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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 »
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
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°—
Q) The angle of elevation of the top of a tower from a point on the ground which is 30 m away from the foot of the tower, is 30°. Find the height of the tower. Ans:   Let the tower be AB and its height be h Now in Δ ABC, tan 300 =
Q) The length of the shadow of a tower on the plane ground is √3 times the height of the tower. Find the angle of elevation of the sun. Ans: Let the tower be AB and its shadow be AC and angle of elevation from point C be θ Given that AC = √3 x
Q) Show that the points (- 2, 3), (8, 3) and (6, 7) are the vertices of a right-angled triangle. Ans: Let’s plot these points on graph, we get: Step 1: Now for a Δ ABC to be an right angled triangle, required condition is: AB2 = AC2 + BC2 Step 2: Let’s calculate the