# October 2023

Q) A pendulum swings through an angle of 30and describes an arc of 8.8 cm in length. Find the length of the pendulum. Ans: Let’s draw a diagram and plot the given information. (Note: your question will become clearer and your answer will never be wrong if you draw a diagram) We know that the circumference of […]

Q) The sum of ages of a father and his son is 45 years. Five years ago, the product of their ages (in years) was 124. Determine their present ages. Ans: Let’s consider the father’s age is X and son’s age is Y. Step 1: It is given that, X + Y = 45 ……

Q) A rocket is in the form of a right circular cylinder closed at the lower end and surmounted by a cone with the same radius as that of cylinder. The diameter and height of cylinder are 6 cm and 12 cm, respectively. If the slant height of the conical portion is 5 cm, then

Q) 150 spherical marbles, each of diameter 1.4 cm, are dropped in a cylindrical vessel of diameter 7 cm containing some water, which are completely immersed in water. Find the rise in the level of water in the vessel. Ans:  Let’s draw a diagram to understand the question: Given that the diameter of the marble

Q) A horse is placed for grazing inside a rectangular field 70 m by 52 m and is tethered to one corner by a rope 21 m long. On how much area can it graze? Ans: Let’s draw a diagram and plot the given information. (Note: your question will become clearer and your answer will never be

Q) If = λ, then find the value of λ. Ans: Solving LHS LHS = ………… (i) We know that = 1 ∴ By substituting this value in equation (i) , we get: = = 1 Since RHS = λ Therefore λ = 1

Q) Vijay is trying to find the average height of a tower near his house. He is using the properties of similar triangles. The height of Vijay’s house if 20m when Vijay’s house casts a shadow 10m long on the ground. At the same time, the tower casts a shadow 50m long on the ground

Q)   Your friend Veer wants to participate in a 200m race. He can currently run that distance in 51 seconds and with each day of practice it takes him 2 seconds less. He wants to do in 31 seconds. 1. Which of the following terms are in AP for the given situationa) 51,53,55….

Q) Raj and Ajay are very close friends. Both the families decide to go to Ranikhet by their own cars. Raj’s car travels at a speed of x km/h while Ajay’s car travels 5 km/h faster than Raj’s car. Raj took 4 hours more than Ajay to complete the journey of 400 km. 1. What

Q) Find the greatest 3-digit number which is divisible by 18, 24 and 36. Ans: Here, this question is slightly tricky one. We need to first find lowest number and then find its largest multiple with 3 digits. Hence, we need to find LCM, not HCF. Let’s start with LCM of 18, 24, 36. By

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