A rectangular loop of length \(2.5 \mathrm{~m}\) and width \(2 \mathrm{~m}\) is placed at \(60^{\circ}\) to a magnetic field of \(4 \mathrm{~T}\). The loop is removed from the field in \(10 \ \mathrm{sec}\). The average emf induced in the loop during this time is

For the circuit shown above, equivalent GATE is :

A person standing on an open ground hears the sound of a jet aeroplane, coming from north at an angle \(60^o\) with ground level. But he finds the aeroplane right vertically above his position. If \(\upsilon \) is the speed of sound, speed of the plane is

Two engines pass each other moving in opposite directions with uniform speed of \(30\,m/s\) . One of them is blowing a whistle of frequency \(540\,Hz.\) Calculate the frequency heard by driver of second engine before they pass each other  ... \(Hz\). Speed of sound is \(330\,m/sec\)

One end of a massless spring of spring constant \(k\) and natural length \(l_{0}\) is fixed while the other end is connected to a small object of mass \(m\) lying on a frictionless table. The spring remains horizontal on the table. If the object is made to rotate at an angular velocity \(\omega\) about an axis passing through fixed end, then the elongation of the spring will be

Net gravitational force at the centre of a square is found to be \( F_{1} \) when four particles having mass M, 2M, 3M and 4M are placed at the four corners of the square as shown in figure and it is \( F_{2} \) when the positions of 3M and 4M are interchanged. The ratio \( \frac{F_{1}}{F_{2}} \) is \( \frac{\alpha}{\sqrt{5}} \). The value of \( \alpha \) is __________ .

The dimensional formula of latent heat is _______.

A circular coil has moment of inertia \(0.8 \,kg m ^{2}\) around any diameter and is carrying current to roduce a magnetic moment of \(20\, Am ^{2}\). The coil is kept initially in a vertical position and it can rotate freely around a horizontal diameter. When a uniform magnetic field of \(4\, T\) is applied along the vertical, it starts rotating around its horizontal diameter. The angular speed the coil acquires after rotating by \(60^{\circ}\) will be

Given below are two statements: statement\(-I\) : The reactance of an ac circuit is zero. It is possible that the circuit contains a capacitor and an inductor. Statement\(-II\) : In \(ac\) circuit, the average power delivered by the source never becomes zero. In the light of the above statements, choose the correct answer from the options given below

Uniform magnetic fields of different strengths \(\left(B_1\right.\) and \(B_2\)), both normal to the plane of the paper exist as shown in the figure. A charged particle of mass m and charge q , at the interface at an instant, moves into the region 2 with velocity \(v\) and returns to the interface. It continues to move into region 1 and finally reaches the interface. What is the displacement of the particle during this movement along the interface?

(Consider the velocity of the particle to be normal to the magnetic field and \(B_2 \gt B_1\))

The region between two concentric spheres ofradii '\(a\)' and '\(b\)', respectively (see figure), have volume charge density \(\rho = \frac{A}{r}\) where \(A\) is a constant and \(r\) is the distance from the centre. At the centre of the spheres is a point charge \(Q\). The value of \(A\) such that the electric field in the region between the spheres will be constant, is :

Vectors \(a \hat{i}+b \hat{j}+\hat{k}\) and \(2 \hat{i}-3 \hat{j}+4 \hat{k}\) are perpendicular to each other when \(3 a+2 b=7\), the ratio of a to \(b\) is \(\frac{x}{2}\). The value of \(x\) is \(..............\)