GATE IN 2026 Question Paper (07-Feb-2026) (Shift-1)

A box contains three apples and two oranges. Two fruits are removed randomly in succession. The probability that the first is an apple and the second is an orange is _____ .

An electric field in free space is
$$\vec{E}=(2x+5y+6z)\hat{i}+(5x+4y+10z)\hat{j}+(6x+10y+2z)\hat{k}\text{ V/m}.$$
The charge density is ____ ${\text{C/m}}^3$. (${ϵ}_0$ is the permittivity of free space)

A straight thin wire carrying a current of $I=1\text{ A}$ in the direction
$$\hat{n}=\frac{1}{\sqrt{6}}\hat{i}+\frac{2}{\sqrt{6}}\hat{j}+\frac{1}{\sqrt{6}}\hat{k}$$
is placed inside a magnetic field of $\vec{B}=(2\hat{i}+2\hat{k})\text{ T}$. The force per unit length on the wire is _____ N/m.

A two-port network has z-parameters $z_{11}=z_{22}=10\Omega$, and $z_{12}=z_{21}=5\Omega$.

The value of $R_L$ such that maximum power is transferred to $R_L$ is _________ $\Omega$.

In the circuit shown below, the value of the output voltage $V_0$ is _____ V.