Riviera International Academy Practice Test – 2076

Subject : BiologySET: A

Class: XII Time: 3 hrs Full Marks: 75

Section A- BOTANY

I. Answer any SEVEN questions in very short. [1X7=7]a. What is plant tissue culture?b. Define photophosphorylation.c. Mention the role of hydathode.d. Distinguish between dominance and epistasis.e. Define genetic code.f. What do you understand by triple fusion?g. How is thigmotropism different from chemotropism?h. Write two characteristics of entomophilous plants.i. Define inbreeding.j. Name any two plants used for green manure.

II. Answer any FIVE in brief. [3X5=15]a. Draw a neat and well-labeled diagram of the anatomical structure

of dorsiventral leaf.b. Explain the mechanism of the opening and closing of stomata.c. What do you understand by Mendel’s 9:3:3:1 ratio?d. Explain the process of crossing over.e. List out the significance of polyploidy.f. Describe microganmetogenesis in angiosperm.g. Mention the application of biotechnology in the field of

agriculture.

III. What is secondary growth? Discuss the activity of cambium in secondary growth in dicot stem.

OrDefine aerobic respiration. Demonstrate CO2 evolved in aerobic respiration. [7.5]

IV. What is genetic material? Describe the mechanism of semi-conservative method of DNA replication with necessary diagrams.

[8]

Section B- Zoology

1. Answer any seven in very short. [7×1=7]a. What is ovulation?b. Define the term deamination.c. What is otolith?d. Who discovered the first antibiotics?e. What is amniocentesis?f. Mention the kinds of teeth found in human.g. What is Hamberger’s phenomenon?h. Write any two symptoms of Hepatitis B.i. Which hormone is called birth hormone?j. What is the significance of keratinization of the outermost layer of the

skin tissue?

2. Answer any five in brief. [5×3=15]a. What are the differences between striped and unstriped muscles?b. Describe the process of neurulation and notochord formation with

diagram.c. Discuss the consequences of rapid population growth.d. Describe the structure and functions of thyroid gland.e. Write a short note on origin and conduction of heart beat.f. Discuss briefly about the fat soluble vitamin.g. Explain ultra-filtration process.

3. Describe the structure and functions of human eye with diagram. [7.5]

OrDescribe the structure of human brain with suitable diagram.

4. What is cancer? Discuss its types, causes, symptoms, diagnosis, control, control measure and treatment. [8]

The End.

Riviera International Academy Practice Test – 2076

Subject : BiologySET: B

Class: XII Time: 3 hrs Full Marks: 75

Zoology

1 Write very short answer to the following questions (any seven): (1x7=7)a) Where do you find transitional epithelium? b) What causes rickets?c) What do you mean by cochlea?d) Define alcoholism.e) Why blood group O is called universal donor?f) What is the role of CSF?g) What do you mean by gametogenesis?h) What is the role of ceruminous gland?i) Which is the largest salivary gland?j) What is IUCD?

2. Write short answers of the following questions (any five). (3x5=15)a) Write down the differences between red bone marrow and yellow bone marrow.b) Describe the process of blastulation in frog.c) Explain the ventricles of brain.d) Describe the homeostatic role of kidney. e) Write short note on population growth curves.f) Write down the differences between rod cell and cone cell.g) Write short note on cardiac cycle.

3) Describe the structure and function of human brain. (7.5)Or

What is ultrafiltration? Describe the mechanism of urine formation.4. What is DOTS? Describe the causative agent, mode of transmission, symptoms, diagnosis, treatment and preventive measures of tuberculosis. (8)

Botany

1. Very short answer questions. (any seven) (7x1=7)A) What is central dogma?

B)Define template DNA.C)What is genetic material?D) Define cistron.E)What is the function of RNA polymerase?F) What is trait?G) What is reciprocal cross?H) What is genotypic ratio of monohybrid cross?I) What is linkage?J) Define incomplete dominance.

2. Short questions.(any five) (5x3=15)a. Describe different types variations.b. Differentiate between DNA and RNA.c. Describe structure of deoxyribonucleic acid.d. What is mutation?Write its types with one beneficial feature.e. Define recessive epistastis with suitable examples.f. Write the characteristics of genetic code.g. Describe the overall process of transcription.

3. What is DNA replication? Describe its overall process. (7.5) Or What is operon concept? Describe tryptophan operon concept.4. Describe Mendel law of segregation with suitable Examples. (8)

The End.

Riviera International Academy Practice Test – 2076

Subject : BiologySET: C

Class: XII Time: 3 hrs Full Marks: 75

Group A (Botany)5. Very short answer questions. (any seven)[1x7=7] K) What is Central dogma?L) Define template DNA.M) What is heridity?N) Define antibiotics?O) What is the function of RNA polymerase?P) What green manure?Q) What is co dominance?R) What is genetic hybridization?6. Short questions (any five) [3x5=15]h. Describe different types of parenchyma tissue tissue.i. Difference between transpiration and translocation.j. Describe the process of DNA replication.k. What is polyploidy write its type with one beneficial features.l. Describe process of complete linkage.m.Significance of plant tissue culture.n. Why Morgan choose dorsophillao. Describe the law of dominance with examples.

7. What is sex linked inheritance. Describe it with suitable examples. [7.5]

Or What is crossing over? Describe with its process.

