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Section-A (Science)

1. (c) As the least distance travelled is 4.8 m, thus friction would have been the largest.

If the magnitude of the force of friction between the breaks pads and discs is large then the distance travelled by car will reduce.

The friction acting on the wheel will bring the car to rest sooner (travelling lesser amount of distance)

2. (c) Statement ‘c’ is a false statement. A compound that allows the electric current to pass through itself, when either in a molten state or in an aqueous solution, is called an electrolyte. Solutions of sodium chloride, copper sulphate, dilute sulphuric acid are examples of strong electrolytes.

Statement ‘b’ is a correct statement. But, statement ‘c’ is a false statement. Thus, it is the wrong option. A solution of copper sulphate or sodium chloride in water will conduct electricity because they are basic in nature.

Statement 'a' is also correct. A solution of sulphuric acid or hydrochloric acid in water conducts electricity. They are considered to be strong electrolytes which dissociate when put in an aqueous medium facilitating the conduction of electric current.

Therefore, only statement c is incorrect. Hence option B is the right answer.

3. (c) When sound wave propagates in a different medium, the frequency of sound does not change. Hence, the frequency of a source of 20 kHz remains same when produced in water or in air.

4. (c) Friction is a phenomenon which resists motion when an object is rubbed against another. Rolling friction is between two objects where one or both of the surface is circular, with only a point in contact. Rolling friction is less than sliding friction.

So rolling friction should be much smaller than the static friction of 20N.

Option C is the answer. 5. (c) Sound is a mechanical wave, it may be defined as a disturbance

which travels through a material medium due to repeated periodic vibrations of the particles of the medium about their mean position, the disturbance is transferred from one particle to the adjoining particle, without any net movement of the medium.

6. (c) Force may bring change in the shape of an object. Although it might not always affect the change in the shape of the object. The change in the shape of the object may occur if the force acting on the object is of greater magnitude.

Hints and Solutions

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Apart from this a force may bring some or all of these affect mentioned in the question.

Hence option C is the correct answer. 7. (c) • Semiconductors are materials which have a conductivity

between conductors (generally metals) and nonconductors or insulators (such as most ceramics).

• Semiconductors can be pure elements, such as silicon or germanium, or compounds such as gallium arsenide or cadmium selenide

• Germanium is neither a good conductor of electricity nor an insulator. It is a semiconductor.

Option B is correct. 8. (c) The Radioactive Isotopes are used as 'tracers' in medicine to

detect the presence of tumors and blood clots in human body. Option A is correct. 9. (c) Cotton is a Natural fibre. Silk is a product of silkworms. Nylon is

a synthetic fibre. Nylon has the highest tensile strength because it is synthetically made followed by silk and cotton.

10. (c) Physical irreversible change: withdrawing money from ATM. Chemical reversible change: charging mobile battery Physical reversible change: filling of water bottle. Chemical irreversible change: boiling an egg. 11. (c) • Potable water refers to water that is fit for human consumption.

Water can be made potable by various methods. • Potable water is also known as drinking water. • One way of making water potable is by boiling it. Option C is correct. 12. (c) A circular blackish ring is formed when a clean glass plate/slide

is introduced into the luminous zone of flame. It indicates the deposition of unburnt carbon particles present in the luminous zone of the flame.

Thus, Option D is the correct answer. 13. (c) As Hari took the powered marble piece, Hari’s test tube will react

faster. For a reaction involving a solid reactant, the smaller in the particle size, i.e., greater is the surface area, the faster is the reaction.

14. (c) Prokaryotes are a group of organisms which lack a well-defined nucleus, nucleolus, and other cell organelle. They have 70S ribosomes in the cytoplasm. Moss, Sponge, Yeast, Amoeba, Penicillium and Spirogyra are eukaryotic organisms, while Bacteria and Blue green algae (like Anabaena and Nostoc) are examples of prokaryotic organisms.

15. (c) Hepatitis B infection is caused by the hepatitis B virus (HBV). The virus is passed from person to person through blood, semen or other body fluids.

16. (c) HIV virus is present in the blood of infected person. So, if this infected blood is transfused to a healthy individual, there are

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chances of the person getting infected by this virus. This virus is also transmitted through shared injection needles, sexual contact, infected mother to child during pregnancy via Placenta.

17. (c) Our modern understanding of the fermentation process comes from the work of the French chemist Louis Pasteur. Moreover, Pasteur demonstrated that only microorganisms are capable of converting sugars into alcohol from grape juice, and that the process occurs in the absence of oxygen.

18. (c) Deforestation is the permanent removal of trees which also remove natural habitat of the animals. This process can include clearing the land for agriculture or grazing, or using the timber for fuel, construction or manufacturing. Forests cover more than 30% of the Earth's land surface, according to the World Wildlife Fund.

19. (c) Puberty usually occurs in girls between the ages of 10 and 14, while in boys it generally occurs later, between the ages of 12 and 16.

20. (c) Harvested grains have less moisture and Specific chemical treatments are required to protect crops from pests and microorganisms. These are the two main characteristics for storage of agriculture goods.

Section B (Mathematics)

21. (c) To find the square root of a decimal number we put bars on the integral part

(i.e., 70) of the number in the usual manner and place bars on the decimal part (i.e., 56) on every pair of digits beginning with the first decimal place. Proceed as usual.

Using long division method for finding

So, the square root of 70.56 is 8.40. 22. (c) (i) Since in the given histogram in the slot 2-3 there are 11

students, therefore there are 11 users whose watch time on YouTube is between 2-3 hours.

