H2S (5 moles) reacts completely with acidified aqueous potassium permanganate solution. In this reaction, the number of moles of water produced is x, and the number of moles of electrons involved is y. The value of (x + y) is ____.
A disc is rolling without slipping on a surface. The radius of the disc is \( R \). At \( t = 0 \), the topmost point on the disc is \( A \) as shown in the figure. When the disc completes half of its rotation, the displacement of point \( A \) from its initial position is:
A projectile is thrown at a speed V and at an angle with the horizontal. If the speed at its maximum height is \(\frac{V}{3}\),then the value of tan θ is:
In cement, generally the increase in strength during a period of 14 days to 28 days is primarily due to
Area of the Region bounded by the curve y=√49-x2 and x-axis is .
Let g(x) = f(x) + f(1 - x) and f''(x) > 0, x ∈ (0,1). If g is decreasing in the interval (0, α) and increasing in the interval (α, 1), then tan-1 (2α) + tan-1 (\(\frac{1}{α}\)) + tan-1\((\frac{α+1}{α})\) is equal to
If (h,k) is the image of the point (3,4) with respect to the line 2x - 3y -5 = 0 and (l,m) is the foot of the perpendicular from (h,k) on the line 3x + 2y + 12 = 0, then lh + mk + 1 = 2x - 3y - 5 = 0.
An object of mass 'm' initially at rest on a smooth horizontal plane starts moving under the action of force $F=2 N$ In the process of its linear motion, the angle $\theta$ (as shown in figure) between the direction of force and horizontal varies as $\theta=k x$, where $k$ is a constant and $x$ is the distance covered by the object from its initial position The expression of kinetic energy of the object will be $E=\frac{n}{k} \sin \theta$ The valte of $n$ is
