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Q) Find the ratio in which the point (8/5, y) divides the line segment joining the points (1, 2) and (2, 3). Also, find the value of y. ns: Let’s make a diagram for the given question: Let’s consider the point C(8/5, y) divides the line AB in ratio of P : 1 Now, by […]
Find the ratio in which the point (8/5, y) divides the line segment joining the points Read More »
Q) In a chemistry lab, there is some quantity of 50% acid solution and some quantity of 25% acid solution. How much of each should be mixed to make 10 litres of 40% acid solution? Ans: Let consider quantity of 50% acid solution be V litres ∵ total quantity of final solution is 10 litres ∴
 Q) Prove that : tan θ /(1 – cot θ) + cot θ / (1 – tan θ) = 1 + sec θ + cosec θ Ans: Here, let’s start by simplifying the LHS in given equation: LHS = = = = = = Now, we know that a3 – b3 = (a – b) (a2
Prove that : tan θ /(1 – cot θ) + cot θ / (1 – tan θ) = 1 + sec θ cosec θ Read More »
Q) In the given figure, AB is a diameter of the circle with centre O. AQ, BP and PQ are tangents to the circle. Prove that ∠POQ = 90°. Ans: Let’s connect Point O with Point R where tangent PQ touches the circle. Let’s consider ∠POR = x and ∠QOR = y Step 1:
In the given figure, AB is a diameter of the circle with centre O. AQ, BP and Read More »
Q) In a teachers’ workshop, the number of teachers teaching French, Hindi and English are 48, 80 and 144 respectively. Find the minimum number of rooms required if in each room the same number of teachers are seated and all of them are of the same subject. Ans: STEP BY STEP SOLUTION The number of
Q)Â A wooden toy is made by scooping out a hemisphere of same radius as of cylinder, from each end of a wooden solid cylinder. If the height of the cylinder is 20 cm and its base is of radius 7 cm, find the total surface area of the toy. Ans: Let’s first make a diagram
Q) A circle with centre O and radius 8 cm is inscribed in a quadrilateral ABCD in which P, Q, R, S are the points of contact as shown. If AD is perpendicular to DC, BC = 30 cm and BS = 24 cm, then find the length DC. Ans:Â To find length of DC, we
Q) A backyard is in the shape of a triangle ABC with right angle at B. AB = 7 m and BC = 15 m. A circular pit was dug inside it such that it touches the walls AC, BC and AB at P, Q and R respectively such that AP = x m. Based
A backyard is in the shape of a triangle ABC with right angle at B. Read More »
Q) Find the smallest number that is divisible by each of 8, 9 and 10. Ans: Since, we need to find the smallest number which has to be multiple of the given numbers, clearly we need to find the LCM of 8,9, and 10 Let’s start with LCM of 8, 9, 10. By prime factorisation, we
Find the smallest number that is divisible by each of 8, 9 and 10. Read More »
Q) If Δ ABC ~ Δ DEF and AB = 4 cm, DE = 6 cm, EF = 9 cm and FD = 12 cm, find the perimeter of Δ ABC. Ans: Let’s start with the diagram for he given question: Step 1: Since we are given that Δ ABC ~ Δ DEF, ∴ Step 2: