JEE | MEDICAL-UG | BOARDS | KVPY | NTSE | …...19. The distance between the points (a, b) and...

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Rao IIT Academy Talent Hunt Paper - 2014

1SANTACRUZ | ANDHERI | GOREGAON | KANDIVALI (E) | KANDIWALI (W) | BORIVALI | BHAYANDER | VASAI | POWAI | DADAR |SION | THANE | LOKPURAM (THANE) | DOMBIVLI | KALYAN | PANVEL / KAMOTHE | NERUL | SANPADA | KHARGHAR |

JEE | MEDICAL-UG | BOARDS | KVPY | NTSE | OLYMPIADS

SAMPLE PAPER 10TH STANDARD FOR STUDENTS ASPIRINGADMISSION IN 11TH STANDARD ENGINEERING STREAM

Date:

Total Marks: 150 Max. Time: 2:00 hr.

1. Read each question carefully.

2. It is mandatory to use black ball point pen to darken the appropriate circle in the OMR sheet.

3. Bubble mark should be dark and fill the circle completely.

4. Here are some examples of incorrect OMR filling. The Correct one is

5. Rough work must not be done on the OMR sheet.

6. Before handing over the OMR sheet to the invigilator, candidate should check that Standard,

Roll No. / Name & Test Date are mentioned correctly.

7. The OMR sheet has to be returned to the invigilator immediately after the examination.

8. There are 75 questions in the paper. Each question carries 2 marks with (– 0.5) Negative marking. The paper

contains questions based on Maths, Science, Logical Reasoning.

9. All questions are single correct answer type.

INSTRUCTIONS FOR CANDIDATES

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MATHS

1. If 216 51 35f x x x , then one of the factors of f x is :

(A) 1x (B) 3x (C) 3x (D) 1x

2. A circular park has sum of its area and perimeter equal to 8 . the diameter of the park equals :

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

3. The A.M. between 2a b and 2a b is

(A) ab (B) 2 2a b (C) 4

2

ab

(D) None

4. If the distance between the point ,2a and 3,4 be 8, then a ?

(A) 2 3 15 (B) 2 3 15 (C) 2 3 15 (D) 3 2 15

5. The root of 2 1 0x x are .....

(A) Real and equal (B) Real and not equal(C) Imaginary (D) None of these

6. A bag contains 3 white and 5 red balls. If a ball is drawn at randam, the probability that the ball is red is .

(A) 38 (B)

58 (C)

315 (D)

515

7. In the following figure, O is the centre of the circle. If 60 ,BAC then OBC ?

(A) 120° (B) 30° (C) 40° (D) 60°

8. The diagonal of a cubical box is 300 cm , the surface area is :

(A) 3600 3 cm (B) 3600cm (C) 31200cm (D) 900 3 cm

9. The probability of getting a prime number when a dice is thrown is,

(A) 16 (B)

13 (C)

12 (D)

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10. The total cost-price of two items is Rs. 10,200 /- and their selling - price are equal if one of the two items issold at a loss of 12% and another is sold at a loss of 18%, then the cost price of the item sold at a loss of18% is

(A) Rs. 4920/- (B) Rs. 5820/- (C) Rs. 5280/- (D) Rs. 4290/-

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11. If m n nma a a then 2 2m n n m is equal is

(A) –1 (B) –2 (C) 0 (D) None of these

12. The discriminant of 2 1x x = 2 is

(A) –3 (B) 13 (C) 11 (D) 12

13. If cos 4 , sin 4x a t y a t , then the value of 2 2x y

(A) 1 (B) a (C) 2a (D) None of these

14. For what value of c does the pair of equations 2cx y and 6 2 3x y have infinitely many solutions ?

(A) 3c (B) 3c (C) 12c (D) Not possible for any value of c

15. Find the roots , of the quadratic equation 2 12 0x kx are such that 1 , then value of k is :

(A) 3 (B) 5 (C) 7 (D) None of these

16. The value of x satisfying the equation 22 2x p q x is :

(A) 2 2

2p q

(B) 2 2

2q p

q

(C) 2 2

2q p

(D) 2 2

2p q

q

17. Two trains of equal length are running on parallel lines in the same direction at the rate of 46 km/hr and 36km/hr. The faster train passes the slower train in 36 seconds, the length of each train is :

(A) 50 m (B) 80 m (C) 72 m (D) None of these

18. If sin sin 41 cos 1 cos

x xx x

and 0 90 ,x then the value of x is equal to

(A) 10° (B) 15° (C) 30° (D) 45°

19. The distance between the points (a, b) and (–a, –b) is :

(A) 2 2a b (B) 2 2a b (C) 0 (D) 2 22 a b

20. The distance between points ,a b b c and ,a b c b is :

(A) 2 22 a b (B) 2 2b c (C) 2 2b (D) 2 2a c

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SCIENCE21. Two charges are placed at a certain distance apart. A brass sheet is placed between them, then force

between them will -

(A) Be zero (B) Increase (C) Decrease (D) Remain the same.

