A square shaped wire with resistance of each side \(3\, \Omega\) is bent to form a complete circle. The resistance between two diametrically opposite points of the circle in unit of \(\Omega\) will be ......

The position of a particle related to time is given by \(x =\left(5 t ^2-4 t +5\right) m\). The magnitude of velocity of the particle at \(t=2\,s\) will be \(...........ms^{-1}\)

A particle of mass \(m\) is moving along the side of a square of side '\(a\)', with a uniform speed \(v\) in the \(x-y\) plane as shown in the figure Which of the following statement is false for the angular momentum \(\vec L\) about the origin ?

A proton moving with one tenth of velocity of light has a certain de Broglie wavelength of \(\lambda\). An alpha particle having certain kinetic energy has the same de-Brogle wavelength \(\lambda\). The ratio of kinetic energy of proton and that of alpha particle is:

A wire of resistance \(160\,\Omega\) is melted and drawn in wire of one-fourth of its length. The new resistance of the wire will be \(......\Omega\)

Two thin metallic spherical shells of radii \({r}_{1}\) and \({r}_{2}\) \(\left({r}_{1}<{r}_{2}\right)\) are placed with their centres coinciding. A material of thermal conductivity \({K}\) is filled in the space between the shells. The inner shell is maintained at temperature \(\theta_{1}\) and the outer shell at temperature \(\theta_{2}\left(\theta_{1}<\theta_{2}\right)\). The rate at which heat flows radially through the material is :-

In an ac circuit, the instantaneous current is zero, when the instantaneous voltage is maximum. In this case, the source may be connected to: \(A\). pure inductor. \(B\). pure capacitor. \(C\). pure resistor. \(D\). combination of an inductor and capacitor. Choose the correct answer from the options given below:

A series LCR circuit with \(R = 20\ \Omega\), \(L = 1.6\text{ H}\) and \(C = 40\ \mu\text{F}\) is connected to a variable frequency a.c. source. The inductive reactance at resonant frequency is _______ \(\Omega\).

Consider an electron in a hydrogen atom, revolving in its second excited state (having radius \(4.65\, \mathop A\limits^o \)). The de-Broglie wavelength of this electron is....\(\mathop A\limits^o \)

In young's double slit experiment, the fringe width is \(12\,mm\). If the entire arrangement is placed in water of refractive index \(\frac{4}{3}\), then the fringe width becomes \((in\,mm)\)

Seven identical circular planar disks, each of mass \(M\) and radius \(R\) are welded symmetrically as shown. The moment of inertia of the arrangement about the axis normal to the plane and passing through the point \(P\) is:

When an external resistance of \(5\ \Omega\) is connected across terminals of a cell, a current of \(0.25\text{ A}\) flows through it. When the \(5\ \Omega\) resistor is replaced by a \(2\ \Omega\) resistor, a current of \(0.5\text{ A}\) flows through it. The internal resistance of the cell is _______ \(\Omega\).

A ball suspended by a thread swings in a vertical plane so that its magnitude of acceleration in the extreme position and lowest position are equal. The angle \((\theta)\) of thread deflection in the extreme position will be :