Class 12th

When a car is approaching the observer, the frequency of horn is 100Hz. After passing the observer, it is 50 Hz. If the observer moves with the car, the frequency will be $\frac{x}{3}$ Ha where x = _________.

Mass numbers of two nuclei are in the ratio of 4 : 3. Their nuclear densities will be in the ratio of

In an experiment to determine the Young's modulus of wire of a length exactly 1m, the extension in the length of the wire is measured as 0.4mm with an uncertainty of $\pm$ 0.02mm when a load of 1kg is applied. The diameter of the wire is measured as 0.4mm with an uncertainty of $\pm$ 0.02mm. The error in the measurement of Young's modulus $\left(\Delta Y\right)$ is found to be x * 10¹⁰Nm^-2. The value of x is _________.

(take g = 10 ms^-2)

Two masses M₁ and M₂ are tied together at the two ends of a light inextensible string that passes over a frictionless pulley. When the mass M₂ is twice that of M₁. The acceleration of the system is a₁. When the mass M₂ is thrice that of M₁ the acceleration of the system is a₂. The ratio $\frac{a_1}{a_2}$ will be:

A disc of mass 1kg and radius R is free to rotate about a horizontal axis passing through its centre and perpendicular to the plane of disc. A body of same mass as that of disc is fixed at the highest point of the disc. Now the system is released, when the body comes to the lowest position, its angular speed will be $\sqrt[]{\frac{x}{3R}rads{}^{-1}}$ where x = __________.

If the initial velocity in horizontal direction of a projectile is unit vector $\widehat{i}$ and the equation of trajectory is y = 5x(1 – x). The y component vector of the initial velocity is ________ $\widehat{j}$ .

A velocity selector consists of electric field $\overrightarrow{E}=E\widehat{k}$ and magnetic field $\overrightarrow{B}=B\widehat{j}$ with B = 12 mT. The value of E required for and electron of energy 728 eV moving along the positive x-axis to pass undeflected is:

(Given. Mass of electron = 9.1 * 1031kg)

Two concentric circular loops of radii r₁ = 30cm and r₂ = 50cm are placed in X – Y plane as shown in the figure. A current I = 7A is flowing through them in the direction as shown in figure. The net magnetic momentum of this system of two circular loops is approximately:

A source of potential difference V is connected to the combination of two identical capacitors as shown in the figure. When key 'K' is closed, the total energy stored across the combination is E₁. Now key 'K' is opened and dielectric of dielectric constant 5 is introduced between the plates of the capacitors. The total energy stored across the combination is now E₂. The ratio E₁/E₂ will be: