PHYSICS
1. Obtain the Dimensional Formulae of ω and k from the equationY = A Sin ( ω t – k x )
2. A Particle locates at x = 0 at time t = 0 starts moving along the positive x – axis with velocity v that varies as
v = x 1 / 2 . How do the displacement , velocity and acceleration of particle vary with time.
3. A small drop of liquid oscillate under the effect of Surface Tension. Assuming the Time Period T depends
upon the force of Surface Tension T , Density d and radius r . Obtain an expression for T ?
4. A stone thrown up is caught by the thrower after 6 seconds. How high will it go and where was it 4 seconds
after start ?
5. A stone is dropped into the Well of depth 67.7 m and sound of splash is heard 3.91 s Later. Find velocity of
sound ?
6. A bouncing ball reaches a maximum height of 10 m. How much time does each up and down cycle take ?
7. A Bullet fired into wall loses half of its velocity after penetrating 3 m.How much further will it penetrate ?
8. A Particle moves along a straight line such that is displacement is given by
S = t 3 – 6 t 2 + 3 t + 4.
Find the velocity when the acceleration is zero ?
9.
Which of the following Forces have the greater inclination with the X axis
(i) 3i+2j
( ii ) 5 i + 3 j
( iii ) 10 i + 12 j
10. A body starts from rest and accelerate uniformly for 30 seconds to the speed of 72 Km/hr. it then moves with
the uniform velocity and finally comes to rest in 50 meters with constant retardation. If Total distance
travelled is 950 m , then Find the acceleration , retardation and Total time taken ?
11. A Stone is dropped from the top of the cliff and is found to travel 14.7 m in the last second to last before it
reaches the ground . Find the height of the cliff ?
12. A bullet fired into a target loses 1 / x of its velocity after travelling a distance S meter into the Target. Show
that it covers further a distance S ( x – 1 )2 / ( 2 x – 1 ) before coming to rest ?
13. A Particle is subjected to an acceleration a = α t + β t2 where α and β are constants. The position and velocity
of the Particles at t = 0 are x0 and v0 respectively. What are the expressions for position x and velocity v of
the Particle after time t.
14. If body travels half its total path in the last second of its fall from rest ,Calculate the time and height of the
fall?
15. The relation between time t and distance x is t = α x2 + β x where α and β are constants Show that
retardation is 2 α v3 , Where v is the instantanuoes velocity.
16. A point moves with uniform acceleration and v1 and v2 and v3 denotes the average velocities in the three
successive intervals of time t1 , t2 and t3. Find the Ratio of ( v1 – v2 ) and ( v2 – v3 ).
17. A bullet loses 1/20 of its velocity in passing through a plank. What is the least number of planks required to
stop the bullet ?
18. Two Forces P and Q acting at a point at an angle θ have the Resultant ( 2n + 1 ) P2 + Q2 and when they act
an angleof 900 – θ, then Resultant is ( 2 n – 1 ) P2 + Q2 . Show that tan θ = ( n – 1 ) / ( n + 1 )
19. A 100 Kg wt. Is suspended from the center of the rope. In equilibrium the two halves of the rope subtend an
angle of 1200 with each other. Find the Tension in the rope ?
20. By the method of dimensions, test the accuracy of the equation : δ 
mg l 3
where δ is the depression
4b d 3 Y
produced in the middle of a bar of length l, breadth b and depth d, when it is loaded in the middle with mass
m. Y is the Young’s modulus of the material of the bar.
21. Find the dimension of a/b in the equation : F  a x  bt 2 , where F is force, x is distance and t is time.
22. Find the dimensions of a × b in the relation : P 
b  x2
; where P is power, x is distance and t is time.
at
23. The Vander Wall’s equation for a gas is
a 

