Byju's: Written Exam ~ I ❤️ Metallurgy

1. Which of the following is not a polynomial?

a) Y^1/2+y²

b) X

c) X+3^1/2

d) X+x²

2. A tent is made in the form of a cone surmounted by the another right circular cone. The diameter of the circular ends of the frustum are 8m and 4m and its height is 3m. the height of the right circular cone is 2m. what is the area of the canvas required for the tent?(take x=3.14, 13^1/2=3.6, 2^1/2=1.41)

a) 87.67m²

b) 86.75m²

c) 86.77m²

d) 85.53m²

3. Nikhil spent 1320 rupees to buy a movie ticket for 20 children and 4 adults. The tickets for adults cost 30 rupees more than those for the children. If A is the price of the ticket for a adults and S is the price of a ticket for children, find the money spend for the adults?

a) 100

b) 320

c) 80

d) 50

4. If 7sin²θ + 3cos²θ, find secθ + cosecθ

a) 2/3^1/2 + 2

b) 2/3^1/2

c) 2/3^1/2 – 3

d) None of these

5. From a pack of 52 cards, ram removes the queen of hearts and the jack of the spades. He now picks a card at random from this reduced pack. What is the probability that ram picks a jack card?

a) 0.06

b) 0.03

c) 0.07

d) 0.05

6. The arithmetic mean of n observations is m. if two observations n and m are added, which of the following is the new mean?

a) m(n+1)/n+1

b) mn+n/n+2

c) mn/n+2

d) m(n+1)+n/n+2

7. An express train takes 1 hour less than a passenger train to travel 132km between mysore and bengaluru (without taking consideration the time they stop at intermediate stations). If the average speed of the express is 11km/h more than that of the passenger train find the average speed of the passenger trainand express train, respectively in km/h

a) 23,34

b) 33,44

c) 29,40

d) 32,43

8. When a ballon bounces, it rises to 3/4^th of the height from which it fell. If the ball is dropped from a height of 32m, how high will it rise at the third bounce?

a) 14¹/₂ m

b) 14m

c) 13m

d) 13¹/₂m

9. The mean of 30 consecutive natural number is x., and the mean of the odd numbers in these30 natural number is y. if the smallest number is an odd number, find the value of x – y.

a) ¼

b) 0

c) 1

d) ½

10. The sum of n terms of three AP’s is S₁, S₂ and S₃. If the first form of each AP is 1 and the common difference is 1, 2 and 3 respectively, find the value of S₁+S₃ / S₂.

a) 1

b) 3

c) 2

d) 5

11. The water in the rectangular reservoir has a base 0f 80m x 60m and is 6.5m deep. At what time (in hours) can the water is emptied by a pipe having a cross section in the form of a square of side 20cm, if water runs through the pipe at the rate of 15km/h?

a) 40

b) 50

c) 52

d) 42

12. Find the area (in cm²) of a quadrant of a circle whose circumference is 22cm.

a) 15

b) 155

c) 9.6

d) 16

13. A triangle ABC is drawn to circumscribe a circle such that the segment BS and SC are of the length 6cm and 8cm respectively. If the length of the segment AT is X cm, then find the perimeter of the triangle.

14. Find the value of m for which the points (3,5), (m,6), and (¹/₂, 15/2) are collinear

a) 4

b) 3

c) 1

d) 2

15. The sum of the first ten terms of an AP is four times the sum of its first five terms. What is the ratio of the first term and the common difference?

a) 1

b) 1/2

c) 4

d) ¼

16. A conical vessel of radius 6 cm and height 8 cm is completely filled with water. A sphere is lowered into the water such that when it touches the sides, it is just immersed. What fraction of the water overflows?

a) 0.375

b) 0.125

c) 0.625

d) 0.875

17. If A, B, C are the angles of a triangle then find sin(^B+C/2)

a) Cot A/2

b) Sin A/2

c) Tan A/2

d) Cos A/2

18. Three consecutives positive integers are taken such that the sum of the squares of the first number and the product of the other two numbers is 232. Find the integers

a) 7, 8, 9

b) 10, 11, 12

c) 8, 9, 10

d) 11, 12, 13

19. A two member committee of one male and one female member is to be constituted out of five males and three females. Amongst the females, Ms. A refuses to be a member of the committee, in which Mr. B taken as the member. In how many ways can a committee can be constituted?