8. Describe different types of mutation with biological role. [8]

Group B (Zoology)

1. Very short answer questions (Any seven) [1x7=7] a. What isograft? b. Name the protein present in bone. c. What is osmoregulation? d. Define pellagra. e. What is biotic potential? f. Define tidal volume. g. Where do you find elastic cartilage? h. Define carrying capacity. i. What is the causative agent of kala-azar? j. What do you call the cavity of blastula?2. Short questions (Any five) [3x5=15] a.Write short notes on decalcified bone.

b. Describe fat soluble vitamins in brief.c. Write short notes on cardiac cycle.d. Describe vaccine in brief.

e. Write down the differences between rod and cone cells.f. What are the control measures of overpopulation? Describe in brief.

g. Write short notes on cleavage.3. Describe the respiratory tract and organ of human. [7.5]

Or Describe the physiology of urine formation in human.

4. What is enteric fever? Describe the causative agent, mode of transmission, symptoms, diagnosis, treatment and control measures of typhoid. [8]

The End.

Riviera International Academy Practice Test – 2076

Subject: ChemistrySET:A

Class :XIITime: 3hrs Full marks:75

Group A

Attempt any fifteen questions: [15×2=30]1. Predict the structure of ammonia molecules using VSEPR Theory.2. Define and give one example of Lewis acid and Lewis base.3. Draw energy profile diagram for catalysed reaction and uncatalysed

reaction.4. 0.53gm of Na2CO3is added to 101 ml of 0.1 N H2SO4 solutions. Will the

resulting solution be acidic, basic or neutral?5. Under what conditions

a. Reaction occurs spontaneously

b. Free energy change becomes zero.

6. What is meant by state function”? Give its example.7. Define equivalent conductance and specific conductance.8. Define order of reaction, and molecularity of reaction.9. Why amino group be protected before nitration in aniline?10. Give brief account on Carbyl amine reaction and Friedel Craft's acylation

reactions.11. Why boiling point of carboxylic acid is higher than alcohol having

comparable molecular mass?12. Identify the major products A and B and give their IUPAC name.

CH3CH2NO2LiAlH4 'A'NaNO2+HCl 'B'13. What is structure of isomeric alcohol of C3H8O that gives Iodoform test?

Write the test reaction.14. Convert ethoxyethane to ethanoyl chloride.15. Prepare Anisole by using Williamson’s ether synthesis.16. What is DNA? Write the name of nitrogen bases found in DNA17. Write the structure of DDT & BHC.18. What is drug? Give name of antipyretic and broad spectrum antibiotics

drugs19. Differentiate between reducing sugar & non reducing sugar

20. How can you prepare Nessler’s reagent?21. What happen when silver nitrate is heated? 22. Write the molecular formula and use of the following

a. Mohr's salt b. corrosive sublimateGroup B

Attempt any five questions: 5×5=2523. What is meant by standard electrode potential? The standard electrode

potential for the following electrode arei. Zn++ + 2e- Zn, E0 = -0.76Vii. Fe+++ + 1e- Fe+2, E0 = 0.77Va. Represent a suitable galvanic cell and point out which one will be

cathode?

b. With 1 M solution of ions what will be E.M.F?

c. Will the reaction Zn++ +2Fe++ Zn + 2Fe+++ occur? Give reason.

24. Define entropy. Derive a relationship ∆G = ∆H - T∆S. A tank of water at 68°C loses 100J of heat energy to the surrounding at 25°C. Calculate the effect of entropy of the universe due to this process.

25. Describe the chemical method of separation of 10, 20, 30 amines from their mixture by Hoffmanm’s method.

26. An alkene “A” undergoes ozonolysis to give two carbonyl compound “B” and “C”. the compound B on reduction with Zn-Hg/H+ gives propane. The compound C reacts with HCN and followed by hydrolysis to produce 2- hydroxypropanoic acid as major product. Write chemical reaction involved and give IUPAC name of A, B and C.

27. Starting from trichloromethane how would you prepare:a. Ethyne b. Carbonyl Chloride

c. Methane d. Chloretone

e. Chloropicrin

28. How is ethanioc acid prepared from methyl magnesium iodide? What happens when ethanoic acid isa. heated with P2O5

b. heated with HI in presence of red phosphorous

c. warmed with ethanol in presence of conc. H2SO4.

29. What is rusting? Describe electrochemical Theory of rusting of iron. List any two methods of prevention of rusting.

Group C

Attempt any two questions 2×10=2030. For the gaseous reaction A(g) + B(g) C(g) + D(g)

It is found that rate = k[A]2[B]1

How many times does the rate of reaction increase or decrease if:a. The partial pressure of both A and B are doubledb. The partial pressure of A doubles but that of B remains constantc. The volume of reacting vessel is doubledd. An inert gas is added which doubles the overall pressure while the

partial pressure of A and B remains constant.e. The temperature rise by 30oC.

31. Explain the laboratory preparation of Aniline with labelled diagram. How would you convert aniline into :a. Phenol b. p-benzoquinone

c. Phenyl isocyanide d. benzene diazonium chloride

e. Para aminobenzenesulphonic acid

32. Explain with neat and clean diagram for laboratory preparation of anhydrous methanoic acid. How does methanoic acid acts upon :a. Fehling’s solutionb. Methanol and H+

c. Conc. H2SO4

33. Write short notes(any two): 2 x 5 = 10a. Victor Mayer test for 10, 20 and 30 alcohol by

b. Extraction of Mercury from cinnabar

c. Ostwald's dilution law

d. Faraday’s 1st law & 2nd laws of electrolysis.

The End.

Riviera International Academy Practice Test – 2076

Subject: ChemistrySET:B

Class :XIITime: 3hrs Full marks:75

Group A [15×2=30]

Attempt any fifteen questions.

1. Draw the orbital picture of ethyne indicating sigma and pi bonds.2. Predict the mode of hybridization of B in BF3. Mention any two features of

this hybridization.3. What mass of 90% pure CaCO3 is required to neutralize 2 litre deci-normal

solution HCl ?4. State Ostwald’s dilution law and mention its limitation.5. How would you justify the value of one Faraday is 96500 coulombs?6. What is meant by single electrode potential? Name any two factors that

affect the magnitude of single electrode potential.7. State Hess’s Law of constant heat summation.8. What is the criterion for a reaction to occur spontaneously?9. Define zero order reaction and find the unit of its rate constant.10. How would you explain that –OH group of phenol is ortho/para directing?11. What is Williamson’s etherification reaction?12. Give an example of Cannizzaro reaction and Aldol condensation of each.13. Why is chloroacetic acid stronger than acetic acid?14. Why are amino acids amphoteric in nature?15. What happens when Grignard’s reagent is treated with CO2?16. Convert benzaldehyde into aniline showing necessary chemical reactions.17. What happens when oil is hydrogenated?18. Define non-reducing sugar and give an example of it.19. What are natural and synthetic dyes? Give an example of each alongwith

structure.20. Give the balanced chemical reaction for the preparation of black oxide of

Copper from blue vitriol. How is black oxide converted into red oxide?21. What is Nesseler’s reagent? How it is prepared?22. What happens when Zinc is exposed in moist air?

Group B [5×5=25]

23. 0.8 g of a divalent metal was dissolved in 100 cc of 1.28 N HCl and the solution was diluted to 200 cc. Then 50 cc of this solution required 54.6 cc of 0.22 N NaOH for neutralization. Find the atomic weight of the metal.

24. State Faraday’s laws of electrolysis. Silver is electrodeposited on a metal plate of surface area 800 mL by passing 0.2 ampere of current for 3 hours. Calculate the thickness of Ag deposited. (Given specific gravity of Ag is 10.47 and atomic mass is 108).

25. Describe Victor Meyer’s method to distinguish primary, secondary and tertiary alcohols.

26. How do you obtain pure chloroform in laboratory from ethanol? Describe along with neat and clean diagram.

27. Briefly describe the metallurgy of Calomel.28. How is steel manufactured by Open Hearth process?29. Write the preparation, properties and uses of white vitriol.

Group C [10×2 = 20]

Attempt any 2 questions.

30. a) State and explain first law of thermodynamics and deduce H = E+PV where all the symbols have their usual meanings.b) The standard heat of formation of SO2 (g) and SO3 (g) are -296.6 kJ and -396 kJ respectively. Calculate ΔH for the reaction;

SO2 (g) + ½ O2 (g) SO3 (g)31. a) An aliphatic compound ‘A’ reacts with SOCl2 to give ‘B’. ‘B’ on

reduction with H2 in presence of Pd/BaSO4 to give ‘C’. When HCN is added to ‘C’ produces ‘D’. On hydrolysis of ‘D’ in acidic medium forms ‘E’. Compound ‘C’ can be obtained by heating the mixture of Sodium formate and Sodium acetate. Identify A,B,C,D,E and write reactions involved.

b) What happens when Nitrobenzene is reduced in acidic, neutral, alkaline and electrolytic conditions?

32. .a) How is pure aniline prepared in the laboratory? Explain.b) Explain why?

i) Amino group of aniline is ortho or para directing.ii) Amino group of aniline is protected before nitration.iii) Aniline is a weaker base than aliphatic amine

33. Write short notes on any two.i) Solubility product principleii) Order and Molecularity of reactioniii) Chemistry of Blue vitrioliv) Theory of Corrosion in Iron

The End.

Riviera International Academy Practice Test – 2076

Subject: ChemistrySET:C

Class :XII Time: 3hrs Full marks:75Group' A'Attempt all the questions.1. Nitrogen of ammonia gets sp3 hybridization but ammonia molecule has trigonal pyramid geometry. Give reason . [2] 2. x cc of 5N HCL was diluted to one liter of normal solution. Calculate the value of x.[2]3. What is pH of solution of NaOH whose concentration is0.4gm/liter?[2]4. What do you mean by Electrolytic Conduction? [2]5. The solubility of CaF2 in water at 180C is 2.05 x10-4mol/L . Calculateits solubility product. [2]6. What volume of decinormal solution of H2SO4 is required toneutralize 50ml of NaOH containing 20 gm/ liter?7. The half-life period of first order rxn is 8 hours. Find the time required to complete 87.5 % of the reaction. [2]8. How would you obtain benzene from.[2]i) Phenol ii) Chlorobenzene9. Convert 1-chloropropane into 2-chloropropane. [2]10. Give an example of Williamson's etherification. [2]11. How would you obtain 2-hydroxy-2-methyl propanoic acid

frompropane ?[2]12. Write an example of each of [1+1] i) Carboxylamine reaction ii) Decarboxylation reaction14. Why does nitrobenzene undergo electrophiticsubstitutionreaction in meta position? [2]15. Why is amine more acidic than ammonia ?[2]16. What happens when fat gets hydrolysed? [2]

17. What is denaturation of protein? Give an example. [2]18. Name the monomers of (i) bakelite (ii) nylon 66 [1+1]19. Give the name of two insecticides with their chemical formulae. [2]20. What happens when zinc white is heated? [2]21. How is corrosive sublimate converted into calomel and vice-versa? [2]22. Write the molecular formula of: [1+1] i) Mohr's salt ii) Green vitriolGroup 'B'Attempt any five questions: [5×5=25]23. Write the chemistry of blue vitriol. [5] Or How is mercury extracted from cinnabar?24. What is Ostwald's dilution law? How much water must beadded to 400 ml of 0.2M solution of ethanoic acid for thedegree of dissociation of the acid to be twice the originalvalue ( Kafor ethanoic acid 1.8 x 10-5).25. Distinguish between electrochemical equivalent and chemical

equivalent. A metallic spoon is coated with silverby passing a current of 5 Amp through AgNO3 solution for 5 hours. What is the thickness of silver plating if the areaof spoon is 12cm2 (density of silver is 10.5 gcm-2)?26. Define the terms: [5] (i) End point (ii) Equivalence point (iii) Indicators(iv) Basicity of acid (v) Acidimetry27. Write any three methods of preparation of chlorobenzene. How does it react with: a. Chloral ? b. Methyl chloride in the presence of sodium and dry ether? [3+2]28. Describe laboratory preparation of ethoxy ethane with a neatandlabeled diagram. [5]

29. Write down the functional isomers of C3H6O with their IUPAC name. Also, give a chemical test to distinguish them one gives Iodoform test and why?