 P  2  (V  b)  RT
V 

Determine the dimensions of a and b. Hence write the Si units of a and b.
24. When white light travels through glass, the refractive index of glass (µ = velocity of light in air/velocity of
light in glass) is found to vary with wavelength as μ  A 
B
. Using the principle of homogeneity of
2
dimensions, find the SI units in which the constants A and B must be expressed
25. What will be the Dimensional Formula of Mass if we choose Length L , time T and Force F as a
Fundamental Quantities ?
26. If Speed of Light c , Planck’s Constant h and Gravitational Constant G are choosen as Fundamental
Quantities , then Find out Dimension of Mass and Time ?
27. Convert an Atmospheric Pressure of 76 cm of Mercury Coulomn into MKS system . Given that Density of
Mercury is 13.6 gm / cm 3 , Accelaration due to Gravity is 980 cm / s 2 ?
28. If force (F ) , acceleration ( A ) and time ( T ) be taken as fundamental physical quantity , then find the
dimension of length in terms of fundamental quantity ?
29. A train starts from rest and moves with constant acceleration of 2 ms 2 for half a minute. The breaks are then
applied and the train comes to rest in one minute. Find (i ) the maximum speed attained by the train and (ii )
the total distance moved by the train and (iii ) the positions ( s ) of the train at half the maximum speed.
30. A car moving along a straight highway with a speed of 72 kmh 1 is brought to a stop within a distance of 100
m. what is the retardation of the car and how long does it take for the car to stop?
CHEMISTRY
31. What is generally used for sterilization of water to make it fit for drinking purposes?
32. What is the number of significant figures in π and 1.051×104?
33. Iron and oxygen combine to form three oxides, FeO, Fe2O3, and Fe3O4. Which law does it prove? Also
state the law.
34. If the speed of light is 3.0×108 m/s, calculate the distance covered by light in 2.00 ns.
35. What is the difference between atomic mass and mass number?
36. What do you mean by saying that energy of the electron is quantized?
37. What happens to the position and momentum of an electron if the photon of a short wavelength hits the
electron?
38. Write IUPAC names of the elements having atomic number 109 and 111. Also write their symbols.
39. What is the basic difference between electron gain enthalpy and electronegativity?
40. Arrange the following in increasing order of their ionic sizes: N-3, Na+, F-, o-2, Mg+2
41. 4 g carbon were heated with 8g of sulphur. How much carbon disulphide is formed when
the reaction is complete. What will the percentage purity?
42. Chlorine is prepared in the lab by treating manganese dioxide with aqueous HCl according to the
equation:MnO2 +4HCl →2H2O +MnCl2 + Cl2 How many grams of HCl react with 5.0 g 0f manganese
dioxide (atomic mass of Mn=55u)
43. a) What is the total number of orbitals associated with the principal quantum number n=3?
b) How many nodes are present in 3d. represent diagrammatically.
44. State Hund’s rule of maximum multiplicity. How is it used for the distribution of electrons in nitrogen
and fluorine.
45. State de-Broglie equation. How would the wavelength of a moving object vary with mass?
46. How are cathode rays originated?
47. Why cations are smaller and anions are larger in radii than parent atom?
48. What are the factors affecting ionization enthalpy?
49. Explain why the electron gain enthalpy of fluorine is less negative than that of chlorine.
50. Justify the presence of 18 elements in 4th period.
51. Butyric acid contains only C, H, and O. A 4.24mg sample of butyric acid is completely burned. It gives
8.45 mg of CO2 and 3.46 mg of H2O. The molecular mass of butyric acid was determined by experiment
to be 88 amu. What is molecular formula?
52. Difference between a) orbit and orbital b) emission and absorption spectrum.
53. How much energy is required to ionise a hydrogen atom if the electron occupies n= 5 orbit? Compare
your answer with the ionization energy of hydrogen atom ( energy required to remove the electron from
n=1)
54. Calculate wave number of the longest wavelength transition in lyman series of hydrogen.
55. What transition in H spectrum would have the same wavelength as balmer transition n=4 to n=2 of He+
spectrum?
56. Arrange the elements N, P, O, and S in order ofa) Increasing first ionisation enthalpy b) in the non metallic character.Give reason.
57. What were the limitation and achievements of Mendeleev periodic table?
58. Define the term diagonal relationship and periodicity. Also give their causes.
59. First member of each group of representative elemnts shows anomalous behaviour. Illustrate with two
examples.
60. Write various characteristics of p-block elements.
Biology
Q61-what is the principle underlying the use of cyanobacteria in agricultural fields for crop improvement? (1)
Q62-Are chemosynthetic bacteria-autotrophic or heterotrophic ?
(1)
Q63-A virus is kept at the border-line of living and non-living. What are the characteristics of virus that are
similar to non-living objects?
(1)
Q64-Diatoms are also called as “pearls of ocean”.Why?
(1)
Q65-What observable features in Trypanosoma would make you classify it under kingdom Protista?
(1)
Q66-Food is stored as Floridean starch in Rhodophyceae. Mannitol is the reserve food material of which group
of algae?
(1)
Q67-Most algal genera show haplontic life sytle. Name an alga which is (a)Haplodiplontic (b)Diplontic.
(1)
Q68-Name the male and female sex organs in bryophytes.
(1)
Q69-In which plant will you look for mycorrhiza and coralloid roots?
(1)
Q70-Name the phylum in which adults show radial symmetry and larva shows bilateral symmetry.
(1)
Q71- Differentiate between a diploblastic and a triploblastic animal.
(2)
Q72-Which group of chordates possess sucking and circular mouth without jaws?
(2)
Q73-Endoparasites are found inside the host body. Mention the special structures they have which enable them
to survive in these conditions?
(2)
Q74-Write two characteristic features of chondrichthyes.
(2)
Q75-Mention two similarities between aves and mammals.
(2)
Q76-Name an animal having canal system and spicules and also name an animal with cnidoblasts.
(2)
Q77- What is metagenesis? Give an example which shows this process.
(2)
Q78-Why are bryophytes called the amphibians of the plant kingdom?
(2)
Q79-The common name of pea is simpler than its scientific name but why it is not in the common practice
worldwide?
(2)
Q80-There is a myth that immediately after heavy rains in forest mushrooms appear in large number and form
fairy-rings. Can you explain this process in biological terms?
(2)
Q81-Neurospora-a fungus has been used as a biological tool to understand plant genetics.What makes it so
special?
(3)
Q82-Brinjal and potato belong to the same genus Solanum but to too different species.Justify the statement. (3)
Q83-Fungi are cosmopolitan, write its role in your daily life.
(3)
Q84-Coment on the lifecycle and nature of a fern prothallus.
(3)
Q85-How are the male and female gametophytes of pteridophytes and gymnosperms different from each
other?
(3)
Q86-Give three major differences between chordates and non-chordates and draw a schematic sketch of
chordates showing those features.
(3)
Q87-What is the relationship between germinal layers and the formation of body cavity in case of coelomates,
acoelomates and pseudocoelomates?
(3)
Q88-Comment upon the habitat and external features of animals belonging to class, amphibia and reptilia. (3)
Q89-Mammals are most adapted among the vertebrates. Elaborate.
(3)
Q90-Draw a flow chart of five kingdom system of classification given by Whittker.
(3)
Note-*Draw diagrams of specimens and slides given in the practical file.
MATHEMATICS
General Instructions:

