(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
- Q4VIEW SOLUTION
- Q5VIEW SOLUTION
- Q6VIEW SOLUTION
In Fig. 2, a quadrilateral ABCD is drawn to circumscribe a circle with centre O in such a way that the sides AB, BC, CD and DA touch the circle at the points P, Q, R and S respectively. Prove that AB+ CD = BC + DA.VIEW SOLUTION
- Q8VIEW SOLUTION
- Q9VIEW SOLUTION
- Q10VIEW SOLUTION
- Q11VIEW SOLUTION
In the figure, a tent is in the shape of a cylinder surmounted by a conical top of same diameter. If the height and diameter of cylindrical part are 2.1 m and 3 m, respectively, and the slant height of conical part is 2.8 m, find the cost of canvas needed to make the tent if the canvas is available at the rate of Rs 500/sq. metre.VIEW SOLUTION
- Q13VIEW SOLUTION
- Q14VIEW SOLUTION
- Q15VIEW SOLUTION
- Q16VIEW SOLUTION
A conical vessel, with base radius 5 cm and height 24 cm, is full of water. This water is emptied into a cylindrical vessel of base radius 10 cm. Find the height to which the water will rise in the cylindrical vessel.VIEW SOLUTION
A sphere of diameter 12 cm, is dropped in a right circular cylindrical vessel, partly filled with water. If the sphere is completely submerged in water, the water level in the cylindrical vessel rises by . Find the diameter of the cylindrical vessel.VIEW SOLUTION
A man standing on the deck of a ship, which is 10 m above water level, observes the angle of elevation of the top of a hill as 60° and the angle of depression of the base of hill as 30°. Find the distance of the hill from the ship and the height of the hill.VIEW SOLUTION
- Q20VIEW SOLUTION
Due to heavy floods in a state, thousands were rendered homeless. 50 schools collectively offered to the state government to provide place and the canvas for 1500 tents to be fixed by the government and decided to share the whole expenditure equally. The lower part of each tent is cylindrical of base radius 2.8 m and height 3.5 m, with conical upper part of same base radius but of height 2.1 m. If the canvas used to make the tents costs Rs 120 per sq.m, find the amount shared by each school to set up the tents. What value is generated by the above problem?VIEW SOLUTION
- Q22VIEW SOLUTION
- Q23VIEW SOLUTION
In the figure, two equal circles, with centres O and O', touch each other at X.OO' produced meets the circle with centre O' at A. AC is tangent to the circle with centre O, at the point C. O'D is perpendicular to AC. Find the value of .VIEW SOLUTION
- Q25VIEW SOLUTION
The angle of elevation of the top Q of a vertical tower PQ from a point X on the ground is 60°. From a point Y, 40 m vertically above X, the angle of elevation of the top Q of tower is 45°. Find the height of the tower PQ and the distance PX.VIEW SOLUTION
The houses in a row are numbered consecutively from 1 to 49. Show that there exists a value of X such that sum of numbers of houses proceeding the house numbered X is equal to sum of the numbers of houses following X.VIEW SOLUTION
In fig. 8, the vertices of ΔABC are A(4, 6), B(1, 5) and C(7, 2). A line-segment DE is drawn to intersect the sides AB and AC at D and E, respectively, such that . Calculate the area of ΔADE and compare it with area of ΔABC.VIEW SOLUTION
- Q29VIEW SOLUTION
- Q30VIEW SOLUTION
- Q31VIEW SOLUTION
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