ijso workshop (4.10.11 to 8.10.11) dignostic test (04.10.11)

IJSO(STAGE-I)

WORK SHOP

DIAGNOSTIC TEST

GENERAL INSTRUCTIONS

1. In addition to this question paper, you are given a separate answer sheet.

2. Fill up all the entries carefully in the space provided on the OMR sheet ONLY IN BLOCK CAPITALS.

Incomplete/incorrect/carelessly filled information may disqualify your candidature.

3. A student has to write his/her answers in the OMR sheet by darkening the appropriate bubble with the

help of HB Pencil as the correct answer(s) of the question attempted.

4. Paper carries 80 questions each of 3 marks.

5. Any rough work should be done only on the blank space provided at the end of question paper.

6. For each correct answer gets 3 marks, each wrong answer gets a penalty of 1 mark.

7. Blank papers, clip boards, log tables, slide rule, mobiles or any other electronic gadgets in any form is

"NOT PERMISSIBLE".

8. Use of nonprogrammable calculator is allowed.

Time : 2 Hr. Max. Marks : 240

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WORK SHOP_IJSO_ STAGE-I _DIAGNOSTIC TEST_PAGE #1

DIAGNOSTIC TEST PAPER

1. The sum of the reciprocals of the roots of the equation,20102009

x + 1 + x1

= 0, is :

(A) 20092010

� (B) � 1 (C) 20102009

(D) 1

2. A round pencil has length 8 units when unstreched and diameter 1/4. It is sharpened perfectly so that itremains 8 units long with 7 units section still cylindrical and remaining 1 unit giving a conical tip. Volumeof the pencil now is :

(A) 9611

(B) 19237

(C) 647

(D) None

3. The four digit number 2652 is such that any two consecutive digits from it make a multiple of 13. Anothernumber N has this same property, is 100 digits long, and begins in a 9. The last digit of N, is :(A) 2 (B) 3 (C) 6 (D) 9

4. Given 2y cos = x sin and 2x sec � y cosec = 3, then the value of x2 + 4y2 is equal to :(A) 1 (B) 2 (C) 3 (D) 4

5. In the diagram B, C and D lie on a straight line, with ACD = 100°, ADB = x°, ABD = 2x° and DAC= BAC = y°. The value of (sin y°. tan y° + sec y°) equals :

A

B C D

2x° 100°x°

y° y°

(A) 7/2 (B) 3 (C) 5/2 (D) 5



6. A sphere is inscribed in a cone of radius 33 and slant height 36 . The radius of the sphere, is :

(A) 0 (B) 3 (C) 36 (D) 233

7. Let A = { x : x N }, B = { x : x is a prime natural number }, then A B is :

(A) N (B) A (C) B (D)

8. In figure, PQ is tangent at point R of the circle with centre O. If TRQ = 30º, find PRS(A) 60º (B) 90° (C) 30° (D) 40°

9. In ABC, segments AD, BE and CF are the altitudes. If AB × AC = 28.80 and BE × CF = 20, then

AD × BC equals :

(A) 24.4 (B) 24.2 (C) 24.0 (D) 23.8

10. If both a and b belong to the set {1, 2, 3, 4}, then the number of equations of the form ax2 + bx + 1 = 0having real roots is :(A) 10 (B) 7 (C) 6 (D) 12

11. Three parallel lines 1,

2 and

3 are drawn through the vertices A, B and C of a square ABCD. If the

distance between 1 and

2 is 7 and between

2 and

3 is 12, then the area of the square ABCD is :

(A) 193 (B) 169 (C) 196 (D) 225



12. Find out (A + B + C + D) such that AB x CB = DDD, where AB and CB are two-digit numbers and DDDis a three-digit number :(A) 21 (B) 19 (C) 17 (D) 18

13. The value of 12 � 22 + 32 � 42 + 52 � 62 + ....+ 992 � 1002 is :(A) � 100 (B) � 5050 (C) � 2500 (D) � 2520

14. Let a and b be distinct real numbers for which a10bb10a

ba

= 2. The value of

ba

is equal to :

(A) 0.5 (B) 0.6 (C) 0.8 (D) 1 or 0.8

15. If xa × xb × xc = 1, then a3 + b3 + c3 is equal to :(A) 9 (B) abc (C) a + b + c (D) 3abc

16. If from the top of a tower 50 m high, the angles of depression of two objects due north of the tower arerespectively 60º and 45º, then the approximate distance between the objects, is ;

(A) 2250 m (B) 3350 m (C) 31 m (D) )13(3

50 m

17. The radius of a cone is 2 times the height of the cone. A cube of maximum possible volume is cut from

the same cone. What is the ratio of the volume of the cone to the volume of the cube ?