Group 'C'Attempt any two questions: [2×10=20]30. (a) Define rate law and rate of a reaction. How dotemperature, catalyst,

concentration of reactant and surfacearea of reactant affect the rate of reaction.

(b) From the following experimental data for the reaction:[2+2]

2A + B 2AB Experiment [A], molL-1 [B], molL-1 Rate, molL-1s-1

1 0.5 0.5 1.6×10-4

2 0.5 1 3.2×10-4

3 1 1 3.2×10-4

(i) Find overall order of reaction.(ii) Find the rate of constant.31. (a) How is pure aniline prepared in the laboratory? [6] (b) Convert aniline into [2+2]

i) azodyeii) n-methyl aniline

32. Describe Victor Meyer's method to distinguish primary,secondary, and tertiary alcohols. Give examples of:a. aldol condensation b. Esterification c. DNPH test d. Fradelcrafts'sallkylation e. Perkin condensation[5+1+1+1+1]33. Write short note on any two: [2×5=10] a. Rusting of iron b. Extraction of zinc from zinc blendec. Solubility product d. Separation of 10, 20, and 30 amine by Hoffmann's method.

The End.

Riviera International Acdemy Practice Test – 2076

Subject : MathematicsSET:A

Class: XII Time: 3 hrs Full Marks: 100

Group : A1. a) In how many ways can the letters of the word “NOTATION” be arranged? (2)

b) Show that 23!

+ 45 !

+ 67 !

+…………..¿∞=1e

. (2)

c) Define identity and inverse element in a group (G ,*). (2)2.a) Find the equation of normal to the parabola y2= 4x perpendicular to the line x+2y+4=0. (2) b) Find the direction cosines of the line whose direction ratio are 2,3,6.

(2) c) If the position vector of M and N are3 i⃗+2 j⃗−3 k⃗∧4 i⃗−2 j⃗+2 k⃗respectively , find M⃗N and its direction cosines. (2)

3. a) Prove that (a⃗ . b⃗¿+(a⃗ × b⃗)2=a2 b2. (2)

b) If x y=e x− y prove that dydx

=(logx )(logex)−2 (2)

c) Evaluate ∫√x2+2x+5dx (2)

4.a) Solve : dydx

= ex+1y

b) Followings are the information about the marks of two students A and B . A B Average marks 84 92 Variance of marks 16 25Examine who has got the uniform marks.c) In the binomial distribution, find mean and standard deviation ifp = 0.33 and n = 100. (2) 5. a) A committee of 5 members is to be selected from 6 boys and 4 girls. In how many ways can this be done so as to include at most threegirls. (4)

b) Evaluate ∫ dx1−2 cosx

OR

Solve: dydx

= x2+ y2

2 x2 (4)

6.a) Define a group. Let ( G , *) be a group then show that (a∗b)−1=b−1∗a−1 for a,b∈G .b) If three successive coefficients in the expansion of (1+x)n are 28,56∧70 , findn . (4)7. a) State and prove the addition theorem of probability. (4) b) Show that the tangent to y2= 8x and x2 = 8y at (2,4) and ( -4,2) respectively are perpendicular to each other. (4)

ORFind the equation of the ellipse whose latus rectum is equal to half its major axis and passes through(√6 ,1¿. (4)

8. a) Find the equation of the plane through the points (-1,1,1) and (1,-1,1) and perpendiculars to the plane x+2y+2z= 5. (4)

ORTheprojection of a line on the axes are 12,4,3 respectively . find the length and the direction cosines of the line. (4)

9. Show that ∑n=1

∞ n2

(n+1) !=e−1.(6)

10. Define vector product of two vectors. Prove by vector method that sin(A+B)= sin A cosB+cosAsinB. (6) 11. Find the derivative of log(cosx) by definition .

ORState mean value theorem . Verify the mean value theorem for the function f(x) = (x-1)(x-2)(x-3) in [1,4]. (6)

Group : B12.a) Two equal forces act on a partical , find the angle between the forces if their square of the resultant is equal to three times their product. (2)

b)If a ball is thrown vertically upwards at a rate of 20ms-1, find the time takento attain the maximum height. (g=10 ms-1)c) A partical projected with a speed of 30m/s reaches its greatest height above the

point of projection 2s econd latter. Find the angle of projection. [g=10m/s].(2)

13. a) If three forces acting at a point are such that each is proportional to the sine of the angle between the other two, then prove that the forces are equilibrium. (4)

ORIf a,b,c be the space described by a particle during the pth,qth and rth second of its motion respectively, prove that a(q-r)+b(r-p)+c(p-q)=0b) A man raise a bucket of water of mass 10kg from a well. When the bucket has risen 18m its velocity is 12m/s. find the work done by the man.

(4)14.ABCD is a square of side 2m. force 1,2,8 and 5N act along the sides AB,BC,

CD and DA respectively and along AC and DB forces 5√2 Nand 2√2Nequally act. Show that the forces are equivalent to a couple

whose moment is 16 Nm. (6)15. A stone is thrown horizontally with velocity √2gh from the top of the tower

of height h. Find where it will strike the ground level through the foot of the water. What will be its striking velocity? (6)

ORP and Q are like parallel forces. If P is moved parallel to itself through a

distance x, show that the resultant of P and Q moves a distance Px

P+Q .