a) 15

b) 11

c) 14

d) 12

20. The ionisation energy of F^- is 320kj/mol. What would be the electron gain enthalpy of fluorine?

a) – 160kj/mol

b) 320kj/mol

c) 160kj/mol

d) – 320kj/mol

21. Beakers A, B and C contain zinc sulphate, silver nitrate, and ferrous sulphate solutions , respectively. If copper pieces are added to each added to each beaker, which of them will change the colour of its solution to blue?

a) B

b) A and C

c) C

d) B and C

22. How many oxygen atoms are present in 5 moles of sulphuric acid (H₂SO₄)?

a) 99.33 x 10²³

b) 75.55 x 10²³

c) 60.22 x 10²³

d) 120.44 x 10²³

23. Out of the people who participated in a survey, 70% owned a car and 75% owned a TV. If 55% owned both a car and a TV, what percent did not own either of them?

a) 5%

b) 25%

c) 10%

d) 20%

24. Which of the following will be the next term in the sequences?

111221

a) 332311

b) 121221

c) 232321

d) 312211

25. If BEAT =25 – 22 – 26 – 7 and RUST = 9 -6 -8 -7, THEN HOW WILL YOU CODE “BURST”?

a) 25-22-9-8-7

b) 25-6-9-8-7

c) 25-9-6-8-7

d) 25-7-8-7-6

26. If A + B means that A is B’s wife, A – B means that A is the son of B, AB means that A is B’s brother, then how is P related to S in P + QR - S?

a) Niece

b) Daughter in law

c) Aunt

d) Daughter

27. If 3.2g of O2 is liberated at the anode when aq.AgNO3 is electrolysed using PI electrodes , find the amount of Ag that will be deposited at the cathode in grams.

a) 4.32g

b) 32g

c) 1.6g

d) 43.2g

28. Select the correct order of the stability of ions of Ge, Sn and Pb.

i.Ge²⁺<Sn²⁺<Pb²⁺

ii.Ge⁴⁺>Sn⁴⁺>Pb⁴⁺

iii.Sn⁴⁺>Sn²⁺

iv.Pb²⁺>Pb⁴⁺

a) Only ii and iii are correct

b) Only I and iv are correct

c) All I, ii, iii and iv are correct

d) Only I, iii and iv are correct

29. Calculate the molarity of the solution when 100ml of 40% (w/v) NaOH solution is mixed in one litre of water

a) 1.00M

b) 0.909M

c) 9.09M

d) 1M

30. Find the exact volume of 1 M NaOH solution required to neutralise 50 ml of 1 M H₂PO₃ solution and 100ml of 2 M H₃PO₂ solution respectively.

a) 100 ml and 200 ml

b) 100 ml and 100 ml

c) 100 ml and 50 ml

d) 50 ml and 50 ml

31. Select the correct det of quantum numbers for the unpaired electrons of a chlorine atom(Z=17)

a) N=3, l=1, m=1

b) n=2, l= 1, m=1

c) n =3, l=1, m=0

d) n=2, l=1, m=0

32. find the respective number of electrons transferred when KMnO4acts as an oxidising agent to give MnO2, Mn²⁺, Mn(OH)₂^2-

a) 1,3,4,5

b) 5,4,3,1

c) 4,3,1,5

d) 3,5,4,1

33. Select the ore from which metals cannot be extracted using the calcination process.

a) ZnS

b) CaCO₃

c) CaCO_3.. Ca(OH)₂

d) Al₂O₃.2H₂O

34. Th belongs to the group 3. It emits an alpha particle , which group does the daughter element belong to ?

a) 1

b) 2

c) 3

d) 4

35. A small bubble rises from the bottom of the lake, where the temperature and pressure are 60 degree Celsius and 6 atm, to the water’s surface, where the temperature is 25 degree Celsius and the pressure is 1 atm. Calculate the final volume of the bubble if its initial volume was 2 ml

a) 14 ml

b) 11.31 ml

c) 12.72 ml

d) 15 ml

36. Find the maximum number of isomers for the compound with the formula C₄H₆

a) 5

b) 6

c) 8

d) 3

37. Among the given four metals , which one will get displacedfrom its salt solution by the other three ?

a) Zinc

b) Magnesium

c) Silver

d) Copper

38. What is the n factor or valency factor for H₂CO₃ ?

a) Either a or b

b) 1

c) Neither a nor b

d) 2

39. How many grams of concentrated nitric acid solution should be used to prepare 250 ml of 2 M HNO₃ ? the concentrated acid is 70%(w/w) HNO₃.

a) 45g of HNO3

b) 54g of HNO3

c) 90g of HNO3

d) 70g of HNO3

40. Which of the following ion is paramagnetic?

a) Mn²⁺

b) Ti²⁺

c) Cu²⁺

d) Mg²⁺

41. Which of the following molecules gives only acids or acidic species on hydrolysis?

i. PCl₃

ii. SF₄

iii. NCl₃

iv. P₄O₆

a) All I , ii , iii, and iv

b) Only I, ii and iii

c) Only ii, iii, and iv

d) Only I, ii, and iv

42. If ‘-’ stands for division , ‘+’ stands for subtraction, and ‘/’ stands for multiplication and ‘x’ stands for addition, then which of the following equations is correct ?

a) 70-2+4/5x6=21

b) 70-2+4/5x6=44

c) 70-2+4/5x6=341

d) 70-2+4/5x6=36

43. A clock gains five minutes every hour. What is the angle traversed by the second hand in one minute?

a) 360.5

b) 380

c) 390

d) 360

44. 56, 90, 132, 184, 248, _{__}?_{_}

a) 362

b) 3687

c) 326

d) 316

45. In a row of boys, A who is 10^th from the left and B who is 9^th from the right interchange their positions, and A becomes 15^th from the left. How many boys are there in the row?

a) 28

b) 23

c) 21

d) 27

46. Choose the correct option to complete from the given series.

NM, PK, SI, ?

a) WG

b) VG

c) VE

d) WF

47. Choose the incorrect number in the given series.

5, 8, 20, 42, 124, 246, 736

a) 124

b) 20

c) 8

d) 246

48. The cost price of 30 articles is the same as the selling price of x articles. If the profit is 20%, then find the vslue of x.

a) 20

b) 12

c) 25

d) 16

49. If 36 % 31= 12 and 92 % 30 + 14 then find the value of 16 % 24

a) 12

b) 25

c) 33

d) 28

50. If 42(49)36 and 87(36)81, then what is the value of ‘A’ in 67(A)58 ?

a) 9

b) 81

c) 26

d) 27

51. Abhishek walks 3 km towards the north from point P and reaches point Q. from Q, he takes a left turn (90 degrees) and walks 4 km to reach point R. From R, he takes a 45 degree left turn and walks 5 km. how he is from point P?

a) 6Ö2 km

b) 8Ö2 km

c) 10 km

d) 8 km

52. Find total numbers of triangles in the given geometric figure

a) 32

b) 36

c) 25

d) 24

53. If ‘NEUROTIC’ can be written as ‘TICRONEU’, then how can ‘PSYCHOTIC ’ be written ?

a) TICCHOPSY

b) TICCOHPSY

c) TICOCHPSY

d) TICHCOPSY

54. How many will be on the face opposite to the one with 2 points ?

a) 5

b) 6

c) 1

d) 4

55. Find the correct water image of given picture

56. One of the following figures doesn’t belong to this group. Which one it is ?

a) 1

b) 2

c) 3

d) 4

57. Find a number to replace (?)

a) 124

b) 31

c) 62

d) 93

58.

a) 51,7

b) 48,5

c) 51,8

d) 56,12

59. What will be the next figure

60. A triangle ABC is drawn to circumscribe a circle such that the segments BS AND SC are lengths of 6 cm and 8 cm respectively. If the length of the segment AT is x cm. then find the perimeter of the triangle.