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Q) Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of Δ PQR. Show that Δ ABC ~ Δ PQR. Ans: Given that, In Δ ABC and Δ PQR, Since AD is median of BC, hence BC = 2BD Similarly, PM is […]
Q) A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarised it in the table given below. Find the mean and median of the following data: Ans: (i) Let’s re-arrange the data with midpoint of each class, frequency, and multiply midpoint with
Q) From a point on the ground, the angle of elevation of the bottom and top of a transmission tower fixed at the top of 30m high building are 30° and 60° respectively. Find the height of the transmission tower. (Use √3 = 1.73) Ans: Let’s consider AD is the tower in the figure above and
Q) As observed from the top of a 75 m high lighthouse from the sea-level, the angles of depression of two ships are 30° and 60°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships. (Use √3 = 1.73) Ans: Let’s consider
Q) How many terms of the arithmetic progression 45, 39, 33, …….. must be taken so that their sum is 180? Explain the double answer. Ans: VIDEO SOLUTION STEP BY STEP SOLUTION We start from the given AP: 45,39, 33, ……. a = 45, d = – 6, Sum of n terms of AP, Sn
Q) ) In the given figure, O is the centre of the circle and QPR is a tangent to it at P. Prove that ∠QAP + ∠APR = 90°. Ans: VIDEO SOLUTION STEP BY STEP SOLUTION Since OA = OP (radii of same circle) In Δ OAP,  ∠OPA = ∠OAP .. (i)
Q) If 217x + 131y = 913 and 131x + 217y = 827, then solve the equations for the values of x and y. Ans: 217 x + 131 y = 913………….(1) 131 x + 217 y = 827………….(2) By adding equations (1) and (2), we get 348 (x + y) = 1740 x + y
Q) If the system of linear equations 2 x + 3 y = 7 and 2 a x + (a + b) y = 28 have an infinite number of solutions, then find the values of ‘a’ and ‘b’. Ans: Step 1: We know that the standard form of a linear equation is: a x
Q) A car has two wipers which do not overlap. Each wiper has a blade of length 21 cm sweeping through an angle of 120°. Find the total area cleaned at each sweep of the two blades. Ans: Area cleaned by a blade = π r2 = x 21 x 21 x = x 21
Q) If Q(0,1) is equidistant from P(5,-3) and R (x,6), find the values of x. Ans: since the Point Q is equidistant, then Distance between P & Q = Distance between R & Q Â (5-0) 2 + (-3-1) 2 = (x-0)2 + (6-1)2 or 25 +16 = x2 + 25 or x2 = 16
If Q(0,1) is equidistant from P(5,-3) and R (x,6), find the values of x. Read More »