NTSE STAGE-1 - Fiitjee PUNE · fiitjeepune centre ntse stage-1 mock test -1(mah) fiitjee ltd.pune...

Scholarship Aptitude Test (SAT)Time:120 Minutes Maximum Marks:100Please read the instructions carefully.

INSTRUCTIONS

A: General :1. Immediately fill in the particulars on this page of the Test Booklet with Blue/Black Ball point

pen.

2. Use Blue/Black Ball Point Pen only for writing particulars on Side-1 and Side-2 of the AnswerSheet. Use of pencil is strictly prohibited.

3. Darken the appropriate bubbles with Blue/Black Ball Point Pen only.4. Blank papers, clipboards, log tables, slide rules, calculators, cellular phones, pagers and

electronic gadgets in any form are not allowed.

5. The answer sheet, a machine-gradable Objective Response Sheet (ORS) is provided separately.

6. Do not Tamper/mutilate the ORS or this booklet.

7. No additional sheets will be provided for rough work

8. On completion of this test, the candidate must hand over the Answer Sheet to the Invigilator onduty in the Room/Hall. However, the candidates are allowed to take away this TestBooklet with them.

B: Questions paper format and Marking Scheme :1. The question paper consists of 100 questions.

2. For each question you will be awarded 1 marks if you darken the bubble corresponding to thecorrect answer and zero mark if no bubbles is darkened. No Negative Mark will be awarded.

Enrollment No. : Batch :

Name :

Candidate’s Signature Invigilator’s Signature:

FIITJEE PUNE CENTRE NTSE STAGE-1 MOCK TEST -1(MAH)

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website: www.fiitjee.com

MOCK TEST-1-SAT-NTSE-S-I -2

PHYSICS

1. A person suffering from defective vision can see objects clearly only beyond 100 cm from the eye. Thepower of the lens required so that he can see clearly is(A) 3 dioptre (B) 3 dioptre(C) 1 dioptre (D) 1 dioptre

2. An automobile travelling with speed of 60 km/h, can brake to stop within a distance of 20 m.If the car is going twice as fast, i.e 120 km/h, the stopping distance will be(A) 20 m (B) 40 m (C) 60 m (D) 80 m

3. Two cars of masses 1m and 2m are moving in circles of radii 1r and 2r , respectively. Their speeds aresuch that they make complete circles in the same time t. The ratio of their centripetal acceleration is(A) 1 1 2 2m r : m r (B) 1 2m : m (C) 1 2r : r (D) 1:1

4. Two lenses of power -15 D and + 5D are in contact with each other. The focal length of the combination is(A) 20 cm (B) 10 cm(C) + 20 cm (D) + 10 cm

5. A satellite of mass m revolves around the earth of radius R at a height x from its surface. If g is theacceleration due to gravity on the surface of the earth, the orbital speed of the satellite is

(A) gx (B)gR

R x(C)

2gR

R x(D)

1/22gR

R x

6. In the circuit, the galvanometer G shows zero deflection. Ifthe batteries A and B have negligible internal resistance, thevalue of the resistor R will be(A) 200 (B) 100 (C) 500 (D) 1000

7. An electric bulb is rated 220 volt − 100 watt. The power consumed by it when operated on 110 volt will be(A) 50 watt (B) 75 watt (C) 40 watt (D) 25 watt

Space for rough work




8. Two concentric coils each of radius equal to 2π cm are placed at right angles to each other. 3 Ampere and4 ampere are the currents flowing in each coil respectively. The magnetic induction in Weber/m2 at thecentre of the coils will be (μ0 = 4 × 10−7 Wb/A-m)(A) 512 10 (B) 510 (C) 55 10 (D) 57 10

9. A 5 kg block slides on a horizontal frictionless floor with a speed of 8 m/s. It strikes a uncompressedspring, and compresses it till the block is motionless. Spring constant is 2,000. N/m. The springcompresses by(A) 50 cm (B) 25 cm(C) 40 cm (D) 80 cm