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(ii)Highest watching hours (6-7) students count - Lowest watching hours (1-2) students count Therefore, their difference =25 – 4 = 21 Hence, Option A is correct.

23. (c) Area of a circle = πr2 Circumference of a circle = 2πr

= 2ax : 1 Hence, A is the correct answer. 24. (c) Let total number of people = x People who like classical music=20

⇒ x = 200 So total number of people surveyed=200 25. (c) Prime factorization of 3267 ⇒ 3267 = 3 × 3 × 3 × 11 × 11 The prime factor 3 appears in group of three, 11 does not appear

in group of three. ∴ To make it a cube, we need to multiply it by 11. 26. (c) Given,

⇒ 2x – 1 = -3 ⇒ 2x = -3 + 1 = -2 ⇒ x = -1 27. (c) 5.05 × 106 = 5.05 × 1000000 = 5050000 28. (c) Lateral surface area of cube = 4a2 4 × 102 = 400 cm2

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Length of cuboidal box = 12.5 cm Breadth = 10 cm Height = 8 cm Lateral surface area = 2[l + b]h = 2[12.5 + 10]8 = 16 × 22.5 = 360 cm2

29. (c) The square of numbers ending with 1 and 9 have 1 in their unit digit.

Therefore, the square roots of 998001 will have 1 or 9 as its unit digit.

Hence, B is the correct answer. 30. (c) (20 + 3-1) × 32

As we know that by the rule 20 = 1

So,

⇒ 4 × 3(2-1) = 4 × 3 = 12

31. (c) Taking the factors of 4096.

Therefore, 4096 = 212 √4096 = √212 By pairing, we will get, √4096 = 26 = 64 Hence, C is the correct answer.

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32. (c) Radius of cap (r) = 7 cm, Height of cap (h) = 24 cm

Slant height of the cone

Area of sheet required to make a cap = CSA of cone = πrl

∴ Area of sheet required to make 10 caps = 10 × 550 = 5500 cm2

33. (c) First consider the case for negative number. Let m = -2 ∴ m2 = (-2)2 = 4 and m3 = (-2)3 = -8 i.e. m2 > m3 Now for positive case, we have Let m = 2 ∴ m2 = (2)2 = 4 and m3 = (2)3 = 8 i.e. m2 < m3 Hence, Option D is correct.

34. (c) 36 < x2 < 49 6 < √44 < 7 6 < x < 7 Hence, A is the correct answer.

35. (c) (35)2 = 1225 (36)2 = 1296 1225 < 1290 < 1296 35 < √1290 < 36 Hence, A is the correct answer. 36. (c) Circumference = length of paper 2π r=44

37. (c) Volume of the cuboid is = 18 cm × 10 cm × 25 cm

⇒ In prime factorization form = 3 × 3 × 2 × 2 × 5 × 5 × 5 We need to make triplets of each prime factor to make a perfect cube. ∴ we need 3 × 2 = 6 cuboids

38. (c) Factorizing 44(x4 – 5x3 – 24x2), we get ⇒ 44(x4 – 5x3 – 24x2) = 2 × 2 × 11 × (x4 – 5x3 – 24x2)

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Taking the common factor x2 out of the bracket, ⇒ 44(x4 – 5x3 – 24x2) = 2 × 2 × 11 × x2(x2 – 5x – 24) = 2 × 2 × 11 × x2(x2 – 8x + 3x – 24) = 2 × 2 × 11 × x2 [x (x – 8) + 3 (x – 8)] = 2 × 2 × 11 × x2 × (x + 3) × (x – 8) Therefore,

Cancelling out all the common factors from the numerator and denominator, we get ⇒ 2 × 2 × x × (x + 3) = 4x(x + 3) Hence, option C is correct.

39. (c)

40. (c) We need to find the 1’s digit. ∴ Our answer will depend only on the 1’s digit of 56985963 which is 3. 1’s digit in cube of 3 = 3 × 3 × 3 = 27 ∴ Correct answer is 7.

Section C (Aptitude)

41. (c) It can be observed from both the dice and if 2, 3, 5 and 6 adjacent to 1, then the number opposite to 1 should be 4. Hence the correct answer is option A.

42. (c) All the other options have at least 1 number that is not a prime number. Only option D has all

43. (c) Here,

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The movement of Rohit is shown in the given figure with the arrow denoting the direction. The distance between his initial position and the final position is AF. AF = AG + GF = 30 + 17 = 47 m. Hence, answer is 47 m towards East.

44. (c) Find out the positions of both the letters from the left and divide the sum of the positions of both the letters from the left by 2. Here 13+23=36. Now divide 36 by 2 , i.e 18. Hence R is the required letter.

45. (c) As Deepak is Amit’s brother. Deepak is grandson of Ramesh therefore, Amit is also grandson of Ramesh.

46. (c) This is an analogy question which shows us the relationship

between two things. Here, the relationship is x : . The first

number is x and the second is Hence, the answer is = 51.

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47. (c) A > B ≥ C < D < E, so E > D > C, so definitely E > C, the rest cannot be surely confirmed like A can be > C but may not be equal to C, similarly D may be > B but may not be equal and A > B and C and C is < D but A may be equal to D also. So only option B remains.

48. (c) First letters are common. Second letters are:b, c, c, c, c. One of the four words having c is the last word. Let us see the third letters now ,there are: t, c, q, h. Clearly t is the last. Hence Actuate is the last word.

49. (c) The word asked to write code for contains all the letters given in the code thus, only find the correct match of the letters. It is A=D, T= W, I- L, U=X, D=G, E=H.

50. (c) After substituting the values given in the question, we get 52 – 12 × 28 ÷ 7 + 15 = 19

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