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In Fig., sides QP and RQ of ΔPQR are produced to points S and T respectively. If SPR = 135° and PQT = 110°, find PRQ.

Solution ∠TQP = 110°, ∠SPR = 135° TQR is a Straight line (from figure) As we have studied in this chapter, TQP... View Article

In the figure, A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC || PR. Show that BC || QR.

Given that A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC || PR To Prove BC || QR Proof In ΔOPQ, AB || PQ... View Article

If 1 part of a red pigment requires 75 mL of base, how much red pigment should we mix with 1800 mL of base?

Solution Let the parts of red pigment mix with 1800 mL base be x. Since the red pigment is in Direct proportion with parts of the base, ... View Article

Aman’s age is three times his son’s age. Ten years ago he was five times his son’s age. Find their present ages.

Solution Let the age of Aman’s son be x Let the age of Aman will be 3x. According to the given details, the equation becomes 5(x... View Article

Express the linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in each case: y-2 = 0

We have to express y–2 = 0 in the form ax + by + c = 0 and indicate the values of a, b and c in each case. Solution The equation... View Article

Express the linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in each case: 2x = -5y

We have to express 2x = –5y in the form ax + by + c = 0 and indicate the values of a, b and c in each case. Solution The equation 2x =... View Article

Find the area of the shaded region in Fig. if ABCD is a square of side 14 cm and APD and BPC are semicircles.

Given ABCD is a square of side 14 cm and APD and BPC are semicircles. Solution Radius =14/2=7 Area of shaded region=Area of square-Area of 2... View Article

Express the linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in each case: 3x + 2 = 0

We have to express 3x+2 = 0 in the form ax + by + c = 0 and indicate the values of a, b and c in each case. Solution The equation 3x+2 = 0 can... View Article

Choose the correct choice in the following and justify: (i) 30th term of the A.P: 10,7, 4, …, is (A) 97 (B) 77 (C) −77 (D) −87

The correct answer is option C -77 Given that A.P. = 10, 7, 4, … Find out 30th term Solution We know that from given series... View Article

A machine in a soft drink factory fills 840 bottles in six hours. How many bottles will it fill in five hours?

Solution Let the number of bottles filled = n Number of bottles 840 a Time in hours 06 5 The ratio of hours and... View Article

An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle.

Given The length of two equal sides of an isosceles triangle is 12 cm. Perimeter = 30 cm. Find out We have to determine the area of a... View Article

How many diagonals does each of the following have? a) A convex quadrilateral (b) A regular hexagon (c) A triangle

a) A convex quadrilateral:2. b) A regular hexagon: 9 c) A triangle: 0... View Article

Express the linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in each case: -2x + 3y = 6

We have to express –2x+3y = 6 in the form ax + by + c = 0 and indicate the values of a, b and c in each case. Solution The equation... View Article

Tick the correct answer and justify: In ΔABC, AB = 6√3 cm, AC = 12 cm and BC = 6 cm. The angle B is: (A) 120° (B) 60° (C) 90° (D) 45°

Given In ΔABC, AB = 6√3 cm, AC = 12 cm and BC = 6 cm. Find out We have to find the measure of angle B On applying pythagoras... View Article

In each of the following find the value of ‘k’, for which the points are collinear. (i) (7, -2) , (5, 1) , (3, -k) (ii) (8, 1) , (k, -4) , (2, -5)

(i) For collinear points, area of triangle formed by them is always zero. Let points (7, -2) (5, 1), and (3, k) are vertices of a triangle. Area... View Article

Can a quadrilateral ABCD be a parallelogram if (i) ∠D + ∠B = 180°? (ii) AB = DC = 8 cm, AD = 4 cm and BC = 4.4 cm? (iii) ∠A = 70° and ∠C = 65°?

(i) Yes, The quadrilateral ABCD be a parallelogram if ∠D + ∠B = 180°, it should also fulfilled some conditions which... View Article

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