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: In AP of 45,39, 33, ……. a = 45, d = – 6, Sum of n terms of AP, Sn = (2a + (n-1)d) 180 = (2 x 45 […]
September 2023
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 (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 »
Q) Prove that: x Ans: Let’s start from LHS LHS = x = x = x = sin θ x cos θ Now, take RHS RHS = = = = sin θ x cos θ Since LHS = RHS Hence proved!
Prove that: (1/cosθ – cos θ) (1/(sin θ) – sin θ) = 1/(tan θ+ cot θ) Read More »
Q) Three bells ring at intervals of 6, 12 and 18 minutes. If all the three bells rang at 6 a.m., when will they ring together again? Ans: VIDEO SOLUTION STEP BY STEP SOLUTION The three bells will ring together again when the time gap is perfect multiple of each bell’s interval Therefore, we will take
Q) Find by prime factorisation the LCM of the numbers 18180 and 7575. Also, find the HCF of the two numbers. Ans: By prime factorisation, we get: 18180 = 22 x 32 x 5 x 101 and 7575 = 3 x 52 x 101 LCM = 22 x 32 x 52 x 101 LCM =
Q) In the given figure, O is the centre of the circle. AB and AC are tangents drawn to the circle from point A. If ∠ BAC = 65°, then find the measure of ∠ BOC. Ans: Since ∠BAC + ∠ BOC = 180° (circle’s identity) ∠ BOC = 180° —∠BAC ∠ BOC = 180°—