Celebrate An Environment Safe Diwali

No Explosives - No Flames & Fire-Crackers , Only Diya’s

Let’s Fill Our Home With Prayers & Lights.

Let Us Have A Pollution Free Diwali...

* Diwali Vacation Assignment *

Ab Ki Diwali… Bina Pradushan Wali….

Diwali which is the contraction of the word Deepawali is known as the “Festival of Light”. Today

we are at a stage when a section of our society is all set to change the meaning of Deepawali, i.e. to transform

Diwali from being the “Festival of Light” into “Festival of Bombs”.

Every year when Diwali comes environmentalists, medical experts and some social activists raise

their voice and warn us of the ill effects of firecrackers, but majority of the people just ignore these warnings

and go around bursting crackers!

It’s time for us to make a difference; it’s time for all of us to unite and shun firecrackers. It’s time

for us to show “We Care”! Care for our environment, our elderly citizens and children’s, our unwell fellow-

humans, our pets, the numerous poor-people who can’t afford a onetime meal and more precisely for our

own health and our future generations. Let’s all pledge to celebrate “Green Diwali”.

It’s time that we completely stop this Fire Cracker menace….! Yes, you read it right Completely

stop.. No ‘Fuljharis’ or Fountain’ or ‘Charkhis’ also as they cause the maximum air pollution moreover

every year several kids end up in burning their hand due to the misuse of these crackers. The only cracker

that can be advocated for is the “Rocket” as it beautifies the Diwali Skyline.

If you hate the word-“Terrorists” and “Bombs” and the two very well resemble each other’ then why

do you start loving the “Bombs” during Diwali? We all know it’s so difficult to walk freely or drive a car

or ride a bike peacefully on Diwali night as there are kids, adults and everyone bursting crackers on the

Roads and the fear remains that the bombs can blast under your car or bike; Yes, this is a sort of terrorism

for the people who are driving! It’s their life at stake, and practically numerous such accidents are reported

every year during Diwali. If you hate Terrorism and their attacks then Stop Bombing Diwali from now!

The noisy crackers sledgehammer our ear drums which may result in temporary or complete hearing

loss or even injure the nervous system! It’s a terrible time for aged people, babies and patients because the

noise affects them the most.

Diwali is the only festival that scares the shit out of the four legged inhabitants; you might have seen

your Tuffy-Tommy-Jimmy running under the bed, chair or sofa for sure! It’s an extreme torture for them

because of their high sensitive hearing ability, he deafening sound of crackers hurt their little brains and

they stop eating-drinking and totally freak out for few days.

The celebration of Diwali can be done peacefully by lighting our houses with “Deeps” or “Dias”.

Instead of literally Burning Money by bursting Firecrackers; it’s better to spend this money for noble causes.

Let’s redefine Diwali celebration and celebrate a cracker-free Diwali, after all any celebration can’t be at

the cost of the environment and general health!

General awareness among the people about the ill effects of firecrackers is of utmost importance and

simultaneously All Fire-Crackers should be Banned and this ban should be implemented stickly. We the

youth, have the power to bring the changes the Change for a Better Tomorrow.

So, On this Diwali Say “No” to Fire Crackers and Say “Yes” to Life! Be responsible citizen.

Wish you all a very Happy, Prosperous & “Green Diwali”.

Diwali Vacation Assignment11th Standard CBSE

Chemistry

Arpita's Science Academy

Date : 02-Nov-18

Reg.No. :            

  How many amny significant figures present in the following? "126000" 3

  45.4 L of dinitrogen reacted with 22.7 L of dioxygen and 45.4 L nitrous oxide wasformed. The reaction is given below                 2  N (g) + O (g)    2 N O (g) Which law is being obeyed in this experiment? Write the statement of the law.

2 2 ⟶ 2

3

  Calculate the amount of carbon dioxide that could be produced when 1 mole ofcarbon is burnt in air.

3

  For the reaction,  ,4.80 g of oxygen is used to burn 0.150mole of iron. What mass of Fe O  will be produced?What mass of Fe will be le� over atthe end of the reaction? What mass of O will be over at the end of the reaction?

