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5 marks Long answer
Check whether a triangle exists for each of the following set of lengths. a. 2, 150, 150 b. 4, 7, 10 c. 2, 2, 6 d. 6, 11, 13
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Use the triangle inequality theorem to check the conditions.
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5 marks Long answer
Using all digits from 0–9 exactly once, create a 10-digit number which is a. the largest multiple of 5. b. the smallest even number.
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Largest multiple of 5: 9876543200; Smallest even number: 1023456789.
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5 marks Long answer
Two consecutive numbers in the Virahāṅka sequence are 987 and 1597. What are the next two numbers in the sequence? Find the previous two numbers in the sequence.
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Next numbers: 2584 and 4181; Previous numbers: 610 and 377.
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5 marks Long answer
Find the value of a in each of the following figures.
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Refer to the specific figures provided.
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5 marks Long answer
Find the area of a rectangle of length 6 4/5 ft and breadth 5 6/7 ft.
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Area = 39 1/5 square feet.
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5 marks Long answer
Construct a triangle with the following measurements: 75°, 5 cm, 75°.
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Use a protractor and ruler to draw the triangle.
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5 marks Long answer
Write the number names of the following numbers in both Indian and International systems of numeration. a. 456111854 b. 5162789 c. 59232731 d. 31133113 e. 357924680
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Refer to the number naming conventions.
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5 marks Long answer
Fill in the blanks. a. 8 mm = .................... cm b. 144 mm = .................... cm c. 456.7 cm = .................... mm d. 63 cm = .................... m e. 567 cm = .................... m f. 348 cm = .................... m g. 576 g = .................... kg h. 79 g = .................... kg i. 2670 g = .................... kg j. 8400 g = .................... kg
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Refer to metric conversions.
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5 marks Long answer
Construct a triangle ABC with BC = 5 cm, AB = 6 cm, CA = 5 cm. Construct an altitude from A to BC.
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Use a compass and ruler to construct the triangle and altitude.
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5 marks Long answer
Evaluate the following. a. 3 ÷ 7/9 b. 5/4 ÷ 4/5 c. 1/6 ÷ 1/8 d. 18/4 ÷ 2 e. 9/5 ÷ 1/9 f. 1/8 ÷ 13/16 g. 3/4 ÷ 3/4 h. 15/3 ÷ 5/8 i. 43/4 ÷ 23/8 j. 21/9 ÷ 14/6
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Follow the division of fractions rules.
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5 marks Long answer
Simplify the following expressions. a. 4a + 10b – 7 + 9a – 3b – 8a + 15 b. 4(2a – 4b) – 7a – 5b – 20 c. 7x – (3x – 4) + 8 d. 9h – (6 + 8h) + 11 e. 32 + 5(5m – 4n) – 6n – 4m – 20
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Combine like terms and apply distributive property.
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4 marks Medium answer
Multiply and then convert it into a mixed fraction. a. 8 × 5/6 b. 11/13 × 7 c. 5 × 2/3
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Results: a. 6 2/3; b. 77/13; c. 10.
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4 marks Medium answer
Compare and write '<', '>', or '='. a. 40 thousand .................... 4 lakhs b. 600 lakhs .................... 6 million c. 750 crore .................... 75 billion
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a.
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4 marks Medium answer
Find the values of the following expressions by writing the terms in each case. a. 48 – 3 × 7 + 12 b. 58 – 20 × 3 + 24 ÷ 4 c. 7 × 5 – 6 × 10 × 3
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a. 9; b. -26; c. -123.
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4 marks Medium answer
Write the following quantities in the decimal form. a. 98 ones, 6 tenths and 70 hundredths b. 21 tens and 21 tenths c. 30 tens, 30 ones 30 tenths and 30 hundredths
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a. 98.67; b. 231; c. 303.30.
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4 marks Medium answer
Write the parity of the following. a. Even number + even number = .............................................. b. Odd number + odd number = .............................................. c. Even number + odd number = .............................................. d. Even number – even number = .............................................. e. Odd number – odd number = .............................................. f. Odd number – even number = ..............................................
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a. Even; b. Even; c. Odd; d. Even; e. Even; f. Odd.
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4 marks Medium answer
Find the third angle of a triangle when two of the angles are: a. 140°, 25° b. 65°, 55° c. 80°, 40°
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Third angle = 180° - (angle1 + angle2).
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2 marks Short answer
Write the following fractions in the decimal form. a. 2/5 b. 5/2 c. 5/4 d. 6/5 e. 1/2
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a. 0.4; b. 2.5; c. 1.25; d. 1.2; e. 0.5.
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