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ICSE Class 10 Mathematics Solved Question Paper 2016

Long Answer Type

21.
If

$R . H . S . = \frac{3 x y z}{a b c} = \frac{3 (a k) (b k) (c k)}{a b c} = 3 k^{3} = L . H . S . \Rightarrow L . H . S . = R . H . S . \Rightarrow \frac{x^{3}}{a^{3}} + \frac{y^{3}}{b^{3}} + \frac{z^{3}}{c^{3}} = \frac{3 x y z}{a b c}$

22.

Draw a line AB = 5 cm. Mark a point C on AB such that AC = 3 cm. Using a ruler and a compass only, construct :

(i) A circle of radius 2.5 cm, passing through A and C.

(ii) Construct two tangents to the circle from the external point B. Measure and record the length of the tangents.

23.

A line AB meets X – axis at A and Y –axis at B. P (4, -1) divides AB in the ratio 1 : 2.

(i) Find the coordinates of A and B.

(ii) Find the equation of the line through P and perpendicular to AB.

24.

A dealer buys an article at a discount of 30 % from the wholesaler, the marked price being Rs. 6000. The dealer sells it to a shopkeeper at a discount of 10 % on the marked price. If the rate of VAT is 6 %, find

(i) The price paid by the shopkeeper including the tax.

(ii) The VAT paid by the dealer.

25.

The given figure represents a kite with a circular and a semicircular motifs stuck on it. The radius of a circle is 2.5 cm and the semicircle is 2 cm. If diagonals AC and BD are of lengths 12 cm and 8 cm respectively, find the area of the:

(i) Shaded part. Give your answer correct to the nearest whole number.

(ii) Unshaded part.

26.

A model of a ship is made to a scale 1 : 300

(i) The length of the model of ship is 2 m. Calculate the lengths of the ship.

(ii) The area of the deck ship is 180,000 m². Calculate the area of the deck of the model.

(iii) The volume of the model in 6.5 m³. Calculate the volume of the ship.

27.

Mohan has a recurring deposit account in a bank for 2 years at 6% p.a. simple interest. If he gets Rs. 1200 as interest at the time of maturity, find:

(i) the monthly installment

(ii) the amount of maturity

28.

$\sum f = 25$

The histogram below represents the scores obtained by 25 students in a mathematics mental test. Use the data to :

(i) Frame a frequency distribution table

(ii) To calculate mean

(iii) To determine the Modal class

29.

A bus covers a distance of 240 km at a uniform speed. Due to heavy rain its speed gets reduced by 10 km/h and as such it takes two hrs longer to cover the total distance. Assuming the uniform speed to be ‘x’ km/h, form an equation and solve it to evaluate ‘x’.