Class 12th

If $\frac{1}{2*3*4}+\frac{1}{3*4*5}+\frac{1}{4*5*6}+...+\frac{1}{100*101*102}=\frac{k}{101},$ then 34 k is equal to………….

A singly ionized magnesium atom (A = 24) ion is accelerated to kinetic energy 5 ke V, and is projected perpendicularly into a magnetic field B of the magnitude 0.5 T. The radius of path formed will be ________cm.

Let p and p + 2 be prime numbers and let

$\Delta =\left|\begin{array}{ccc}\hfill p!\hfill & \hfill \left(p+1\right)!\hfill & \hfill \left(p+2\right)!\hfill \\ \hfill \left(p+1\right)!\hfill & \hfill \left(p+2\right)!\hfill & \hfill \left(p+3\right)!\hfill \\ \hfill \left(p+2\right)!\hfill & \hfill \left(p+3\right)!\hfill & \hfill \left(p+4\right)!\hfill \end{array}\right|$

Then the sum, of the maximum values of and , such that p and (p + 2) divide $\Delta ,$ is………….

A wire $A$ , bent in the shape of an arc of a circle, carrying a current of $2\mathrm{A}$ and having radius $2\mathrm{c}\mathrm{m}$ and another wire $B$ , also bent in the shape of arc of a circle, carrying a current of $3\mathrm{A}$ and having radius of $4\mathrm{c}\mathrm{m}$ , are placed as shown in the figure. The ratio of the magnetic fields due to the wires $A$ and $B$ at the common centre $O$ is:

The total internal energy of two mole mono atomic ideal gas at temperature T = 300K will be __________J. (Given R = 8.31 J/mol.K)

The number of matrices of order 3 * 3, whose entries are either 0 or 1 and the sum of all the entries is a prime number, is……….

A hanging mass M is connected to a four times bigger mass by using a string-pulley arrangement, as shown in the figure. The bigger mass is placed on a horizontal ice-slab and being pulled by 2 Mg force. In this situation, tension in the string is $\frac{x}{5}Mg$  for x_________. Neglect mass of the string and fiction of the block (bigger mass) with ice slab.

Particle $A$ of mass $m_A=\frac{m}{2}$ moving along the $x$ -axis with velocity $v_0$ collides elastically with another particle $B$ at rest having mass $m_B=\frac{m}{3}$ . If both particles move along the $x$ axis after the collision, the change $\mathrm{\Delta }\lambda$ in de-Broglie wavelength of particle $A$ , in terms of its de-Broglie wavelength $\left({\lambda }_0\right)$ before collision is:

Let the ratio of the fifth term from the beginning to the fifth term from the end in the binomial 

A man of 60kg is running on the road and suddenly jumps into stationary trolly car of mass 120kg. Then, the trolly car starts moving with velocity 2ms^-1. The velocity of the running man was _________ ms^-1, when he jumps into the car