List of practice Questions

Explain with the help of suitable example polar covalent bond.
Find \(\frac {dy}{dx}:\) \(y=cos^{-1}(\frac {1-x^2}{1+x^2}),\ \ 0<x<1\)
Find \(\frac {dy}{dx}:\) \(sin^2x+cos^2y=1\)
\(Find\  \frac {dy}{dx}:\) \(y=tan^{-1}( \frac {3x-x^3}{1-3x^2}),\ \ -\frac {1}{\sqrt 3}<x<\frac {1}{\sqrt 3}\)
How much electricity is required in coulomb for the oxidation of 
(i) 1 mol of H2O to O2. 
(ii) 1 mol of FeO to Fe2O3.

How much electricity in terms of Faraday is required to produce
 (i) 20.0 g of Ca from molten CaCl2.
 (ii) 40.0 g of Al from molten Al2O3.

Conductivity of 0.00241 M acetic acid is 7.896 × 10-5 S cm-1 . Calculate its molar conductivity and if \(\land^0_m\) for acetic acid is 390.5 S cm2 mol-1 , what is its dissociation constant?
The resistance of a conductivity cell containing 0.001M KCl solution at 298 K is 1500 Ω. What is the cell constant if conductivity of 0.001M KCl solution at 298 K is 0.146 x 10-3 S cm-1 .
Define conductivity and molar conductivity for the solution of an electrolyte. Discuss their variation with concentration.
Calculate the standard cell potentials of galvanic cells in which the following reactions take place: 
 (i)  \(2Cr_{(S)}+3Cd^{2+}_{(aq)} \rightarrow 2Cr^{3+}_{(aq)}+3Cd\)
 (ii) \(Fe^{2+}_{(aq)}+Ag^+_{(aq)} \rightarrow Fe^{3+}_{(Aq)}+Ag(s)\)
Calculate the \(\triangle_rG^\ominus\) and equilibrium constant of the reactions.
Given the standard electrode potentials, 
K+/K = -2.93V, Ag+/Ag = 0.80V, 
Hg2+/Hg = 0.79V 
Mg2+/Mg = -2.37 V, Cr3+/Cr = - 0.74V 
Arrange these metals in their increasing order of reducing power.
Arrange the following metals in the order in which they displace each other from the solution of their salts.
Al, Cu, Fe, Mg and Zn
A cross was made by Mendel with pea plant between violet flower (VV) in axial position (AA) and while flower (vv) in terminal position (aa). What ratio of white flowers (vv) phenotypically he had received in F2 generation?
Determine the volume contraction of a solid copper cube, 10 cm on an edge, when subjected to a hydraulic pressure of 7.0 × 106 Pa.
Differentiate w.r.t. \(x\) the function: \((3x^2-9x+5)^9\)
Differentiate the following w.r.t. x: \(e^{sin^{-1}x}\)
Differentiate the following w.r.t. x: \(\frac {e^x}{sin\ x}\)
What is the maximum value of the function sin x + cos x?
If $y = \cot^{-1} \, (x^2)$, then the value of $ \frac{dy}{dx}$ is equal to
  1. A child stands at the centre of a turntable with his two arms outstretched. The turntable is set rotating with an angular speed of 40 rev/min. How much is the angular speed of the child if he folds his hands back and thereby reduces his moment of inertia to 2/5 times the initial value ? Assume that the turntable rotates without friction. 
  2. Show that the child’s new kinetic energy of rotation is more than the initial kinetic energy of rotation. How do you account for this increase in kinetic energy?
Find the mean deviation about the median for the data 36, 72, 46, 42, 60, 45, 53, 46, 51, 49.

Find the mean deviation about the mean for the given data.

\(x_i\)510152025
\(f_i\)74635
A metre-long tube open at one end, with a movable piston at the other end, shows resonance with a fixed frequency source (a tuning fork of frequency 340 Hz) when the tube length is 25.5 cm or 79.3 cm. Estimate the speed of sound in air at the temperature of the experiment. The edge effects may be neglected.

A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of 45 Hz. The mass of the wire is 3.5 × 10–2 kg and its linear mass density is 4.0 × 10–2 kg m–1. What is (a) the speed of a transverse wave on the string, and (b) the tension in the string?

A rocket with a lift-off mass 20,000 \(\text {kg}\) is blasted upwards with an initial acceleration of 5.0 \(\text \,m \text s^{-2}\). Calculate the initial thrust (force) of the blast.