**Section A** (Each question carries 2 marks)

Q.1: Simplify the expression and evaluate it as directed:

x (x – 3) + 2 for x = 1

Q.2: An electric pole, 14 metres high, casts a shadow of 10 metres. Find the height of a tree that casts a shadow of 15 metres under similar conditions.

Q.3: Express 0.0000000000025 in standard form.

Q.4: Factorise: 12x + 36

Q.5: Name any two three dimensional shapes.

**Section B** (Each question carries 3 marks)

Q.6: Plot the following points on a graph paper. Verify if they lie on a lie.

A(1,1), B(2,2), C(3,3), D(4,4)

Q.7: There are 100 students in a hostel. Food provision for them is for 20 days. How long will these provisions last, if 25 more students join the group ?

OR

Evaluate: (5/8) ^{(-7)} x (8/5) ^{(-4)}

Q.8: Using the Euler’s formula find the vertices, if faces are 5 and edges are 9.

Q.9: Multiply: ( a^{2} + 2b^{2} ) ( 5a – 3b )

Q.10: Using suitable identity find the product of (6x – 7) (6x + 7)

**Section C** (Each question carries 5 marks)

Q.11: Find the value of:

i) (1/2) ^{(-2)} + (1/3) ^{(-2)} + (1/4) ^{(-2)}

ii) (-3) ^{4} x (5/3) ^{4}

Q.12: A factory requires 42 machines to produce a given number of articles in 63 days.

i) How many machines would be required to produce the same number of articles in 54 days ?

ii) How many days would it take to produce the same number of articles in 21 days ?

Q.13: Factorise the following:

i) 121b^{2} – 88bc + 16c^{2}

ii) q^{2} – 10q + 21

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