Fe+ 3 ⟶ 2FO2 e2O3

2 3

2

3

  According to de-Broglie, matter should exhibit dual behaviour, that is both particleand wave like properties.However, a cricket ball of mass 100g does not move like awave when it is thrown by a bowler at a speed of 100km/h.Calculate the wavelength ofthe ball and explain why it does not show wave nature?

3

  Explain, giving reasons which of the following sets of quantum are not possible? n = 0, l = 0, = 0, = ±1/2m1 ms

3

  An ion with mass number 56 contains 3 unit of positive charge and 30.4% moreneutrons than the electrons. Assign the symbol to this ion.

3

  In a hydrogen atom, the energy of an electron in first Bohr's orbit is 13.12 x10  mol . What is the energy required for its excitation to Bohr's second orbit?5 -1

3

  Assign the position of the element having outer electronic configuration. (i) ns  np  for n=3 (ii) (n-1) d  ns  for n=4 and (iii) (n-2) f  (n-1) d  ns for n=6, in the periodic table.

2 4

2 2

7 1 2 

3

  Arrange the elements N, P, O, and S in the order of Increasing non-metalliccharacter. Give the reason for the arrangement assigned.

3

  Define electronegativity. How does it di�er from electron gain enthalpy? 3

  The dipole moment of molecule AB is 0.54D and the bond distance is 1.41 

. Calculate the fractional change    on A and B atom in AB molecule (electroniccharge, e = 4.8 x 10 esu.Ao

δ-10

3

1)2)

3)

4)

5)

6)

7)

8)

9)

10)

11)12)

  Predict the hybridisation of each carbon in the molecule of organic compoundgiven below. Also indicate the total number of  -bonds in this molecule. σ and π

3

  Consider structure I to VII and answer the following questions (i) and (ii). I.    II.   

III.  

IV.  

V.  VI.   VII.  

Identify the pairs of compounds that represent position isomerism.

− − − −OHCH3 CH2 CH2 CH2

− −CH −CH3 CH2 CH3

|

OHCH3

|

−C −CH3 CH3

|

OH−CH −C −OHCH3 H2

|

CH3

− −O− −CH2 CH2 CH2 CH3

−O− − −CH2 CH2 CH2 CH3

−O−CH −CH3 CH3

|

CH3

3

  Arrange the following  in order of decreasing

stability.C , , (C ,C = CHH3CH

+2 C6H5CH

+2 H3)3C

+ H2 CH+2

3

  An alkane has a molecule mass of 72. Give all the possible structural isomersalong with their IUPAC names.

3

13)

14)

15)

16)

  Write IUPAC names of the following compounds: (a) CH CH = C(CH ) (b) CH = CH-C C-CH (c)

 

(d) 

(e) 

(g) 

3 3 2

2 ≡ 3

C ( ) (CH3 CH2 CH

−CH(CCH2 H3

|

)2

H2)3CH3

−CH = CH − −CH = CH − − −CH =CH3 CH2 CH

C2H5

|CH2 CH2

3

  An alkene 'A' on ozonolysis gives a mixture of ethanal and pentan-3-one. Write thestructure and IUPAC name of 'A'.

3

  How will you convert ethanoic acid into ethene? 3

  A measured temperature on Fahrenheit scale is 200  F. What will this reading beon Celsius scale ?

0 3

  How many should significant figures should be present in the answer calculation?  (i)   0.02856×298.15×0.112

0.5785

3

  In a reaction,  identify the limiting reagent if any in the followingreaction mixtures. (iii) 100 atoms of A+100 molecules of B

A+ →B2 AB2 3

  Calculate wave number and  frequency of yellow radiation having wavelength

5800Ao

3

  A golf ball has a mass of 40g and a speed of 25 m/s. If the speed can be measuredwithin accuracy of 2%, calculate the uncertainty in the position.

3

  If uncertainties in the measurement of position and momentum of an electron arefound to be equal in magnitude, what is the uncertainty in the measurement of velocityof the electron? Comment on the result obtained?

