Let x=tanθ, so 1+x2=secθ. Then (secθ−1)/tanθ=(1−cosθ)/sinθ=tan(θ/2). Hence tan−1(tan(θ/2))=θ/2=(1/2)tan−1x.
A swimmer's speed in swimming pool is 6 km/hr. He swims between two points in a river and returns back to the starting point. He took 24 minutes more to cover the distance upstream than downstream. If the speed of the stream is 4 km/hr, then the distance between two points is:
Held on 23 May 2023 · Verified 13 Jul 2026.
0.5 km
1 km
1.5 km
2 km
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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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