(A) 3.18 (B) 2.25 (C) 2.35 (D) can�t be determined

18. Alloy A contains 40% gold and 60% silver. Alloy B contains 35% gold and 40% silver and 25%copper. Alloys A and B are mixed in the ratio of 1 : 4. What is the ratio of gold and silver in the newlyformed alloy is :(A) 20% and 30% (B) 36% and 44% (C) 25% and 35% (D) 49% and 36%

19. PQ is a chord of a circle. The tangent XR at X on the circle cuts PQ produced at R. If XR = 12 cm, PQ = x cm,

QR = x � 2 cm, then x in cm is :

X

12

RP Q

x x� 2

(A) 6 (B) 7 (C) 10 (D) 14



20. If the decimal 0.d25d25d25 ..... is expressible in the form n/27, then d + n must be :(A) 9 (B) 28 (C) 30 (D) 34

21. A particle moves on x axis according to equation, x = t2 + 2t + 1 [Here x is in metre and t is in second ]Its displacement in t = 0 to t = 1 sec. is :(A) 4 m (B) 2 m (C) 3 m (D) 1 m

22. Impossible graph in the case of a particle in one dimensional motion is :

(A) (B)

(C) (D)

23. Particles are projected from the top of a tower with same speed at different angles as shown. Which of thefollowing are True ?

(A) All the particles would strike the ground with (same) speed.(B) All the particles would strike the ground with (same) speed simultaneously.(C) Particle 1 will be the first to strike the ground.(D) (A) & (C) are correct



24. An object is thrown horizontally from a point �A� from a tower and hits the ground 3s later at B. The line from

�A� to �B� makes an angle of 30° with the horizontal. The initial velocity of the object is: (Take g = 10 m/s2):

(A) 15 3 m/s (B) 15 m/s (C) 10 3 m/s (D) 25/ 3 m/s

25. A fully loaded elevator has a mass of 6000 kg. The tension in the cable as the elevator is accelerateddownward 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

26. A body of mass M is dropped from a height h on a sand floor. If the body penetrates x cm into the sand,the average resistance offered by the sand to the body is :

(A) Mg

x

h(B) Mg

x

h1 (C) Mgh + Mgx (D) Mg

x

h�1

27. The radius of curvature of the convex surface of a plano-convex lens is 10 cm. What is the focal length of

the plano-convex lens ? (Here = 1.5)

(A) 10 cm (B) 20 cm (C) 15 cm (D) 5 cm

28. Two identical heater wires are first connected in series and then in parallel with a source of electricity.The ratio of heat produced in the two cases is :(A) 2 : 1 (B) 1 : 2 (C) 4 : 1 (D) 1 : 4

29. In a transformer the output current and voltage are 4 A and 20 V respectively. If the ratio of numberof turns in the primary and secondary coil is 2 : 1 respectively, what is the input current andvoltage ?(A) 2 A and 40 V (B) 1 A and 20 V (C) 4 A and 10 V (D) 8 A and 40 V



30. Starting from rest, a particle moves along a circle of radius 2 m with an angular acceleration of ( / 4) rad s �2.

During the time the particle covers a quarter of the circle, the magnitude of average velocity is:(A) 1.50 m/s (B) 2,00 m/s (C) 1..00 m/s (D) 1.25 m/s

31. A stationary ball weighing 0.25 kg acquires a speed of 10 m/s when hit by a hockey stick. The impulseimparted to the ball is :(A) 0.25 N × s (B) 2.5 N × s (C) 2 N × s (D) 0.5 N × s

32. A thin lens is made with a material having refractive index µ = 1.5. Both the sides are convex. It is dipped

in water (µ = 1.33), it will behave like :

(A) a convergent lens (B) a divergent lens

(C) a rectangular slab (D) a prism

33. A machine, which is 75% efficient, uses 12 J of energy in lifting up a 1 kg mass through a certain distance.The mass is then allowed to fall through that distance. The velocity at the end of its fall is (in m/s) :

(A) 24 (B) 12 (C) 18 (D) 9

34. A 3 kg ball strikes a heavy rigid wall with a speed of 10 m/s at an angle of 60°. It gets reflected with the

same speed and angle as shown here. If the ball is in contact with the wall for 0.20 s, what is the averageforce exerted on the ball by the wall?

