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ICSE Class 10 Mathematics Solved Question Paper 2014

Short Answer Type

A die has 6 faces marked by the given numbers as shown below:

The die is thrown once. What is the probability of getting
(i) a positive integer.
(ii) an integer greater than - 3.
(iii) the smallest integer.

Find x, y if $[\begin{matrix} - 2 & 0 \\ 3 & 1 \end{matrix}] [\begin{matrix} - 1 \\ 2 x \end{matrix}] + 3 [\begin{matrix} - 2 \\ 1 \end{matrix}] = 2 [\begin{matrix} y \\ 3 \end{matrix}]$ .

Shahrukh opened a ‘Recurring Deposit’ account in a bank and deposited Rs. 800 per month for 1½ years. If he received Rs. 15,084 at the time of maturity, find the rate of interest per annum.

Without using trigonometric tables, evaluate

$\sin^{2} (34^{°}) + \sin^{2} (56^{°}) + 2 \tan (18^{°}) \tan (72^{°}) - \cot^{2} (30^{°})$

Using the Remainder and Factor Theorem, factorise the following polynomial:
x³ + 10x² - 37x + 26

The numbers 6, 8, 10, 12, 13 and x are arranged in an ascending order.
If the mean of the observations is equal to the median, find the value of x.

7.
In the figure, m∠DBC = 58°. BD is the diameter of the circle. Calculate:
(i) m∠BDC
(ii) m∠BEC
(iii) m∠BAC

Consider the followiong figure:

(i) Given that BD is a diameter of the circle.

The angle in a semi circle is a right angle.

So, we can write, $∠ BCD = 90^{°}$

Also, given that $∠ DBC = 58^{°}$

In $∆$ BDC, by angle sum property, we have

$∠ DBC + ∠ BCD + ∠ BDC = 180^{°}$

$\Rightarrow 58^{°} + 90^{°} + ∠ BDC = 180^{°}$

$\Rightarrow 148^{°} + ∠ BDC = 180^{°}$

$\Rightarrow ∠ BDC = 180^{°} - 148^{°}$

$\Rightarrow ∠ BDC = 32^{°}$

(ii) $□ BECD$ is cyclic quadrilateral.

we know that, opposite angles are supplementary

$\Rightarrow ∠ BEC + ∠ BCD = 180^{°}$

$\Rightarrow ∠ BEC + 32^{°} = 180^{°}$

$\Rightarrow ∠ BEC = 148^{°}$

(iii) Angles in the same segment are equal.

$\Rightarrow ∠ BAC = ∠ BDC = 32^{°}$

Use graph paper to answer the following questions. (Take 2 cm = 1 unit on both axes)
(i) Plot the points A( - 4, 2) and B(2, 4)
(ii) A' is the image of A when reflected at the y-axis. Plot it on the graph paper and write
the co-ordinates of A'.
(iii) B' is the image of B when reflected on the line AA'. Write the co-ordinates of B'.
(iv) Write the geometric name of the figure ABA'B'.
(v) Name a line of symmetry of the figure formed.

A shopkeeper bought a washing machine at a discount of 20% from a wholesaler, the printed price of the washing machine being Rs. 18,000. The shopkeeper sells it to a consumer at a discount of 10% on the printed price. If the rate of sales tax is 8%, find:
(i) the VAT paid by the shopkeeper.
(ii) the total amount that the consumer pays for the washing machine.