List of practice Questions

Find the mean deviation of the following data: 

Evaluate the following integral: \[ \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \left( x^4 + x^3 + x \right) \cos x \, dx \]
Find the minimum of the function \[ f(x) = |x+2| \]
Find the center of the ellipse given by the equation \[ 4x^2 + 24x + 9y^2 - 18y + 9 = 0 \]
Water flows through a pipe with velocity \( V_1 = 3 \, \text{m/s} \) where the area of the pipe is \( A_1 \). What is the velocity \( V_2 \), where the diameter of the pipe is half of that at area \( A_1 \)?
When a rotating disc suddenly shrinks in radius, what happens to the angular velocity \( \omega \)?
The center of mass of a rod of length \( l \) is at a distance ______ from one end of the rod.
The acceleration of a particle varies with time as \( a = 6t \). What is the displacement and velocity of the particle at \( t = 4s \)?
What is the potential energy of an object of mass \( m \) placed on the surface of the Earth? (Mass of Earth = \( M \), radius of Earth = \( R \))
A block is tied to a string of length 98 cm and is rotated in a horizontal circle. Find the angular velocity if the centripetal acceleration \( a = g \).
If \( n \) cells of emf \( E \) and internal resistance \( r \) are connected in parallel, what is the equivalent emf and internal resistance of the combination?
A guitar string is vibrating in the third harmonic. The number of nodes and antinodes present are:
A rod of length 0.5 m moves with a velocity of 3 m/s in a perpendicular magnetic field of strength 2 T. Find the emf induced across its ends.
According to Huygen's principle, secondary wavelets move:
Coefficient of friction is the ratio of?
Electric field lines around a positive charge are directed:
The temperature of the source and sink of a heat engine are 127°C and 27°C respectively. By how much should the temperature of the source be increased so as to double the efficiency?
Which of the following is an ambidentate ligand? a) \( \text{C}_2 \text{O}_4^{2-} \) b) \( \text{CN}^- \) c) \( \text{NH}_3 \)
10 g of (90 percent pure) \( \text{CaCO}_3 \), treated with excess of HCl, gives what mass of \( \text{CO}_2 \)?
Pressure of pure benzene is 0.75. When 0.2g of a non-volatile solute is added to 39g of benzene, pressure changes to 0.745. The molar mass of solute is?
In which of the following \( K_c = K_p \)? a) \( \text{PCl}_5(g) \rightleftharpoons \text{PCl}_3(g) + \text{Cl}_2(g) \) b) \( \text{H}_2(g) + \text{I}_2(g) \rightleftharpoons 2\text{HI}(g) \)
Given the following concentrations and rates, which one corresponds to the rate law for the reaction? \[ [A] = 0.10 \quad [D] = 0.2 \quad \text{Rate} = 0.2 \] \[ [A] = 0.2 \quad [D] = 0.2 \quad \text{Rate} = 0.4 \] \[ [A] = 0.10 \quad [D] = 0.1 \quad \text{Rate} = 0.05 \]
Friedel Craft's reaction is an example of:
Find the \( \Delta G \) during the reaction: \[ \text{H}_2\text{O}(l) \rightleftharpoons \text{H}_2\text{O}(g) \quad \Delta S = +1 \, \text{kJ/mol} \, \text{at} \, 100^\circ C \]
\( E^\circ_{\text{Cell}} = 1.1 \, \text{V}. \, \text{Find} \, E_{\text{Cell}} \, \text{for the reaction:} \, \text{Zn} + \text{Cu}^{2+} \, (0.1M) \rightleftharpoons \text{Zn}^{2+} \, (0.001M) + \text{Cu} \)