22. The ratio of SI unit to C.G.S unit for magnetic flux density is

(A) 103 (B) 104 (C) 10–4 (D) 10–3

23. Process of fusion is used for construction of

(A) Atom bomb (B) Ordinary bomb (C) Hydrogen Bomb (D) Neutron

24. The SI unit of coefficient of mutual inductance of a unit is

(A) Henry (B) Volt (C) Farad (D) Weber

25. The focal length of a lens is greatest for the colour

(A) Violet (B) Red (C) Yellow (D) Orange

26. Electron volt is a unit of

(A) Potential difference (B) Charge(C) Energy (D) Capacity

27. Power of a lens whose focal length is one meter is .....dioptre.

(A) One (B) Ten (C) Hundred (D) None of these

28. At magnetic poles, the angle of dip is

(A) 45° (B) 30° (C) 0° (D) 90°

29. Proton donor is

(A) Arrhenius Base (B) Bronsted acid (C) Lewis acid (D) Lewis base

30. Which one of the following oxides is neutral ?

(A) Co (B) SnO2 (C) ZnO (D) SiO2

31. The diamagnetic molecules are -

(A) B2, C2, N2 (B) O2, N2, F2 (C) C2, N2, F2 (D) B2, 2–2O , N2

32. Which ore contains both iron and copper ?

(A) Cuprite (B) Chalcocite (C) Chalcopyrite (D) Maldehite

33. The first use of quantum theory to explain the structure of atom was made by

(A) Heisenberg (B) Bohr (C) Planck (D) Einstein

34. Number of bonds present in C20 H42 is :

(A) 62 (B) 61 (C) 63 (D) 60

35. Which metal can be purified by distillation :

(A) Cu (B) Ag (C) Fe (D) Hg

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36. S.I. unit of Surface Tension is :(A) Degree/Cm (B) Nm (C) N/m2 (D) N/m

37. Resolving power of a telescope increases with(A) Increase in focal length of eye-piece (B) Increase in focal length of objective(C) Increase in aperture of eye piece (D) Increase in aperture of objective

38. The value of current i in the given circuit is

(A) Zero (B) 5 A (C) 7 A (D) 11 A

39. What is the effective Resistance of the following circuit :

(A) 5R (B) 2R (C) R (D) 5R

40. Half - life of radioactive element depends on(A) Temperature (B) Pressure(C) Nature of element (D) Quantity of radioactive material

41. Nuclear force exists between.(A) Neutron - Neutron (B) Proton - Proton(C) Neutron - Proton (D) All of these

42. Unit of coefficient of viscosity are :

(A) 1Nms (B) 2 1Nm s (C) 2Nm (D) None of thes

43. Two media are seperated by a plane surface, speed of light in one medium is 102 10 cm/sec and in other thespeed it is 102.4 10 / seccm . deduce the critical angle for a ray going from the first medium into the second.

(A) 1 1sin

2

(B) 1 5sin

6

(C) 1 5sin

12

(D) 1 5sin

2

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44. A solution reacts with crushed egg - shells to give a gas that turns lime - water milky. The solution contains

(A) NaCl (B) HCl (C) LiCl (D) KCl

45. Ethane, with the molecular formula 2 6C H has

(A) 6 Covalent bonds. (B) 7 Covalent bonds(C) 8 Convalent bonds (D) 9 Covalent bonds

46. Which of the following statements is not a correct statement about the trends when going from left to rightacross the periods of periodic table.

(A) The elements become less metallic in nature

(B) The number of valence less electrons increase

(C) The atoms lose their electrons more easily

(D) The oxides become more acidic

47. Which one of the following type sof medicines is used for treating indigestion ?

(A) Antibiotic (B) Analgesic (C) Antacid (D) Antiseptic

48. 10 ml of a solution of NaOH is found to be completely neutralised by 8ml of a given solution of HCl. If wetake 20 ml of the same solution of NaOH the amount HCl solution required to neutralise it will be

(A) 4 ml (B) 8 ml (C) 12 ml (D) 16 ml

49. Which pair represents chain isomers ?

(A) CH3CHCl2 and ClCH2CH2Cl (B) Propyl alcohol and isopropyl alcohol(C) 2-methylbutane and neo-pentane (D) Diethyl ether and methylpropyl ether.

50. Which formula represents an alkyne ? (Assume all are non - cyclic).

(A) C2H6 (B) C2H2 (C) C5H10 (D) C8H8

LOGICAL REASONING51. Ravi traveled 4 km straight towards south. He turned left and travelled 6 km straight, then turned right and

travelled 4 km straight, how far is he from the starting point ?(A) 8 (B) 10 (C) 12 (D) 12

52. Hour is related to Second in the same way as Tertiary is related to ... ?

(A) Ordinary (B) Secondary (C) Primary (D) Intermediary

53. If D = 4 & COVER = 63 then BASES = ?

(A) 49 (B) 46 (C) 54 (D) 55

Direction: (54 to 55) In the following example which is from the different group ?