10. A material ‘B’ has twice the specific resistance of ‘A’. A circular wire made of ‘B’ has twice the diameter ofa wire made of ‘A’. Then for the two wires to have the same resistance, the ratio l A / l B of their respectivelengths must be

(A) 2 (B) 1 (C)1

2(D)

1

4

11. A stone is dropped into a well of depth 80 m, the sound of splash is heard 4.20 sec after the time is stoneis dropped the velocity of sound in air is(A) 200 m/s (B) 300 m/s (C) 400 m/s (D) 500 m/s

12. The ratio of the heights from which two bodies are dropped is 3 : 5 respectively. The ratio of their finalvelocities is(A) 5 : 3 (B) 3 : 5 (C) 9 : 25 (D) 5 : 3

13. The main constituent of bio gas is(A) methane (B) carbon dioxide (C) hydrogen (D) ethane

CHEMISTRY

14. Which of the following is least ionic?(A)AgCl (B) KCl (C) BaCl2 (D) NaCl

15. The process requiring the absorption of energy is:(A) F F (B) Cl Cl (C) 2O O (D) H H

16. Among the following statements the correct one is(A)Calamine and siderite are carbonates (B) Argentite and cuprite are oxides(C) Zinc blende and pyrites are oxides (D) Malachite and Azurite are ores of copper





17. The set representing the correct order of first ionisation potential is:(A)K > Na > Li (B) Be > Mg > Ca (C) B > C > N (D) Ge > Si > C

18. The valency shell of element A contains 3 electrons while the valency shell of element B contains 6electrons. If A combines with B, the probable formula of the compound formed will be:

(A)AB2 (B) A2B (C) A2B3 (D) A3B2

19. Which of the following has shortest carbon bond length?(A) C6H6 (B) C2H6 (C) C2H4 (D) C2H2

20. In the hydrocarbon,CH3 6

CH5

CH4

CH23

C2

CH1

The state of hybridization of carbons 1, 3, 5 are in the following sequence(A) sp, sp2, sp3 (B) sp3, sp2, sp (C) sp2, sp, sp3 (D) sp, sp3, sp2

21. In the following reaction,2 2 22 3 2SO H S S H O

(A) Sulphur is oxidized and hydrogen is reduced(B) Hydrogen is oxidized and sulphur is reduced(C) Sulphur is both oxidized and reduced(D) Sulphur is reduced and oxygen is oxidized

22. Which of the following has the smallest size ?(A) Na (B) 2Mg (C) Cl (D) F

23. The soap molecule has(A) Hydrophobic head and hydrophilic tail (B) Hydrophilic head and hydrophobic tail(C) Hydrophilic head and hydrophilic tail (D) Hydrophobic head and hydrophobic tail

24. The pH of 101 10 M 2 4H SO H solution is(A) 8 (B) 7 (C) 10 (D) None of these

25. Carbonisation is favoured by(A) high T, low P and air (B) high T, high P, no air(C) low T, high P, no air (D) any T and P

26. Which of the following does not conduct electricity?(A) fused NaCl (B) solid NaCl(C) brine solution (D) copper.





BIOLOGY

27. Golgi bodies of plants are usually called as(A) Dictyosomes (B) Lysosomes (C) Peroxisomes (D) Spherosomes

28. The function of light in photosynthesis is(A) Photolysis of water(B) Assimilation of CO2

(C) Production of starch(D) Activation of enzymes

29. Which of the following acts as middle man?(A) WBC (B) Plasma (C) Blood (D) Lymph

30. The wave of contractions that pushes the food through alimentary canal is called(A) Peritoneum (B) Peristalsis (C) Stomatisis (D) Polarisation

31. Histamine secreting cells are found in(A) Connective tissue (B) Nervous Tissue(C) Lungs (D) Muscular tissue

32. The largest part of the brain is(A) Cerebrum (B) Medulla oblongata (C) Cerebellum (D) Corpora quadrigermine

33. Cnidaria is characterized by(A) Nematocysts (B) Coelenteron(C) tissue level of organization (D) All the above

34. Location of Leydig cells and their secretions are(A) Ovary - estrogens (B) Pancreas – Glucagon(C) Testis – Testosterone (D) Liver - Cholestrol

