(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
In Figure 1, a tower AB is 20 m high and BC, its shadow on the ground, is m long. Find the Sun's altitude.
- Q3VIEW SOLUTION
In Figure 2, PQ is a chord of a circle with centre O and PT is a tangent. If ∠QPT = 60°, find ∠ PRQ.
In Figure 3, two tangents RQ and RP are drawn from an external point R to the circle with centre O. If ∠PRQ = 120°, then prove that OR = PR + RQ.
In figure 4, a triangle ABC is drawn to circumscribe a circle of radius 3 cm, such that the segments RD and DC are respectively of lengths 6 cm and 9 cm. If the area of ∆ABC is 54 cm2, then find the lengths of sides AB and AC.
- Q7VIEW SOLUTION
- Q8VIEW SOLUTION
- Q9VIEW SOLUTION
- Q10VIEW SOLUTION
- Q11VIEW SOLUTION
Solve for x :VIEW SOLUTION
The angle of elevation of an aeroplane from a point A on the ground 60°. After a flight of 15 seconds, the angle of elevation changes to 30°. If the aeroplane is flying at a constant height of 1500 m, find the speed of the plane in km/hr.VIEW SOLUTION
- Q14VIEW SOLUTION
The probability of selecting a red ball at random from a jar that contains only red, blue and orange balls is The probability of selecting a blue ball at random from the same jar is If the jar contains 10 orange balls, find the total number of balls in the jar.VIEW SOLUTION
- Q16VIEW SOLUTION
Due to sudden floods, some welfare associations jointly requested the government to get 100 tents fixed immediately and offered to contribute 50% of the cost. If the lower part of each tent is of the form of a cylinder of diameter 4.2 m and height 4 m with the conical upper part of same diameter but of height 2.8 m, and the canvas to be used costs Rs. 100 per sq. m, find the amount, the associations will have to pay. What values are shown by these associations?VIEW SOLUTION
A hemispherical bowl of internal diameter 36 cm contains liquid. This liquid is filled into 72 cylindrical bottles of diameter 6 cm. Find the height of the each bottle, if 10% liquid is wasted in this transfer.VIEW SOLUTION
A cubical block of side 10 cm is surmounted by a hemisphere. What is the largest diameter that the hemisphere can have ? Find the cost of painting the total surface area of the solid so formed, at the rate of Rs 5 per 100 sq. cm. [Use π =3.14]VIEW SOLUTION
- Q20VIEW SOLUTION
- Q21VIEW SOLUTION
- Q22VIEW SOLUTION
A train travels at a certain average speed for a distance of 54 km and then travels a distance of 63 km at an average speed of 6 km/h more than the first speed. If it takes 3 hours to complete the total journey, what is its first speed ?VIEW SOLUTION
- Q24VIEW SOLUTION
- Q25VIEW SOLUTION
- Q26VIEW SOLUTION
At a point A, 20 metres above the level of water in a lake, the angle of elevation of a cloud is 30°. The angle of depression of the reflection of the cloud in the lake, at A is 60°. Find the distance of the cloud from A.VIEW SOLUTION
A card is drawn at random from a well-shuffled deck of playing cards.VIEW SOLUTION
Find the probability that the card drawn is
(i) a card of spade or an ace
(ii) a black king
(iii) neither a jack nor a king
(iv) either a king or a queen
Find the values of k so that the area of the triangle with vertices (1, –1), (–4, 2k) and (–k, –5) is 24 sq. units.VIEW SOLUTION
Find the ratio in which the point divides the line segment joining the points and B(2, −5).
In Figure 5. PQRS is a square lawn with side PQ = 42 metres. Two circular flower beds are there on the sides PS and QR with centre at O, the intersection of its diagonals. Find the total area of the two flower beds (shaded parts).
From each end of a solid metal cylinder, metal was scooped out in hemispherical form of same diameter. The height of the cylinder is 10 cm and its base is of radius 4.2 cm. The rest of the cylinder is melted and converted into a cylindrical wire of 1.4 cm thickness. Find the length of the wire.VIEW SOLUTION
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