The distance between object and its two times magnified real image as produced by a convex lens is \(45 \mathrm{~cm}\). The focal length of the lens used is _______ \(\mathrm{cm}\).

Match List \(- I\) (Electromagnetic wave type) with List \(- II\) (Its association/application) and select the correct option from the choices given below the lists

લિસ્ટ\(-I\)	લિસ્ટ\(-II\)
\(a\). Infrared waves	\(i\). To treat muscular strain
\(b\). Radio waves	\(ii\). For broadcasting
\(c\). \(X-\)rays	\(iii\). To detect fracture of bones
\(d\). Ultraviolet rays	\(iv\). Absorbed by the ozone layer of the atmosphere

\(a\)         \(b\)         \(c\)         \(d\)

Two concentric circular coils with radii \(1\,cm\) and \(1000\,cm\), and number of turns \(10\) and \(200\) respectively are placed coaxially with centers coinciding. The mutual inductance of this arrangement will be \(.........\times 10^{-8}\,H\)(Take, \(\pi^2=10\))

The velocity of sound in a gas. in which two wavelengths \(4.08\,m\) and \(4.16\,m\) produce \(40\) beats in \(12\,s\), will be ..............\(ms ^{-1}\)

The maximum percentage error in the measurment of density of a wire is [Given, mass of wire \(=(0.60 \pm 0.003) \mathrm{g}\)
radius of wire \(=(0.50 \pm 0.01) \mathrm{cm}\)
length of wire \(=(10.00 \pm 0.05) \mathrm{cm}]\)

The current gain of a common emitter amplifier is \(69\). If the emitter current is \(7.0\,mA\), collector current is.....\(mA\)

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 \(9.85\) ]

A transverse harmonic wave on a string is given by \(y(x, t)=5 \sin (6 t+0.003 x)\) where \(x\) and \(y\) are in \(cm\) and \(t\) in \(sec\). The wave velocity is \(...........\,ms ^{-1}\).

The energy released when \(\dfrac{7}{17.13}\) kg of \(^{7}_{3}\text{Li}\) is converted into \(^{4}_{2}\text{He}\) by proton bombardment is \(\alpha \times 10^{32}\) eV. The value of \(\alpha\) is _______. (Nearest integer) (Mass of \(^{7}_{3}\text{Li} = 7.0183\) u, mass of \(^{4}_{2}\text{He} = 4.004\) u, mass of proton \(= 1.008\) u and \(1\) u \(= 931\) MeV/c\(^2\) and Avogadro number \(= 6.0 \times 10^{23}\))