Submit your work in the separate notebook.

Present your work neatly.

Holidays home weightage will be counted.
Q1. Out of 100 students : 15 passed in English, 12 passed in Mathematics , 8 in Science 6 in English and
Mathematics , 7 in Mathematics and Science; 4 in English and Science ; 4 in all the three . Find how many
passed
(i)
(ii)
(iii)
(iv)
in English and Mathematics but not in Science
in Mathematics and Science but not in English
in Mathematics only
in more than one subject only
Q.2 In a town of 10,000 families it was found that 40% families buy newspaper A, 20% families buy newspaper
B, 10% families buy newspaper C, 5% families buy A and B, 3% buy B and C and 4% buy A and C. if 2%
families buy all the three newspaper. Find
(a) The newspaper of families which buy newspaper A only.
(b) The number of families which buy none of A, B and C
Q.3 Let A, B and C be sets. Then show that A  B  C    A  B   A  C  .
Q4. From 50 students taking examinations in Mathematics, Physics and Chemistry, each of the student has
passed in at least one of the subject, 37 passed Mathematics, 24 Physics and 43 Chemistry. At most 19 passed
Mathematics and Physics, at most 29 Mathematics and Chemistry and at most 20 Physics and Chemistry. What
is the largest possible number that could have passed all three examinations?
Q5. Fill in the blanks in each of the following:
1. The set {x  R : 1 ≤ x < 2} can be written as ______________.
2. When A = φ, then number of elements in P(A) is ______________.
3. If A and B are finite sets such that A  B, then n (A U B) = ______________.
4. If A and B are any two sets, then A – B is equal to ______________.
5. Power set of the set A = {1, 2} is ______________.
6. Given the sets A = {1, 3, 5}. B = {2, 4, 6} and C = {0, 2, 4, 6, 8}. Then the universal set of all the three sets
A, B and C can be ______________.
7. If U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {1, 2, 3, 5}, B = {2, 4, 6, 7} and C = {2, 3, 4, 8}. Then
(i) (B U C)′ is ______________. (ii)(C – A)′ is ______________.
8. For all sets A and B, A – (A ∩ B) is equal to ______________.
Q6. Let A = {1, 2, 3, 4} and B = {5, 7, 9}. Determine
(i) A × B
(ii) B × A (iii) Is A × B = B × A ? (iv) Is n (A × B) = n (B × A) ?
Q7. Find x and y if: (i) (4x + 3, y) = (3x + 5, – 2) (ii) (x – y, x + y) = (6, 10).
Q8. If A = {2, 4, 6, 9} and B = {4, 6, 18, 27, 54}, a  A, b  B, find the set of ordered pairs such that ‘a’
factor of ‘b’ and a< b.
6
Q9. Find the domain and range of the relation R given by R = {(x, y) : y =x + ; where x, y  N and x < 6}.
x
Q10. State True or False for the following statements:
(i) The ordered pair (5, 2) belongs to the relation R = {(x, y) : y = x – 5, x, y  Z}
(ii) If P = {1, 2}, then P × P × P = {(1, 1, 1), (2, 2, 2), (1, 2, 2), (2, 1, 1)}
(iii). If A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6}, then (A × B) U (A × C) = {(1, 3), (1, 4), (1, 5), (1, 6),
(2, 3), (2, 4), (2, 5), (2, 6), (3, 3), (3, 4), (3, 5), (3, 6)}.
1
14

(iv). If (x – 2, y + 5) =   2,  are two equal ordered pairs, then x = 4, y = 
3
3

(v). If A × B = {(a, x), (a, y), (b, x), (b, y)}, then A = {a, b}, B = {x, y}.
Q11. Prove the following by using the principle of mathematical induction for all n  N:
(i) 3 2n – 1 is divisible by 8, for all natural numbers n.
(ii) n3+ 7n + 3 is divisible by 3, for all natural numbers n.
(iii) For any natural number n, xn – yn is divisible by x – y, where x and y are any integers with x ≠ y.
(v) (1 + x)n ≥ (1 + nx).
Q.12 Solve the following system of inequations graphically.
2x + y -3  0
x – 2y + 1  0
x0
y  0.
Q13. Solve the following system of inequations graphically.
2x + y  24
x + y  11
2x + 5y  40
x0
y  0.
Q14.
Solve the graphically the following system of inequations.
x+ 2y  3
3x + 4y  12
x  0.
y  1.
Q15. (i) Prove : Tan3  - Tan2  - Tan  = Tan  Tan2  Tan3 
(ii) Tan500 =Tan400 + 2Tan100
(iii) Prove: 2Tan 700 = Tan800 – Tan100
(iv) Cotx Cot2x – Cot2x.Cot3x – Cot3x.Cotx = 1
Q16Find the value of
 19 
(i) Sin 

 6 
 17 
(ii) Cos 

 4 
15
4
(iv) Tan
13
12
9
3
5
 cos
 cos
0
13
13
13
13
1
Q18 .Prove cos200 cos400 cos600 cos800 =
16
3
Q19. Prove sin200 sin400 sin600 sin800 =
16
1
Q20. Prove cos40o cos800 cos1600 = 8
3
Q21. Sin100 Sin500 Sin600 Sin700 =
16

9
5
Q22 Prove cos 2 cos  cos 3 cos
 sin 5 sin
2
2
2


3
Q23Prove cos2A + cos2(A + ) + cos2(A  ) =
2
3
3
x
x
x
Q24 Find sin , cos , tan in each following
2
2
2
4
1
(i) Tanx =  , x in quadrant II
(ii) cosx =  , x in quadrant III
3
3
Q25Solve the following the equations:
i. Sin + Sin3x + Sin5x = 0
ii. Cos  + Cos3  - 2Cos2  = 0
Q17. Prove 2cos

(iii) Cot
cos
Note: Write and Learn all the trigonometric formulae .