Q) Prove that: = 2 cosec θ Ans: LHS = = = = = = = = 2 cosecθ = RHS ……… Hence Proved !
Prove that: sin θ / (1 + cos θ) + (1 + cos θ) / sin θ = 2 cosec θ Read More »
September 2023
Q) Prove that 4n can never end with digit 0, where n is a natural number. Ans: Let’s assume that 4n ends with 0. Since now it ends with zero, it is multiple of 10 and hence, it must be divisible by 2 and 5 both. This clearly means, that the factors of 4n should include
Prove that 4^n can never end with digit 0, where n is a natural number. Read More »
Q. Computer-based learning (CBL) refers to any teaching methodology that makes use of computers for information transmission. At an elementary school level, computer applications can be used to display multimedia lesson plans. A survey was done on 1000 elementary and secondary schools of Assam and they were classified by the number of computers they had.
Q) In a coffee shop, coffee is served in two types of cups. One is cylindrical in shape with diameter 7 cm and height 14 cm and the other is hemispherical with diameter 21 cm. Based on the above, answer the following questions: (i) Find the area of the base of the cylindrical cup. (ii)
Q) In an annual day function of a school, the organizers wanted to give a cash prize along with a memento to their best students. Each memento is made as shown in the figure and its base ABCD is shown from the front side. The rate of silver plating is Rs. 20 per cm2. Based
Q) Through the mid-point M of the side CD of a parallelogram ABCD, the line BM is drawn intersecting AC in LL and AD (produced) in E. Prove that EL = 2BL. Ans: In Δ BMC and Δ EMD, MC = MD (given) ∠ CMB = ∠ EMD (Opposite angles) ∠ MBC = ∠
Q) Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of Δ PQR. Show that Δ ABC ~ Δ PQR. Ans: Given that, In Δ ABC and Δ PQR, Since AD is median of BC, hence BC = 2BD Similarly, PM is
Q) A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarised it in the table given below. Find the mean and median of the following data: Ans: (i) Let’s re-arrange the data with midpoint of each class, frequency, and multiply midpoint with
Q) From a point on the ground, the angle of elevation of the bottom and top of a transmission tower fixed at the top of 30m high building are 30° and 60° respectively. Find the height of the transmission tower. (Use √3 = 1.73) Ans: Let’s consider AD is the tower in the figure above and
Q) As observed from the top of a 75 m high lighthouse from the sea-level, the angles of depression of two ships are 30° and 60°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships. (Use √3 = 1.73) Ans: Let’s consider