Group : C16.a) Determine the fessible region of the following system of inequalities: 2x+y≤ 8 , x+2 y ≤10 x , y ≥ 0. (2)

b) Convert the decimal number ( 2567)10 to octal form. (2)

c) Use the trapezoidal rule , evaluate ∫0

1 dx1+x2 n=2. (2)

17. a)Using the Gauss elimination method, solve the following system of equations: x+3y-z=-2, 3x+2y-z= 3,-6x-4y-2z =18. (4)

ORUsing inverse matrix method , solve the following system of equations: 3x+y+z =15; x+y+z=3; y-z=-1.

b) Using simpson’s13 rule ,evaluate;∫

0

1

√1+2 x2 dx ,h=0.25 .(4)

18. Using simplex method , maximize Z= 15X+10Y subject to 2x+y≤ 10; x+3 y ≤10 x , y ≥ 0. (6)19. Find the root of an equation x3+x-4=0 in the interval [1,4] upto two decimal

places. By using bisection method. (6)OR

Find a root of the equation x3-x-4=0 between 1 and 2 to three places of decimal by newton’s method. (6)

The End.

Riviera International Acdemy Practice Test – 2076

Subject : MathematicsSET:B

Class: XII Time: 3 hrs Full Marks: 100Attempt all the questions:

Group 'A' [15×2=30]1. a) In how many ways can four boys and three girls be seated in a row

containing seven seats,if the boys and girls must alternate.

b) If 3⃗ i+ j⃗ − k⃗ and d⃗i− 4⃗ j+ 4⃗ k are collinear vectors, find the value of d.

c) If a⃗ and b⃗ are two vectors of unit length and is the angle between them show that :

|⃗ a − b⃗ | = sin

d) Prove that if a⃗ + b⃗ + c⃗ = 0, prove that :

a⃗ × b⃗ = b⃗ × c⃗ = c⃗ × a⃗ and intercept it geometrically. e) Find the equations of the tangent and normal to

y = x3 - 2x2 + 4 at (2, 4).

f) Find of xcos h2 x

a .

g) Integrate: ∫ dx

√2 ax−x2

h) Solve: dy = ex - y + x3 e-y

i) Shade the feasible region under the constraints.2x + y 40 x + 2y = 50 x,y 0

j) Find the correction coefficient between the two variables under the following conditions n = 10, x = 5, y = 3 x2 = 290, y2 = 300, xy = 115.

k) If fx = 110, fx2 = 1650, N = 10 and M0 = 12.45. Find the skewness based on mean mode and standard deviation.

l) Find the inverse of the matrix A =

(12¿ )¿¿

¿¿.

m) Using the Simpson's rule ∫ dx

1+x2 n = 2.

n) Solve the following system of equations using Gauss Elimination Method : x + 2y = 5.

o) |⃗ a + b⃗ |=|⃗a − b⃗ |, then, prove that a⃗ is a per perpendicular to b⃗ .

Group 'B' [(5×2)×4=40]2. a) Solve :

b) Solve :

3. a) Integrate : ∫ dx

( x−2 )2( x−3 )3

b) Integrate: ∫ dx

3+4 cos hx4. a) Find from first principle: log (sin x/a).

b) In how many ways can the letters of the word CALCULUS be arranged so that the two c's do not come together?

5. a) Apply the method of successive bisection to find the root of the equation x3

- 4x + 1 = 0 lying between 1 and 2 correct to the two places of decimal. b) Using Newton Raphson method find a positive root of x 3 + 3x - 5 = 0

lying between 1 and 2 correct to three places of decimals. 6. a) Solve the following system of equations by Gauss Seidel Method.

3x1 + x2 = 5

x1 - 4x2 + x3 = -2x1 + x2 - 3x3 = -1

b) The regression coefficient of x on y and y on x are 1.5 and 0.65 respectively. If the arithmetic mean's x and y are 36 and 52 respectively, find the two regression equations. Also find the value of y when x = 60.

Group 'C' [5×6=30]7. Apply simplex method to maximize f = 15x1 + 10x2

subject to 2x1 + x2 10x1 + 3x2 10x1 x2 0

8. Define cross product of two vectors prove vectorically:sin (A + B) = sin A cos B + cos A sin B

9. State trapezoidal rule.Hence, evaluate ∫ dx

1+x2n=4

.10. Define Largrange's mean value theorem. Also verify the theorem for the

function f(x) = 2x2 - 10x + 29 in [27].11. Scores of two golfers for 6 rounds were as follows: Golfer A 74 75 80 78 72 77Golfer B 86 84 80 88 87 85

Find which golfer may be considered to be a more consistent player.

The End.

Riviera International Acdemy Practice Test – 2076

Subject : MathematicsSET:C

Class: XII Time: 3 hrs Full Marks: 100Group – A [5×3× 2 = 30 ]

1.a. Let f(x) = {xsin 1x

0, for x≠ 0

Show that f(x) is continuous at x = 0

b. Find the derivative of (sinx)cosx.

c. Find the derivative of logsinhxa .

2. a. Find the approximate increase in the volume of sphere when its radius increases from 2cm to 2.1cm. Also find the actual change.

b.Evaluate: xlim ¿→

∞ 3 x2+4 x−72 x2+5 x+8

¿

c. In how many ways can 4 boys and 3 girls be seated in a row containing 7 seats if they may sit anywhere?

