# June 2024

Q) Find the area of the minor and the major sectors of a circle with radius 6 cm, if the angle subtended by the minor arc at the centre is 60 deg (Use pi = 3 * 14 ) Ans: Let’s draw the diagram for better understanding:  Step 1: Here, we are given that θ  […]

Q) If a chord of a circle of radius 10 cm subtends an angle of 60 deg at the centre of the circle, find the area of the corresponding minor segment of the circle. (Use pi = 3.14 and sqrt(3) = 1.73 ) Ans: Let’s draw the diagram for better understanding:  Step 1: Here, we

Q) A tent is in the shape of a right circular cylinder up to a height of 3 m and then a right circular cone, with a maximum height of 13.5 m above the ground. Calculate the cost of painting the inner side of the tent at the rate of 2 per square metre, if

Q) A solid wooden toy is in the shape of a right circular cone mounted on a hemisphere of same radius. If the radius of the hemisphere is 4.2 cm and the total height of the toy is 10.2 cm, find the volume of the wooden toy. Also, find the total surface area of the

Q) A survey regarding the heights (in cm) of 50 girls of class X of a school was conducted and the following data was obtained : Find the mean and mode of the above data. Ans: 1. Mean value of the data: Let’s re-arrange the data with midpoint of each class, frequency, and multiply midpoint with frequency:

Q) As observed from the top of a lighthouse, 100 m above sea level, the angle of depression of a ship, sailing directly towards it, changes from 30° to 45°. Determine the distance travelled by the ship during the period of observation. (Use √3 = 1.732) Ans:  Let’s start with the diagram for this question:

Q) Evaluate: Ans: We need to find the value of: We know that cos 45 = , sec 30 = , cosec 30 = 2 by substituting these values in the given expression, we get: =  = = = …. Answer or to further simplify, we can multiply and divide the expression by (√3 –

Q) Prove that Ans: Method 1: We need to prove that Let’s start with squaring in both sides: We know that:  and ∴ ∴ Since LHS = RHS Hence Proved ! Method 2: Let’s start from LHS: Since, and ∴ LHS = = = Since, ∴ LHS = = =     = = =

Q) If x sin3 θ + y cos3 θ = sin θ cos θ and x sin θ = y cos θ, prove that x2 + y2 = 1 Ans: Given that x sin3 θ + y cos3 θ = sin θ cos θ ∴  x sin θ sin2 θ + y cos θ cos2 θ = sin θ

Q) In a park, four poles are standing at positions A, B, C and D around the circular fountain such that the cloth joining the poles AB, BC, CD and DA touches the circular fountain at P, Q, R and S respectively as shown in the figure. Based on the above information, answer the following

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