3

  Iron pieces are attracted towards a magnet but zinc pieces are not. Why? 3

  How would you justify the presence of 18 elements in the 5th period of theperiodic table?

3

17)

18)

19)20)

21)

22)

23)

24)

25)

26)27)

  The first   and the second  ionization enthalpies (in kJ mol ) andthe   electron gain enthalpy (in kJ mol ) of a few elements are given belowElementsI 520 7300 -60II 419 3051 -48III 1681 3374 -328IV 1008 1846 -295V 2372 5251 +48VI 738 1451 -40Which of the above elements is likely to be  (i)   the least reactive element? (ii)  the most reactive metal? (iii)  the most reactive non-metal? (iv)  the least reactive non-metal? (v)   the metal which can form a stable binary halide of the formula MX (X = halogen)? (vi)  the metal which can form a predominantly stable covalent halide of the formulaMX (X = halogen)?

( )△iH1 ( )△iH2-1

( H)△eg-1

△iH1△iH2 H△eg

2

3

  On the basis of VSEPR theory, predict the shapes of the following NH−

2

3

  A Compound of analysis gave the following percentage composition Na=14.31%,S=9.97%, H=6.22% and O=69.50%. Calculate the molecular formula of the compound assuming that all the hydrogen inthe compound is present in combination with oxygen as the water of crystallization.The molecular mass of the compound is 322.

3

  (i) A sample of drinking water was found to be severely contaminated withchloroform CHCL3 which is Carcinogenic in nature. The level of contamination was15ppm (by mass). (b) Determine the molarity of chloroform in the water in which the mole fraction ofethanol is 0.040

3

  Calcium carbonate reacts with aqueous HCI to give CaCL  and CO  according tothe reaction given below CaCO (s) + 2HCI(aq)  CaCl (aq) + CO (g) + H O(l) What mass of CaCl  will be formed when 250 mL of 0.76 M HCI reacts with 1000 g ofCaCO  ? Name the limiting reagent. Calculate the number of moles of CaCL  formed inthe reaction.

2 2

3 ⟶ 2 2 2

2

3 2

3

  A photon of wavelength 4 X 10 m strikes on the metal surface, the work functionof the metal being 2.13 eV. Calculate The energy of the photon (eV).

-7 3

  Why was the change in the Bohr model of atom is required, due to whichimportant development(s), concept of movement of an electron in an orbit wasreplaced by the concept of probability of finding an electron in an orbital?What is thename given to the changed model of an atom?

3

  A neutral atom of an element has 2K, 8L and 5M electrons. Find out the following. Atomic number of the element

3

28)

29)

30)

31)

32)

33)

34)

35)

  Write the electronic configurations of the following ions. a) H  b) Na  c) O  d) F- + 2- -

3

  Which atoms are indicated by the following configuration? a) [He]2s  b) [Ne] 3s 3p  c) [Ar]4s 3d1 2 3 2 1

3

  In p-block elements form acidic, basic and amphoteric oxides. Explain eachproperty by giving two examples and also write the reactions of these oxides withwater

3

  Define electron gain enthalpy. What are its units? Discuss the factors whichinfluence the electron gain enthalpy.

3

  (a) How does atomic radius vary in group in the periodic table? (b) Explain (i) Radius of cation is less than that of the atom. (ii) Radius of anion is more than that of the atom. (iii) In iso-electronic ion, the ionic radii decreases with increase in atomic number

3

  Discuss the shape of the following molecules using VSEPR model , , , , S,BeCl2 BCl3 SiCl4 AsF5 H2 PH3

3

  What is the type of hybridisation of carbon atoms marked with star? 3

  Explain the terms inductive and electromeric e�ects. Which electron displacemente�ect explain the following correct orders of acidity of the carboxylic acids? (a) Cl CCOOH > Cl CHCOOH > ClCH COOH (b) CH CH COOH > (CH ) CHCOOH > (CH ) C.COOH

3 2 2

3 2 3 2 3 3

3

  Explain hyperconjugation e�ect. How does hyperconjugation e�ect explain thestability of alkenes?

