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An observer looks at a distant tree of height 10 m with a telescope of magnifying power of 20. To the observer the tree appears :

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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 :

The vapour pressure of acetone at $20_{∘}C$ is 185 torr. When 1.2 g of a non - volatile substance was dissolved in 100 g of acetone at $20_{∘}C$, its vapour pressure was 183 torr. The molar mass $(gmol_{−1})$ of the substance is :

A diode detector is used to detect an amplitude modulated wave of 60% modulation by using a condenser of capacity 250 pico farad in parallel with a load resistance 100 kilo ohm. Find the maximum modulated frequency which could be detected by it.

A uniformly charged solid sphere of radius R has potential $V_{0}$ (measured with respect to $∞$ ) on its surface. For this sphere the equipotential surface with potentials $23V_{0} ,45V_{0} ,43V_{0} and4V_{0} $ have radius \displaystyle{R}_{}

If a piece of metal is heated to temperature $θ$ and then allowed to cool in a room which is at temperature $θ_{0}$ the graph between the temperature T of the metal and time t will be closest to :

The area (in sq. units) of the region described by ${(x,y):y_{2}≤2x$and $y≥4x−1}$is :

For a simle pendulum, a graph is plotted between its kinetic energy (KE) and potential energy (PE) against its displacement d. Which one of the following represents these correctly ? (Graphs are schematic and not drawn to scale)

$(lim)_{x0}((1−cos2x)xtan4x3+cosx $ is equal to: