tan−1x+cot−1x=2π for all real x. So expression =2π+sin−1x. Since sin−1x∈[−2π,2π], expression ranges from 0 to π. Hence α=0, β=π.
A motor boat goes 20 km downstream and comes back to the starting point in 6 hours. If the speed of the boat in still water is 12 km/h, then the speed of the stream is :
Held on 30 May 2023 · Verified 13 Jul 2026.
10 km/h
15 km/h
8 km/h
6 km/h
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If the total cost and total revenue of a company that produces and sells $x$ units of a particular product are $C(x) = 5x + 350$ and $R(x) = 50x - x^2$ respectively, then which of the following is/are the breakeven values: (A) $x = 10$ (B) $x = 25$ (C) $x = 45$ (D) $x = 30$ Choose the correct answer from the options given below:
The supply function of a commodity is P = $x^3+2x+18$. When 4 units of commodity are sold , then producer surplus is:
The demand function P for maximising a profit monopolist is given by P=274-x², while the marginal cost is 4+3x for x units of commodity. The consumer surplus is
If $y = e^{\frac{1}{2}\log(1+ \tan^2 x)}$, then $\frac{d^2y}{dx^2}$ is equal to:
If the random variable X follows the Poisson distribution such that P[X = k] = P[X = k+1], then the mean value of X is:
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