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KISHORE VAIGYANIK PROTSAHAN YOJANA

PRACTICE PAPER# 1

CLASS-XI

GENERAL INSTRUCTIONS

1. The question paper consists of two parts (Part- A contains multiple choice questions and Part- B contains descriptive type questions) for 100 marks. It consists of 40 questions of 1 mark each and 12 questions of 5 marks each. There will be four sections allotted for (1) Mathematics, (2) Physics, (3) Chemistry and (4) Biology. All questions are compulsory.

2. The question paper CODE is printed on the right hand top corner on this sheet of this booklet. 3. The composition of the question paper is given in the table below :

SI.

No. Subjective Part-A (Objective Type) Part-B (DescriptiveType)

1 Mathematics 10 questions - 1 mark each 03 questions - 5 marks each 2 Physics 10 questions - 1 mark each 03 questions -- 5 marks each 3 Chemistry 10 questions - 1 mark each 03 questions - 5 marks each

4 Biology 10 questions - 1 mark each 03 questions - 5 marks each

4. The answer paper for ‘Part-A’ is machine readable. Do not forget to mention your paper code and Roll Number neatly and clearly in the blank space provided in the Objective Response Sheet (ORS)/Answer Sheet.

5. For each question, indicate your answer by filling the corresponding oval with a HB pencil only.

6. There is negative marking for wrong answers in Part - A. Unanswered questions will not be evaluated and will not be penalized as a wrong answer.

7. In Part - A each correct answer gets 1 mark and for each incorrect answer 0.25 mark will be deducted. 8. In Part - B each correct answer gets 5 marks. There will be no negative marking for

Part - B. Part-B will be evaluated only for the top 50 students based on the marks obtained in Part - A. 9. You are permitted to use a non programable calculator.

10. Kindly note that both ‘Part-A' ORS Sheet and ‘Part-B' booklet have to be returned to the invigilator at the end of the respective sessions.

11. Candidates are permitted to carry only the 'Part-A' question paper after the examination.

Time : 3 Hr. Max. Marks : 100

PCCP Head Office / Talwandi Campus :

CODE

1

PART-A (1 Mark)

MATHEMATICS

1. Let s₁ (n) be the sum of the first n terms of the arithmetic progression 8, 12, 16, ... and let s₂(n) be the sum of the first n terms of arithmetic progression 17, 19, 21 ... If for some value of n, s₁(n) = s₂(n) then this common sum is :

(A) not uniquely determinable (B) 260

(C) 216 (D) 200

2. The number of solutions are in [0, 2] such that (sin(2x))4 = 1/8 is

(A) 2 (B) 4 (C) 8 (D) 16

3. The set of real numbers r satisfying :

0 7 r . 3 – r . 4 5 r . 8 – r . 3 2 2    is

(A) the set of all real numbers

(B) the set of all positive real numbers

(C) the set of all real numbers strictly between 1 and 5/3

(D) the set of all real numbers which are either less than 1 or greater than 5/3 4. If a, b and c are distinct real numbers such that a : (b + c) = b : (c + a) then

(A) a, b, c are all positive (B) a, b, c are all negative

(C) a + b + c = 0 (D) ab + bc + ca + 1 = 0

5. How many positive real numbers x are there such that _xx x

_

_

 ?

(A) 1 (B) 2 (C) 4 (D) infinite

6. Let [x] denote the greatest integer part of a real number x. If



7. Suppose for fixed real numbers a and b.f(x) = x3 _{+ ax}2 _{+ bx + c}

has 3 distinct roots for c = 0. Then (A) f_c(x) has 3 distinct roots for all real c

(B) f_c(x) has 3 distinct roots for all real c > 0 or for all real c < 0, but not for both (C) f_c(x) has 3 distinct roots for all real c in (p, q) for some p < 0 and q > 0 (D) f_c(x) need not have 3 distinct roots for any real c other than zero

8. Given a semicircle of radius 1, let a be the side of an equilateral triangle which is inscribed in the semicircle with its vertices on the boundary of the semicircle (boundary includes the bounding diameter also). Then the set of possible values of a is

(A) {1}

(B) {1, 3 2

}

(C) the set of all positive real numbers not exceeding 3 2

(D) the set of all real numbers which are greater than or equal to 1, but less than or equal to 3 2

9. A ray of light originating at the vertex A of a square ABCD passes through the vertex B after getting

reflected by BC, CD and DA in that order. If  is the angle of the initial position of the ray with AB then sin

equals.

