Q) In a school, there are two sections of class X. There are 40 students in the first section and 48 students in the second section. Determine the minimum number of books required for their class library so that they can be distributed equally among students of both sections. Ans: STEP-BY-STEP SOLUTION To get a […]

Q) If sin θ + cos θ = p and sec θ + cosec θ = q, then prove that q (p2 – 1) = 2 p. Ans: Let’s take the components one by one: Step 1: Given that sin θ + cos θ = p ∴ p = sin θ + cos θ ….. (i)

If sin θ + cos θ = p and sec θ + cosec θ = q, then prove that q (p2 – 1) = 2p Read More »

Q) A man starts his job with a certain monthly salary and earns a fixed increment every year. If his salary was Rs. 15,000 after 4 years of service and Rs. 18,000 after 10 years of service, what was his starting salary and what was the annual increment? Ans: Step 1: Let’s consider the starting

A man starts his job with a certain monthly salary and earns a fixed increment Read More »

Q) Find the value of ‘k’ for which the quadratic equation (k + 1) x 2 – 2 (3 k + 1) x + (8 k + 1) = 0 has real and equal roots. [CBSE 2024 – Series 4 – Set 2] Ans: Given quadratic equation is: (k + 1) x

Find the value of c for which the quadratic equation (c + 1) y2 – 6(c+1) y + 3(c+9)= 0 Read More »

Q) A 2-digit number is such that the product of its digits is 18. When 63 is subtracted from the number, the digits interchange their places. Find the number. Ans: Step 1: Let’s consider X and Y are the digits of the given number. Hence the given number is 10 X + Y ∴ the

A 2-digit number is such that the product of its digits is 18. When 63 is subtracted Read More »

Q) The angles of depression of the top and the bottom of a 50 m high building from the top of a tower are 45° and 60°, respectively. Find the height of the tower. (Use √3 = 1·73) Ans: Let’s start with the diagram for this question: Here we have tower AB is the tower

The angles of depression of the top and the bottom of a 50 m high building from the Read More »

Q) Find the length of the arc of a circle which subtends an angle of 60° at the centre of the circle of radius 42 cm. Ans: Since the length of an arc with angle θ, L = 2 π r x here, r = 42 cm, θ = 600 ∴ L = = 2

Q) The minute hand of a clock is 14 cm long. Find the area on the face of the clock described by the minute hand in 5 minutes. Ans: Step 1: ∵ Angle subtended by minute hand in full one hour or 60 mins = 3600 ∴ Angle subtended by minute hand in 5 mins

Q) Three bells ring at intervals of 9, 12 and 15 minutes respectively. If they start tolling together, after what time will they next toll together? Ans: STEP-BY-STEP SOLUTION The three bells will ring together again when the time gap is perfect multiple of each bell’s interval Therefore, we will take LCM of three time

Q) Evaluate: Ans: Let’s take the components one by one: Step 1: we know that cos 60 = , sec 30 = , tan 45 = 1, sin 30 = , sin 60 = Step 2: Let’s put these values in the given expression, we get: ∴ ∴ ∴ ∴ ∴ ∴ Therefore the value of

Evaluate: (5 cos 2 60 + 4 sec 2 30 – tan 2 45) / (sin 2 30 + sin 2 60) Read More »