List of practice Questions

Answer the following :
(a) You can shield a charge from electrical forces by putting it inside a hollow conductor. Can you shield a body from the gravitational influence of nearby matter by putting it inside a hollow sphere or by some other means ?
(b) An astronaut inside a small space ship orbiting around the earth cannot detect gravity. If the space station orbiting around the earth has a large size, can he hope to detect gravity ?
(c) If you compare the gravitational force on the earth due to the sun to that due to the moon, you would find that the Sun’s pull is greater than the moon’s pull. (you can check this yourself using the data available in the succeeding exercises). However, the tidal effect of the moon’s pull is greater than the tidal effect of sun. Why ?
Let R be a relation from N to N defined by R = {(a, b): a, b ∈ N and a = b2}. Are the following true?
  1. (a, a) ∈ R, for all a ∈ N
  2. (a, b) ∈ R, implies (b, a) ∈ R
  3. (a, b) ∈ R, (b, c) ∈ R implies (a, c) ∈ R.
Justify your answer in each case.
If A and G be A.M. and G.M., respectively between two positive numbers, prove that the numbers are A±√(A+G)(A-G).

Choose the correct alternative : 
(a) Acceleration due to gravity increases/decreases with increasing altitude.
(b) Acceleration due to gravity increases/decreases with increasing depth (assume the earth to be a sphere of uniform density).
(c) Acceleration due to gravity is independent of mass of the earth/mass of the body.
(d) The formula –G Mm  \(\frac{1}{r_2 }– \frac{1}{r_1}\)  is more/less accurate than the formula mg(r2 – r1) for the difference of potential energy between two points r2 and r1 distance away from the centre of the earth.

Suppose there existed a planet that went around the Sun twice as fast as the earth. What would be its orbital size as compared to that of the earth?

The number of bacteria in a certain culture doubles every hour. If there were 30 bacteria present in the culture originally, how many bacteria will be present at the end of 2nd hour, 4th hour and nth hour ?

Let A = {1, 2, 3, 4}, B = {1, 5, 9, 11, 15, 16} and f = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}. Are the following true?
  1. f is a relation from A to B.
  2. f is a function from A to B.
Justify your answer in each case.
Io, one of the satellites of Jupiter, has an orbital period of 1.769 days and the radius of the orbit is 4.22 × 108 m. Show that the mass of Jupiter is about one-thousandth that of the sun.
Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola \(16x^ 2 - 9y^2 = 576\)
Let us assume that our galaxy consists of 2.5 × 1011 stars each of one solar mass. How long will a star at a distance of 50,000 ly from the galactic centre take to complete one revolution ? Take the diameter of the Milky Way to be 105 ly.
What will Rs 500 amounts to in 10 years after its deposit in a bank which pays annual interest rate of 10% compounded annually?
Choose the correct alternative:
(a) If the zero of potential energy is at infinity, the total energy of an orbiting satellite is negative of its kinetic/potential energy.
(b) The energy required to launch an orbiting satellite out of earth’s gravitational influence is more/less than the energy required to project a stationary object at the same height (as the satellite) out of earth’s influence.

Does the escape speed of a body from the earth depend on 

(a) the mass of the body, 

(b) the location from where it is projected, 

(c) the direction of projection, 

(d) the height of the location from where the body is launched?

If A.M. and G.M. of roots of a quadratic equation are 8 and 5, respectively, then obtain the quadratic equation.
A comet orbits the sun in a highly elliptical orbit. Does the comet have a constant
(a) linear speed,
(b) angular speed,
(c) angular momentum,
(d) kinetic energy,
(e) potential energy,
(f) total energy throughout its orbit?
Neglect any mass loss of the comet when it comes very close to the Sun.
If f is a function satisfying \(f (x +y) = f(x) f(y)\text{ for all}\, x, y ∈ N\) such that f(1) = 3 and \(∑_{x = 1}^n f(x) = 120 \), find the value of n.
Draw the diagram of a sarcomere of skeletal muscle showing different regions.
The first\((\triangle_ iH_1)\) and the second \((\triangle_iH)\) ionization enthalpies (in \(kJ\; mol ^{-1}\) ) and the \((\triangle_{eg}H)\) electron gain enthalpy (in \(kJ \;mol^{ -1}\) ) of a few elements are given below: 
Elements                       \(\triangle_iH\)                \(\triangle_iH\)                \(\triangle_{eg}H\) 
   I                                    520                   7300                    -60 
  II                                    419                   3051                    -48 
  III                                  1681                  3374                    -328  
  IV                                  1008                 1846                    -295 
  V                                   2372                  5251                   +48 
  VI                                  738                    1451                    -40
Which of the above elements is likely to be : 
  1. the least reactive element.
  2. the most reactive metal.
  3. the most reactive non-metal.
What is the significance of juxta glomerular apparatus (JGA) in kidney function?
Use the periodic table to answer the following questions.
  1. Identify an element with five electrons in the outer subshell.
  2. Identify an element that would tend to lose two electrons. 
  3. Identify an element that would tend to gain two electrons.
  4. Identify the group having metal, non-metal, liquid as well as gas at the room temperature.
The increasing order of reactivity among group 1 elements is \(Li\) \(<Na\) \(<K\) \(<Rb\) \(<Cs\) 
whereas that among group 17 elements is \(F>Cl>Br>I\) Explain.
Assign the position of the element having outer electronic configuration
  1. \(ns^ 2 np^ 4\) for \(n\) = \(3\) 
  2. \((n - 1)d^ 2 \;ns^ 2\) for \(n\) =\( 4\), and 
  3. \((n - 2) f ^7 (n - 1)d ^1 ns^ 2\) for \(n\) = \(6\), in the periodic table.
Predict the formula of the stable binary compounds that would be formed by the combination of the following pairs of elements.
  1. Lithium and oxygen 
  2. Magnesium and nitrogen 
  3. Aluminium and iodine 
  4. Silicon and oxygen
  5. Phosphorus and fluorine 
  6. Element 71 and fluorine
A liquid is in equilibrium with its vapour in a sealed container at a fixed temperature. The volume of the container is suddenly increased.
  1. What is the initial effect of the change on vapour pressure?
  2. How do rates of evaporation and condensation change initially?
  3. What happens when equilibrium is restored finally and what will be the final vapour pressure?
In the modern periodic table, the period indicates the value of: