KENDRIYA VIYALAYA AFS GURGAON Winter BREAK HOME WORK

SUBJECT-ENGLISH

Class XII A & B -

03 Question papers (First Pre Board 2016-17)

Revision of complete syllabus for 2nd Pre Board

SUBJECT OF ACCOUNTANCY CLASS XII A

Scanner-

1. Chapter 1 to 6 Chapter in 1st Book2. Chapter 7 to 8,9, 2 Book3. Chapter 10,11,12,13, 3rd Book

Project work

Specific Project-1 Company .s Bal.Sheet Down Load of Any Company and

Calculate ratoio no1

liquidyed ratio and

Solvency ratio,

Activity,

Profebilitiy ratio.

Project Work

Purchase 10 days Economics Times and Cut And Paste 5 Different Companies And Draw Bar Diagram.

Business Study

Sold Question Papers

Modal Question Paper 1,2,3, Backside of Business Study Book, Project in Markting

Chemistry

XII A 1. Learn & Write 20 name reactions.

2. Solve the all the three sets of P.B.1

3. Write all formulae of phy.Chem & learn.

4. Solve 10 numerical from chapter 1to 4 involving different formulae

Of a particular chapter.

5. Complete one investigatory project from the given topics.

SUBJECT- HINDI

SUBJECT –PHYSICS

Class-XII

UNIT – VI OPTICS

CBSE 2014:(Delhi Sets)

1. A convex lens is placed in contact with a plane mirror. A point object at a distance of 20 cm on the axis of this combination has its image coinciding with itself. What is the focal length of the lens?

[1

2. For a single slit of width "a", the first minimum of the interference pattern of a l monochromatic

light of wavelength λ occurs at an angle of . At the same angle of we get a maximum for two narrow slits separated by a distance "a". Explain. [2

3. (a) Draw a labelled ray diagram showing the formation of a final image by a compound microscope at least distance of distinct vision. (b) The total magnification produced by a compound microscope is 20. The magnification

produced by the eye piece is 5. The microscope is focussed on a certain object. The distance between the objective and eyepiece is observed to be 14 cm. If least distance of distinct vision is 20 cm, calculate the focal length of the objective and the eye piece.

[3

4. (a) A mobile phone lies along the principal axis of a concave mirror. Show, with the help of a suitable diagram, the formation of its image. Explain why magnification is not uniform. (b) Suppose the lower half of the concave mirror's reflecting surface is covered with an opaque

material. What effect this will have on the image of the object? Explain.

5. (a) (i) 'Two independent monochromatic sources of light cannot produce a sustained interference pattern'. Give reason.

(ii) Light waves each of amplitude "a" and frequency "ω", emanating from two coherent light sources superpose at a point. If the displacements due to these waves is given by

, and where ϕ is the phase difference between the two, obtain the expression for the resultant intensity at the point.

(b) In Young's double slit experiment, using monochromatic light of wavelength λ, the intensity of light at a point on the screen where path difference is A, is K units. Find out the intensity of light at a point where path difference is λ/3.

OR

(a) How does one demonstrate, using a suitable diagram, that unpolarised light when passed through a Polaroid gets polarised?

(b) A beam of unpolarised light is incident on a glass-air interface. Show, using a suitable ray

diagram, that light reflected from the interface is totally polarised, when , where µ, is the refractive index of glass with respect to air and iB is the Brewster's angle.

CBSE 2013:(Delhi Sets)

1. Write the relationship between angle of incidence ‘I’ and angle of prism ‘A’ and angle of minimum deviation for a triangular prism.

[1

2. Which of the following wave can be polarized [1(i) heat wave (ii) sound wave? Give reason to support your answer.

3. (a) Write the necessary conditions for the phenomenon of total internal reflection to occur. [2(b) Write the relation between the refractive index and critical angle for a given pair of optical

media.

4. A convex lens of focal length 25 cm is placed coaxially in contact with a concave lens of focal length 20 cm. Determine the power of the combination. Will the system be converging or diverging in nature?

[2

5. (a) In what way is diffraction from each slit related to the interference pattern in a double slit experiment?

[3(b) Two wavelengths of sodium light 590 nm and 596 nm are used, in turn, to study the

diffraction taking place at a single slit of aperture 2 × 10 – 4 m. The distance between the slit and the screen is 1.5 m. Calculate the separation between the positions of the first maxima of the diffraction pattern obtained in the two cases.

6. (a) Draw a ray diagram showing the image formation by a compound microscope. Hence obtain expression for total magnification when the image is formed at infinity. [5

(b) Distinguish between myopia and hypermetropia. Show diagrammatically how these defects can be corrected.

OR

(a) State Huygen's principle. Using this principle draw a diagram to show how a plane wave front incident at the interface of the two media gets refracted when it propagates from a rarer to a denser medium. Hence verify Snell's law of refraction.

(b) When monochromatic light travels from a rarer to a denser medium, explain the following, giving reasons:

(i) Is the frequency of reflected and refracted light same as the frequency of incident light?

(ii) Does the decrease in speed imply a reduction in the energy carried by light wave.

CBSE 2011:(Delhi Sets)

7. A convex lens made up of glass of refractive index 1.5 is dipped, in turn, in (i) a medium of refractive index 1.65, (ii) a medium of refractive index 1.33.

[3(a) Will it behave as a converging or a diverging lens in the two cases? (b) How will its focal length change in the two media?

8. Use the mirror equation to show that[3

(a) an object placed between f and 2f of a concave mirror produces a real image beyond 2f.(b) a convex mirror always produces a virtual image independent of the location of the object. (c) an object placed between the pole and focus of a concave mirror produces a virtual and enlarged

image.

9. A compound microscope uses an objective lens of focal length 4 cm and eyepiece lens of focal length 10 cm. An object is placed at 6 cm from the objective lens. Calculate the magnifying power of the compound microscope. Also calculate the length of the microscope. [3

ORA giant refracting telescope at an observatory has an objective lens of focal length 15 m. If an eyepiece lens of focal length 1.0 cm is used, find the angular magnification of the telescope.

If this telescope is used to view the moon, what is the diameter of the image of the moon formed by the objective lens? The diameter of the moon is 3.42 × 106 m and the radius of the lunar orbit is 3.8 × 108 m.

10. State the importance of coherent sources in the phenomenon of interference.In Young's double slit experiment to produce interference pattern, obtain the conditions for constructive and destructive interference. Hence deduce the expression for the fringe width.How does the fringe width get affected, if the entire experimental apparatus of Young is immersed in water? [5

OR(a) State Huygens Principle. Using this principle explain how a .-diffraction pattern is obtained on a

screen due to a narrow slit on which a narrow beam coming from a monochromatic source of light is incident normally.

(b) Show that the angular width of the first diffraction fringe is half of that of the central fringe. (c) If a monochromatic source of light is replaced by white light, what change would you observe in

the diffraction pattern?11. A convex lens made up of glass of refractive index 1.5 is dipped, in turn, in (i) a medium

of refractive index 1.6, (ii) a medium of refractive index 1.3.(a) Will it behave as a converging or a diverging lens in the two cases?(b)How will its focal length change in the two media? [3

12. A converging lens has a focal length of 20 cm in air. It is made of a material of refractive index 1.6. It is immersed in a liquid of refractive index 1.3. Calculate its new focal length.[3

CBSE 2010:

1. A converging lens is kept coaxially in contact with a diverging lens - both the lenses being of equal focal lengths. What is the focal length of the combination?

[12. When light travels from a rarer to denser medium, the speed decreases. Does this decrease in

speed imply a decrease in energy carried by the light wave? Justify your answer. [13. (i) Draw a neat labelled diagram of an astronomical telescope in normal adjustment. Explain

briefly its working. [3

(ii) An astronomical telescope uses two lenses of power 10 D and 1 D. what is the magnifying power in normal adjustment.

OR

(i) Draw a neat labelled diagram of a compound microscope. Explain briefly its working. (ii) Why must both the objective and eyepiece of a compound microscope have short focal

length? 4. In Young’s double slit experiment, the two slits 0.15 mm apart are illuminated by

monochromatic light of wavelength 450 nm. The screen is 1 m away from the slits [3

(a) Find the distance of the second (i) bright fringe, (ii) dark fringe from the central maximum. (b) How will the fringe pattern change if the screen is moved away from the slits?

