List of practice Questions

If \( x_1, i=2, 3, \ldots, n \) are \( n \) observations such that \( \sum_{i=1}^{n} x_i^2 = 550 \), mean \( \bar{x} = 5 \) and variance is zero, then the number of observations is equal to:

The approximate value of \( \sqrt[3]{730} \) obtained by the application of derivatives is:

A ball is projected in still air. With respect to the ball the streamlines appear as shown in the figure. If speed of air passing through the region 1 and 2 are \( v_1 \) and \( v_2 \), respectively and the respective pressures, \( P_1 \) and \( P_2 \), respectively, then

If the voltage across a bulb rated 220V – 60W drops by 1.5% of its rated value, the percentage drop in the rated value of the power is:

The electric power delivered by a transmission cable of resistance \( R_c \) at a voltage \( V \) is \( P \). The power dissipated is

Mobility \( \mu \) of an electron is related to average collision time \( \tau \) as: \[ \mu = \frac{e \tau}{m} \] (where \( e \) is the electronic charge, and \( m \) is the mass of the electron)

A line makes angles \( \alpha, \beta, \gamma \) with \( x, y \), and \( z \)-axes respectively. Then the value of \( \sin^2\alpha + \sin^2\beta - \cos^2\gamma \) is:

The area of the triangle formed by the coordinate axes and a line whose perpendicular from the origin makes an angle of 45° with the x-axis is 50 square units. Then the equation of the line is:

The vapour pressure of H\(_2\)O at 323K is 95 mm of Hg. 176g of sucrose (Molar mass = 342 gmol\(^{-1}\)) is added to 900g of H\(_2\)O at 323K.
The vapour pressure of solution is about

If 25th February, 2008 was a Monday, then what was the day of 15th March, 2008?

Identify the wrong pair: