CHEMISTRY MODEL QUESTION PAPER -2009-2010-

Q 1. What designation is given to an orbital having n=3, l=0

Q 2. What are the units of surface tension?

Q 3. State modern periodic law.

Q 4. Give the IUPAC name of tertiary butyl alcohol.

Q 5. Write conjugate acid and base NH3.

Q 6. Give the relation between standard Free energy change and Equilibrium constent.


Q 7. An alkene A on ozonolysis gives a mixture of Ethanal & Propanal. Write the
structure of A

Q 8. Determine the oxidation number of underlined element in.
NaBH4

Q 9. What do you understand by the term Electron gain enthalpy ? How it is different
from Electro negativity

Q 10. What are the various factors due to which the Ionisation enthalpy of the main group
Element tends to decrease down a group.?

Q 11. Define the terms -: ( a) Entropy ( b) Enthalpy of combustion
OR
Explain Hess law of constant heat summation with the help of an example

Q 12. In what ways Be shows anomalous behavior than other elements of same group
chemically ( Give equations).
Q 13. Complete the following reactions.
(a) CH3-CH=CH2 + H2O HgSO4 /H+ ?
( b) CH3-CH2-Br + Na Ether ?

Q 14. Explain Why ?
(a) Pb (IV) is less stable than Pb (II).
(b) BCl3 Molecule has Zero dipole moment.

Q 15. Balance the given redox reaction in acidic medium.
MnO4
-
+ SO2 Mn2+ + HSO4
-

Q 16. What is the maximum number of emission lines obtained when the exited electron
of a H atom in n=6 drops to the ground state .

Q 17. Compare the relative stability of the following species and indicate their magnetic
Properties on the basis of MOT (i) O2, (ii) O2
2-

Q 18 Explain why ?
(a) Cs is used in photoelectric cell.
(b) Potassium carbonate can not be prepared by solvey process.

Q 19. (a)Calculate the molarity of Oxalic acid in the solution prepared by dissolving its
2.52 gm in enough water to form 250 ml of the solution.
(b)Round off the following in three significant figures
(a) 3289 (b) 0.03265

Q 20 (a) State Pauli’s exclusion principle.
(b) Write the electronic configuration of Co+3. & find out the number of unpaired
electrons present in it.

Q 21. Calculate the enthalpy of combustion of Ethylene gas to form carbon dioxide and
water at 298 K and 1 atm preassure. The enthalpies of formation of CO2, H2O &
C2H4 are -393.5,-241.8 & +52.4 kj mol-1 respectively.

Q 22. Explain the following.
(a) (i) Carbon monoxide is more dangerous than carbon dioxide .why ?
(ii) Statues and monuments in India are affected by acid rain How?
(b)What are the full forms of MIC & BOD.?

Q 23. (a) What are Electrophiles explain with example
(b) Define Position isomerism with example.

Q 24. (a) 0.50 gm of an organic compound was Kjeldahlised and the ammonia obtained
was passed into 100 ml of M/10 H2SO4 .The excess acid required 160 ml of M/10 NaOH
for neutralization .calculate the percentage of nitrogen in the compound.

Q 25. (a) Write the favorable factors for the formation of Ionic bond.
(b ) Discuss the shape of NH3 molecule using VSEPR theory.
.

Q 26. Density of a gas is found to be 5.46 g/dm3 at 27C at 2 bar pressure . calculate the
density at STP.
OR
(a) Explain the physical significance of van dar waals parameter also give their
units.
(b) In terms of Charle’s law explain why -273C is the lowest possible
temperature?

Q27. What causes the temporary and permanent hardness of water .discuss the method of
softening of hard water by ion exchange method.

Q28 (a) write short notes on -:
(i) common ion effect
(ii) PH
(iii) Heterogeneous equilibrium
(b)A sample of HI (g) is placed in a flask at a pressure of 0.2 atm .At equilibrium
partial pressure of HI (g) is 0.04 atm. What is Kp for the given equilibrium?
reaction
2HI (g)  H2 (g) + I2 (g)
OR
(a) What are the application of equilibrium constant.
(b) Write expression for Kc for the reaction
CaCO3 (s)  CaO(s) + CO2(g)
(c) Discuss the effect of catalyst & addition of inert gas at constant pressure for
the reaction
2SO2 (g) + O2 (g)  2SO3 (g)

Q29 (a) Write the IUPAC names of the product obtained by the ozonolysis of
following compounds
(i) Hex-2-ene (ii) 2-Ethyl but –1-ene
(b) Why is Wurtz reactionnot preferred for alkanes containing odd number of
carbon aatoms ? Illustrate your answer by taking one example
OR
(a) Complete the following equations
(i)CH3-CH=C-CH3 + H2O H+/Hg++

CH3
(ii) CH3-CH2-CH =CH2 + HBr Peroxide
(iii) C6H6 + Cl2 AlCl
3
(b) What are the necessary conditions for any system to be aromatic ?

Q30. (a) Assign reason for each of the following
(i) Ga (I) undergoes disproportionation reaction.
(ii) Anhy. AlCl3 used as catalyst
(iii) Boron is unable to form BF6
-
ion explain
(b)Complete the following equation.
(i) SiO2 + HF  ?
(ii) BCl3 + H2O  ?
OR
(a) Write equation to justify amphoteric nature of Aluminium.
(b) Give reasons :
(i) Conc HNO3 can be stored in Aluminium container
(ii) Ionization enthalpy decreases from carbon to silicon.
(iii)

PARABOLA -1-

CONIC SECTION

PARABOLA

Conics or conic sections are the curves corresponding to various plane sections of a right circular cone by cutting that cone in different ways.

Each point lying on these curves satisfies a special condition, which actually leads us towards the mathematical definition of conic sections.

If a point moves in plane in such a way that the ratio of its distance from a fixed point to its perpendicular distance from a fixed straight line, always remains constant, then the locus of that point I called a Conic Section.

The fixed point is called the focus and the fixed line is called directrix of the conic. The constant ratio is called the eccentricity and is denoted by e.

According to the value of there are three types o conic i.e. for e = 1, e <> 1 the corresponding conic is called parabola, ellipse and hyperbola respectively.

A conic section or conic is the locus of a point, which moves so that its distance from a fixed point is in a constant ratio to its distance from a fixed straight line, not passing through the fixed point.

The fixed point is called the focus.

• The fixed straight line is called the directrix.

• The constant ratio is called the eccentricity and is denoted by e.

• When the eccentricity is unity i.e. e = 1, the conic is called a parabola; when e <> 1, the conic is called a hyperbola.

• The straight line passing through the focus and perpendicular to the directrix is called the axis of the parabola.

• The point of intersection of a conic with its axis is called vertex.

• The chord passing through focus and perpendicular to axis is called latus rectum.

• Any chord of the parabola which is perpendicular to the axis is called double ordinate.

• The straight line perpendicular to axis of the parabola passing through vertex is called tangent at the vertex.


Axis of the conic:

The line through focus and perpendicular to the directrix is called the axis of the conic. The intersection point o conic with axis is known as the vertex of the conic.

Enquiry: How do we mathematically define a parabola and what are its various features?

The locus of the point, which moves such that its distance from a fixed point (i.e. focus) is always equal to its distance from a fixed straight line (i.e. directrix), is called parabola.

Equation of Parabola:

Let S be the focus, V be the vertex, ZM be the directrix and x-axis be the axis of parabola. We require therefore the locus of a point P, which moves so that its distance from S, is always equal to PM i.e. its perpendicular distance from ZM. After appropriate configuration let S = (a, 0)

We have ten SP2 = PM2

⇒ (x – a)2 + y2 = (a + x)2

⇒ y2 = 4ax This is the standard equation of a parabola.

PARABOLA -2-

There are four common forms of parabola according to their axis, with their vertex at origin (0, 0).

PARABOLA -3-

Let us understand some other features of a parabola.

(a) Focal Distance:

The distance of a point on the parabola from its focus is called the focal distance of the point Focal distance of P = SP = x + a.

(b) Focal Chord:

A chord of the parabola, which passes through its focus, is called Focal chord.

(c) Latus Rectum:

The chord through focus and perpendicular to the axis of the parabola is called the latus rectum.

The co-ordinates of the end point of the latus rectum are (a, 2a) and (a, –2a) and length of latus rectum = 4a.


For horizontal parabola

Let us consider origin (0, 0) as the vertex A of the parabola and two equidistant points S(a, 0) as focus and Z(–a, 0) a point on the directrix now let P(x, y) be the moving point. Draw SZ perpendicular from S on the directrix. Then SZ is the axis of the parabola. Now the middle point of SZ, that is A, will lie on the locus of P.

i.e. AS = AZ

The x-axis along AS, and the y-axis along the perpendicular to AS, as A, as in the figure. Now by definition PM = PS ⇒ MP2 = PS2

So, that, (a + x)2 = (x – a)2 + y2.

Hence, the equation of horizontal parabola is y2 = 4ax.


Similarly for the vertical parabola

Let us consider origin (0, 0) as the vertex A of the parabola and two equidistant points S(0, b) as focus and Z(0, –b) a point on the directrix now let P(x, y) be the moving point. Draw SZ perpendicular from S on the directrix. Then SZ is the axis of the parabola. Now the middle point of SZ, that is A, will lie on the locus of P i.e. AS = AZ.

The y-axis along AS, and the x-axis along the perpendicular to AS at A, as in the figure.




Now by definition PM = PS

⇒ MP2 = PS2

So that, (b + y)2 = (y – b)2 + x2.

Hence, the equation of vertical parabola is x2 = 4by.


Finding the end points of latus Rectum

For finding the end points of latus rectum LL’ of the parabola y2 = 4ax, we put x = a as latus rectum passes through focus (a, 0) therefore we have

y2 = 4a2

⇒ y = + 2a

Hence the end points are (a, 2a) and (a, – 2a).

Also LSL’ = 2a – (–2a) = 4a = length of double ordinate through the focus S.


Note:

Two parabolas are said to be equal when their latus recta are equal.

The important points & lines related to standard Parabola

Note:

1. The points and lines of two parabolas can be interchanged by transformations.

2. If a > 0 & a <> 0 & b <>

PARABOLA -4-

Parametric Form of a Parabola

Suppose that the equation of a tangent to the parabola y2 = 4ax. … (i)

is y = mx + c. … (ii)

The abscissa of the points of intersection of (i) and (ii) are given by the equation (mx + c)2 = 4ax. But the condition that the straight line (ii) should touch the parabola is that it should meet the parabola in coincident points hence discriminant should be zero

⇒ (mx – 2a)2 = m2c2 … (iii)

⇒ c = a/m.

Hence, y = mx + a/m is a tangent to the parabola y2 = 4ax, whatever be the value of m.

Equation (mx + c)2 = 4ax now becomes (mx – a/m)2 = 0.

⇒ x = a/m2 and y2 = 4ax

⇒ y = 2a/m.

Thus the point of contact of the tangent y = mx + a/m is (a/m2 ,2a/m).

Taking 1/m = t where t is a parameter, i.e., it varies from point to point. The parabola y2 = 4ax as a parametric form is given by the co-ordinate (at2, 2at) and we refer to it as point ‘t’.


Illustration:

Prove that the area of the triangle inscribed in the parabola y2 = 4ax is a2 (t1 – t2) (t2 – t3) (t3 – t1) where t1, t2 and t3 are the vertices.

Solution:

The three points on the parabola are (at12, 2at1), (at22, 2at2) and (at32, 2at3).

PARABOLA -5-

THE GENERAL EQUATION OF A PARABOLA

We shall now obtain the equation of a parabola when the focus is any point and the dircectrix is any line.

Let (h, k) be the focus S and lx + my + n = 0 the equation of the directrix ZM of a parabola. Let (x, y) be the coordinates of any point P on the parabola. Then the relation, PS = distance of P from ZM, gives

(x – h+) + (y – k)2 = (lx + my + n)2/(l2 + m2)

⇒ (mx – ly)2 + 2gx + 2fy + d = 0.

This is the general equation of a parabola. It is clear that second-degree terms in the equation of a parabola form a perfect square.

The converse is also true, i.e. if in an equation of the second degree, the second-degree terms from a perfect square then the equation represents a parabola, unless it represents two parallel straight lines.


