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ICSE Class 10 Mathematics Solved Question Paper 2016

Short Answer Type

Using remainder theorem, find the value of k if on dividing $2 x^{3} + 3 x^{2} - k x + 5 by x - 2$ , leaves a remainder 7.

If ( 3 a + 2 b ) : ( 5 a + 3 b ) = 18 : 29. Find a : b.

Long Answer Type

Given $A = [\begin{matrix} 2 & 0 \\ - 1 & 7 \end{matrix}] and I = [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}]$ and A² = 9 A + mI. find m.

The mean of following numbers is 68. Find the value of ‘x’. 45, 52, 60, x, 69, 70, 26, 81 and 94 Hence estimate the median.

The slope of a line joining P ( 6, k ) and Q (1- 3k, 3 ) is $\frac{1}{2}$ . Find

(i) k

(ii) Midpoint of PQ, using the value of ‘k’ found in (i).

Without using trigonometrical tables, evaluate:

${cosec}^{2} 57 ° - \tan^{2} 33 ° + \cos 44 ° cosec 46 ° - \sqrt{2} \cos 45 ° - \tan^{2} 60 °$

7.
A certain number of metallic cones, each of radius 2 cm and height 3 cm are melted and recast into a solid sphere of radius 6 cm. Find the number of cones.

Let the number of cones be n.

Let the radius of the sphere be r_s = 6 cm

Radius of a cone be r_c = 2 cm

And height of the cone be h = 3 cm

Volume of sphere = n ( Volume of a metallic cone )

$\Rightarrow \frac{4}{3} π {r_{s}}^{3} = n (\frac{1}{3} π {r_{c}}^{2} h) \Rightarrow \frac{4}{3} π {r_{s}}^{3} = n (\frac{1}{3} π {r_{c}}^{2} h) \Rightarrow \frac{4 {r_{s}}^{3}}{{r_{c}}^{2} h} = n \Rightarrow n = \frac{4 (6)^{3}}{(2)^{2} (3)} \Rightarrow n = \frac{4 x 216}{4 x 3} \Rightarrow n = 72$