(Set II) In Young’s double slit experiment, the two slits 0.12 mm apart are illuminated by monochromatic light of wavelength 420 nm. The screen is 1 m away from the slits

(a) Find the distance of the second (i) bright fringe, (ii) dark fringe from the central maximum. (b) How will the fringe pattern change if the screen is moved away from the slits? (Set III) In Young’s double slit experiment, the two slits 0.2 mm apart are illuminated by monochromatic light of wavelength 600 nm. The screen is 1 m away from the slits

(a) Find the distance of the second (i) bright fringe, (ii) dark fringe from the central maximum. (b) How will the fringe pattern change if the screen is moved away from the slits?

5. How does an unpolarised light gets polarised when passed though a polaroid? [3

Two polaroids are set in the crossed positions. A third polaroid is placed between the two making an angle θ with the pass axis of the first polaroid. Write the expression for the intensity of light transmitted from the second polaroid. In what orientation the intensity of the transmitted light will be (i) minimum and (ii) maximum.

6. An illuminated object and a screen are placed 90 cm apart. Determine the focal length and nature of lens required to produce a clear image on the screen, twice the size of the object.

[3(Set II) The image obtained with a convex lens is erect and its length is four times the length of the object. If the focal length of the lens is 20 cm, calculate the object and image distances.

(Set III) A convex lens is used to obtain image of an object on screen 10 m from the lens. If the magnification is 19, find the focal length of the lens.

INVESTIGATORY PROJECTS FOR FINAL PRACTICAL EXAM

KENDRIYA VIDYALAYA No-1 AFS GURGAON.ACHIEVEMENT TEST : 2016-17

Subject: Mathematics Time: 3 hours Class : XII Max. Marks : 100

General Instructions:

(i) All questions are compulsory.(ii) Question numbers 1-4 in section A are very short-answer type

questions carrying 1 mark each.(iii) Question numbers 5-12 in section B are short-answer type questions

carrying 2 marks each.(iv) Question numbers 13-23 in section C are long –answer-I type

questions carrying 4 marks each.(v) Question numbers 24 -29 in section D are long –answer-II type

questions carrying 6 marks each.

SECTION-A

Question numbers 1 to 4 carry 1 mark each.

Q1) Let f: R → R such that f(x) =sin x and g: R→R such that g(x)=x2, find fog.

Q2) Evaluate: |cos15 ° sin 15°sin75 ° cos75°| .

Q3) If y= log5 x , find dydx

.

Q4) Find ∫ sin xsin(x+a)

dx

SECTION-B

Question numbers 5 to 12 carry 2 marks each.

Q5) Prove that 2tan−1 12 + tan−1 1

7 = tan−1 3117

Q6) Find non zero value of x, satisfying the matrix equation: x(2 x 2

3 x) + 2 (8 5 x4 4 x ) = 2 (x2+8 24

10 6x )Q7) Prove that the function f given by f(x) =¿ x−1∨¿, xϵ R is not differentiable at x=1.Q8) Differentiate: sin2 x w.r.t. ecos x .

Q9) Using differentials, find the approximate value of f (2.01 ), where f(x) = 4x2 + 5x +2.

Q10) Evaluate : ∫2

8

¿ x−5∨¿¿ dx.

Q11) Find ∫ x3 sin ¿¿¿¿ dx

Q12) Show that the function f: N → N given by f (x) =2x is one - one but not onto.

SECTION – C

Question numbers 13 to 23 carry 4 marks each.

Q13) Let A={1,2,3,….9} and R be the relation defined on A ×A by (a,b) R(c,d)

iff a + d = b + c. Prove that R is an equivalence relation. Also find the equivalence class [(2,5)].

Q14) Consider the binary operations * : R x R → R and O : R x R → R defined as a* b =| a-b | and a o b =a for all a,b ϵ R .Show that * is commutative but not associative and o is associative but not commutative.

Q15) Show that sin−1( 1213 )+cos−1( 4

5 )+ tan−1( 6316 )=π

OR Solve: sin−1 (1−x )−2sin−1 x= π

2

Q16) Using properties of determinants,

prove that | 3 a −a+b −a+c−b+a 3 b −b+c−c+a −c+b 3 c |=3(a+b+c). (ab+bc+ca).

