NTA JEE Main 9th April 2014 Online

An experiment is performed to obtain the value of acceleration due to gravity g by using a simple pendulum of length L. In this experiment time for 100 oscillations is measured by using a watch of 1 second least count and the value is 90.0 seconds. The length L is measured by using a meter scale of least count 1 mm and the value is 20.0 cm. The error in the determination of g would be:

The position of a projectile launched from the origin at t = 0 is given by $$\vec{r} = (40\hat{i} + 50\hat{j})$$ m at t = 2s. If the projectile was launched at an angle $$\theta$$ from the horizontal, then $$\theta$$ is (take g = 10 ms$$^{-2}$$).

Water is flowing at a speed of 1.5 m s$$^{-1}$$ through a horizontal tube of cross-sectional area $$10^{-2}$$ m$$^2$$ and you are trying to stop the flow by your palm. Assuming that the water stops immediately after hitting the palm, the minimum force that you must exert should be (density of water = $$10^3$$ kg m$$^{-3}$$)

A block A of mass 4 kg is placed on another block B of mass 5 kg, and the block B rests on a smooth horizontal table. If the minimum force that can be applied on A so that both the blocks move together is 12 N, the maximum force that can be applied on B for the blocks to move together will be:

A cylinder of mass M$$_C$$ and sphere of mass M$$_S$$ are placed at points A and B of two inclines, respectively. (See figure). If they roll on the incline without slipping such that their accelerations are the same, then the ratio $$\frac{\sin\theta_C}{\sin\theta_S}$$ is:

India's Mangalyan was sent to the Mars by launching it into a transfer orbit EOM around the sun. It leaves the earth at E and meets Mars at M. If the semi-major axis of Earth's orbit is $$a_e = 1.5 \times 10^{11}$$ m, that of Mar's orbit $$a_m = 2.28 \times 10^{11}$$ m, taking Kepler's laws, give the estimate of time for Mangalyan to reach Mars from Earth.

In materials like aluminium and copper, the correct order of magnitude of various elastic modulii is:

A capillary tube is immersed vertically in water and the height of the water column is $$x$$. When this arrangement is taken into a mine of depth d, the height of the water column is $$y$$. If R is the radius of earth, the ratio $$\frac{x}{y}$$ is:

Water of volume 2 L in a closed container is heated with a coil of 1 kW. While water is heated, the container loses energy at a rate of 160 J/s. In how much time will the temperature of water rise from 27°C to 77°C? (Specific heat of water is 4.2 kJ/kg and that of the container is negligible).

The equation of state for a gas is given by $$PV = nRT + \alpha V$$, where n is the number of moles and $$\alpha$$ is a positive constant. The initial temperature and pressure of one mole of the gas contained in a cylinder are T$$_0$$ and P$$_0$$ respectively. The work done by the gas when its temperature doubles isobarically will be: