Q) A sum of Rs. 1400 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is Rs. 40 less than the preceding price, find the value of each of the prizes. Ans: It is given that each prize money is less than the […]
February 2024
Q) Find two consecutive odd positive integers, the sum of whose squares is by using the quadratic formula. Ans: Let’s consider the 1st odd positive integer be XThen the next consecutive odd positive integers will be X + 2 Now it is given, that the sum of the squares of these two numbers is 290∴ X2
Q) A train travels at a certain average speed for a distance 63 km and then travels a distance of 72 km at an average speed of 6 km/hr more than the original speed. If it takes 3 hours to complete total journey, what is its original average speed? Ans: Let’s consider the original average speed
Q) The following table gives the distribution of the life time of 400 neon lamps. Find the median lifetime of a lamp. Ans: Let’s re-organize the data in the frequency table to find out each part: To find the median, we need to identify middle value of the data. Let’s rearrange the data: First, we
Q) A gulab jamun, contains sugar syrup up to about 30% of its volume. Find approximately how much syrup would be found in 45 gulab jamuns, each shaped like a cylinder with two hemispherical ends with length 5 cm and diameter 2.8 cm. Ans: STEP BY STEP SOLUTION Let’s understand the steps to calculate: First, we
Q) A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface area. Ans: STEP BY STEP SOLUTION We reconstruct the diagram of capsule as combination
Q) A train travels 360 km at a uniform speed. If the speed had been 5 km/hr more, it would have taken 1 hour less for the same journey. Find the speed of the train. Ans: Let’s consider the speed of the train is X km/hr. Now, to cover distance of 360 km, it will take
Q) If the sum of m terms of an A.P. is the same as the sum of its n terms, show that the sum of its (m+n) terms is zero. Ans: Let = First term of the given A.P. and = Common difference . Then, . Now, Hence Proved! Please do press “Heart”
Q) The ratio of the sum of m and n terms of an A.P. is . Show that the ratio mth and nth term is (2m-1) : (2n-1). Ans: Let: First term of given A.P. = , Common difference = , Then, the sums of m and n terms are given by Then, Please do