Q17) If A= [ 0 −tan α2

tan α2

0 ] and I is the Identity matrix of order 2,

show that (I+A)=(I–A). [cosα −sin αsin α cos α ].

Q18) If x = a (cos t + log tan t2 ), y = a sin t, find d2 y

dt 2 and d2 ydx2 .

Q19) Find the derivative of the function given by f(x) = (1+x) (1+x2¿ (1+ x4)(1+x8) and hence find f '(1).

Q20) Find the values of x for which f(x) = [x (x–2)]2 is an increasing function. Also find the points on the curve, where the tangent is parallel to x- axis.

OR

A man of height 2 meters walks at uniform speed of 5 kilometers/ hour away from a lamp post which is 6 meters high. Find the rate at which the length of his shadow increases.

Q21) ∫ xsin−1 x√1−x2 dx OR ∫ (√ tan x+√cot x¿)dx¿

Q22) Using the properties of definite integrals, evaluate: ∫π /6

π /3 dx1+√ tan x

Q23) Express tan−1[ a cos x−b sin xbcos x+a sin x ] in simplest form if a

b tan x > –1.

SECTION-C

Question numbers 24 to 29 carry 6 marks each.

Q24) Usingintegration , find the area of the region bounded by the triangle whose vertices are (-1, 0), (1, 3), and (3, 2).

OR

Find the area lying above x-axis and included between the circle x2+ y2 = 8 x and the parabola y2= 4 x.

Q25) Find : ∫ ( x2+1 )( x2+2)( x2+3 )(x2+4)

dx.

OR

Evaluate ∫0

4

( x+e2x ) dx as the limit of a sum.

Q26) Two sign boards, one circular and another square are to be made cutting a wire of length 40 m into two pieces. The sign boards are to depict ‘BE HONEST’ & ‘BE PUNCTUAL’ and these are to be displayed near the main gate of school. What should be the length of the two pieces, so that the combined area of the square & the circle is minimum.

Q27) Three friends A, B and C visited a super market for purchasing fresh fruits. A purchased 1kg apples, 3kg grapes and 4kg oranges and paid £ 800. B purchased 2kg apples, 1kg grapes and 2kg oranges and paid £ 500. C

purchased 5kg apples, 1kg grapes and 1kg oranges and paid £ 700. Find the cost of each fruit per kg by matrix method. Why fruits are good for health?

OR Using elementary row transformations, find the inverse of the matrix

[ 1 3 −2−3 0 −12 1 0 ]

Q28) Given that cos x2

. cos x4

. cos x8

… ….= sin xx , prove that

122 sec2( x

2 )+ 124 sec2( x

4 )+… ..=cosec2 x− 1x2 .

Q29) Show that semi-vertical angle of right circular cone of given surface area and

maximum volume issin−1( 13 ).

Test – chapter-1,2 & 3 Class –XII Duration : 90 min Mathematics Max. Marks : 50

Note : i) All questions are compulsory.

ii) Question numbers 1 to 6 carry 1 mark each.

iii) Question numbers 7 to 12 carry 4 marks each.

iv) Question numbers 13 to 16 carry 5 marks each.

1.Write the identity element for the binary operation * defined on set R of all real numbers by the rule a* b = 3 ab

7 for all a, b € R.

2. If f: R →R is defined by f(x) =x2 - 3x +2, find f(f(x)).

3. If A={ a, b, c, d },find the number of binary operations on A.

4. Consider the set A={ 1, 2, 3 } and relation R ={(1, 2), (1, 3)}. Is R a transitive relation ? Justify your answer.

5.Ifsin−1 x + sin−1 y + sin−1 z=3π2 ,then find the value of x + y + z

6. If the matrix A =5 2 x2 7 −34 t −7

is a symmetric matrix, find the

value of x and t.