(A) 150 N (B) Zero (C) N3150 (D) 300 N

35. A mass of 0.5 kg moving with a speed of 1.5 m/s on a horizontal smooth surface, collides with a nearlyweightless spring of force constant k = 50 N/m. The maximum compression of the spring would be :

(A) 0.5 m (B) 0.15 m (C) 0.12 m (D) 1.5 m



36. Four masses are located as shown in the figure. Acceleration due to gravity is same everywhere. What isthe position of centre of gravity for the system ?

1m 2m 3m 4m

1kg 2kg 3kg 4kg

O

(A) 2m (B) 2.5 m (C) 3 m (D) 2.7 m

37. A large water tank is filled at a constant rate of 10 litres/ min. It has an outlet of maximum flow of 10 litres/min at the bottom of the tank, but the output is proportional to the water present in the tank at any giventime. How will the �v�, volume of water content in the tank, change with time ?

(A)

v

t(0.0)

(B)

v

t(0.0)

(C)

v

t(0.0)

(D)

v

t(0.0)

38. When a ray of white light enters a prism, it begins to spread out in rainbow colours.An inverted prism is brought close to this prism as shown in the Fig 2,Both the prisms are made of same material. If a ray of white light is incident on surface A and �d� is made

zero then output from �B� will be :

Ad

d

B

(A) white light.(B) rainbow colours which are converging(C) rainbow colours which are spreading out(D) no light comes out from surface B.



39. A set of vectors taken in a given order gives a closed polygon. Then the resultant of these vectors is a(A) scalar quantity (B) pseudo vector (C) unit vector (D) null vector

40. If P

+ Q

= P

� Q

and is the angle between P

and Q

, then

(A) = 0° (B) = 90° (C) P

= 0 (D) Q

= 0

41. Which of the following is an example of emulsion ?(A) Face cream (B) Shaving cream (C) Honey (D) Smoke

42. When a green iron salt is heated strongly, its colour finally changes to black and odour of burning sulphuris given out the iron salt is -(A) FeSO

4(B) FeCl

3(C) FeS (D) None of these

43. In the reaction 2H2S + SO

2 2H

2O + 3S, the substance that is oxidized is -

(A) Hydrogen sulphide (B) Sulphur dioxide (C) Sulphur (D) Water

44. Match the following(i) Hydrochloric acid (a) Organic acid(ii) Phosphoric acid (b) Strong acid(iii) Citric acid (c) Vinegar(iv) Acetic acid (d) Weak acid (i) (ii) (iii) (iv)(A) a, c, b, d(B) b, d, a, c(C) a, d, b, c(D) d, b, a, c

45. Which of the following is lewis base ?(A) BCl

3(B) H

2O (C) NH

4+ (D) CH

4

46. The concept of an acid as an acceptor of a pair of electron was introduced by -(A) Lowry (B) Bronsted (C) Arrhenius (D) Lewis

47. Which of the following metals will not give H2 with dil. HNO

3 ?

(A) Mg (B) Mn (C) Al (D) None of these

48. Which of the following reactions is not possible ?(A) Zn(s) + CuSO

4(aq) ZnSO

4(aq) + Cu(s)

(B) 2Ag(s) + Cu(NO3)

2(aq) 2AgNO

3 (aq) + Cu(s)

(C) Fe(s) + CuSO4(aq) FeSO

4(aq) + Cu(s)

(D) Mg(s) + 2HCl (dil) MgCl2 (aq) + H

2(g)



49. The main purpose of alloy making is -(A) to decrease the hardness. (B) to increase the melting point.(C) to increase resistance to corrosion. (D) to decrease tensile strength.

50. Many salts absorb water from the atmosphere. This property is called -(A) hydration (B) dehydration (C) efflorescence (D) deliquescence

51. The number of molecules in one litre of water is close to

(A) 4.23

10023.6 23

(B) 18 × 6.023 × 1023 (C) 4.22

18×1023 (D) 55.5 × 6.023 × 1023

52. The mass of sodium in 11.7 g of sodium chloride is -(A) 2.3 g (B) 4.6 g (C) 6.9 g (D) 7.1 g

53. A sample of ammonium phosphate (NH4)

3 PO

4 contains 3.18 moles of hydrogen atoms. The number of

moles of oxygen atoms in the sample is -(A) 0.265 (B) 0.795 (C) 1.06 (D) 4.00

54. 2 g of a base whose eq. wt. is 40 reacts with 3 g of an acid. The eq. wt. of the acid is-(A) 40 (B) 60 (C) 10 (D) 80