35. BCG vaccine is used to cure which of the following disease(A) Pneumonia (B) Tuberculosis (C) Polio (D) Amoebiasis

36. Pyramids of energy are(A) always upright (B) always inverted(C) mostly upright (D) mostly inverted

37. Which of the following disease is caused by air pollution?(A) Rheumatism (B) Scurvy (C) Haemophilia (D) Bronchitis

38. Green house effect is caused by(A) Green plants (B) Infrared rays (C) UV-rays (D) X-rays

39. When both crops and livestock are raised on the same farm, it is known as(A) Mixed farming (B) Mixed cropping (C) Intercropping (D) Crop rotation

40. The inheritance of skin colour in humans is an example of which of the following?(A) Epistasis (B) Gene linkage(C) Polygeneric inheritance (D) Codominance





MATHEMATICS

41. A, B and C all three consecutive even integers such that three times the first is two more than twice thethird one. What is the third one?(A) 11 (B) 12 (C) 14 (D) 10

42. Find the distance between P and Q if P is a point on the x-axis with abscissa 12 and Q is (8, 3).(A) 4 (B) 7 (C) 5 (D) None of these

43. Solving:2a bax by

and 3 5 4x y gives (x, y).

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

44. In ABC, points P, Q and R are the midpoints of the sides AB, BC and CA respectively. If area of ABC is32 square units, then area of PQR is(A) 8 square cm (B) 16 square cm (C) 64 square cm (D) 24 square cm

45. If 2sin sin 1, then 2 4cos cos is(A) 0 (B) –1 (C) 1 (D) 2

46. In a Derby Race, the horse cusac’s, chance of winning is 1/6, that of Lydo’s winning is 1/12 and of horseDerco’s is 1/8. If the race starts with 18 horses and only one horse wins, what is the probability that one ofthese 3 horses will win?(A) 1/8 (B) 3/8 (C) 1/4 (D) None of these

47. There is a certain number consisting of two digits, to the sum of whose digits if we add 7, the result will be3 times the left hand digit, and if from the number itself we subtract, 18 the digits will be reversed. Thenumber is(A) 47 (B) 52 (C) 61 (D) 53

48. Solve for 1 1: 0.0.5 .05 .005 .0005x xx

(A) 20 (B) 100 (C) 10 (D) 200





49. The expression ax + b is equal to 13 when x is 5 and ax + b is equal to 29 when x is 13. The value of theexpression when x is 0.5.

(A) 2.9 (B) 29 135 (C) 4 (D) 29 5

13

50. O is the centre of the circle ABC = then x° + y° is

A

D C

BO

x°y°

(A) 180 – (B) 90 + (C) 3/2 (D) 180 +

51. A cylindrical drum which is 32 cm in diameter and 28 cm in height contains water to a depth of 18 cm. Asolid sphere of radius 8 cm is placed in the drum. How far below the top of the drum is the level of water?(A) 8.5 cm (B) 10.5 cm (C) 19.5 cm (D) None of these

52. The angle of elevation of the top of a tower from a point P on the ground is found to be such that2tan .5

The tower is at a distance of 300 m away from the point P. On walking 140 m towards the

tower, the angle of elevation at the point is found to be°, then tan P.(A) 3/4 (B) 2/3 (C) 2/5 (D) 3/5

53. In ABC, AB = AC = b, ,2bAQ AP = a then AB is

AP

Q

CB

(A) b/a (B) 4a (C) 3a/b (D) 2a2/b





54. In ABC, D and E are the midpoints of AB and BC respectively and ABC = 90°, then

(A) 2 2 2AE CD AC (B) 2 2 254

AE CD AC

(C) 2 2 234

AE CD AC (D) 2 2 245

AE CD AC

55. In the given figure ABO = 15°, OBC = 45°, find OCA?A

15°45°

B C

O

(A) 20° (B) 45° (C) 60° (D) 30°

56. Ram’s age is 1/3 of his father’s age. Ram’s father’s age will be 12 years more than twice of Shyam’s ageafter 10 years. If Shyam’s 8th birthday was celebrated 3 years before, then what is Ram’s age at present?(A) 14 years (B) 16 years (C) 11 years (D) 13 years

