JEE Main Test 1...

Weight of a body of mass m decreases by 1% when it is raised to height h above the earth\'s surface. If the body is taken to a depth h in a mine, change in its weight is

If the both the root of the quadratic equation χ² - 2kχ + k² + k - 5 = 0 are less than 5, then k lies in the interval

A spring of force constant 800 Nm^-1 has an extension of 5cm. The work done in extending it from 5 cm to 15 cm is

The kinetic energy of a body becomes four times its initial value. The new momentum will be

The sum of infinity of the series 1 + 2/3 + 6/3² + 10/3³ + 14/3⁴ + ... is

A lead bullet strikes against a steel plate with a velocity 200 m/s. If the impact is perfectly inelastic and the heat produced is equally shared between the bullet and the target, then the rise in temperature of the bullet is (specific heat capacity of lead =125 Jkg ^-1 K ^-1)

The figure shows a system of two concentric spheres of radii r₁ and r₂ and kept at temperatures T₁ and T₂ respectively. The radial rate of flow of heat in a substance between the two concentric spheres, is proportional to

The cylindrical tube of a spray pump has a cross-section of 8 cm², one end of which has 40 fine holes each of area 10^-8 m². If the liquid flows inside the tube with a speed of 0.15 m min^-1, the speed with which the liquid is ejected through the holes is

The number of times the digit 5 will be written when listing the integers from 1 to 1000, is

5.6 L of helium gas at STP is adiabatically compressed to 0.7 L. Taking the initial temperature to be T₁, the work done in the process is