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Section-A (Science)

1. (c) The image formed by a plane mirror is always erect and of the

same size as that of the object. Therefore, Anuj has a plane mirror. Also, when the image is erect and of small size than object then it is a convex mirror so Priya has a convex mirror.

2. (b) When we blow air into the mouth of the bottle, the air near the mouth has higher speed. This decreases the air pressure at the mouth of the bottle. The air pressure inside the bottle is higher than it is near the mouth which pushes the ball outwards.

Thus option B is the correct answer. 3. (c) Let us assume that the total time taken to cover the distance of

100 m by Rahul is tA and by Rohan is tB. Time can be expressed in terms of;

Now if the average speed of Rahul (vA) is 8.41 ms-1 and of Rohan (vB) is 12.2 ms1. Time taken by Rahul to cover 100m race (tA),

Time taken by Rohan to cover 100m race (tB),

Since the school record was 12 s. Therefore, both Rahul and Rohan has broken the record. Hence, option C is the correct answer.

4. (a) Pin on the wire in figure A will fall first since we know that heat travels by conduction in solid and the distance (which is PQ) is less in fig A as compared to fig B (which is CE) so heat reaches pin in fig A faster and makes it fall down.

5. (c) According to the law of reflection, the angle of incident is equal to the angle of reflection. (i = r)

As the ray incident on the mirror A at an angle 25 degree with the mirror, the ray will reflect making an angle of 25 degrees with the normal. The ray will then strike the surface of the mirror B at an angle of 65 degrees with the normal;

Hints and Solutions

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6. (d) 35° is equivalent to 308.13 K; which is greater than the

temperature of water in the mug i.e. 305 K. Therefore, the heat is going to flow from the iron ball to the water instead. Hence, the assertion is false.

Although, the reason is true as in the process of convection the water molecule of the liquid moves themselves.

7. (c) • An indicator prepared from natural substances is known as natural indicator. Examples are Litmus, Turmeric, China Rose petals, snowball plant, Red Cabbage and Grape Juice.

• An indicator prepared from artificial substances is known as synthetic indicator Examples are Phenolphthalein and Methyl Orange.

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• Methyl orange is a pH indicator frequently used in titration because of its clear and distinct color variance at different pH values. Methyl orange shows red color in acidic medium and yellow color in basic medium.

8. (d) In dish X, two substances are just mixed and can be seen separately. As the mixture is not heated. so no chemical reaction takes place and no new compound is formed. Thus it is a physical change. In dish Y, the mixture is heated so, a chemical reaction takes place new compound (iron sulphide) is formed. Thus, it is a chemical change. We cannot get back iron supplied by any physical method. So it is irreversible.

9. (d) At standard temperature and pressure, hydrogen gas is a colourless, odorless, tasteless, non-toxic, non-metallic, highly combustible diatomic gas with the molecular formula H2.

10. (b) The fabric of clothes made by synthetic fibres melt easily and can stick to the person’s body. They should not be worn at laboratories and in the kitchen.

Hence, option B is correct. 11. (b) An acid which can be dissociated completely or almost completely

in water is known as a strong acid. For e.g. Sulphuric acid, nitric acid, hydrochloric acid, etc

12. (d) Methods of purification of organic compounds are sublimation, distillation and crystallization.

13. (d) Azo dyes are the synthetic colour that contain an azo group, -N=N-, as part of the structure. Azo groups do not occur naturally. Most azo dyes contain only one azo group, but some contain two (di azo), three (tri azo) or more.

14. (c) Platelets are tiny blood cell fragments that help your body form clots to stop bleeding. If one of your blood vessels gets damaged, it sends out signals that are picked up by platelets. The platelets then rush to the site of damage and form a plug, or clot, to repair the damage.

15. (a) Insects also have similar openings. These openings are called spiracles. Insects have a network of air tubes called tracheae for gas exchange. Oxygen rich air rushes through spiracles into the tracheal tubes, diffuses into the body tissue, and reaches every cell of the body.

16. (a) Light energy is used to synthesize food from carbon dioxide and water. Thus, chlorophyll, sunlight, carbon dioxide and water help to carry out the process of photosynthesis. The solar energy

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captured by the leaves is stored in the plant in the form of chemical energy.

17. (b) Animals which are ruminants have a large sac-like structure between the small intestine and large intestine, which is not present in humans. Hence the doctor is veterinary surgeon.

Hence Option B is correct. 18. (c) Yeast and mushroom obtain nutrients from dead and decayed

organisms. Hence, they have saprophytic mode of nutrition. 19. (c) Haemoglobin is a protein in red blood cells that carries oxygen to

body's organs and tissues and transports carbon dioxide from organs and tissues back to lungs. It abbreviated Hb or Hgb, is the iron-containing oxygen-transport metalloprotein in the red blood cells of almost all vertebrates as well as the tissues of some invertebrates. Haemoglobin in blood carries oxygen from the lungs or gills to the rest of the body.

20. (c) A fertilized egg is called a zygote. A zygote is the single cell created when the sperm and egg combine (product of fertilization).

Section-B (Mathematics)

21. (d) We know that, Distance curved by a circle in n revolutions = 2πrn

484 × 1000

⇒ n = 55,000 22. (b) Let the width of the rectangle = x cm ∴ Length of rectangle = (10 + x) cm Now, Perimeter = 240 cm 2[length + width] = 240 2[10 + x + x] = 240 2[10 + 2x] = 240 10 + 2x = 120 2x = 110 ⇒ x = 55 cm ∴ Length of rectangle = 10 + x = 10 + 55 + 65 cm

23. (d)

24. (b) We have, 8x3 + 12y2 – 13xy - ? = 3x3 + 9y2 – 7xy ⇒ 8x3 + 12y2 – 13xy - 3x3 + 9y2 – 7xy = ? ⇒5x3 + 3y2 – 6xy

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25. (c) We know that, in a right angled triangle, the square of hypotenuse in equal to the sum of the square of other two sides.

