $-1.602×10^{-19}\;C$

RPSC Lecturer - Q8

🌾Which of the following is zero?

a) grad div A

b) div gradient V

c) div curl A

d) curl curl A

Correct Answer: Option B

Charge of an electron is $-1.602×10^{-19}\;C$