Q) If pth term of an A.P. is q and qth term is p, then prove that its nth term is (p + q – n). Ans: We know that nth term of an A.P. = a + (n-1) d Therefore, pth term Tp = a + (p – 1) x d = q Similarly, […]
Q) The traffic lights at three different road crossings change after every 48 seconds, 72 seconds and 108 seconds respectively. If they change simultaneously at 7 a.m., at what time will they change together next? Ans: The three traffic light will change together again when the time gap is perfect multiple of each light’s interval. Therefore,
Q) Prove that: = 2 cosec Ans: Let’s start from LHS LHS = Since sec A = LHS = LHS = = = = = = = = = 2 cosec = RHS …………… Hence Proved
Prove that root[(sec A – 1)/(sec A + 1)] + root[(sec A + 1)/(sec A – 1)] = 2 cosec A Read More »
Q) If a cos θ + b sin θ = m and a sin θ – b cos θ = n, then prove that a2 + b2 = m2 + n2 Ans: Since a cos θ + b sin θ = m By squaring on both sides, we get: (a cos θ + b sin θ)2
If a cos θ + b sin θ = m and a sin θ – b cos θ = n, then prove that a2 + b2 = m2 + n2 Read More »
Q) Using prime factorisation, find HCF and LCM of 96 and 120. Ans: By prime factorisation, we get: 96 = 25 x 3 and 120 = 23 x 3 x 5 ∴ LCM = 25 x 3 x 5 = 480 And HCF = 23 x3 = 24 Therefore, LCM of given numbers is 480
Using prime factorisation, find HCF and LCM of 96 and 120. Read More »
Q) Find the ratio in which y-axis divides the line segment joining the points (5, – 6) and (- 1, – 4). Ans: Let’s draw the diagram to solve: Let’s consider the coordinates of point P is (0,y) Also consider that the line AB is divided in ratio of m : n. By section formula,
Q) Point P(x, y) is equidistant from points A(5, 1) and B(1,5). Prove that x = y. Ans: Let’s draw the diagram to solve: Given that PA = PB Hence, PA2 = PB2 (x – 5)2 + (y – 1)2 = (x – 1)2 + (y – 5)2 – 10 x – 2y = –
Point P(x, y) is equidistant from points A(5, 1) and B(1, 5). Prove that x = y. Read More »
Q) The line segment joining the points A(4,-5) and B(4,5) is divided by the point P such that AP : AB = 2 : 5. Find the coordinates of P. Ans: Let’s draw the diagram to solve: Given that (AB = AP + PB) by cross multiplication, we get: 5 AP = 2 (AP
Q) A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in the figure. If the height of the cylinder is 10 cm and its base is of radius 3.5 cm, find the total surface area of the article. Ans: The curved surface area of the
Q) In the given figure, Δ ABC and ΔDBC are on the same base BC. If AD intersects BC at O, prove that Ans: Let’s draw perpendicular from points A and D on line BC: In Δ AON and Δ DOM, ∠ AON = ∠ DOM (interior angles) ∠ ANO = ∠ DMO (given that AN and