(i) All questions are compulsory.
(ii) The question paper consists of 31 questions divided into four sections – A, B, C and D.
(iii) Section A contains 4 questions of 1 mark each, Section B contains 6 questions of 2 marks each, Section C contains 10 questions of 3 marks each and Section D contains 11 questions of 4 marks each.
(iv) Use of calculated is not permitted.
- Q1VIEW SOLUTION
- Q2VIEW SOLUTION
- Q3VIEW SOLUTION
In Fig. 1, PA and PB are tangents to the circle with centre O such that ∠APB = 50°. Write the measure of ∠OAB.
In Fig. 2, AB is the diameter of a circle with centre O and AT is a tangent. If ∠AOQ = 58°, find ∠ATQ.
- Q6VIEW SOLUTION
- Q7VIEW SOLUTION
- Q8VIEW SOLUTION
- Q9VIEW SOLUTION
- Q10VIEW SOLUTION
- Q11VIEW SOLUTION
- Q12VIEW SOLUTION
The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 45°. If the tower is 30 m high, find the height of the building.VIEW SOLUTION
- Q14VIEW SOLUTION
- Q15VIEW SOLUTION
In Fig. 3, APB and AQO are semicircles, and AO = OB. If the perimeter of the figure is 40 cm, find the area of the shaded region.
In Fig. 4, from the top of a solid cone of height 12 cm and base radius 6 cm, a cone of height 4 cm is removed by a plane parallel to the base. Find the total surface area of the remaining solid.
A solid wooden toy is in the form of a hemisphere surrounded by a cone of same radius. The radius of hemisphere is 3.5 cm and the total wood used in the making of toy is . Find the height of the toy. Also, find the cost of painting the hemispherical part of the toy at the rate of Rs 10 per cm2.VIEW SOLUTION
In Fig. 5, from a cuboidal solid metallic block, of dimensions
15cm ✕ 10cm ✕ 5cm, a cylindrical hole of diameter 7 cm is drilled out. Find the surface area of the remaining block
In Fig. 6, find the area of the shaded region [Use π = 3.14]
The numerator of a fraction is 3 less than its denominator. If 2 is added to both the numerator and the denominator, then the sum of the new fraction and original fraction is . Find the original fraction.VIEW SOLUTION
Ramkali required Rs 2,500 after 12 weeks to send her daughter to school. She saved Rs 100 in the first week and increased her weekly saving by Rs 20 every week. Find whether she will be able to send her daughter to school after 12 weeks.
What value is generated in the above situation?VIEW SOLUTION
Solve for x :VIEW SOLUTION
- Q24VIEW SOLUTION
In Fig. 7, tangents PQ and PR are drawn from an external point P to a circle with centre O, such that ∠RPQ = 30°. A chord RS is drawn parallel to the tangent PQ. Find ∠RQS.
- Q26VIEW SOLUTION
From a point P on the ground the angle of elevation of the top of a tower is 30° and that of the top of a flag staff fixed on the top of the tower, is 60°. If the length of the flag staff is 5 m, find the height of the tower.VIEW SOLUTION
- Q28VIEW SOLUTION
- Q29VIEW SOLUTION
- Q30VIEW SOLUTION
Water is flowing at the rate of 2.52 km/h through a cylindrical pipe into a cylindrical tank, the radius of whose base is 40 cm. If the increase in the level of water in the tank, in half an hour is 3.15 m, find the internal diameter of the pipe.VIEW SOLUTION
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