57. Which one of the following cannot be the ratio of angles in a right angled triangle?(A) 2 : 3 : 5 (B) 1 : 3 : 6 (C) 1 : 2 : 3 (D) 1 : 3 : 4

58. An AP has 23 terms, sum of the middle three terms is 144, the sum of last three terms is 264. Find the 8th

term.(A) 32 (B) 37 (C) 38 (D) 28

59. A 20 m deep well with diameter 7 m is dug and earth from digging is evenly spread out to form a platform22 m by 14 m. The height of the platform is(A) 2.3 m (B) 2.5 m (C) 3 m (D) 2.7 m

60. In what ratio does the point 3 11,5 5

C

divide the line segment joining the points A(3, 5) and B(3, 2)?

(A) 1 : 3 (B) 2 : 5 (C) 3 : 5 (D) 2 : 3







61. Study of inscriptions is called as (A) Numismatics (B) Epigraphy (C) Genealogy (D) Inscriphiology 62. Original name of Voltaire was A) Georg wilhem B) Rene Descartes C) Frances- marie arovet D) Hegal 63. Earliest written hand written documents are in form of inscriptions, those were dated as A) 3rd Century after Christ B) 3rd century B.C.E. C) 4th Century after Christ D) 4th century B.C.E 64. Sab hasad Bakhar was written by A) James mili B) Savitribai C) V. K. Rajwade D) Krishanaji anant 65. INTACH stands for A) Indian National Trust for Art and Craft. B) Indian National Troop for artificial and cultural intelligence. C) Indian National Trust for art and cultural Heritage. D) Indian National Trust for articians. 66. Radio was named Akashvani on the suggestion of A) C.V.Raman B) Narendra Sharma C) Nageshwar Rao D) Pandit Jawaharlal Nehru 67. Who was the editor of Darpan. A) Balshastri Jambekar B) Bhau Mahajan C) Gohal Hari D) Balgangadhar Tilak 68. During Julius Caesar’s regin newspaper were known as A) Acts of sins B) Mery of God C) Act a diurna D) Act a sinis 69. Who was the first author who wrote the script of thorale madhavarao peshwe A) I . J. Powdas B) J.V. Bhave C) V.J. Kirtane D) Ram Gopal Rao 70. Clay art in Sanskrit is known as A) Mitti Khel B) Mrichchha Katika C) Khel sang D) Shudraka. 71. Indian Athlete who won 5 gold medals Continuously? A) Dutte Chand B) Hima das C) P.T. Usha D) Sania Mirza. 72. Gandharva School Came into existence by A) 6th century B.C.E B) 8th Century B.C.E C) 9th century B.C.E D) 2nd Century B.C.E

HISTORY




73. Which city entered in UNESCO world heritage site in 2019? A) Delhi B) Mumbai C) Pune D) Jaipur 74. Mahatma Phule wrote a book Named as A) Gulamgiri B)The high Caste Hindu Women C) Primitive communism to slavery D) The untouchables 75. Five volumes of Cambridge history of india was published in the year? A) 1922- 1937 B) 1963- 1967 C) 1967-1975 D) 1918-1937 76. Karl Marx had written a book named as A) Annales School B)The secret of world history C) Das Kahital D) The working women




77. Self governing institutions got constitutional status in which amendment A) 67th B) 96th C) 73rd & 74th D) 75th 78. RTI came into existence in which year A) 2007 B) 2006-2007 C) 2009 D) 2005 79. Which article of Indian constitution talks about elections commission A) 448 B) 367 C) 324 D) 114 80. Who was the first voter in India A) Girja Prasad B) Hanumant Sharma C) Sham Sharan Neg D) Lal Bhadur Shastri 81. Communist Party of India was established in A) 1927 B) 1925 C) 1926 D) 1924 82. Identify the Regional Party Statement I : Signed agreement in 1985. II : Protect cultural, linguist and Social Identify. III : Oil producing state. A) Assam Gram Parishad B) Assam National Conference C) Assam National Party D) Assam Janta Party. 83. Consumer protection act came into existence In A) 1985 B) 1987 C) 1989 D) 1986 84. First organisation of Trade union in India was A) Railway federation B) All india Trade Party C) All India Trade Union Congress D) Railway trade union Congress.

