# August 2023

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 …

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) Its given that: CD is median of ΔABC RS is median of ΔPQR ΔABC∼ΔPQR AB = …

Q) PA, QB and RC are each perpendicular to AC. If AP = x, QB = z, RC = Y, AB = a and BC = b, then prove that  +   = Ans: Let’s look at Δ CQB & Δ CPA, By AA similarity theorem, ∠PAC = ∠QBC  (perpendicular to AC) ∠PCA = ∠QCB …

Q) A ladder set against a wall at an angle 45° to the ground. If the foot of the ladder is pulled away from the wall through a distance of 4 m, its top slides a distance of 3 m down the wall making an angle 30° with the ground. Find the final height of …

Q)Solve the pair of equations x = 5 and y = 7 graphically. Ans:  Plot both the equations on the graph. Increase till intersection point (5,7)

Q) Prove that (cosec A – sin A) (sec A- cos A) = Ans:  Let’s start with LHS: (cosec A – sin A) (sec A- cos A) =   ( – A) ( – A) =   () () =   () () =   cos A . sin A Now, Let’s solve RHS: =      =      = …

Q) The centre of a circle is (2a, a-7). Find the values of ‘a’ if the circle passes through the point (11,-9). Radius of the circle is 5√2cm. Ans:  Let’s find out radius of the circle by co-ordinate method. Therefore, (2a – 11)2 + (a -7 + 9)2 = (5√2 )2 or (4a2 + 121 …

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