Time allowed 1 hr 30 mins Class IX – Mathematics - Lesson 1 & 2 28 Jun 2018, 4.30 pm IST MM 40 1 State whether the following are polynomials or not 0 2 2 If 5x + 2y = 12 and xy = 10, find the value of 25x2 + 4y2. 2 3 Find the value of p, if (x – 2) is a factor of 4x3 - 3x2 – 4x - p. 2 4 Find the value of a, if 2 5 Express $0.1\stackrel{‾}{23}$ in the form $\frac{\mathrm{p}}{\mathrm{q}}$, where p and q are integers and q ≠ 0. 2 6 If then find the value of x3 - y3 2 7 Without actually calculating the cubes, find the value of 483 – 303 – 183. 2 8 Simplify 3 9 If the polynomials az3 + 4z2 + 3z – 4 and z3 – 4z + a leave the same remainder when divided by z – 3, find the value of a. 3 10 If , find the values of each of the following $\mathrm{x}+\frac{1}{\mathrm{x}}$ ${\mathrm{x}}^{3}+\frac{1}{{\mathrm{x}}^{3}}$ 4 11 If a + b + c = 9 and ab + bc + ca = 26, find the value of a3 + b3 + c3 - 3abc. 4 12 Classify the following numbers as rational or irrational with justification (i) $\sqrt{196}$ (ii) $3\sqrt{18}$ (iii) 10.124124... (vi) 1.010010001... 4 13 Locate $\sqrt{10}$ on the number line Represent $\sqrt{5.6}$ on the number line 4 14 Factorise 6