3.a. Let S= {1, -1} and o denotes the usual operation of multiplication. Represent it by Cayley’s table and show that the multiplication is a binary operation.

b. Find the eccentricity and the foci of the hyperbola 3x2-4y2 = 36.

c. Find the area of the parallelogram determined by the vectors i⃗+2 j⃗+3 k⃗ and -3i⃗−2 j⃗+k⃗ .

4. a. Find the regression equation of y on x when:∑ x=15 ,∑ y=25 ,∑ x2=55 ,∑ y2=140 ,∑ xy=78 ,n=5. b. From 20 tickets marked from 1 to 20, one is drawn at random. Find the

probability that it is a multiple of 4 or 5.

c. Find the equation of tangent and normal to the parabola y2 = 12x at the point (-1, 4).

5 a. Find the feasible region determined by the inequalities: 3x+4y≤ 24 , x≥ 2 , y ≥ 1.

b. Evaluate the following integral using composite trapezoidal rule: ∫1

5

x2

dx, n = 4.

c. Compute the integrals ∫0

1 11+x2 dx, n = 4 using Simpson’s 1/3 rule.

Group – B [5×2 × 4 = 40]

6.a. If siny = xsin(a+y), prove that: dydx

= sin2(a+ y )sina

.

b. Find the point on the curve y = 3x2+4x-5 where the tangent is parallel to the line 16x+2y = 3.

7. a. In how many ways the letter of the word MONDAY be arranged? How many of these arrangements do not begin with M? How many begin with M and do not end with N?

b. Define Group. Let G = {1, -1, i, -i} where i is the imaginary unit and o stands for the binary operation of multiplication. Show that (G, o) forms a group.

8 a. Find the eccentricity, coordinates of vertices and focus of the ellipse 9x2+5y2-30y = 0.

b. Find the condition under which the line y = mx+c is tangent to the parabola y2 = 4ax. Find the equation of tangent in slope form and also find the point of contact.

9.a. A bag contains 5 red and 6 black balls. Two balls are drawn at random. Find the probability that i. both are red ii. both are of same color.

b. If 20% of the electric bulbs manufactured by a company are defective, find the probability that out of 4 bulbs chosen at random i. 1 bulb is defective ii. at most 2 bulbs are defective.

10 a. Compute Bowley’s coefficient of skewness for the following data:

Variables 10-15 15-20 20-25 25-30 30-35Frequency

8 12 20 18 2

b. If I = ∫0

4

x2dx , n = 4,

i. Find the approximate value of each integral using the trapezoidalrule.

ii. Calculate the exact value of the integral.

iii. Determine the error.

Group – C [5×6= 30]

11. Find from first principles the derivativeof etanx.

12. State Rolle’s theorem and interpret geometrically.VarifyRolle’s theorem for f(x) = x2-4 in -3≤ x≤ 3.

13. Use simplex method to find the optimal solutions of the following LP problem.

Max.Z = 7x+5y Subject to x+2y≤ 6 ,4 x+3 y≤ 12 , x ≥ 0 , y ≥ 0

14. Define scalar product of two vectors. Prove by vector method: Cos (A-B) = cosAcosB+sinAsinB

15. Prove that the latus rectum of a parabola bisects the angle between the tangent and the normal at either extremity of the latus rectum.

The End.

Riviera International Academy

Practice Test – 2076Subject : Physics

SET:AClass: XII Time: 3 hrs Full Marks: 75

Candidates are required to give their answer in their own words as far as practicable. The figure in the margin indicates full marks.

Group A(1) Answer in brief, any four questions: (4×2=8)

(a) You are given ‘n’ wires each of resistance R. What is the ratio of maximum to minimum resistance that can be obtained from these wires?

(b) ‘Potentiometer is equivalent to a voltmeter of infinite resistance’. Explain?(c) How is Seebeck effect different from Peltier effect? Explain.(d) What will be the path of charged particle moving along uniform magnetic

field?(e) If the horizontal and vertical components of earth’s field are equal at a

certain place, what is the angle of dip at that place?

(f) Why is a choke coil preferable to a resistor in an AC circuit?(2) Answer in brief any four questions: (4×2=8)

(a) One electron and one proton moving with the same velocity are passing through the same electric field. Which one gains more energy and why? What about velocity?

(b) Differentiate between excitation potential and ionization potential.(c) Why the base region of a transistor is lightly doped compared to the

collector and emitter region?(d) How do you get emission of β-particles from the nucleus although there

are no electrons within it?(e) What is Green house effect and Global warming?(f) What is critical density? State Hubble's law.

(3) Answer in brief any one question :(a) What is change in fundamental frequency of a tube open at both ends if

half of it is dipped vertically in water?(b) What happens when a tuning fork has only one prong?

(4) Answer in brief any one question.(a) What are advantages of Michelson's method over Foucault's Method for

the determination of speed of light?(b) ‘Sunglasses are made of Polaroid glasses but not of coloured glasses’.

Why?Group B

(5) Answer any three questions: (3×4=12)(a) State and explain Faraday's laws of electrolysis and verify second law

experimentally.(b) What is shunt? Describe the use of shunt to convert galvanometer into

ammeter?(c) Describe theory and working of an AC generator.(d) State Ampere Circuital law. Use it to find magnetic field intensity due to a

current carrying solenoid.(6) Answer any three questions: (3×4=12)

(a) Discuss the Millikan’s experiment to determine the value of plank's constant.

(b) What is Bragg’s law? Discuss how the crystal plane spacing is determined by using Bragg’s law.

(c) What is Zener diode? Discuss how it is used as voltage stabilizer.(d) What is nuclear fission? Give an example to illustrate your answer. Also

calculate energy released in a typical fission reaction.