(A) 2/ 13 (B) 3/ 13 (C) 3/5 (D) 4/5

10. Let ABC be triangle with AB = AC = 6. If the circumradius of the triangle is 5, then BC equals

(A) 25/3 (B) 9 (C) 48/5 (D) 10

PHYSICS

11. A fully loaded elevator has a mass of 6000 kg. The tension in the cable as the elevator is accelerated downward with an acceleration of 2ms–2 _{is (Take g = I0 ms}–2₎

(A) 7·2 × 104 N (B) 4.8 × 104 N (C) 6 × 104 N (D) 1.2 × 104 N

12. A body is moving with constant acceleration from A to B in a straight line. C is the mid-point of AB. If u and v are the speeds at A and B respectively. The speed at C is

(A) 2 v u (B) 2 u – v (C) 2 v u2 2 (D) 2 u – v2 2

13. A ray of light enters a slab of material with increasing refractive index. Four possibilities of the trajectory of the ray are shown below.

Slab with increasing Refractive index D C B A

The correct choice is :

14. The isotope 238 92

U decays through a chain of  and  emissions ending up at the product Pb20682 . This

chain involves

(A) 8  emission and 6  emissions

(B) 8  emission and 8  emissions

(C) 6  emission and 8  emissions

(D) 6  emission and 6  emissions

15. Figure shows an assembly consisting of a number of pendulums of varying lengths. The driver pendulum is pulled aside and released so that it oscillates in a plane perpendicular to that of the diagram. It will be observed that

String Driver pendulum

(A) all pendulums oscillate with the frequency of the driver pendulum and have the same amplitude. (B) pendulums oscillate with different frequencies but equal amplitude, the shortest pendulum oscillating with the highest frequency.

(C) all pendulums oscillate with the frequency of the driver pendulum; the pendulum with length equal to that of the driver has the greatest amplitude.

(D) pendulums oscillate with different frequencies and different amplitudes.

16. You are riding on your bicycle with inflated tyres. Your friend asks for a lift and sits on the carrier behind you :

(A) The air pressure in the tyres increases. (B) The air pressure in the tyres decreases. (C) The air pressure in the tyres remains the same.

(D) Nothing in the system changes except the reaction of the ground

17. The circuit shown has 3 identical light bulbs A, B, C and 2 identical batteries E₁, E₂ . When the switch is open, A and B glow with equal brightness. When the switch is closed:

A B C S E1 E2

(A) A and B will maintain their brightness and C will be dimmer than A and B. (B) A and B will become dimmer and C will be brighter than A and B.

18. A boat at rest has two persons of unequal weights seated at either end. If they walk across the boat and interchange their positions,

(A) the boat will move in the direction of walking of the lighter person. (B) the boat will move in the direction of walking of the heavier person. (C) the boat will not move at all.

(D) the boat will oscillate about a mean position and stop once the persons have moved to the new positions.

19. A physical quantity that is conserved in a process (A) must have the same value for all observers. (B) can never take negative values.

(C) must be dimensionless.

(D) need not necessarily be a scalar.

20. A coolant in a chemical or nuclear plant is a liquid that is used to prevent different parts of a plant from getting too hot. One important property of coolant is that it

(A) should have low specific heat. (B) should have high specific heat.

(C) high density and low thermal conductivity. (D) low density and high thermal conductivity.

CHEMISTRY

21. The half-life of 60₂₇Co is 5.3 years. How much of 20 g of 60₂₇Co will remain radioactive after 21.2 years ?

(A) 10 g (B) 1.25 g (C) 2.5 g (D) 3.0 g

22. The element which reacts both with acids and bases to produce a salt and hydrogen gas is

-(A) Zn (B) Mg (C) Li (D) S

23. The compound having a triple bond is

-(A) Benzene (B) Cyclohexane (C) Acetylene (D) Glucose

24. An element which has 2 electrons less than that in Ne is

-(A) Mg (B) Na (C) O (D) F

25. Chlorine gas is produced from HCI by the addition of

-(A) K₂SO₄ (B) KCl (C) KNO₃ (D) KMnO₄

26. Among HCl, HBr, HF, and HI the weakest acid in water is

-(A) HCl (B) HF (C) HBr (D) HI

27. Products of the reaction Ca(OH)₂ + 2NH₄Cl, are

(A) CaCI₂ + 2NH₃ + 2H₂O (B) CaCl₂ + NH₄OH + H₂

(C) CaO + 2NH₃ + 2H₂O (D) CaO + NH₄OH + H₂

28. When a few drops of concentrated sulphuric acid are added to a few drops of a clear sugar (sucrose) solution in a test tube, the solution

(A) remains colorless (B) turns black (C) turns blue (D) turns white 29. The reaction ZnO + C  Zn + CO is an example of a

(A) Combination reaction (B) Reduction-oxidation reaction

(C) Displacement reaction (D) Decomposition Reaction

30. The monomer of Teflon is : (A) Me (B) Cl (C) CN (D) F F F F

BIOLOGY

(A) A mixture of destroyed germs, killed leucocytes and damaged tissue cells (B) Concentrated blood plasma

