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

The value of the surface integral ${\iint }_S(2x+z)dydz+(2x+z)dxdz+(2z+y)dxdy$ over the sphere $S:x^2+y^2+z^2=9$ is

Newton-Raphson method is used to compute the inverse of the number 1.6. Among the following options, the initial guess of the solution that results in non-convergence of the iterative process is

The value of the integral ${\int }_{-\pi }^{\pi }({\cos }^{6}x+{\cos }^{4}x)dx$ is

Let $y[n]=\frac{1}{\alpha }y[n-1]+x[n]$, where $\alpha >1$ and real, represent a difference equation of a causal discrete-time linear time invariant system. The system is initially at rest. If $x[n]=\delta [n-p]$ where $p>10$, the value of $y[p+1]$ is

The clock frequency of the digital circuit shown in the figure is 12 MHz. The frequencies of the output (F) corresponding to Control = 0 and Control = 1, respectively, are