(7) Answer any one question: (1×4=4)(a) What is standing wave? Derive an expression for it. Discuss positions of

nodes and antinodes on it.(b) What is end correction? How can end correction be calculated by using

resonance tube experiment?(8) Answer any one question: (1x4=4)

(a) State and prove law of refraction on the basis of wave theory.

(b) What is interference of light? Shows that the width of bright and dark fringes obtained in Double Slit's experiment are equal.

Group C

(9) Answer any two numerical questions: (2×4=8)

(a) A wire of resistance 0.5Ωm-1 is bent into a circle of radius 1m. The same material wire is connected across a diameter AB of circle. What is the equivalent resistance between two ends of the diameter of the circle?

(b) A horizontal straight wire 5cm long weighting 1.2g/m is perpendicular to a uniform of flux density 0.6T.If resistance of wire is 3.8Ω/m. Calculate the potential difference applied between ends of wire to make it just in balance.

(c) A constant AC supply is connected to a series circuit consisting of a resistance of 300 W in series with a capacitor of capacitance 6.67 mF, the frequency of the supply being 3000/2p Hz. It is desired to reduce the current in the circuit to half its value. Show how this could be done by placing an additional resistance.

(10) Solve any two numerical problems: (2×4=8)

(a) A beam of electron moving with velocity 107m/s enters midway between two horizontal parallel plates, in the direction parallel to the plates 5cm long and 2cm apart having potential difference V volt. Calculate V if the beam just grazes the edge of lower plate.(e/m = 1.8x 1011C/kg)

(b) An X-ray tube works at a DC potential difference of 50 kV. Only 0.4% of the energy of the cathode rays is converted into X-radiation and heat is generated in the target at a rate of 600 W. Estimate (i) the current passed into the tube (ii) the velocity of the electrons striking the target. (Electron mass = 9.10´10-31 kg, electron charge = -1.60´10-19 C)

(c) A radioactive source has decayed to one tenth of one percent of its initial activity in one hundred days. What is its half life period and mean life?

(11) A car travelling at 10ms-1 sounds its horn, which has a frequency of 500Hz and this is heard in another car which is travelling behind the first car in the same direction, with a velocity of 20ms-1. The sound can also be heard in the second car by reflection from a cliff. What frequencies will the driver of the second car hear?(velocity of sound in air=340ms-1 ) (4)

(12) A diffraction grating 2 cm wide has 2400 lines and is used in first order. What is the diffraction angle for light of wavelength 6000 Å? (3)

The End.

Riviera International Academy Practice Test – 2076

Subject : PhysicsSET:B

Class: XII Time: 3 hrs Full Marks: 75

Candidates are required to give their answer in their own words asfar as practicable. The figure in the margin indicates full marks.

Group A 1. Answer in brief, any FOUR questions. [4×2 = 8]

a. Two wires one of copper and other of Iron have the same diameter and carry the same current. In which wire will the drift velocity of electrons will be more?

b. Differentiate between fuse wire and heating wire.c. Does a charged particle moving through a magnetic field always

experience force?

d. Why do we prefer a potentiometer to measure emf of a cell than a voltmeter?

e. How is galvanometer converted into voltmeter?.f. Point out the difference between peltier effect and seeback effect..

2. Answer in brief, any FOUR questions. [4×2 = 8]a. Cathode rays cannot regarded as electromagnetic waves, why?b. What is the specific charge? What are the values of specific charge

of electron and proton?c. What do you mean by stopping potential?d. Does the threshold frequency depend on the intensity of light?e. What are the differences between Intrinsic and Extrinsic

semiconductors?.f. Why does the width of depletion layer of a p-n junction increase in

reverse biasing?3. Answer in brief, any ONE question. [1×2 = 2]

a. A tuning fork produces a feeble sound. But when it is pressed against a table, a loud sound is produced, why?

b. What happens to a frequency of transverse vibration of stretched string if its tension is halved and area of cross-section is doubled?

4. Answer in brief, any ONE question. [1×2 = 2]a. What are the conditions for constructive and destructive interference

of light?b. Define polarizing angle. How it is related with the refractive index

of the medium.

Group B5. Answer any THREE questions. [3×4 = 12]

a. State principle of Meter Bridge. Describe how it is used to determine the resistance of a wire.

b. Define drift velocity of electrons. Establish a relation between drift velocity of electrons and current density in the conductor.

c. State and explain Biot-Savart law. Use this law to find the magnetic field due to a long straight current carrying conductor.

d. What is electromagnetic induction? Explain Faraday's law of

electromagnetic induction a nd prove E =−d∅dt¿

¿

6. Answer any THREE questions. [3×4 = 12]a. Describe with necessary theory,Thomsons method to determine

specific charge of an electron..b. What is photoelectric effect? Discuss Einstein's photoelectric

equation.c. What is p-n junction diode? Describe forward and reverse bias

characteristics of a junction diode.d. Describe the working of center tapped full wave rectifier..

7. Answer any ONE question. [1×4 = 4]a. How are the beats formed when two waves are superimposed?

Deduce the expression for the beat frequency.b.What is Doppler's effect? Deduce the formula for the apparent

frequency of sound wave when the source and listener move towards each other.

8. Answer any ONE question. [1×4 = 4]a. Show that in Young double slit experiment of interference, width of

dark and bright fringes are equal.b. Discuss Fraunhofer diffraction at a single slit..

