If ∆ is an operation such that for integers a and b we have a ∆ b = a × a + b × b – a × b, then find (–3) ∆ 2
A loop of wire with an area of 0.05 m² is placed perpendicular to a magnetic field of strength 0.2 T. If the magnetic field is reduced to zero in 0.1 seconds, calculate the induced EMF in the loop using Faraday’s law.
A simple pendulum with a length of 2 meters is displaced by a small angle and released. Calculate the time period of oscillation, assuming that the acceleration due to gravity is 9.8 m/s².
If a is an integer other than 1 and –1, match the following:
Column I Column II
(a) a ÷ (–1) (i) a
(b) 1 ÷ (a) (ii) 1
(c) (–a) ÷ (–a) (iii) Not an integer
(d) a ÷ (+1) (iv) –a
Calculate the area between the curves y = x^2 and y = 4x – x^2 over the interval [0, 2].
A factory makes two products, P and Q. Each unit of P requires 3 hours of labor and 2 units of raw material, while each unit of Q requires 2 hours of labor and 1 unit of raw material. The factory has a maximum of 60 hours of labor and 40 units of raw material available. If the profit per unit of P is 50 rupees and of Q is 40 rupees, determine the production plan to maximize profit.
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