The cell reaction $Mn + 2Ag_{(C_1)}^{+} (aq) \to Mn_{(C_2)}^{+2} (aq) + 2Ag$ is represented by

In the sequence of sets $(1,2,3), (4,5,6), (7,8,9,10), \ldots$,the sum of elements in the $50^{th}$ set is

The path length of oscillation of a simple pendulum of length $1 \ m$ is $16 \ cm$. Its maximum velocity is $(g = \pi^2 \ m/s^2)$

Let $y = y(x)$ be the solution of the differential equation $\sin x \frac{dy}{dx} + y \cos x = 4x$,where $x \in (0, \pi)$. If $y(\frac{\pi}{2}) = 0$,then find the value of $y(\frac{\pi}{6})$.

Aluminium reacts with $NaOH$ and forms compound '$X$'. If the coordination number of aluminium in '$X$' is $6$,the correct formula of $X$ is

Suppose,the acceleration due to gravity at the Earth's surface is $10\, m\, s^{-2}$ and at the surface of Mars it is $4.0\, m\, s^{-2}$. $A$ $60\, kg$ passenger goes from the Earth to the Mars in a spaceship moving with a constant velocity. Neglect all other objects in the sky. Which part of the figure best represents the weight (net gravitational force) of the passenger as a function of time?