Maharashtra SSC Class 10 Geometry March 2018 question paper

Maximum marks 40 · Time 2 hours

Try each question first, then open its model answer. Where the paper offers a choice, both questions are shown with OR between them.

Q.1

1 mark each · attempt any 5

Q.1 (i)1 mark $\triangle DEF \sim \triangle MNK$
Q.1 (ii)1 mark $8$
Q.1 (iii)1 mark $6$
Q.1 (iv)1 mark $\theta = 45^\circ$
Q.1 (v)1 mark $3$
Q.1 (vi)1 mark $V$

Q.2

2 marks each · attempt any 4

Q.2 (i)2 marks $10 : 7$
Q.2 (ii)2 marks $A$
Q.2 (iii)2 marks $\angle XYZ$
Q.2 (iv)2 marks $\cos\theta = \dfrac{24}{25}$
Q.2 (v)2 marks $216$
Q.2 (vi)2 marks $10$

Q.3

3 marks each · attempt any 3

In the following figure, seg $DH \perp$ seg $EF$ and seg $GK \perp$ seg $EF$ . If $DH = 12$ cm, $GK = 20$ cm and $A(\triangle DEF) = 300$ cm $^2$ , then find the following.
Q.3 (i) (a)3 marks $EF$
Q.3 (i) (b) $A(\triangle GEF)$
Q.3 (i) (c) $A(\square DFGE)$
Q.3 (ii)3 marks $PA$
Q.3 (iii)3 marks $C$
Q.3 (iv)3 marks $\sqrt{\dfrac{1 - \cos A}{1 + \cos A}} = \operatorname{cosec} A - \cot A$
Q.3 (v)3 marks $A(-2, -3)$

Q.4

4 marks each · attempt any 2

Q.4 (i)4 marks $Prove that, "the lengths of the two tangent segments to a circle drawn from an external point are equal".$
Q.4 (ii)4 marks $30^\circ$
Q.4 (iii)4 marks $A(5, 4)$

Q.5

5 marks each · attempt any 2

Q.5 (i)5 marks $Prove that, in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the remaining two sides.$
Q.5 (ii)5 marks $\triangle SHR \sim \triangle SVU$
Q.5 (iii)5 marks $V$