GATE IN 2025 Question Paper (01-Feb-2025) (Shift 2)

A $2n\times 2n$ matrix $A=[a_{ij}]$ has its elements as
$a_{ij}=\{\begin{array}{ll}\beta & \text{if }(i+j)\text{ is odd,}\\ -\beta & \text{if }(i+j)\text{ is even,}\end{array}$
where $n$ is any integer greater than 2 and $\beta$ is any non-zero real number. The rank of $A$ is

The solution of the differential equation $\frac{dy}{dx}=9\frac{x}{y}$ represents

The working of the hand-held metal detector most widely used by security personnel for human frisking is based on the principle of

The primary coil of a linear variable differential transformer (LVDT) is supplied with AC voltage as shown in the figure. The secondary coils are connected in series opposition and the output is measured using a true RMS voltmeter. The displacement $x$ of the core is indicated in mm on a linear scale. At the null position $x=0$, the voltmeter reads 0 V. If the voltmeter reads 0.2 V for a displacement of $x=+2$ mm, then for a displacement of $x=-3$ mm, the voltmeter reading, in V, is

In the force transducer shown in Figure (a), four identical strain gauges S1, S2, S3, and S4 are mounted on a cantilever at equal distance from its base. S1 and S2 are mounted on the top surface and S3 and S4 are mounted on the bottom surface, as shown in the Figure (a). These strain gauges are to be connected to form a Wheatstone bridge consisting of four arms A, B, C, and D, as shown in the Figure (b). From the following options, the correct order to maximize the measurement sensitivity is