A balloon was moving upwards with a uniform velocity of \(10\, {m} / {s}\). An object of finite mass is dropped from the balloon when it was at a height of \(75\, {m}\) from the ground level. The height of the balloon from the ground when object strikes the ground was around.(In \({m}\)) (Takes the value of \(g\) as \(10 \,{m} / {s}^{2}\) )

The trajectory of projectile, projected from the ground is given by \(y=x-\frac{x^2}{20}\). Where \(x\) and \(y\) are measured in meter. The maximum height attained by the projectile will be \(...........\,m\)

Two shorts dipoles \((A, B), A\) having charges \(\pm 2 \mu C\) and length 1 cm and \(B\) having charges \(\pm 4 \mu C\) and length 1 cm are placed with their centres 80 cm apart as shown in the figure. The electric field at a point \(P\), equi-distant from the centres of both dipoles is ___________ N/C.

A small block of mass \(100\,g\) is tied to a spring of spring constant \(7.5\,N / m\) and length \(20\, cm\). The other end of spring is fixed at a particular point \(A\). If the block moves in a circular path on a smooth horizontal surface with constant angular velocity \(5\,rad / s\) about point \(A\), then tension in the spring is \(.........\,N\)

In a radioactive decay chain, the initial nucleus is \({}_{90}^{232}Th\).  At the end there are \(6\,\,\alpha -\) particles and \(4\,\,\beta -\) particles with are emitted. If the end nucleus is \({}_Z^AX\,,\,A\) and \(Z\) are given by

Which of the following will NOT be observed when a multimeter (operating in resistance measuring mode) probes connected across a component, are just reversed?

The current sensitivity of a galvanometer can be increased by: \((A)\) decreasing the number of turns \((B)\) increasing the magnetic field \((C)\) decreasing the area of the coil \((D)\) decreasing the torsional constant of the spring Choose the most appropriate answer from the options given below.

The output of the given combination gates represents

A wire of length \(L\, (=20\, cm)\), is bent into a semicircular arc. If the two equal halves of the arc were each to be uniformly charged with charges \( \pm Q\,,\,\left[ {\left| Q \right| = {{10}^3}{\varepsilon _0}} \right]\) Coulomb where \(\varepsilon _0\) is the permittivity (in \(SI\, units\)) of free space] the net electric field at the centre \(O\) of the semicircular arc would be

A conical pendulum of length \(1\,m\) makes an angle \(\theta \, = 45^o\) w.r.t. \(Z-\) axis and moves in a circle in the \(XY\) plane.The radius of the circle is \(0.4\, m\) and its centre is vertically below \(O\). The speed of the pendulum, in its circular path, will be ..... \(m/s\) (Take \(g\, = 10\, ms^{-2}\))

The difference of temperature in a material can convert heat energy into electrical energy. To harvest the heat energy, the material should have _________.

Two coherent sources of sound, \(S_{1}\) and \(S_{2}\) produce sound waves of the same wavelength, \(\lambda=1\, m ,\) in phase. \(S_{1}\) and \(S_{2}\) are placed \(1.5\, m\) apart (see fig.) A listener, located at \(L,\) directly in front of \(S_{2}\) finds that the intensity is at a minimum when he is \(2\,m\) away from \(S _{2}\). The listener moves away from \(S _{1},\) keeping his distance from \(S_{2}\) fixed. The adjacent maximum of intensity is observed when the listener is at a distance \(d\) from \(S\)\(_{1}\). Then, \(d\) is\(......m\)