54. (A) Sun (B) Moon (C) Venus (D) Mars

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55. (A) Milk (B) Syrup (C) Cake (D) Tea

56. The day of the week on 15 Aug. 1947 , was

(A) Tuesday (B) Friday (C) Wednesday (D) Thursday

57. If it was saturday on 17th November 1962, what will be the day on 22nd November 1964 ?

(A) Monday (B) Tuesday (C) Wednesday (D) Sunday

58. Which two months in a year have the same calendar ?

(A) June, October (B) April, November (C) April, July (D) October, December

59. Find the missing number

6 9 15 8 12 20 4 6 ?

(A) 5 (B) 10 (C) 15 (D) 2160. MANTEL : NAMLET : : VANITY : ?

(A) NAVYIT (B) NAVYTI (C) NAVIYI (D) AVINTIY

61. Find the missing term

2Z5 , 7Y7 , 14X9 , 23W11 , 34V13 ?

(A) 27U24 (B) 45U15 (C) 47U15 (D) 47U14

62. India Gate : Delhi :: _________:__________

(A) Chicago : USA (B) Albany : New York(C) Agar : Taj Mahal (D) Chandigarh : Rock Garden

63. If JUMP is coded as KVLO then GIVE will be coded

(A) HHWD (B) HIUE (C) HJUD (D) HJVD

64. Arrange the given words in he order they occur in dictionary

1. SIGN 2. SOLID 3. SCENE 4. SIMPLE

(A) 3,1,2,4 (B) 3.1.4.2 (C) 3,4,1,2 (D) 3,4,2,1,

Direction : - In the following question:

means ‘is equal to’ means ‘ is not equal to’

+ menas ‘is greater than’ – means ‘is ;less than’

× means ‘is not greater than’ means ‘is not less than’

Now select the correct alternative in each of the following question:

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65. a – b – c implies

(A) a – b + c (B) b + a – c (C) c × b + a (D) b + a c

66. Correct the following equation by interchanging two signs

5 9 45 16 3 5

(A) + and – (B) × and + (C) × and + (D) × and –

67. Pointing towards a man in the photograph, lady said “ the father of his brother is the only son of my mother”.How is the man releated to lady ?

(A) Brother (B) Son (C) Cousin (D) Nephew

68. Pointing to a girl in the photograph, Ramesh said “Her mother’s brother is the only son of my mother’sfather. Hwo is the girl’s mother related to Ramesh ?

(A) Mother (B) Sister (C) Aunt (D) Grandmother

69. Light : Ray : : Sound : ?

(A) Hear (B) Wave (C) Audio (D) Pitch

Direction : Question consists of a particular pattern. Find the pattern and answer the question

70. Given set : 992, 733, 845, 632

(A) 114 (B) 326 (C) 425 (D) 236Direction(Question 71 to 75) : Study the figure carefully and answer the given :

Here, big triangle represents artists, samll triangle reprsensts scientists, rectangle representsdancers and cirlce represents doctors.

71. Which letter represent the artists who are doctors and dancers only ?(A) A (B) D (C) G (D) H

72. Which letters represent the artists who are neither scientists nor doctors ?(A) A and B (B) A and L (C) B and G (D) L and H

73. Which letters represent the artists who are dancers as well as doctors?(A) A and D (B) C and A (C) C and D (D) G and H

74. Which letter represents the artists who are neither doctors nor scientists nor dancers?(A) A (B) D (C) F (D) G

75. Which letter represents the scientists who are not artists ?(A) B (B) D (C) F (D) L4

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Answer Key

1. (D) 2. (A) 3. (B) 4. (D) 5. (C)

6. (B) 7. (B) 8. (B) 9. (C) 10. (C)

11. (C) 12. (B) 13.(C) 14. (A) 15. (C)

16. (B) 17. (A) 18.(C) 19. (D) 20. (C)

21. (C) 22. (B) 23. (C) 24. (A) 25. (B)

26. (C) 27. (A) 28. (D) 29. (B) 30. (A)

31. (C) 32. (C) 33. (B) 34. (B) 35. (D)

36. (D) 37. (D) 38. (D) 39. (C) 40. (C)

41. (D) 42. (D) 43. (B) 44. (B) 45. (B)

46. (C) 47. (C) 48. (D) 49. (C) 50. (B)

51. (B) 52. (C) 53. (B) 54. (B) 55. (C)

56. (B) 57. (D) 58. (C) 59. (B) 60. (B)

61. (C) 62. (B) 63. (C) 64. (B) 65. (B)

66. (D) 67. (D) 68. (A) 69. (B) 70. (C)

71. (A) 72. (C) 73.(C) 74. (B) 75. (C)

JEE | MEDICAL-UG | BOARDS | KVPY | NTSE | …...19. The distance between the points (a, b) and...

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