7. Check whether the relation R on R, defined as R = { ( a , b ) :a ≤ b3 } is reflexive symmetric or transitive.

8. Let f : N→ Y : f (x) = 4 x2 + 12 x + 15 and Y = range( f ). Show that f is invertible and find f−1.

9. Prove that cos−112/13+¿ sin−13 /5¿ = sin−156 /65 .

10. Prove that tan−1{ √1+x2+√1−x2

√1+x2 – √1−x2 } = π4 + 1/2 cos−1 x2

11. Prove that tan−11 /4+¿¿ tan−12 /9 = ½ cos−13 /5. 12. Express the following matrix as the sum of a symmetric and a

skew symmetric matrix and verify your result :3 −2 −43 −2 −5

−1 1 2

13. Find the inverse of the following matrix by using elementary

row transformation : 2 3 12 8 13 7 2

14. Check whether the operation * defined on set A =R x R as ( a, b )* ( c , d ) = ( a + c , b + d ) is a binary operation or not, where R is the set of all real numbers . If it is a binary operation , is it commutative and associative too ? Also find the identity of *. Also write the inverse element of the element ( 3, - 5 ) in A.

15. Let R be the relation on N x N defined by

( a , b ) R (c , d ) ⇔ ad (b+c )=¿ bc ( a + d ). Check whether R is an equivalence relation on NxN.

16. Prove that tan ⌈ π4

+ 12

cos−1( ab )⌉ + tan ⌈ π

4−1

2cos−1( a

b )⌉ =2b/a

ORSolve : tan−12 x+tan−13 x= nπ + 3π /4 where n € Z.

Test – chapter-4 & 5

Class XII- Mathematics

Time allowed – 90 min. Max Marks: 50

Note:- (i) All questions are compulsory.

(ii) Question numbers 1 to 10 carry 1 mark each.

(iii) Question numbers 11 to 20 carry 4 mark each.

1. Examine the applicability of Rolle’s theorem for the function f(x)= |x| in [-2,2].

2. If y = ¿)n , prove that dydx =

ny√x2+a2 .

3. If y = log5 (log x), find dydx

.

4. Find the derivative of Sin(Sin x2) at x = √ π2

.

5. Differentiate xSinx , x > 0, w . r . t . ‘x’.

6. A balloon, which always remains spherical, has a variable diameter 32

(2 x+1 ) .

Find the rate of change of its volume with respect to x .

7. Find points on the curve x2

9 + y2

16 = 1 at which the tangents are parallel to

y axis.

8. Find the approximate change in the volume ‘V’ of a cube of side x meters caused by increasing the side by 2%.

9. The amount of pollution content added in the air in a city due to x- diesel vehicles is given by P(x) = 0.005x3 + 0.02x2 + 30x. Find the marginal increase in pollution content when 3 diesel vehicles are added and write which value is indicated in the above question.

10. Find the maximum and minimum values of the function ‘ f ’ given by f(x) Sin x + Cos x.

11.For a positive constant ‘a’ find dydx where y= a¿¿and x= ( t + 1

t ) .

12. If y =ea cos−1 x, -1 ≤ x ≤1, show that (1-x2) d2y/dx2 – x dydx - a2 y2 = 0.

13. It is given that for the function f(x) = x3 + bx2 +ax +5 on [1,3], Rolle’s

theorem holds with C= 2+ 1√3 . Find the values of ‘a’ and ‘b’.

14. Differentiate tan-1 ¿) w.r.t. Sec-1 ¿) .

15. If the function ‘f’ defined by f(x) = 1-sin 3 x , x ˂ π2 3cos2x

a , x = π2

b(1−sin x )( π−2 x )2

, x ˃ π2

is continuous at x= π2 , find the values of a and b.

16. Find the equation of the tangent to the curve y= x−7( x−2 )(x−3) at the point

where it cuts the x-axis.17. Show that the right circular cone of least curved surface and given volume

has an altitude equal to √2 times the radius of the base.

18. A window is in the form of a rectangle above which there is a semicircle. If the perimeter of the window is P cm, show that the window will admit

maximum possible light only when the radius of semicircle is Pπ+4 cm.

19. Find the interval in which the function f(x) = [x (x-2)]2 is strictly increasing or strictly decreasing.

20. Sand is pouring from a pipe at the rate of 12cm3/s. The falling sand forms a cone on the ground in such a way that the height of the curve is always one sixth of the radius of the base. How fast is the height of the sand cone increasing when the height is 4cm?