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Hydrogen peroxide oxidises $[Fe(CN)_{6}]_{4−}$ to $[Fe(CN)_{6}]_{3−}$ in acidic medium but reduces $[Fe(CN)_{6}]_{3−}$ to $[Fe(CN)_{6}]_{4−}$ in alkaline medium. The other products formed are, respectively

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Let O be the vertex and Q be any point on the parabola,$x_{2}=8y$. It the point P divides the line segment OQ internally in the ratio 1 : 3, then the locus of P is :

Distance of the centre of mass of a solid uniform cone from its vertex is $Z_{0}$. If the radius of its base is R and its height is h then $Z_{0}$ is equal to :

A piston filled with 0.04 mol of an ideal gas expands reversibly from 50.0 mL to 375 mL at a constant temperature of $37.0_{∘}C.$ As it does so, it absorbs 208J of heat. The values of q and w for the process will be: (R = 8.314 J/mol K) (l 7.5 = 2.01)

The I - V characteristic of an LED is

If the vectors $AB=3i^+4k^$ and $AC=5i^−2j^ +4k^$are the sides of a triangle ABC, then the length of the median through A is

At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production P w.r.t. additional number of workers x is given by \displaystyle\frac{{{d}{P}}}{{{\left.{d}{x}\right.}}}={100}-{12}\sqrt{{{x}{\dot}}}If the firm employs 25 more workers, then the new level of production of items is

The supply voltage to a room is 120 V. The resistance of the lead wires is 6 $Ω$ A 60 W bulb is already switched on. What is the decrease of voltage across the bulb, when a 240 W heater is switched on in parallel to the bulb?

The area (in square units) bounded by the curves $y=x ,2y−x+3=0$, x-axis, and lying in the first quadrant is