Q). Prove that: sin θ/(cot θ + cosec θ) = 2 + sin θ /(cot θ – cosec θ) Ans. Let’s start from LHS: Step 1: LHS = = = = Step 2: We know that sin2 θ + cos2 θ = 1 ∴ sin2 θ = 1 – cos2 θ ∴ LHS = Step […]
Prove that: sin θ/(cot θ + cosec θ) = 2 + sin θ /(cot θ – cosec θ) Read More »
Q). Solve for x: , x ≠ 1, – , – 4 Ans: ∴ ∴ ∴ ∴ (8 x + 4) (x + 4) = 5 (x + 1)(5 x + 1) ∴ 8 x2 + 4 x + 32 x + 16 = 5 ( 5 x2 + 5 x + x + 1)
Solve for x: 1/ x + 1 + 3 / 5 x + 1 = 5 / x + 4, x ≠ 1, – 1/5, – 4 Read More »
Q). If the zeroes of the polynomial x2 + p x + q are double in values to the zeros of 2 x2 – 5 x – 3 Find the value of p and q. Ans: Step 1: Given polynomial equation 2 x2 – 5 x – 3 = 0 Comparing with standard polynomial, ax2
Q). If 𝛼 and β are zeroes of a polynomial x2 – 7 x + 10, then form a quadratic polynomial whose zeroes are 𝛼2 and 𝛽2 . Ans. For detailed solution to this question, please refer to the solution of a similar question – the link is given below: Click here for solution to similar question.
Q) In an A.P. of 50 terms, the sum of first 10 terms is 210 and the sum of last 15 terms is 2565. Find the A.P. Ans: We can find the AP, if we find its first term and common difference. Let’s consider the first terms of AP is “a” and the common difference
Q). Find the value of X, when in the A.P. given below 2 + 6 + 10 + …… + X = 1800 Ans: Step 1: In the given AP: a = 2, d = 4, Let’s consider there are n terms in this AP, Given that the sum of AP is 1800
Find the value of X, when in the A.P. given below 2 + 6 + 10 + …… + X = 1800 Read More »
Q). Sum of the areas of two squares is 157 m2. If the sum of their perimeters is 68 m, find the sides of the two squares. Ans: Let’s consider that the side of a square is X m and the side of the other square is Y m. Step 1: By 1st given condition,
Q) How many terms of the arithmetic progression 24, 21, 18, …….. must be taken so that their sum is 78? Explain the double answer. Ans: We start from the given AP: 24, 21, 18, ……. a = 24, d = – 3, Sn = 78 (given) Sum of n terms of AP, Sn
Q. In a fight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. Find the duration of the flight. Ans: Step 1: Let’s consider that the aircraft’s original average speed was X