(C) Thick mucus secretion

(D) Concentrated secretion of the sebaceous gland

32. Discovery of fossils has provided biologists with significant clues as in the steps in evolution. Archaeop-teryx one such example, which is connection link between :

(A) Pisces and amphibian (B) Amphibia and reptilia

(C) Reptilia and aves (D) Aves and mammalian

33. Which of the following is a bacterial disease ?

(A) Smallpox (B) Measles (C) Meningitis (D) Rabies

34. During photosynthesis, light energy :

(A) Is converted to chemical energy (B) Is converted to kinetic energy

(C) Is the catalyst (D) Dissociates CO₂ directly

35. Majority of the world population depends largely on the following for their staple food :

(A) Fungi and algae (B) Animal products

(C) Dicotyledenous (D) Monocotyledenous plants

36. If you put a nail at the middle of a young plant and allow it to grow, then : (A) You will find the nail at the same position after the tree is fully grown (B) The nail will fall out

(C) The nail will rise along with the tree (D) The nail will come closer to the ground

37. If you are asked to write on a topic of interest, you can read as many books as you want but never copy someone else's writing on the same topic. The act is called plagiarism and is morally incorrect, as : (A) You are stealing someone else's labor (B) It is a punishable offence in court

(C) You have not paid money to do so (D) A patent exists on the writing

38. A couple has 8 children, all boys. What is the chance that their ninth child will be another boy ?

(A) 1/2 (B) 1/4 (C) 1/8 (D) 1/16

39. Grapes were put in a concentrated sugar solution. On examination after 12 hours, the grapes were shrunken. This is because :

(A) Grapes become sweeter (B) Water evaporates from the solution

(C) Sugar induces disintegration of grapes (D) Loss of water from grapes by osmosis 40. On a normal sunny day, rate of photosynthesis (per unit time) is maximum during :

(A) Early morning (B) Between late morning to before noon

PART-B (5 Mark)

MATHEMATICS

1. A square ABCD is constructed inside a triangle PQR having sides 10, 17 and 21 as shown in figure. Find the perimeter of the square ABCD.

2. 10 parallel lines of length 5 cm each are drawn such that the distance between any two consecutive lines is 1 cm. One line is selected randomly and its ends are marked as A and B. One other line is selected and its midpoint is marked as M. Find the sum of the areas of all the possible triangles ABM.

3. C₁ and C₂ are centres of two identical semi circles with radius ‘r’ units. The ratio of C1P1 to PQ is 1

: 7, as shown in the figure. Find the radius of the circle inscribed in the region common to the identical semicircles, given that the circle touches the two semicircles and the line segment P₁P₂.

P C1 P1 P2 C2 Q

PHYSICS

4. Find the force F to be applied on M, so that m remains stationary with respect to M ?

M F

m

5. Two identical plano-convex lenses can be combined in three ways, as shown. Find theratio of the focal lengths of these combinations.

(i) (ii) (iii)

6. Find the Current in the branch CD of the circuit as given below :

CHEMISTRY

7. A solid mixture (5.0g) consisting of lead nitrate and sodium nitrate was heated below 600ºC unit the

weight of the residue was constant. If the loss in weight is 28.0 percent, find the amount of lead nitrate and sodium nitrate in the mixture.

8. One mole of an ideal gas undergoes a series of changes as shown in the graph in which X, Y, Z mark the three stages of the system. At each stage the variables are shown in the graph.

x y 20.0L 10.0L V z 300K 600K T

(a) Calculate the pressure at three stages of the system. (b) Name the processes during the following changes.

(i) X to Y (ii) Y to Z

(iii) Z to X and (iv) overall change.

9. The pH of an aqueous solution of ammonia is 11.5. Find the molarity of the solution. K_b(NH₄OH) = 1.8 × 10–5

BIOLOGY

(i) Name the blood vessel that brings oxygenated blood to human heart. (ii) Which chamber of human heart receives oxygenated blood ?

(iii) Name the types of flowers present in Cyathium. (iv) What is Kieselguhr ?

(v) Define Metamorphosis.

11. Answer the following Questions :

(i) What are the anticoagulants present in blood? (ii) Name the breakdown products of haemoglobin . (iii) What are Maurer's dots ?

(iv) In human beings, blue eye colour is recessive to brown eye .A brown eyed man has a blue eyed mother.

(A) What is the genotype of man and his mother? (B) what are possible genotypes of his father ? 12. Define the following terms :

(i) Erythroblastosis foetalis (ii) Serum

(iii) Hole in the heart. (iv) Pacemaker of heart. (v) Scutellum,