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Q) An aeroplane when flying at a height of 3000 m from the ground passes vertically above another aeroplane at an instant when the angles of elevation of the two planes from the same point on the ground are 60° and 45° respectively. Find the vertical distance between the aeroplanes at that instant. Also, find […]
Q) ABCD is a parallelogram. P is a point on side BC and DP when produced meets AB produced at L. Prove that: (i) (ii) (iii) If LP : PD = 2 : 3, then find BP : BC Ans: (i) Solution for : Step 1: Since DC ǁ AB (and hence AL) and Line
Q) Sides AB and AC and median AM of a Δ ABC are proportional to sides DE and DF and median DN of another Δ DEF. Show that Δ ABC ~ Δ DEF. Ans: Construction: Extend AM to A’ such that AM = A’M and extend DN to D’ such that DN = D’N Join
Q)Jaya scored 40 marks in a test getting 3 marks for each correct answer and losing 1 mark for each incorrect answer., Had 4 marks being awarded for each correct answer and 2 marks were deducted for each incorrect answer then Jaya again would have scored 40 marks. How many questions were there in the
Q) Prove that, 2(sin6 θ + cos6 θ) – 3 (sin4 θ + cos4 θ) +1 = 0 Ans: We know that, (a-b)3 = a3 – b3 – 3ab (a – b) And (a-b)2 = a2 + b2 – 2ab LHS: 2(sin6 θ + cos6 θ) – 3 (sin4 θ + cos4 θ) +1 = 2[sin6
Prove that, 2(sin^6 θ + cos^6 θ) – 3 (sin^4 θ + cos^4 θ) +1 = 0 Read More »
Q) In the given figure, ABCD is a parallelogram. AE divides the line segment BD in the ratio 1:2. If BE = 1.5 cm, then find the length of BC. Ans: Since AD ǁ BC, and EA cuts these lines, ∠DAE = ∠AEB or (∠OEB) Similarly, Line DB cuts these parallel lines, ∠ADB = ∠DBC
Q) If tan θ = , then show that = Ans: Given that, tan θ = cot θ = √7 Let’s start from numerator of LHS: cosec2 θ – sec2 θ = (1 + cot2 θ) – (1 + tan2 θ) = cot2 θ – tan2 θ = (√7)2 – = 7 – = …………………
Q) If sin θ + sin2 θ = 1, then prove that cos2 θ + cos4 θ = 1. Ans: Given that sin θ + sin2 θ = 1 sin θ = 1 – sin2 θ LHS: cos2 θ + cos4 θ = (1- sin2 θ) + (1- sin2 θ)2 = sin θ + (sin
If sin θ + sin^2 θ = 1, then prove that cos^2 θ + cos^4 θ = 1. Read More »
Q) India meteorological department observes seasonal and annual rainfall every year in different sub-divisions of our country. It helps them to compare and analyse the results. The table given below shows sub-division wise seasonal (monsoon) rainfall (mm) in 2018: Based on the above information, answer the following questions: (I) Write the modal class. (II) Find
Q) In the given figure, CD and RS are respectively the medians of Δ ABC and Δ PQR. If Δ ABC ~ Δ PQR then prove that: (i) Δ ADC ~ Δ PSR (ii) AD x PR = AC x PS Ans: (i) Δ ADC ~ Δ PSR Step 1: Since it is given that: