An electron is made to enter symmetrically between two parallel and equally but oppositely charged metal plates, each of 10 cm length. The electron emerges out of the electric field region with a horizontal component of velocity \(10^6 \mathrm{~m} / \mathrm{s}\). If the magnitude of the electric field between the plates is \(9.1 \mathrm{~V} / \mathrm{cm}\), then the vertical component of velocity of electron is (mass of electron \(=9.1 \times 10^{-31} \mathrm{~kg}\) and charge of electron \(=1.6 \times 10^{-19} \mathrm{C}\) )

Pressure inside two soap bubbles are \(1.01\) and \(1.02\) atmosphere, respectively. The ratio of their volumes is

A convex lens made of glass (refractive index \(=1.5\) ) has focal length 24 cm in air. When it is totally immersed in water (refractive index \(=1.33\) ), its focal length changes to ________.

A damped harmonic oscillator has a frequency of \(5\) oscillations per second. The amplitude drops to half its value for every \(10\) oscillations. The time it will take to drop to \(\frac{1}{1000}\) of the original amplitude is close to .... \(s\)

A convex mirror of radius of curvature \(30 \mathrm{~cm}\) forms an image that is half the size of the object. The object distance is :

A vessel contains \(0.15\) m\(^3\) of a gas at pressure \(8\) bar and temperature \(140°\)C with \(c_p = 3R\) and \(c_v = 2R\). It is expanded adiabatically till pressure falls to \(1\) bar. The work done during this process is _______ kJ. (\(R\) is gas constant)

The source that illuminates the double - slit in 'double - slit interference experiment' emits two distinct monochromatic waves of wavelength \(500\,nm\) and \(600\, nm\), each of them producing its own pattern on the screen. At the central point of the pattern when path difference is zero, maxima of both the patterns coincide and the resulting interference pattern is most distinct at the region of zero path difference. But as one moves out of this central region, the two fringe systems are gradually out of step such that maximum due to on wavelength coincides with the minimum due to the other and the combined fringe system becomes completely indistinct. This may happen when path difference in \(nm\) is

Let \(y=y(x)\) be the solution of the differential equation \(\frac{d y}{d x}=2 x(x+y)^3-x(x+y)-1, y(0)=1\). Then, \(\left(\frac{1}{\sqrt{2}}+\mathrm{y}\left(\frac{1}{\sqrt{2}}\right)\right)^2\) equals :

Suppose \(a_1, a_2, 2, a_3, a_4\) be in an arithmeticogeometric progression. If the common ratio of the corresponding geometric progression is \(2\) and the sum of all \(5\) terms of the arithmetico-geometric progression is \(\frac{49}{2}\), then \(a_4\) is equal to \(...........\).

Let \(\alpha, \beta, \gamma\) be the real roots of the equation, \(x ^{3}+ ax ^{2}+ bx + c =0,( a , b , c \in R\) and \(a , b \neq 0)\) If the system of equations (in, \(u,v,w\)) given by \(\alpha u+\beta v+\gamma w=0, \beta u+\gamma v+\alpha w=0\) \(\gamma u +\alpha v +\beta w =0\) has non-trivial solution, then the value of \(\frac{a^{2}}{b}\) is

A moving coil galvanometer has a coil with \(175\, turns\) and area \(1\, cm^2\) It uses a torsion band of torsion constant \(10^{-6}\, N\, -m/rad\). The coil is placed in a magnetic field \(B\) parallel to its plane. The coil deflects by \(10\) for a current of \(1\, mA\). The value of \(B\) (in Tesla) is approximately

Let a complex number \(z ,| z | \neq 1\), satisfy \(\log _{\frac{1}{\sqrt{2}}}\left(\frac{| z |+11}{(| z |-1)^{2}}\right) \leq 2 .\) Then, the largest value of \(|z|\) is equal to ............

The equation \(\lambda=\frac{1.227}{ x } nm\) can be used to find the de-Brogli wavelength of an electron. In this equation \(x\) stands for : Where,\(m =\) mass of electron \(P =\) momentum of electron \(K =\) Kinetic energy of electron \(V =\) Accelerating potential in volts for electron