POLITICAL SCIENCE




GEOGRAPHY

85. In india elephants are found in which type of climate A) Hot and Humid B) Cold and Dry C) Hot and Dry D) Mixed. 86. What is the average population density of India? A) 372 Person/ Sq Km B) 467 Person / Sq km C) 382 Person/ Sq Km D) 380 Person / Sq Km 87. Which is he Plateave located between aravali ranges and Chhota Nagpur Plateau. A) Deccan B) The Baghel Khand. C) Malwa D) Marwar Uhland 88. Identify the true statement/ Statements. A) Himalaya’s are old fold of mountains B) Arc of Himalaya is near about 1800 km. C) Himalaya’s can be divided into three parts i.e. Himadri, Shimla and Himachal. D) It can be divided into 4 parts on the basis of river flowing across it. 89. Tributaries of Indus South to North are A) Beas, Chenab, Ravi, Satluj, Jhelum. B) Satluj, Beas, Ravi, Chenab, Jhelum. C) Chenab, Beas, Ravi, Satluj, Jhelum. D) Jhelum, Chenab, Beas, Ravi, Satluj. 90. Identify the false statement 1) Waterways are cheap means of transport 2) Roadways constitute 85 % of passenger and 70 % of freight traffic. 3) Near about 85 % of India’s foreign trade moves through ocean routes. 4) Railway are dense in hilly regions. A) 1 , 4 B) 3, 4 C) 2, 4 D) 1, 3 91. BRICS nations lies in which continent ? A) South America, Asia. B) North America and Asia. C) Asia D) Europe. 92. In India reserve of oil is found in . A) Himalayan region B) Goa Maharashtra belt C) Jamnagar D) Mouth of river Godavari 93. Brazil lies in which hemisphere A) Southern B) Northern C) Eastern D) Both a and b 94. Identify the correct are out with respect to brazils international borders. A) Peru, Bolivia, Paraguay, Uruguay B) Namibia, Botswana, Peru, Bolivia C) Sweden, Fairland, Venezuela, Ecuador D) Argentina, Uruguay, Paraguay, Alaska 95. Highest Peak of brazil is A) Pico de Neblina B) Pico das Agulhas C) Pico da Bandeira D) Mount Roraima.



96. Choose the right statement/statements. 1) Amazon basin is quite wide in West and it narrows eastward. 2) Amazon forest is covered with tropical forest 3) Only major river of eastern coast is sao fransica which meets the atlantic ocean. 4) Brazil has a coast line of 3400 km A) 1, 2, 3 , 4 B) 2, 3 C) 2, 3, 4 D) 1, 2, 3 97. Identify the wrong statement/ statements 1) Tropic of Capricorn as well as Trophic of cancer passes through Brazil 2) Rainfall in brazil is because of south -east Trade winds and the north west trade winds. 3) Northern part is hot whereas southern part is cool. 4) The average temperature of amazon valley = 21℃ - 29℃ A) 1, 2, 3 B) 1, 2, 3, 4 C) 1, 2, 4 D) 2, 3 98. Brazil occupies how much of total worlds land? A) 5.3 % B) 3.2 % C) 5.4% D) 5.6 % 99. Identify two of the cities of brazil? A) Rio – De Janeiro and Asuncion B) Rio- De Janeiro and Sao Paulo C) Sao Paulo and Regina D) Regina and Asuncion 100. Identify the true statement A) Brazil has three time zones B) GMT – 03 is the official Brazilian time C) Brazil have developed inland water ways on commercial Basis. D) Major coffee growing areas in brazil are minas Gerais and Sao Paulo a) A, B, C b) C, B c) B, C, D d) All of the above.



