# March 2024

Q) The difference between the outer and inner radii of a hollow right circular cylinder of length 14 cm is 1 cm. If the volume of the used in making the cylinder is 176 cm³, find the outer and inner radii of the cylinder. Ans. Let’s draw the diagram for the given question: Here, Cylinder […]

Q) From the top of a building 60 m high, the angles of depression of the top and bottom of the vertical lamp post are observed to be 30° and 60° respectively.(i) Find the horizontal distance between the building and the lamp post.(ii) Find the distance between the tops of the building and the post.

Q) BINGO is game of chance. The host has 75 balls numbered 1 through 75. Each player has a BINGO card with some numbers written on it. The participant cancels the number on the card when called out a number written on the ball selected at random. Whosoever cancels all the numbers on his/her card, says

Q) An arc of a circle of radius 21 cm subtends an angle of 60° at the centre. Find:(i) the length of the arc(ii) the area of the minor segment of the circle made by the corresponding chord radius r of in-circle. Ans: Let’s draw the diagram for better understanding:  (i) length of the arc: We

Q) In the given figure PA, QB and RC are each perpendicular to AC. If AP = x, BQ = y and CR = z, then prove that 1/x + 1/z = 1/y Ans: Step 1: In Δ APC and Δ BQC, ∠ PCA = ∠  QCB  (common angle) ∠ PAC = ∠  QBC  (900)

Q) A pole 6m high is fixed on the top of a tower. The angle of elevation of the top of the pole observed from a point P on the ground is 60 and the angle of depression of the point P from the top of the tower is 45. Find the height of the tower

Q) The sum of first and eighth terms of an A.P. is 32 and their product is 60. Find the first term and common difference of the A.P. Hence, also find the sum of its first 20 terms. Ans: Let’s consider the first terms of AP is a and the common difference is d. (i). Calculating

Q) In an A.P. of 40 terms, the sum of first 9 terms is 153 and the sum of last 6 terms is 687. Determine the first term and common difference of A.P. Also, find the sum of all the terms of the A.P. Ans: VIDEO SOLUTION   STEP BY STEP SOLUTION Let’s consider the

Q) A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area and the volume of the vessel. Ans. Let’s start with the diagram of the question: We

(Q) A rectangular floor area can be completely tiled with 200 square tiles. If the side length of each tile is increased by 1 unit, it would take only 128 tiles to cover the floor.(i) Assuming the original length of each side of a tile be x units, make a quadratic equation from the above information.

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