Note:
The general equation of second degree i.e. ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 represents a parabola if Δ ≠ 0 and h2 = ab. (Δ = abc + 2fgh – af2 – bg2 – ch2).

Special case:

Let the vertex be (α, β) and the axis to be parallel to the x-axis. Then the equation of parabola is given by (y – β)2 = 4a (x – α) which is equivalent to x = Ay2 + By + C.

If three points are given we can find A, B and C.

Similarly, when the axis is parallel to the y-axis, the equation of the parabola is y = A’x2 + B’x + C’.


Illustration:

Find the equation of the parabola whose focus is (3, –4) and directrix
x – t + 5 = 0.

Solution:

Let P(x, y) be any point on the parabola. Then

√((x-3)2 (y+4) )=x-y+5/√(1+1)

⇒ (x – 3)2 + (y + 4)2 = (x-y+5)2/2

⇒ x2 + y2 + 2xy – 22x + 26y + 25 = 0.

⇒ (x + y)2 = 22x – 26y – 25.


Illustration:

Find the equation of the parabola having focus (–6, 6) and verte (–2, 2).

Solution:

Let S(–6, –6) be the focus and A(–2, 2) the vertex of the parabola. On SA take a point K (x1, y1) such that SA = AK. Draw KM perpendicular on SK. Then KM is the directrix of the parabola.

Since A bisects SK, ((-6+x1)/2,(-6+y1)/2) = (–2, 2)

⇒ – 6 + x1 = – 4, and – 6 + y1 = 4

Or (x1, y1) = (2, 10).

Hence the equation of the directrix KM is y – 10 = m (x + 2). … (1)

Also gradient of

SK = (10-(-6))/(2-(-6) )=16/8 = 2; ⇒ m = (-1)/2

So that equation (1) becomes y – 10 = –1/2 (x – 2)

or x + 2y – 22 = 0 is the directrix.

Next, let PM be a perpendicular on the directrix KM from any point

P(x, y) on the parabola.

Form SP = PM, the equation of the parabola is

√({(x+6)+(y+6)2 } )=(x+2y-22)/((12+22 ) )

or 5 = (x2 + y2 + 12x + 12y + 72) = (x + 2y – 22)2

or 4x2 + y2 – 4xy + 104x + 148 y – 124 = 0.

or (2x – y)2 + 104x + 148y – 124 = 0.


Illustration:

If the point (2, 3) is the locus and x = 2y + 6 is the directrix of a parabola, find

(i) the equation of the axis,

(ii) the co-ordinates of the vertex,

(iii) length of the latus rectum,

(iv) equation of the latus rectum.


Solution:

(i) We know that the axis of a parabola is the line through the focus

And perpendicular to the directrix.

The equation of any line passing through the focus (2, 3) is

y – 3 = m (x – 2) ⇒ mx – y = 3 – 2m

If the line be perpendicular to the directrix x – 2y = 6, we have,

m (1/2) = – 1 ⇒ m = – 2.

Hence the equation of the axis is y – 3 = – 2 (x – 2) ⇒ 2x + y = 7.

(ii) The co-ordinates of the point of intersection (say) A of the directrix x – 2y = 6 and the axis 2x + y = 7 are obtained by solving the two equations; thus they are (4, –1). Since the vertex is the middle point of A (4, –1) and the focus S(2, 3); the co-ordinates of the vertex are ((4+2)/2,(3-1)/2), i.e. (3, 1).

(iii) Since OS = √((3-2)2+(1-3)2 )=√5,

The length of the latus rectum = 4OS = 4√5.

(iv) Since the latus rectum is the line through the focus parallel to the directrix, its equation is x – 2y + c = 0, where c is given by 2 – 2.3 + c = 0, i.e. c = 4.

Please join the blog and comment ..... you can add questions based on any lessons (XI class )

PHYSICS HELPER

PHYSICS MODEL QUESTION PAPER 2009 - 2010

Q.1 What happens to coefficient of friction when weight of body is doubled?

Q.2 A body is traveling with a constant speed in on the circumference of a circle, of the quantities –
a) Linear velocity b) Linear Acceleration
c) Acceleration toward the centre and d) Centripetal force,
Which remains constant?

