Let x=sinα,y=sinβ. The equation becomes cosα+cosβ=a(sinα−sinβ). Using sum-to-product, this simplifies to cot2α−β=a. So sin−1x−sin−1y= constant. Differentiating: 1−x21−1−y21dxdy=0, giving dxdy=1−x21−y2.
The minimum value of Z=30x+10y subject to the constraints x+2y≤30,3x+y≥30,4x+3y≥60,x,y≥0 is
Held on 25 May 2023 · Verified 13 Jul 2026.
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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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