55. Which of the following has the highest normality ?(A) 1 M H

2SO

4(B) 1 M H

3PO

3(C) 1 M H

3PO

4(D) 1 M HNO

3

56. The nitrogen atom has 7 protons and 7 electrons. The nitride ion will have -(A) 10 protons and 7 electrons (B) 7 protons and 10 electrons(C) 4 protons and 7 electrons (D) 4 protons and 10 electrons

57. Which of the following contains both polar and non-polar bonds ?(A) NH

4Cl (B) HCN (C) H

2O

2(D) CH

4

58. The empirical formula of a compound is CH2O and its vapour density is 30, then the molecular formula of

the compound will be :(A) CH

2O (B) C

2H

4O

2(C) C

4H

8O

4(D) C

3H

6O

3

59. The element with highest electronegativity is -(A) carbon (B) chlorine (C) fluorine (D) oxygen



60. The transition elements have a characteristic electronic configuration which can be represented as -(A) (n�2) s2p6d1�10 (n�1) s2p6ns2 (B) (n�2) s2p6d1�10 (n�1) s2p6d1 or 2 ns1

(C) (n�1) s2p6d10 ns2np6 nd1�10 (D) (n�1) s2p6d1�10 ns1 or 2

61. During cell division, DNA duplication occurs in(A) Prophase (B) G1 - of interphase (C) S - phase (D) early telophase

62. The ribosomes are mainly composed of(A) RNA core and lipid envelope (B) DNA core and lipid envelope(C) RNA and proteins (D) DNA and proteins

63. Best stage to observe shape, size and number of chromosomes is :(A) Prophase (B) Metaphase (C) Anaphase (D) Interphase

64. The minimum number of meiotic divisions required to obtain 100 pollen grains of wheat(A) 25 (B) 50 (C) 100 (D) 150

65. Transfer of genes from one chromosome to another and vice versa during synapsis is called :(A) Exchange (B) Chiasmata (C) Crossing over (D) Translocation

66. In which group Balanoglossus is classified ?(A) Urochordata (B) Cephalochordata (C) Hemichordata (D) Tunicata

67. Four chambered heart occurs in(A) amphibia (B) crocodile (C) bird (D) both B and C

68. The familiar disease Amoebiasis is caused by(A) Entamoeba histolytica (B) Taenia solium(C) Ascaris lumbricoides (D) Wuchereria bancrofti

69. Oral vaccine of Polio was developed by -(A) Jenner & Sabin (B) Koch & Salk (C) Salk and Jenner (D) Salk & Sabin

70. Which of the following is sexually transmitted disease ?(A) Syphilis (B) Gonorrhoea (C) AIDS (D) All of these

71. The disease which begins abruptly and last only for a short duration is known as :(A) Acute disease (B) Chronic disease (C) Congenital disease (D) Both B and C



72. If Henle�s loop were absent from mammalian nephron which of the following is to be expected.

(A) There will be no urine formation(B) There will be hardly any change in the quality and quantity of urine formed.(C) The urine will be more concentrated.(D) The urine will be more dilute

73. End product of glycolysis is(A) Acetyl CoA (B) Pyruvic Acid(C) Glucose 1 phosphate (D) Fructose 1 phosphate

74. Uric acid is nitrogenous waste in(A) Mammals and Molluscs (B) Birds and Lizards(C) Frog and cartilaginous fishes (D) Insects and Bony fishes

75. Blood transfusion is not possible from.(A) AB to O (B) O to AB (C) O to B (D) O to A

76. Trypsin digests protein in(A) Stomach in acidic medium (B) stomach in alkaline medium(C) Duodenum in acidic medium (D) Duodenum in alkaline medium

77. Which one is the emergency gland ?(A) Testis (B) Adrenal (C) Thymus (D) Pituitary

78. Testis descend into scrotum in mammals for(A) Spermatogenesis (B) Fertilization(C) Development of sex organs (D) Development of visceral organs

79. A frog with crushed brain is pinched on the leg. The leg is drawn away . It is(A) Automatic motor response(B) Neurotransmitter induced response(C) Conditional reflex(D) Simple reflex

80. Which is mismatched ?(A) Cerebrum - Memory (B) Medulla oblongata - Temperature regulation(C) Cerebellum - equilibrium (balance of body) (D) Olfactory lobes - smell

ijso workshop (4.10.11 to 8.10.11) dignostic test (04.10.11)

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