JEE Main Test 1...

If p, q, r and s are positive real numbers such that p + q + r + s = 2, then M = (p + q) (r + s) satisfies the relation

A cube of side 40 mm has its upper face displaced by 0.1 mm by a tangential force of 8 kN. The shearing modulus of cube is

A thermodynamic system is taken from an initial state i with internal energy U_i =100 J to the fmal state f along two different paths iaf and ibf as schematically shown in the figure. The work done by the system along the paths af, ,ib and bf are W_af = 200 J, W_ib = 50 J and W_bf =100 J, respectively. The heat supplied to the system along the path iaf, ,ib and bf are Q_iaf ,Q_ib and Q_bf respectively. If the internal energy of the system in the state b is U_b = 200 J and Q_iaf = 500 J, the ratio Q_bf/Q_ib is

Three liquids of equal masses are taken in three identical cubical vessels A, B and C. Their densities are ρ_A , ρ_B and ρ_C respectively but ρ _A< ρ_B < ρ_C . The force exerted by the liquid on the base of the cubical vessel is

If (1 + χ )¹⁵ = a₀ + a₁ χ +...+ a₁₅ χ¹⁵ , then

The sink temperature of a heat engine 77°C. The efficiency is 30%. The source temperature is

Two point objects of mass 1.5 g and 2.5 g respectively are at a distance of 16 cm apart, the centre of gravity is at a distance x from the object of mass 1.5 g, where x is

One solid sphere A and another hollow sphere B are of same mass and same outer radius. Their moments of inertia about their diameters are respectively I_A and I_B such that

Note: d_A and d_B are their densities.

If I denotes the 3 × 3 identity matrix and P is a matrix obtained by rearranging the columns of I. Then,