The aperture diameter of a telescope is \(5\; \mathrm{m} .\) The separation between the moon and the earth is \(4 \times 10^{5} \;\mathrm{km} .\) With light of wavelength of \(5500\;\mathring A\), the minimum separation between objects on the surface of moon, so that they are just resolved, is close to......\(m\)

One main scale division of a vernier caliper is equal to \(m\) units. If \(n^{\text {th }}\) division of main scale coincides with \((n+1)^{\mathrm{th}}\) division of vernier scale, the least count of the vernier caliper is _______.

Statement \(I :\)Two forces \((\overrightarrow{{P}}+\overrightarrow{{Q}})\) and \((\overrightarrow{{P}}-\overrightarrow{{Q}})\) where \(\overrightarrow{{P}} \perp \overrightarrow{{Q}}\), when act at an angle \(\theta_{1}\) to each other, the magnitude of their resultant is \(\sqrt{3\left({P}^{2}+{Q}^{2}\right)}\), when they act at an angle \(\theta_{2}\), the magnitude of their resultant becomes \(\sqrt{2\left({P}^{2}+{Q}^{2}\right)}\). This is possible only when \(\theta_{1}<\theta_{2}\). Statement \(II :\) In the situation given above. \(\theta_{1}=60^{\circ} \text { and } \theta_{2}=90^{\circ}\) In the light of the above statements, choose the most appropriate answer from the options given below

If \(x\) and \(y\) coordinates of a projectile as a function of time \((t)\) are given as \(24t\) and \(43.6t-4.9t^2\), respectively, then the angle (in degrees) made by the projectile with horizontal when \(t=2\) s is ______.

Three point charges of magnitude \(5 \mu C , 0.16 \mu C\) and \(0.3 \mu C\) are located at the vertices \(A , B , C\) of a right angled triangle whose sides are \(AB =3\,cm\), \(BC =3 \sqrt{2}\,cm\) and \(CA =3\,cm\) and point \(A\) is the right angle corner. Charge at point \(A\) experiences \(N\) of electrostatic force due to the other two charges.

In a uniform magnetic field, the magnetic needle has a magnetic moment \(9.85 \times 10^{-2} \,{A} / {m}^{2}\) and moment of inertia \(5 \times 10^{-6} \,{kgm}^{2}\). If it performs \(10\) complete oscillations in \(5\, seconds\) then the magnitude of the magnetic field is \(....\,mT.\) [ Take \(\pi^{2}\) as \(9.85\) ]

The balancing length for a cell is \(560 \;\mathrm{cm}\) in a potentiometer experiment. When an external resistance of \(10 \;\Omega\) is connected in parallel to the cell, the balancing length changes by \(60\; \mathrm{cm} .\) If the internal resistance of the cell is \(\frac{\mathrm{N}}{10} \;\Omega,\) where \(\mathrm{N}\) is an integer then value of \(\mathrm{N}\) is

A liquid column of height \(0.04 \mathrm{~cm}\) balances excess pressure of soap bubble of certain radius. If density of liquid is \(8 \times 10^3 \mathrm{~kg} \mathrm{~m}^{-3}\) and surface tension of soap solution is \(0.28 \mathrm{Nm}^{-1}\), then diameter of the soap bubble is _______ \(\mathrm{cm}\). \(\text { (if } g=10 \mathrm{~ms}^{-2} \text { ) }\)

A mass \('m'\) is supported by a massless string wound around a uniform hollow cylinder of mass \(m\) and radius \(R\). If the string does not slip on the cylinder, with what acceleration will the mass fall on release?

A cord is wound round the circumference of wheel of radius \(r\). The axis of the wheel is horizontal and the moment of inertia about it is \(I. \,A\) weight \(mg\) is attached to the cord at the end. The weight falls from rest. After falling through a distance \( 'h '\), the square of angular velocity of wheel will be ..... .

The photodiode is used to detect the optiocal signals. These diodes are preferably operated in reverse biased mode because.