3

  Arrange the following set of compounds in order of their decreasing relativereactivity with an electrophile, E+. (i) Chlorobenzene, 2, 4-dinitrochlorobenzene, p-nitrochlorobenzene (ii)Toluene, 

Also explain ur answer.

p− C − − ,H3 C6H4 NO2

p− N − −O2 C6H4 NO2

3

36)

37)

38)

39)

40)

41)

42)

43)

44)

45)

Wish You All Happy and Prosperous Diwali..Happy Dipawali

Arpita's Science Academy

Wanowrie / B.T Kawade / Hadapsar 9970787007        www.arpitasacademy.com

*****************************************

  (a) What type of isomerism is shown by methoxymethane and ethanol? (b) How will you bring out the following conversions. (i) Acetylene to ethane (ii) Benzene to Toluene (iii) Ethanol to ethene?

3

  (a) Why are alkenes called unsaturated hydrocarbons? (b) How will you test the presence of double bond in an alkene? (c) Name the products formed when propene is subjected to ozonolysis.

3

46)

47)

Diwali Break Practice Worksheet11th Standard CBSE

Mathematics

Arpita's Science Academy

Date : 02-Nov-18

Reg.No. :            

  If A = {3, 5, 7,9, 11}, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17};find: (l) A  B (ii) B C (iii) A C D (iv) A C (v) B D (vi)A (B  C) (vii) A  D (viil) A (B D) (ix) (A  B) (B C) (x) (A  D) (B C)

∩

∩

∩ ∩

∩

∩

∩ ∪

∩

∩ ∪

∩ ∩ ∪

∪ ∩ ∪

4

  If A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12, 16,20}, C= {2, 4, 6, 8,10,12,14, 16}, D = {5,10, 15, 20}, find: (i) A - B (ii) A - C (iii) A - D (iv) B - A (v) C - A (vi) D - A (vii) B - C (viii) B - D (ix) C - B (x) D-B (xi) C-D (xii) D - C

4

  In a survey of 60 people, it was found that 25 people read newspaper H, 26 readnewspaper T, 26 read newspaper I, 9 read both H and I, 11 read both H and T, 8 readboth T and I, 3 read all three newspapers. Find: (i) the number of people who read at least one of the newspapers. (ii) the number of people who read exactly one newspaper.

4

1)

2)

3)

  In a survey of 25 students, it was found that 15 had taken mathematics, 12 hadtaken physics and 11 had taken chemistry. 5 had taken mathematics and chemistry, 9had taken mathematics and physics, 4 had taken physics and chemistry and 3 hadtaken all the three subjects. Find the number of students who had (i) only chemistry (ii) only physics (iii) only mathematics (iv) physics and chemistry but not mathematics (v) mathematics and physics but not chemistry (vi) at least one of the three subjects. (vii) only one of the subjects. (viii) none of the subjects.

4

  Find the domain of the function f(x) = +2x+1x2

−8x+12x24

  = cot3xcos 4x+cos 3x+cos 2xsin 4x+sin3 x+sin 2x

4

  Find the value of [1 + cos ][1 + cos ][1 + cos ][1 + cos ]π8

3π8

5π8

7π8

4

  Find the general solution for each of the following equations cos 3x + cos x - cos 2x = 0

4

  Find the general solution for each of the following equations: sec 2x = 1- tan 2x2

4

  Find the general solution for each of the following equations: sin x + sin 3x + sin 5x = 0

4

  Prove that 2cos cos +cos + cos =0π

139π13

3π13

5π13

4

  sin x + sin 3x + sin 5x + sin 7x = 4 cos x cos2x sin 4x 4

  Find sin  in each of the following: sin x = ,x in quadrant II.

