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 Model Activity Task Solved Paper

MODEL ACTIVITY TASK

CLASS – X

MATHEMATICS

Answer the following questions:

1. Multiple choice questions (MCQs): 1 × 4 = 4

(i) If A α B then

• (a)A²αB³
• (b) A³αB²
• (c) AαB³
• (d) A²αB²

(ii) A and B started a business. A invested ₹1000 for 9 months and B invested some money for 6 months. If they make a profit of ₹600 in a year and B gets profit share ₹400 then capital of B in the business is

• (a)₹ 2000
• (b) ₹ 3000
• (c) ₹4000
• (d) ₹6000

(iii) The lengths of radii of two circles are 7cm. and 4cm respectively. The two circles touch each other internally. The distance between the two centres of the two circles is

• (a) 5.5 cm.
• (b) 1.5 cm.
• (c) 11 cm.
• (d) 3 cm.

(iv) The volume of a solid sphere having radius of r/2 unit length is

• (a) π r² sq unit
• (b) 4/3 πr³ cubic unit
• (c) 4πr² sq. unit
• (d) 1/6 πr³cubic unit

2. Write true/false (T/F): 1 × 4 = 4

(i) Two similar triangles are always congruent.

(ii) The height, radius and slant height of a right circular cone are always the three sides of an acute angled triangle.

(iii) If in a partnership business the ratio of capitals of Pretom, Nirja and Tatha is as 1/2:1/3:1/4then the ratio of their profit shares will be 3:4:6.

(iv) If a α 1/b and b α 1/a then a α 1/c.

3. Fill in the blanks: 1 × 3 = 3

(i) If we double the length of radius of a solid sphere, the area of curved surface of the sphere will be ________.

(ii) In a business, if Shobha contributedtimes more than Masud and Priya contributed times more than Masud then the ratio of the capitals of Masud, Shobha and Priya will be ________ .

(iii) Two circles touch each other externally at the Point A. The number of common tangent drawn to the two circles at the point A is ________ .

4. Short answer type questions: 2 × 2 = 4

(i) If a α b,b α c and c α a, then find the relation between three variation constants.

(ii)

In the adjoining figure, Δ ABC circumscribes a circle and touches the circle at the points P, Q, R. If AP = 4 cm., BP = 6 cm., AC = 12 cm. and BC = x cm., find the value of x.

5. Prove with reason that the tangent to a circle at any point on it is perpendicular to the radius that passes through the point of contact. 5

Class 10 Model Activity Task All Subject October 

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