Sujeet Kumar

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

Question 1.Radius of circle is 10 cm. There are two chords of length 16 cm each. What will be the distance of these chords from the centre of the circle ?Given: In a circle with centre O,OR and OP are radii and RS and PQ are its congruent chords.PQ = RS= 16 cm,OR = OP … Read more

Question 1.Distance of chord AB from the centre of a circle is 8 cm. Length of the chord AB is 12 cm. Find the diameter of a circle.Given: In a circle with centre O,OA is radius and AB is its chord,seg OP ⊥ chord AB, A-P-BAB = 12 cm, OP =8 cmTo Find: Diameter of … Read more