,cos and tanx

2x

2x

214

4

  Find the sin 18° 4

  Prove the following by using the principle of mathematical induction for all n ∊N:1.2.3+2.3.4+...+n(n+1)(n+2)=  n(n+1)(n+2)(n+3)

4

4

  Prove the following by using the principle of mathematical induction for all n ∊ N:

1.3+3.5+5.7+....+(2n-1)(2n+1) =  n(4 +6n−1)n2

3

4

  Prove the following by using the principle of mathematical induction for all n ∊ N: ++ + +.. .1

1.2.31

2.3.41

3.4.5=1

n(n+1)(n+2)

n(n+3)

4(n+1)(n+2)

4

  Prove the following by using the principle of mathematical induction for all n ∊ N:n(n + 1) (n + 5) is a multiple of 3

4

  Prove the following by using the principle of mathematical induction for all n ∊ N:3 -8n-92n+1

4

  If x-iy =  prove that (x +y ) = a−ib

c−id

− −−−√ 2 2 2 +a2 b2

+c2 d24

  If a+i=  ,prove that a +b =( +ix2 )2

+12x22 2 ( +ix2 )2

( +12x2 )2

4

  Find the square root of -8i. 4

4)

5)

6)

7)

8)

9)

10)

11)

12)13)

14)15)

16)

17)

18)

19)

20)

21)

22)

  Find the square root of  .3 − 4 i7√ 4

  If α and β are di�erent complex numbers with =1then find  .Here α and

β are di�erent complex numbers such that |β|=1

|β| ∣∣β−α

1− βα∣∣ 4

  If a+ib =  where x is real,prove that  a +b =1 and x+i

x−i2 2 =b

a2x−1x2

4

  Solve the inequalities graphically 3x+2y 150, x+4y 80, x 15, y 0,x 0≤ ≤ ≤ ≥ ≥ 4

  How many litres of water will have to be added to 1125 litres of the 45% solutionof acid so that the resulting mixture will contain more than 25% but less than 30% acidcontent?

4

  In how many ways can the letters of the word PERMUTATIONS be arranged if the (i) words start with P and end with S (ii) vowels are all together (iii) there are always 4 letters between P and S

4

  How many numbers are there between 100 and 1000 such that at least one of theirdigits is 7?

4

  Expand using binomial theorem  0.,x ≠[1 + ( − )]x

22x

44

  Find the expansion of (3x - 2ax + 3a ) using binomial theorem.2 2 3 4

  Find the middle terms in the expansion of (2x− )x2

6

94

  Find a, b and n in the expansion of (a + b) if the first three terms of the expansionare 729, 7290 and 30375 respectively.

n  4

  If the fourth term in the expansion of  then find the value of aand n.

is(ax+ )1x

n 2027

4

  The coe�icient of (m + 1) term in the expansion of (1 +x) is equal to thecoe�icient of (m + 3) term. Show that m + 1 = n.

th  2n

th4

  The sums of n terms of two arithmetic progressions are on the ratio 5n + 4; 9n + 6.Find the ratio of their 18 terms.th 

4

  The ratio of the sum of m and n terms of an A.p. is m :n . Show that the ratio ofm  and n term is (2m - 1): (2n - 1).

2 2

th th 4

  Find the Sum to n terms of the sequences 8,88,888,8888.... 4

  Find the Value of n so that   may be the geometric mean between a and

b 

+an+1 bn+1

+an bn4

  The sum of two numbers is 6 times their geometric mean, show that numbers arein the ratio (3 + 2 ) : (3 − 2 )2√ 2√

4

  Let sum of n, 2n, 3n terms of an A.P. be S , S  and S  respectively, show that S  = 3(S - S )

1 2 3 3

2 1

4

  The sum of the first four terms of an A.P. is 56. The sum of the last four terms is112. If its first term is 11, then find the number of terms.

4

  If the sum of n terms of an A.P. is 8n + 3n and its mth term is 507, find the value ofm.

2 4

  Find the sum to n terms in the series 1 x 2 x 3 + 2 x 3 x 4 + 3 x 4 x 5 + ..... 4

  Find the sum to n terms in the series 3 x 1  + 5 x 2  + 7 x 3  + ......2 2 2 4

23)24)

25)

26)27)

28)

29)

30)

31)32)

33)

34)

35)

36)

37)

38)39)

40)

41)

42)

43)

44)45)

*****************************************

  if (b-c) , (c-a) ,(a-b)  are in A.P., Prove that   are in A.P2 2 2 , ,1b−c

1c−a

1a−b

4

  Find the equation of the line passing through the point of intersection of the lines4x + 7y - 3 = 0 and 2x - 3y + 1 = 0 that has equal intercepts on the axis.