FIITJEE MOCK TEST-1For NTSE STAGE-1

Scholarship Aptitude Test (SAT)ANSWERS



1. C 2. D 3. C 4. B5. D 6. B 7. D 8. C9. C 10. C 11. C 12. B13. A 14. A 15. C 16. D17. B 18. C 19. D 20. D21. C 22. D 23. B 24. D25. B 26. B 27. A 28. A29. D 30. B 31. A 32. A33. D 34. C 35. B 36. A37. D 38. B 39. A 40. C41. C 42. C 43. D 44. A45. C 46. B 47. D 48. C49. C 50. D 51. A 52. A53. B 54. B 55. D 56. A57. B 58. A 59. B 60. D

61. C 62. C 63. B 64. D 65. C 66. B 67. A 68. B 69. C 70. B 71. C 72. D 73. D 74. A 75. A 76. C 77. C 78. D 79. C 80. C 81. B 82. A 83. D 84. C 85. A 86. C 87. C 88. D 89. B 90. B 91. A 92. D 93. D 94. A 95. A 96. D 97. C 98. D 99. B 100. C


HINTS & SOLUTIONS

1. C

Sol.1 1

11

P DF m

2. DSol. If the initial speed is doubled, the stopping distance becomes four times, i.e. 80 m.3. CSol. a r4. BSol. P = P1 + P2 = 10

1fP 0.1 m 10 cm

5. DSol. For the satellite, the gravitational force provides the necessary centripetal force i.e.

2

e 0 e2 2

GM m Mv GMand g

R X RR X

1/22

e

gRv

R X

6. BLet 1I and 2I are the currents from 12 V and 2 V battery respectively,

1 1 2500 12VI R I I

1 2 2R I I V Given that I2 = 0

1 1500 12I RI …(i)and 1 2RI …(ii)On solving (i) and (ii), we getR = 100

7. DSol. V = 220 Volt, P = 100 Watt

220 220

484100

R

2 110 110

25watt484

VP

R

8. C

Sol.2 7

0 4 10 3

2 2 2

iB

r

= 3 × 10–7 weber/m2

2 70 4 10 4

2 2 2

iB

r

= 4 × 10–7 weber/m2

2 2res 1 2B B B 55 10 weber/m2

9. C

Sol. 2 21 1

2 2mv kx

m

x vk

= 5 28 m

2000 5

10. C




Sol. A BR R2B A

2 A BD D

A A B B

A B

l l

A A

2

4B

A

ll

1

2A

B

l

l

11. C

Sol. 1

24

ht s

g

2

Dt

S

1 2 4.2t t s t2 = 0.2 s0.2 = 80/S S = 80/0.2 = 400

12. BSol. Applying, 2 2 2v u gh v h

13. A 14. A 15. C 16. D17. B 18. C 19. D 20. D21. C 22. D 23. B 24. D25. B 26. B27. ASol. Golgi bodies of plants are called dictyosomes.28. ASol. Light causes photolysis of water in photosynthesis.29. DSol. Lymph acts as middle man.30. BSol. Peristalsis helps to move food through alimentary canal.31. ASol. The mast cells of connective tissue secrete histamine.32. ASol. The largest part of the brain is cerebrum.33. DSol. Cnidaria is characterized by tissue level of organization, gastro vascular cavity coelenterons and

nematocysts.34. CSol. Leydig cells are present in testis and secrete testosterone.35. BSol. BCG vaccine is used to cure Tuberculosis.36. ASol. Pyramids of energy are always upright.37. DSol. Bronchitis caused due to air pollution.38. BSol. Infrared rays causes greenhouse effect as they are absorbed by the green house gases in the

atomosphere.39. ASol. Mixed farming is when both crops and livestock are raised on same farm.40. CSol. The inheritance of skin colour in humans is an example of polygeneric inheritance.27. ASol. Golgi bodies of plants are called dictyosomes.28. ASol. Light causes photolysis of water in photosynthesis.




