JEE Advanced Mi...

Two blocks of masses m₁ = 5kg and m₂ = 2 kg are connected by threads which pass over the pulleys as shown in the figure. The threads are massless, and the pulleys are massless and smooth. The blocks can move only in the vertical direction. If the acceleration of m₁, if expressed in simplest from, is equal to  calculate 'n'. (Take g = 10 m/s²)

A long, square wooden block is pivoted along one edge as shown. The block is in equilibrium when immersed in water to the depth shown.

Assuming friction in the pivot is negligible. Let the density of wood be 170α. Hence α is (in SI unit, up to two significant digit).

Two particles are projected horizontally in opposite directions from a point in a smooth inclined plane of inclination θ=60^∘ with the horizontal as shown in the figure. Find the separation between the particles in the inclined plane when their velocity becomes perpendicular to each other. v₁ = 1 m/s, v₂ = 3 m/s. Express your answer in the form of k/5 metre. Then, find the value of k.

Graph shows variation of internal energy U with density ρ of one mole of an ideal monoatomic gas. Process AB is a part of rectangular hyperbola. Find work done in the process (in Joules)

If molar mass of C is P, find value of P.

How many maximum numbers of cyclic isomer(s) is/are possible with formula C₅H₁₀? (consider stereoisomers)

The least degree of a polynomial with integer coefficients, whose one of the roots be cos 12⁰, is

Consider n x n graph paper, where n is a natural number. Consider the right-angled isosceles triangles, whose vertices are integer points of this graph and whose sides forming right angle are parallel to x and y axes. If the number of such triangle is 2/kn(n + 1)(2n + 1), the numerical quantity k must be equal to