A torque meter is calibrated to reference standards of mass, length and time each with \(5 \%\) accuracy. After calibration, the measured torque with this torque meter will have net accuracy of\(............\%\)

Two projectiles are projected at \(30^{\circ}\) and \(60^{\circ}\) with the horizontal with the same speed. The ratio of the maximum height attained by the two projectiles respectively is:

Pressure inside a soap bubble is greater than the pressure outside by an amount _______. (given : \(\mathrm{R}=\) Radius of bubble, \(\mathrm{S}=\) Surface tension of bubble)

A block of mass \(5 \mathrm{~kg}\) is placed on a rough inclined surface as shown in the figure.If \(\vec{F}_1\) is the force required to just move the block up the inclined plane and \(\vec{F}_2\) is the force required to just prevent the block from sliding down, then the value of \(\left|\vec{F}_1\right|-\left|\vec{F}_2\right|\) is _______. [Use \(g=10 \mathrm{~m} / \mathrm{s}^2\) ]

In a reflecting telescope, a secondary mirror is used to:

A transverse wave on a string is described by \(y = 3\sin(36t + 0.018x + \pi/4)\), where \(x, y\) are in cm and \(t\) in seconds. The least distance between the two successive crests in the wave is _____ cm. (Nearest integer)
(\(\pi = 3.14\))

In the given circuit- the value of current \(I _{ L }\) will be \(mA\). (When \(R _{ L }=1 \,k\, \Omega\) )

For \(z=a^{2} x^{3} y^{\frac{1}{2}}\), where \(a\) is a constant. If percentage error in measurement of \(x\) and \(y\) are \(4 \%\) and \(12 \%\), respectively, then the percentage error for \(z\) will be \(%\)

The radii of two soap bubbles are \(r_1\) and \(r_2\). In isothermal conditions, two meet together in vaccum. Then the radius of the resultant bubble is given by

Match List \(I\) with List \(II\)

LIST\(-I\)	LIST\(-II\)
\((A)\)  Torque	\((I)\)    \(ML ^{-2} T ^{-2}\)
\((B)\)   Stress	\((II)\)   \(ML ^2 T ^{-2}\)
\((C)\)   Pressure of gradient	\((III)\)   \(ML ^{-1} T ^{-1}\)
\((D)\)   Coefficient of viscosity	\((IV)\)   \(ML ^{-1} T ^{-2}\)

Choose the correct answer from the options given below