29. DSol. Lymph acts as middle man.30. BSol. Peristalsis helps to move food through alimentary canal.31. ASol. The mast cells of connective tissue secrete histamine.32. ASol. The largest part of the brain is cerebrum.33. DSol. Cnidaria is characterized by tissue level of organization, gastro vascular cavity coelenterons and

nematocysts.34. CSol. Leydig cells are present in testis and secrete testosterone.35. BSol. BCG vaccine is used to cure Tuberculosis.36. ASol. Pyramids of energy are always upright.37. DSol. Bronchitis caused due to air pollution.38. BSol. Infrared rays causes greenhouse effect as they are absorbed by the green house gases in the

atomosphere.39. ASol. Mixed farming is when both crops and livestock are raised on same farm.40. CSol. The inheritance of skin colour in humans is an example of polygeneric inheritance.

41. CSol. Let three consecutive even numbers be A, A + 2, A + 4

3A = 2(A + 4) + 2A = 10 A + 4 = 14

42. CSol. Coordinates of P(12, 0)

2 212 8 3 0 5d

43. DSol. Putting the options in the second equation and check for LHS = RHS.

1 1, ,2 2

x y 44. ASol. PQR is formed by joining mid-point, sides of PQR is half of each side, so in PQR

Area of PQR 14 Area of ABC

Area of PQR 1 32 84 square cm

45. C

Sol. 22 4 2 2cos cos cos cos

2 22 2 2 2cos 1 sin cos sin sin 1 sin

2 2cos sin 1 46. B

Sol. Required probability 1 1 1 36 12 8 8

47. DSol. Let the number be xy (10x + y)




Then x + y + 7 = 3x 2x – y = 7 … (i)and 10x + y – 18 = 10y + x 9x – 9y = 18 … (ii)Solving (i) and (ii) we getx = 5, y = 3 Number = 53

48. C

Sol. 1 2 2 20 200 2000 00.5

x x

x = 1049. CSol. 5a + b = 13 and 13a + b = 29

Solving both we geta = 2, b = 3When x = 0.5ax + b = 2 × 0.5 + 3 = 4.

50. DSol. Angle at centre = 2 × angle at circumference

x = 2In a cyclic quadrilateral ABCDy + = 180° y = 180 Adding x to both sidesx + y = 180 – + 2[x + y = 180 + ]

51. ASol. Volume of sphere = volume of water raised.

3 24 8 163

x

x = 1.5 cmLevel of water below the top = 28 (18 + 1.5) = 8.5 cm.

32cm

18cm28cm

52. ASol. Let AB is a tower of height h.

In rt ABP,2tan

300 5h

h = 120 m

ln rt ABQ, tan hBQ

120 120 3300 140 160 4




Q

h

B

A

P

140m300m

53. BSol. AQ is tangent and AB is secant

2AQ AP AB 2

44 4b ba b a b a

54. BSol. From ABC

2 2 2AE CD AC The only option (2) satisfies the condition.

E

D

B

A

C

55. DSol. OBC = OCB = 45°

BOC = 90°

BAC 902

= 45°

ACB = 180 (45 + 60) = 75° OCA = 75 – 45 = 30°

56. ASol. Shyam’s age after 10 years = 8 + 3 + 10 = 21

Ram’s father’s age after 10 years = 42 + 12 = 54His present age = 42 years Ram’s age = 14 years.

57. BSol. Check with option

(i) 2x + 3x + 5x = 180° x = 18°s are 36°, 54°, 90°

(ii) x + 3x + 6x = 180°x = 18Angles 18°, 54°, 108°, cannot be a right triangle.

58. ASol. Given that

11 12 13 144t t t

3 36 3 144a d … (i)

21 22 23 264t t t

3 66 3 264a d … (ii)Subtracting (i) from (ii)




d = 4 and a = 48 7 4 7 4 32t a d

59. BSol. Let the height raised = h m

222 722 14 207 2

h h = 2.5 m

60. D

Sol. 3 3 31 5xx

23

x 1(3, 5) (–3, –2)3 11,

5 5C

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