4

  The hypotenuse of a right angled triangle has its ends at the points (1, 3) and (-4,1). Find the equation of the legs (perpendicular sides) of the triangle.

4

  Find the equations of the medians of a triangle formed by the lines x + y - 6 = 0, x -3y - 2 = 0 and 5x - 3y + 2 = 0.

4

  Find the equation of the line through the intersection of 5x - 3y = 1 and 2x + 3y - 23= 0 and perpendicular to the line 5x - 3y - 1= 0.

4

46)

47)

48)

49)

50)

Diwali Vacation Assignment11th Standard CBSE

Physics

Arpita's Science Academy

Date : 02-Nov-18

Reg.No. :            

  Match the technology in column A to its related scientific principle(s) in column B.A. Technology B. Scientific principle(s)1. Steam engine Propagation of electromagnetic waves2. Nuclear reactor Newton's laws of motion3. Radio and television Superconductivity4. Computers Role of DNA in heredity5. Lasers Thermodynamics6. Production of ultrahigh magnetic fields

Faraday's law of induction

7. Rocket propulsionConversion of gravitational potential energy intoelectrical energy

8. Genetic engineeringMotion of charged particles in electromagneticfields.

9. Electric generator Fission of uranium by slow neutrons10. Hydroelectric power Amplification by population inversion11. Aeroplane Digital logic of electronic circuits12. Particle accelerators Bernoulli's principle in fluid dynamics

3

  A capacitor of capacitance is charged to a voltage . Calculate the charge Q with error limits.

C = (2.0 ± 0.1)μF

V = (20 ± 0.5)V

3

  It is a well-known fact that during a total solar eclipse the disk of the moon almostcompletely covers the disk of the sun. The distance of moon (r and sun (r ) from theearth surface is 3.84 x 10 m and 1.496 x 1011 m while the diameter of Sun is 1.390 x10  m. Determine the approximate diameter of the moon.

ME) SE8

9

3

  A player throws a ball upwards with an initial speed of 29.4 ms-1. (i)What is the direction of acceleration during the upward motion of the ball? (ii)What are the velocity and acceleration of the ball at the highest point of its motion? (iii)Choose x=0 and t=0 be the location and time at its highest point, verticallydownward direction to be the positive direction of x-axis and give the signs of position,velocity and acceleration of the ball during its upward and downward motion. (iv)To what height does the ball rise and a�er how long does the ball return to theplayer's hands?(Take g=9.8ms and neglect air resistance)-2 

3

  Read each statement below carefully and state with reasons and examples if ittrue or false. A particle in 1-D motion with zero speed may have non-zero velocity.

3

1)

2)

3)

4)

5)

  State which of the following situations are possible and give an example for eachof these? An object moving in a certain direction with acceleration in the perpendiculardirection.

3

  A man walks on a straight road from his home to a market 2.5 km away with aspeed of 5 km/h. Finding the market closed, he instantly turns and walks back wth aspeed of 7.5 km/h. What is the (i) magnitude of average velocity (ii) average speed ofthe man, over the interval of time  0 to 40 min?

3

  Figure gives the x-t plot of a particle executing one-dimensional simple harmonicmotion. Give the signs of position, velocity and acceleration variables of the particles att == 0.3 s, 1.2s, - 1.2s.

3

  If unit vector  and  are inclined at angle then prove that a b − = 2sin∣∣a b∣∣θ

23

  The maximum height attained by a projectile is increased by 10% by increasing itsspeed of projection, without changing the angle of projection. What will thepercentage increase in the horizontal range?

3

  In a harbour, wind is blowing at the speed of 72 km/h and the flag on the mast of aboat anchored in the harbour flutters along the N-E direction. If the boat starts movingat a speed of 51 km/h to the North, what is the direction of flag on the mast of theboat?

