Which of the following trigonometric identities are true? A. \(\sin^2(41^\circ) + \sin^2(49^\circ) = 1\) B. \(\sin^2(60^\circ) - 2\tan(45^\circ) - \cos^2(30^\circ) = -1\) C. \(\sin^2(\theta) + \frac{1}{1+\tan^2(\theta)} = 1\) Choose the correct answer from the options given below:

If A earns \(33\frac{1}{3}\)% more than B, then percentage B earns less than A will be

Which of the following is the value of m for which the polynomial \(x^4 + 10x^3 + 25x^2 + 15x + m\) is exactly divisible by \(x + 7\)?

The population of a village is 5000. If in a year, the number of males were to increase by 5% and that of females by 3% annually, the population would grow to 5202 at the end of the year. If M is the number of males and F is the number of females in the village, then (M,F) =

The area of a circular play ground is 22176 cm\(^2\). What is the cost of fencing this ground at the rate of ₹50 per metre?

Match List I with List II List I (Quadratic Equation) | List II (Roots) A. \(6x^2 + x - 12 = 0\) | I. \((-6, 4)\) B. \(8x^2 + 16x - 10 - 202\) | II. \((9, 36)\) C. \(x^2 - 15x + 324 = 0\) | III. \(\left(3, -\frac{1}{2}\right)\) D. \(2x^2 - 5x - 3 = 0\) | IV.…

The sum of n-terms of sequence \(\frac{1}{1 \times 2}, \frac{1}{2 \times 3}, \frac{1}{3 \times 4}, \ldots\) is

P, Q and R invested Rs. 25,000, Rs. 50,000 and Rs. 25,000 respectively to start a business. At the end of two years, they earned a profit of Rs. 48,000. What will be Q's share?

If 'A' can do \(\frac{1}{4}\) of a work in 3 days and 'B' can do \(\frac{1}{6}\) of same work in 4 days, how much will 'A' get if both work together and are paid ₹180 in all