Q.3 which of the two, Kilowatt hour or electron volt is a bigger unit of energy and by what factor?

Q.4 Why is the tip of the nib of a pen slit?

Q.5 State Newton’s law of Cooling ?

Q.6 What is Reynolds’s Number?

Q.7 The length of a string tied to two rigid supports is 40 cm . What is the maximum wave length of the stationary wave produced on it ?

Q.8 Standing is not allowed in a double Decker bus . Why ?

Q.9 Two straight lines drawn on the same displacement time graph make angles. 30 º & 60 º with time axis respectively which line represents greater velocity? What is the ratio of the two velocities?

Q.10. Why fruits fall down from a tree, when its branches are shaken?

(OR)

In a tug of war, the team that pushes harder against the ground wins why?

Q.11 A light body and a heavy body have the same momentum. Which one will have greater kinetic energy ?

Q.12 Define the Torque. Give its unit and dimension.

Q.13. State the conditions necessary for a satellite to appear stationary?

Q.14 Derive the expression for work done during an adiabatic process

Q. 15 At what temperature is the rms velocity of hydrogen molecule equal to that of an oxygen
molecule at 47 º ?

Q.16 A transverse harmonic wave on a string is described by Y (x , t) = 3 Sin (36 t + 0.018 x + Π/4) Where x and y are in cm and t in sec. The positive direction of x is from left to right.
a) Is this a travelling or a stationary wave? If it is travelling, what are the speed and direction of its
propagation?
b) What are its amplitude and frequency?


Q.17 Write Newton’s Formula for the speed of sound in air. What correction was made by
Laplace in this formula?

Q.18 Apply first law of thermodynamics to
1) An Isochoric process 2) An Isothermal process

Q.19. Assuming that the mass M of the largest stone that can be moved by a flowing river depends
upon ‘v’ the velocity, ‘ρ’ the density of water and on ‘g’ the acceleration due to gravity.
Using dimensions show that M varies with the sixth power of the velocity of flow.


Q.20. Two balls are thrown simultaneously, A vertically upwards with a speed of 20 m/s from the ground and B vertically downwards from a height of 40 m/s with the same speed and along the same line of action. At what points do the balls collide? (g = 9.8 m/s2 )


Q.21. Show that Newton’s second law of motion is the real law of motion.
(OR)
State the principle of conservation of linear momentum. Explain why the gun recoils when a bullet is fired from it .


Q.22 Derive a relation for the optimum velocity of negotiating a curve by a body in a banked curve.


Q.23 What is meant by elastic collision? Show that in case of one dimensional elastic collision of two bodies, the relative velocity of separation after the collision is equal to the relative velocity of approach before the collision.


Q.24 State the laws of moments of Inertia. The M. I. of a solid sphere about tangent is (5/3)MR2 Where M is mass and R is radius of the sphere. Find the M.I. of the sphere about its diameter .


Q.25 Define acceleration due to gravity show that the value of ‘g’ decreases with altitude?


Q.26. A liquid drop of diameter 4mm breaks into 1000 droplets of equal size. Calculate the
resultant change in energy.
(The surface tension of the liquid is 0.07 N/m)


Q.27. Show that the pressure exerted by a gas is two – third of the average kinetic energy per unit volume of the
gas molecules.


Q.28. (a) Show that for two complementary angles of projection of a projectile thrown with the same velocity,
the horizontal ranges are equal.
(b) For what angles of projection of a projectile is the range maximum.
(c) For what angle of projection of a projectile, are the horizontal range and maximum height attained by the projectile equal.

OR

Deduce expressions for (a) Time of flight (b) Horizontal range and (c) Maximum height reached by a projectile, in terms of its initial velocity and angle of projection.


Q.29 State and prove Bernoulli’s theorem. Give two applications of it?
(OR)
Describe stress strain relationship for a loaded steel wire and hence explain the terms elastic limit, yield point, tensile strength?


Q.30 Derive expressions for the kinetic and potential energies of a harmonic oscillator. Hence show that total energy is conserved in SHM.

OR

What is SHM? Show that the acceleration of a particle in SHM is proportional to its displacement. Also derive expression for the time period.