Half-lives of two radioactive elements A and B are 20 minutes and 40 minutes, respectively. Initially, the samples have equal number of nuclei. After 80 minutes, the ratio of decayed numbers of A and B nuclei will be :
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A particle of mass m moving in the x direction with speed 2v is hit by another particle of mass 2m moving in the y direction with speed v. If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to
The angle between the lines whose direction cosines satisfy the equations l+m+n=0and l2=m2+n2is
If x=−1and x=2are extreme points of f(x)=αlog∣x∣+βx2+x, then
The statement (p↔ q) is
A piston filled with 0.04 mol of an ideal gas expands reversibly from 50.0 mL to 375 mL at a constant temperature of 37.0∘C. As it does so, it absorbs 208J of heat. The values of q and w for the process will be: (R = 8.314 J/mol K) (l 7.5 = 2.01)
On a hot summer night, the refractive index of air is smallest near the ground and increases with height from the ground. When a light beam is directed horizontally, the Huygens' principle leads us to conclude that as it travels, the light beam :
The gas leaked from a storage tank of the Union Carbide plant in Bhopal gas tragedy was:
A uniform cylinder of length L and mass M having cross-sectional area A is suspended, with its length vertical, from a fixed point by a massless spring, such that it is half submerged in a liquid of density σ at equilibrium position. The extension x0 of the spring when it is in equilibrium is: