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Question 1.Perpendicular height of a cone is 12 cm and its slant height is 13 cm. Find the radius of the base of the cone.Given: Height (h) = 12 cm, length (l) = 13 cmTo find: Radius of the base of the cone (r)Solution:l2 = r2 + h2∴ 132 = r2 + 122∴ 169 = r2 + 144∴169 – 144 … Read more

Question 1.Length, breadth and height of a cuboid shape box of medicine is 20 cm, 12 cm and 10 cm respectively. Find the surface area of vertical faces and total surface area of this box.Given: For cuboid shape box of medicine,length (l) = 20 cm, breadth (b) = 12 cm and height (h) = 10 … Read more

Question 1.Choose the correct alternative answer for the following multiple choice questions. i. Which of the following statements is true?(A) sin θ = cos (90 – θ)(B) cos θ = tan (90 – θ)(C) sin θ = tan (90 – θ)(D) tan θ = tan (90 – θ)Answer:(A) sin θ = cos (90 – θ) … Read more

Question 1.In the following table, a ratio is given in each column. Find the remaining two ratios in the column and complete the table. Solution:In right angled ∆ABC,∠C = θ.Let the common multiple be k.∴ BC = 35k and AC = 37kNow, AC2 = AB2 + BC2 …[Pythagoras theorem]∴ (37k)2 = AB2+ (35k)21369k2 = AB2 + 1225k2AB2 = 1369k2 – 1225k2= 144k2AB … Read more

Question 1.In the given figure, ∠R is the right angle of ∆PQR. Write the following ratios. i. sin Pii. cos Qiii. tan Piv. tan QSolution: Question 2.In the right angled ∆XYZ, ∠XYZ = 90° and a, b, c are the lengths of the sides as shown in the figure. Write the following ratios. i. sin … Read more

Question 1.Choose the correct alternative answer for the following questions. i. What is the form of co-ordinates of a point on the X-axis?(A) (b,b)(B) (0, b)(C) (a, 0)(D) (a, a)Answer:(C) (a, 0) ii. Any point on the line y = x is of the form _____.(A) (a, a)(B) (0, a)(C) (a, 0)(D) (a, -a)Answer:(A) (a, … Read more

Question 1.On a graph paper plot the points A(3, 0), B(3, 3), C(0, 3). Join A, B and B, C. What is the figure formed?Soiution: d(O, A) = 3 cm, d(A, B) = 3 cm, d(B, C) = 3 cm, d(O, C) = 3 cm and each angle of □ OABC is 90°∴ □ OABC … Read more

Question 1.State in which quadrant or on which axis do the following points lie.i. A(-3, 2)ii. B(-5, -2)iii. K(3.5, 1.5)iv. D(2, 10)V. E(37, 35)vi. F(15, -18)vii. G(3, -7)viii. H(0, -5)ix. M(12, 0)x. N(0, 9)xi. P(0, 2.5)xii. Q(-7, -3)Solution: Question 2.In which quadrant are the following points?i. whose both co-ordinates are positive.ii. whose both co-ordinates are … Read more

Question 1.Choose correct alternative answer and fill in the blanks. i. Radius of a circle is 10 cm and distance of a chord from the centre is 6 cm. Hence, the length of the chord is ____.(A) 16 cm(B) 8 cm(C) 12 cm(D) 32 cmAnswer: ∴ OA2 = AC2 + OC2∴ 102 = AC2 + 62∴ AC2 = 64∴ AC … Read more

Question 1.Construct ∆ABC such that ∠B =100°, BC = 6.4 cm, ∠C = 50° and construct its incircle.Solution: Steps of construction:i. Construct ∆ABC of the given measurement.ii. Draw the bisectors of ∠B and ∠C. Let these bisectors intersect at point I.iii. Draw a perpendicular IM on side BC. Point M is the foot of the … Read more