The initial speed of a projectile fired from ground is \(u\). At the highest point during its motion, the speed of projectile is \(\frac{\sqrt{3}}{2} u\). The time of flight of the projectile 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

The percentage error in the calculated volume of a sphere, if there is \(2\%\) error in its diameter measurement, is __________.

Two sources of light emit with a power of \(200 \mathrm{~W}\). The ratio of number of photons of visible light emitted by each source having wavelengths \(300\  \mathrm{nm}\) and \(500 \mathrm{~nm}\) respectively, will be _______.

In a building there are \(15\) bulbs of \(45\; \mathrm{W}, 15\) bulbs of \(100\; \mathrm{W}, 15\) small fans of \(10 \;\mathrm{W}\) and \(2\) heaters of \(1 \;\mathrm{kW}\). The voltage of electric main is \(220\; \mathrm{V}\). The minimum fuse capacity (rated value) of the building will be: .......... \(A\)

A body of mass \(4 \mathrm{~kg}\) experiences two forces \(\overrightarrow{\mathrm{F}}_1=5 \hat{\mathrm{i}}+8 \hat{\mathrm{j}}+7 \hat{\mathrm{k}}\) and \(\overrightarrow{\mathrm{F}}_2=3 \hat{\mathrm{i}}-4 \hat{\mathrm{j}}-3 \hat{\mathrm{k}}\). The acceleration acting on the body is _______.

Two cells are connected between points \(A\) and \(B\) as shown. Cell \(1\) has emf of \(12\,V\) and internal resistance of \(3\,\Omega\). Cell \(2\) has emf of \(6\,V\) and internal resistance of \(6\,\Omega\). An external resistor \(R\) of \(4\,\Omega\) is connected across \(A\) and \(B\). The current flowing through \(R\) will be \(.............A\).

A current of \(2\, mA\) was passed through an unknown resistor which dissipated a power of \(4.4\, W\). Dissipated power when an ideal power supply of \(11\, V\) is connected across it is

A particle performs simple harmonic motion with amplitude \(A\). Its speed is trebled at the instant that it is at a distance \(\frac{{2A}}{3}\) from equilibrium position. The new amplitude of the motion is

The maximum rated power of the LED is \(2\) mW and it is used in the circuit with input voltage of \(5\) V as shown in the figure below. The current through resistance \(R_S\) is \(0.5\) mA. The minimum value of the resistance of \(R_S\), to ensure that the LED is not damaged is _______ k\(\Omega\).

The quantities \(\quad x=\frac{1}{\sqrt{\mu_{0} \epsilon_{0}}}, y=\frac{E}{B}\) and \(z=\frac{l}{C R}\) are defined where \(C-\) capacitance \(R-\)Resistance, \(l-\)length, \(E-\)Electric field, \(B-\)magnetic field and \(\varepsilon_{0}, \mu_{0},\) -free space permittivity and permeability respectively. Then....

A simple harmonic oscillator of angular frequency \(2\,rad\,s^{-1}\) is acted upon by an external force \(F = sin\,t\,N .\) If the oscillator is at rest in its equilibrium position at \(t = 0,\) its position at later times is proportional to