3

  If the position vectors of P and Q be respectively  and 

, find  .

( + 3 − 7 )i j k

(5 − 2 + 4 )i j k PQ→

3

  A stone of mass 0.25 kg tied to the end of a string is whirled round in a circle ofradius 1.5m with speed 40 rev/min in a horizontal plane. What is the tension in thestring? what is the maximum speed with which the stone can be whirled around if thestring can withstand a maximum tension of 200 N?

3

6)

7)

8)

9)

10)

11)

12)

13)

  Two bodies A and B of masses 5 kg and 10 kg in contact with each other rest on atable is against a rigid wall as shown in figure. The coe�icient of friction between thebodies and the table 0.15.A force of 200 N is applied horizontally at A What are (i) thereaction of the partition or wall (ii) the action- reaction forces between A and B? Whathappens when the partition is removed? Does the answer to (ii) change, when thebodies are in motion? Ignore di�erence between  and   ? μs μk

3

  A light, inextensible string connects two blocks of mass M , and M . A force Factsupon M . Find acceleration of the system and tension in siring.

1 2

I

3

  A car of mass 1000 kg moving with a speed of 30 ms collides with the back of astationary lorry of mass 9000 kg. (Fig.). Calculate the speed of the vehicles immediatelya�er the collision if they remain jammed together.

-1 3

  A Carnot engine absorbs 6 X 10  cal at 227   C. Calculate work done per cycle bythe engine if its sink is maintained at 127  C.

5 o

o3

  Periodic Motion of a Clock The period of oscillation of a simple pendulum is  Measured value of L is

20.0 cm known to 1mm accuracy and time for 100 oscillations of the pendulum isfound to be 90 s using a wrist watch of 1 s resolution. What is the accuracy in thedetermination of g?

T = 2π Lg

−−√

3

  Energy Estimation A calorie is a unit of heat or energy and it equals about 4.2j, where 1J=1 kg-m /s. Suppose we employ a system of units in which the unit of mass equals kg, the unit oflength is m, the unit of time is s. Show that a calorie has a magnitude interms of new units.

2 2

4.2α−1β−2γ2

3

  Power Estimation Find the value of 60J per min on a system that has 100g, 100cm and 1 min as the baseunits.

3

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  The shadow of a tower standing on a level plane is found to be 50 m longer whenSun's altitude is 30° than when it is 60°. Find the height of the tower.

3

  A boy starts moving from -20 m towards + x-axis as shown in figure. He turns attime instant t  and starts moving towards - x-axis. At time t  he reached at -50 m asshown in the figure. Find the displacement and distance for the time interval (i) t  to t and (ii) t  to t

2 3

1 2 1 3

3

  Two trains, each having a speed of 30 km/h. are headed towards each other on thesame track. A bird that can fly 60 kru/h flies o� the front of one train when they were 60km apart and heads directly to the other train. On reaching the train, the bird flies backto the first train. What is the total distance the bird travels before the trains collide?

3

  The position of a particle is given by 

where, t is in seconds and the coe�icients have the proper units for r to be in metres. Find the magnitude and direction of v(t) at t=2.0s

r = 3.0t + 2.0 + 5.0i∧

t2j∧

k∧

3

21)

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24)

  Figure shows a pirateship 560 m from a fort defending a harbour entrance. Adefence cannon, located at sea level, fires balls at initial speed, u =82 m/s.

  

(i) At what angle, from the horizontal must a ball be fired to hit the ship? (ii) What is the maximum range of the cannon balls?

0

θ0

3

  A girl riding a bicycle along a straight road with a speed of 5 m/ s throws a stone ofmass 0.5 kg which has a speed of 15 m /s with respect to the ground along her directionof motion. The mass of the girl and bicycle is 50 kg. Does the speed of the bicyclechange a�er the stone is thrown ? What is the change in speed, if so ?

3

  'A hockey puck with a mass of 0.3 kg slides on the 1 N = 105 dyne C1 horizontalfrictionless surface of an ice rink. Two forces act on the puck as shown in figure. Theforce F  has a magnitude of 5 Nand F  has a magnitude of 8 N. Determine theacceleration of the puck.

