Q) In an AP first term is 2 and the sum of the first five terms is one- fourth of next five terms, show that 20th term is -112. [Practice Paper 1, 2023-24, Dir of Edu, GNCT of Delhi] Ans: [Here, we are given value of a, value of d […]
In an AP first term is 2 and the sum of the first five terms is one- fourth Read More »
Q) If the coefficient of (r-5)th and (2r-1)th term in the expansion of (1+x)34 are equal, then find the value of r. [Practice Paper 1, 2023-24, Dir of Edu, GNCT of Delhi] Ans: Step 1: Since in binomial expansion of (x + y)n, the term Tr+1 is given by: Tr+1 = Xn-r
If the coefficient of (r-5)th and (2r-1)th term in the expansion of (1+x)34 Read More »
Q) In the given figure, and AB = 5 cm. Find the value of DC. [UP Board Exam paper, 2024] Ans: Step 1: Lets start with Δ AOB and Δ COD: If these triangles are similar, then: Since it is given that , Therefore, by SAS criterion of similarity, Δ
In the given figure, AO/OC=BO/OD=1/2 and AB = 5 cm. Find the value of DC. Read More »
Q) Both the ends of a metallic solid cylinder are semi-spherical. Its total height is 19 cm and diameter of the cylinder is 7 cm. Find the weight of the solid if weight of 1 cm³ of the metal is 4.5 g. Ans: Step 1: Let’s make diagram for our
Q) Find the number of bricks, each measuring 25 cm x 12.5 cm x 7.5 cm, required to construct a wall 24 m long, 20 m high and 0.5 m thick while the cement and sand mixture occupies 1/20th of the volume of the wall. Ans: [Approach: A wall consists of bricks and sand-cement mixture.
Q) A cone and a cylinder have the same base radius and height. If the volume of the cylinder is 300 cm 3, find the volume of the cone. Ans: [Approach: Given that the radius and height are the same, we will find a relation of r and h from
Q) The sum of the squares of two consecutive natural numbers is 365. Find the numbers. Ans: Step 1: Let the first number be X. Since the numbers are consecutive, hence next number will be: X + 1 Step 2: According to the given condition, sum of the squares of
The sum of the squares of two consecutive natural numbers is 365. Find the numbers. Read More »
Q) If sin A = , find the values of cos A and tan A Ans: [Approach: We can calculate the value of cos A by trigonometric identity of sin2 A + cos2 A = 1, and then calculate tan A = sin A / cos A] Step 1: Since we
If sin A = 3/5, find the values of cos A and tan A Read More »
Q) The perimeter of a rectangular park is 120 m, and its length is 10 m more than its width. Find the dimensions of the park. Ans: Step 1: Let the width of the park be X meters. Since the length is 10 meters more than the width: Length =
Q) A shopkeeper buys an article for Rs. 500 and sells it for Rs. 650. Find the profit percentage. Ans: [Approach: % Profit is calculated by x 100″. Hence, if we calculate the profit, we can calculate % profit] Step 1: Profit = Selling Price – Cost Price = 650