Clearly, (13)2 = (12)2 + (5)2 169 = 144 + 25 169 = 169 Therefore, 5 cm, 10 cm and 13 cm will from a right angled

triangle. 26. (a) Given, Length of minute hand = r = 12 cm In 30 minutes the minute hand will cover the distance which in

equal to circumference of a semi-circle whose radius is 12 cm. ∴ Distance covered by minute hand in 30 minutes = πr

27. (b) Let Mohit’s age be x years ∴ Ajeet’s age = (2x + 5) years According to question. x + 2x + 5 = 20 3x = 15 x = 5 Therefore, Mohit’s age is 5 years. 28. (b) Length of wire = Perimeter of rectangle = 2 (40 + 24) = 128 cm Perimeter of square = 128 cm 4 × side = 128 Side = 32 cm Area of square = (side)2 = (32)2 = 1024 cm2 Hence, B is the correct answer.

29. (d)

Here, AC is the original height of tree Now, tree has broke down from B. ∴ AB = BD

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Given, BC = 6 m & CD = 8 m In ΔBCD, By Pythagoras Theorem, (BD)2 = BC2 + CD2 (BD)2 = (6)2 + (8)2 (BD)2 = 36 + 64 (BD)2 = 100 ∴

Also, AB = BD = 10 m Now, Original height of tree = AC = AB + BC = 10 + 6 = 16m 30. (d) Consider 451,679,449,432,479,500 Arrange the data in ascending order i.e.

432,449,451,479,500,679. Since number of observations is even, the median is given by

finding the average or mean of the two middle most observations:

So, median is:

= 465 Hence, option D is correct. 31. (b) Consider the table,

As 126 has the highest frequency that is 14. So, mode of the data is 126.

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32. (a) From the double bar graph given we can see that cost of apples in city 1 is Rs 90/kg and in city 2 is Rs 75/kg.

The ratio of cost of apples in city 1 to the cost of apples in city 2 is

.

Hence, option A is correct. 33. (b) Area of circle = πr2 We know that r = ½d Area of circle

Circumference of circle = πd

Hence, B is the correct answer. 34. (d) Perimeter of given semicircle = πr + 2r

= 66 + 42 = 108 cm

35. (d) The perimeter of square = 4 × side 4 × sides = x

Area of square = (side)2

Hence, D is the correct answer. 36. (d) Area of a rectangle = length × breadth Area of given rectangle= (0.4×100 cm) × 0.25 cm = 10 cm2

37. (b)

38. (c) The exterior angle of a triangle equals to the sum of interior opposite angles.

90° = x + x 2x = 90° x = 45° Also, Sum of angles of a triangle = 180° x + x + y = 180° 90° + y = 180° y = 90° y – x = 90° - 45° = 45° Hence, C is the correct answer.

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39. (a) In a triangle, the sum of two sides is always greater than the third side.

Therefore, a + b > c a + c > b b + c > a Hence, A is the correct answer. 40. (b) 1 hectare = 10, 000 m2 Now, Area of Square = 1 ha (Side)2 = 10, 000 m2 ∴ side = = 100m

Section-C (Aptitude)

41. (a) The pattern is - 45, - 35, - 25, ..... i.e. 125 - 45 = 80 80 – 35 = 45 45 – 25 = 20 So, missing term = 20 - 15 = 5. 42. (d) The way carpenter make use of saw; which is a tool to saw wood,

the same way a mason uses trowel to place bricks. Thus option D is the correct answer. 43. (b) You can see that in KING and RING, ING is common. Therefore,

the three letters which represent ING should be ‘bde’ which are also common in the given code. The left out letter in the word KING is K i.e. m in the given code. Similarly, in RING the left out letter is R which is ‘o’ in the code. Similarly, in RING the left out letter is R which is ‘o’ in the code.

44. (d) All schools have teachers and students. No teacher is a student. Therefore, these two are independent of each other but part of the school. Therefore, alternative D is the answer wherein the big circle represents school and two small circles within it represent teachers and students separately.

45. (a) The following figures explain the soln.

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46. (d) Here,

The man moves as shown in the direction of the arrow. AD = BC = 20 m Thus, D is 20 m to the west of A. 47. (b) Sheetal is 10th from left and Hina is 9th from Right. If they

interchanged their positioned Sheetal become 15th from left. So, Sheetal has gained its position from left.

15th Positions + 8th positions = Total girls Total Girls = 23. 48. (d) In all the numbers, sum of the first 2 digits is equal to the third

digit, like 2 + 4 = 6, so 246, 6 + 3 = 9 so 639 etc. Only D is the odd one out, so answer is D.

49. (c) According to the question; + → – - → × × → ÷ ÷ → + Now, the above equation becomes; 15 ÷ 3 + 15 – 5 × 2 Applying BODMAS rule; (Bracket of; Division; Multiplication;

Addition; Subtraction)

Hence, option C is correct. 50. (d) ABCD is written as A – D – C – B and the next four term EFGH

follows the similar pattern i.e. E – H – G – F Thus if M – P – O – N then the next 4 terms Q R S T will be as Q

– T – S – R Hence option D is the correct answer.

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