Group C9. Solve any TWO numerical problems. [2×4 = 8]a.A resistance of 1000W and of 2000W is placed in series with a 100V main supply. What will be the reading on a voltmeter of internal resistance 2000W when placed across?

i. 1000W resistance and ii. 2000W resistanceb. The driver cell of a potentiometer has an emf of 2V and negligible internal resistance. The potentiometer wire has a resistance of 3W. Calculate the resistance needed in series with the wire if a p.d of 5mv is required

across the whole wire. The wire is 100cm long and a balance length of 60cm is obtained for a thermocouple emf E. What is the value of E?c. A wire 28m long is bent into N terms of circular coil of diameter 14cm forming a solenoid of length 60cm. Calculate the flux density inside it, when a current of 5 ampere passes through it. (μ=12.57 X 10-7 m)10. Solve any TWO numerical problems. [2×4 = 8]

a. An oil drop of density 960kg/m3 and radius 10-6 m is driven vertically upwards through air by an electric field of 1.95 × 105 v/m with a constant velocity of 3.5 × 10-4 m/sec. If the viscosity of air is 1.8 × 10-5 Nsm-2, calculate the number of electronic charges on the drop. (Neglect up thrust due to air)

b. The photoelectric threshold wavelength of a tungsten surface is 272 nm. Calculate the maximum velocity of electrons ejected from this tungsten surface by ultraviolet radiation of frequency 1.45×1015 Hz. (h= 6.6 × 10-32Js, C=3×108 m/s, me= 9.1×10-31kg).

c. An electron moves in a circular path of radius 20cm in a magnetic field of 2 × 10-3 Tesla. Find the speed of the electron. What is the potential through which the electron must be accelerated to acquire this speed?

11. An open pipe 30 cm long and a closed pipe 23cm long, both of same diameters. Each are sounding its first overtone and these are in conison. What is the end correction of these pipes? [4]

12. A beam of light is reflected by a rotating mirror on to fixed mirrors which sends it back to the rotating mirror from which it is again reflected and then makes an angle of 18° with its original direction. The distance between the two mirrors is 104 m and the rotating mirror is making 375 revolutions per second. Calculate the velocity of light.[3]

The End.

Riviera International Academy Practice Test – 2076

Subject : PhysicsSET:C

Class: XII Time: 3 hrs Full Marks: 75

Candidates are required to give their answer in their own words asfar as practicable. The figure in the margin indicates full marks.

Group-A

1. Answer any FOUR questions in brief. [4x2=8]

a. Hall voltage is much more measurable in semiconductors than in metals. Why?

b. Will the drift velocity of electrons change if the diameter of a connecting wire is halved? Why?

c. Why do we prefer a potentiometer to measure emf of a cell rather than a voltmeter?

d. What are eddy currents? Write down its uses.e. What is meant by faraday’s constant?f. Write down the faraday’s laws of electromagnetic induction.

2. Answer any FOUR questions in brief. [4x2=8]

a. What do you mean by ionization potential?b. If the discharge tube is filled up with various gases in turn, will the

discharge in all gases take place at the same electrode potential?c. Explain the difference between stimulated and spontaneous emission

of radiation.d. Give circuit symbol and truth table of NAND gate.e. Gases become conducting at low pressure. Why?

3. Answer any ONE question in brief. [2x1=2] a. Longitudinal waves cannot be polarized. Why?b. What is the threshold of hearing? Define one bel.

4. Answer any ONE question in brief. [2x1=2] a. Differentiate between wave front and wavelet.b. Does the energy of light change when it travels from one medium to

another? Give reason.

Group-B5. Answer any THREE questions in brief. [4x3=12]

a. State Biot and Savart’s law and use it to obtain an expression for the magnetic field at the center of the circular coil.

b. State Lenz’s law and explain it is an example of conservation of energy.

c. State and verify Joule’s law of heating.d. Discuss the principle of potentiometer and use it to determine the

internal resistance of a cell.

6. Answer any THREE questions in brief. [4x3=12]

a. Discuss the laboratory method to determine the specific charge of an electron by J.J Thomson’s method.

b. What is rectifier? Describe the working of full wave rectifier using two semiconductors diodes.

c. Discuss photoelectric effect and derive Einstein’s photoelectric equation. What is stopping potential?

d. What are Bohr’s postulates of hydrogen atom? Derive an expression for the radius of Bohr’s orbit.

7. Answer any one question in brief. [4x1=4]

a. Show that both harmonics odd and even can be produced in an organ pipe open at both ends.

b. What is Doppler’s effect? Obtain an expression for the apparent pitch when a source moves towards stationary observer.

8. Answer any one question in brief. [4x1=4]

a. Describe the Michelson’s method of determining thespeed of light.

b. Discuss the young’s double slit experiment and show that the width of bright and dark fringes is equal.

Group-C9. Solve any TWO numerical problems. [4x2=8]

a. A standard cell of 1.0185volt, when used in a one meter long slide wire potentiometer balances at 60cm. Calculate the percentage error in a voltmeter which balances at 65cm when reading is 1.2volt.

b. A straight conductor of length 15cm is moving with uniform speed of 10m/s making an angle of 300 with uniform magnetic field of 10-

4Tesla. Calculate the emfinduced across the length.

c. A coil consisting of 100 circular loops with radius 0.60m carries a current of 5A. At what distance from the center along the magnetic field of magnitude 1/8 as great as it is at the center.

10. Solve any TWO numerical problems. [4x2=8] a. A hydrogen atom is in ground state. What is the quantum number to

which it will be excited absorbing a photon of energy 12.75eV?b. A clean nickel surface of work function 5.1eV is exposed to light of

wavelength 235nm. What is the maximum speed of the photoelectrons emitted from this surface?

c. Obtain the de-Broglie wave length of the electron having the kinetic energy of 3600eV. (Mass of electron=9.1×10-31, electronic charge= 1.6×10-19c, Planck’s constant= 6.6×10-34Js).

11. What is the difference between the speed of longitudinal waves in air at 270 C and their speed at -130 C? What is the speed at 00 C? 4

12. Calculate the polarizing angle for light traveling from water of refractive index 1.33 to glass of refractive index 1.5. 3

The End.