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,... View Article
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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... 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... 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... 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... 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... 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... 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... 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... 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... 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... 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
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... 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... 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... View Article
Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other.
Let us assume ABCD be a quadrilateral and P, Q, R and S are the mid points of AB, BC,... View Article
Prove that the sum of the squares of the sides of rhombus is equal to the sum of the squares of its diagonals.
Given: ABCD is a rhombus To prove: AB2 + BC2 + CD2 + DA2 Poof: ABCD is rhombus and let diagonals AC and BD bisect each... View Article
Draw a pie chart showing the following information. The table shows the colours preferred by a group of people.
Solution: Here, central angle = 360o Total number of people = 36
ABCD is a parallelogram. The circle through A, B and C intersect CD (produced if necessary) at E. Prove that AE, = AD.
Solution Given ABCD is a ||gm. The circle through A,B and C intersect at E. To prove: AE=AD Proof: ABCE... 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
