Sujeet Kumar

Question 1.The radii of two circular ends of frustum shaped bucket are 14 cm and 7 cm. Height of the bucket is 30 cm. How many litres of water it can hold? (1 litre = 1000 cm3)Given: Radii (r1) = 14 cm, and (r2) = 7 cm,height (h) = 30 cmTo find: Amount of water … Read more

Question 1. Find the volume of a cone if the radius of its base is 1.5 cm and its perpendicular height is 5 cm.Given: For the cone,radius (r) = 1.5 cm,perpendicular height (h) = 5 cmTo find: Volume of the cone.Solution:Volume of cone = 1/3 πr2h∴ The volume of the cone is 11.79 cm3. Question 2. Find … Read more

Question 1.Choose the correct alternative answer for the following questions. i. sin θ.cosec θ = ?Answer:(A) ii. cosec 45° = ? Answer:(B) iii. 1 + tan2 θ = ?(A) cot2 θ(B) cosec2 θ(C) sec2 θ(D) tan2 θAnswer:(C) iv. When we see at a higher level, from the horizontal line, angle formed is ______(A) angle of elevation.(B) angle of depression.(C) 0(D) … Read more

Question 1.A person is standing at a distance of 80 m from a church looking at its top. The angle of elevation is of 45°. Find the height of the church.Solution:Let AB represent the height of the church and point C represent the position of the person.BC = 80 mAngle of elevation = ∠ACB = … Read more

Question 1.We know that,sin2 θ + cos2 θ = 1 LetAB = 7k and AC = 25kIn ∆ABC, ∠B = 90°∴ AB2 + BC2 = AC2 … [Pythagoras theorem]∴ (7k)2 + BC2 = (25k)2∴ 49k2 + BC2 = 625k2∴ BC2 = 625k2 – 49k2∴ BC2 = 576k2∴ BC = 24k …[Taking square root of both sides] Question 2.If tan θ = 3/4, find the values of sec θ … Read more

Question 1.Fill in the blanks using correct alternatives. i. Seg AB is parallel to Y-axis and co-ordinates of point A are (1, 3), then co-ordinates of point B can be _______.(A) (3,1)(B) (5,3)(C) (3,0)(D) (1,-3)Answer: (D)Since, seg AB || Y-axis.∴ x co-ordinate of all points on seg ABwill be the same,x co-ordinate of A (1, 3) … Read more

Question 1. Angles made by the line with the positive direction of X-axis are given. Find the slope of these lines.i. 45°ii. 60°iii. 90°Solution:i. Angle made with the positive direction ofX-axis (θ) = 45°Slope of the line (m) = tan θ∴ m = tan 45° = 1∴ The slope of the line is 1. ii. … Read more

Question 1.Find the co-ordinates of point P if P divides the line segment joining the points A (-1, 7) and B (4, -3) in the ratio 2:3.Solution:Let the co-ordinates of point P be (x, y) and A (x1, y1) B (x2, y2) be the given points.Here, x1 = -1, y1 = 7, x2 = 4, y2 = -3, m … Read more

Question 1. Find the distance between each of the following pairs of points.i. A (2, 3), B (4,1)ii. P (-5, 7), Q (-1, 3)iii. R (0, -3), S (0,52)iv. L (5, -8), M (-7, -3)v. T (-3, 6), R (9, -10)Solution:i. Let A (x1, y1) and B (x2, y2) be the given points.∴ x1 = 2, … Read more

Question 1.Select the correct alternative for each of the following questions. i. The number of tangents that can be drawn to a circle at a point on the circle is ______(A) 3(B) 2(C) 1(D) 0Answer:(C) ii. The maximum number of tangents that can be drawn to a circle from a point outside it is ______(A) … Read more