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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
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 »
Q) If sin (A – B) = , cos (A + B) = ; 0 < A + B <= 90°, A > B; find ∠A and ∠B. Ans: Let’s take the components one by one: Step 1: sin (A – B) = Since we know that sin 300 = ∴ sin (A –
If sin (A – B) = 1/2, cos (A + B) = 1/2; 0 < A + B B; find ∠A and ∠B. Read More »