∫((1+ln x)³)/x dx
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Define Binomial, Poisson and Normal distribution with appropriate equation and name their terms.
1.50 mol of PCl₅(g) is decomposes at room temperature to form PCl₃(g) and Cl₂(g). Determine their concentration at equilibrium, when K_c = 1.80.
In an iron determination from the same amount of sample, the five replicate results were obtained: 20.1, 19.6, 20.0 and 19.9 and 20.4 mg iron.
Calculate the standard deviation, variance, standard deviation of mean, coefficient of variation and relative standard deviation in ppm of the given data.
Solve the following differential equation:
(1/y²) (dy/dt) = 1 - e⁻³ᵗ
(c) Show that the equation
(y - 2x³)dx = x(1 - xy)dy
becomes exact on multiplication by x⁻² and solve it.
Find A⁻¹, where
(a) Evaluate the following limit.
(b) If the law of motion of a particle is given as: s = -t³ + 3t² + 25, then (2+1)
i) find its velocity and acceleration.
ii) find the distance covered by the particle in time t = 5 units
Find the equation of tangent and normal to the curve f(x) = x³ - 3x² + 6x - 1 at x = 2.