Maths (212)
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1. Answer any one of the following question.
(a) i) Find five rational numbers between 3/5 and 4/5.
ii) Are the square roots of all positive integers irrational? If not, give an example of the square root of a number that is a rational number.
(b) Simplify the following
(i) 3 (a⁴b³)¹⁰×5(a²b²)³
(ii) (2x-²y³)³
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2. Answer any one of the following question.
(a) (i) Solve: (5m-3)/4+ (3m-2)/5 = (m+6)/7
(ii) The sum of two numbers is 82 and their product is 1456, find the two numbers.
(b) For the polynomial (x³ + 2x + 1)/5-(7/2)x²-x⁶, write
(i) the degree of the polynomial
(ii) the coefficient of x³
(iii) the coefficient of x⁶
(iv) the constant term
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3. Answer any one of the following question.
(a) In Fig. 1, lines XY and MN intersect at O. If ∠POY = 90° and a: b = 2 : 3, find c.
(b) In Fig. 1, ∠PQR = ∠PRQ, then prove that that ∠PQS = ∠PRT.
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4. Answer any one of the following questions.
(a) Find all the angles of a parallelogram if one angle is 80°.
In a rectangle, one diagonal is inclined to one of its sides at 25°. Measure the acute angle between the two diagonals.
(b) Prove that the angle bisectors of a parallelogram form a rectangle.
In a trapezium ABCD, AB||CD. Calculate ZC and ZD if angle A = 55° and angle B = 70°
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5. Answer any one of the following questions.
(a) (i) Prove that the tangents drawn at the ends of a diameter of a circle are parallel.
(ii) Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.
In the figure 3, DE||AC and DF||AE. Prove that BF/FE = BE/EC
(b) AD and BC are equal perpendiculars to a line segment AB. Show that CD bisects AB.
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6. Prepare any one Project out of the following projects given below:
(a) Draw the frequency polygon for the following data