1 2

3

  What is the acceleration of the block and trolley system shown in a figure. If thecoe�icient of kinetic friction between the trolley and the surface is 0.04, what is thetension in the string? (take g = 10ms ). Neglect the mass of the string. -2

3

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  Abody of mass m1 equal to 20 kg is placed on a smooth horizontal table. Thisbody is connected to a string which passes over a frictionless pulley. The string alsocarries another body of mass m  equal to 10 kg at the other end. Find out theacceleration which will be produced when the nail fixed on the table is removed, alsofind out the tension in the string during the motion of the bodies. What is the= result,when the bodies stop? Take g = 10 N/kg.

2

3

  Horizontal Force Applied on Rope Hanging Vertically See in figure a mass of 6 kg is suspended by a rope oflength 2 m from the ceiling. Aforce of 50Nin the horizontal direction is applied at the mid-point P of the rope asshown. What is the angle, the rope makes with the vertical in equilibrium? (Take g = 10 ms ). Neglect the mass of the rope. -2

3

  The sun is a hot plasma (ionised matter) with its inner core at a temperatureexceeding 10 K and its outer surface at a temperature of about 6000 K. At these hightemperatures, no substance remains in a solid or liquid phase. In what range do youexpect the mass densities of solids and liquids or gases? Check if your guess is correctfrom the following data. Mass of the Sun =   and radius of the Sun = .

7

2.0 × kg1030

7.0 × m108

3

  The diameter of a wire as measured by a screw gauge was found to be 1.328,1.330, 1.325, 1.334 and 1.336 cm. Calculate percentage error.

3

  A three wheeler starts from rest, accelerates uniformly with 1ms  on a straightroad for 10 s, and then moves with uniform velocity. Plot a graph between the distancecovered by the vehicle during the nth second (n = l, 2, 3, ...) versus n.What do youexpect the plot to be during accelerated motion a straight line or a parabola?

-2 3

  If A and B are two vectors such that  Then, Also, find the value of  

|A × B| = A.A3√

|A × B|

3

  Give the magnitude and direction of the net force acting on a stone of mass 0.1 kg. (i) Just a�er it is dropped from the window of a stationary train. (ii) Just a�er it is dropped from the window of a train running at a constant velocity of36 km / h (iii) Just a�er it is dropped from the window of a train accelerating with 1 m /s2

3

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  A block of mass 25 kg is raised by a 50 kg man in two di�erent ways as shown infigure. What is the action on the floor by the man in the two cases? If the floor yields anormal force of 700 N, which mode should the man adopt to li� the block without thefloor yielding?

3

  Figure below shows the position-time graph of a body of mass 0.04 kg. Suggest asuitable physical context for this motion. What is the time between two consecutiveimpulses received by the body? What is the magnitude of each impulse?

3

  Masses M , M and M are connected by light strings which pass over pulleys Pand P as shown. The masses move such that the string between P and P is parallel toincline and the string between P and M is horizontal, M = M = 4kg. The coe�icient ofkinetic friction between masses and tile surface is 0.25. The angle of inclination ofplane is 37° to the horizontal. If the mass M  moues downwards with uniform velocity,find M and the tension in the horizontal string. Given g = 9.8 m/s and sin 37° = 3/5.

1 2 3 1

2 1 2

2 3 2 3

1

12

3

  A Carnot cycle is performed by 1 mole of air (r = 1.4) initially at 327  C. Each stagerepresents a compression or expansion in the ratio 1:6 Calculate e�iciency of theengine Take R = 8.31 J/ mol

o

-K

3

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Happy Diwali

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  When a system is taken from state i to state f along the path iaf, it is found that theheat Q absorbed by the system is 50 cal. and work done W by the system is equal to 20cal. along the path ibf; Q = 36 cal

(i) What is W along the path ibf? (ii) If W = -13 cal. for the curved return path fi what is Q for this path? (iii) Take U, = 10 cal, what is U ? (iv) If U = 22 cal. what are Q for the processes bf and ib?

f

b

340)