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What is the expression equal to ∫(1/(x² + a²)) dx?

tan⁻¹(5/12) is equal to:

For solving:
(i) 3x + 4y = 18
(ii) 3y − x = 7

Using Gauss elimination, apply:

Solve by simplex method the LP problem to maximize
Z = 7x + 5y

subject to
x + 2y ≤ 6,
4x + 3y ≤ 12,
x ≥ 0, y ≥ 0.

Using Simpson’s one-third rule, compute ∫₀² (3x + 1) dx. Also, find the error of approximation from its actual value.

Write the binomial theorem for any positive integer n in expansion form.

If a = 2i and b = 3j, then b × a is:

Show that more than 95% of students will be infected after 10 days.

Four unbiased coins are tossed successively. The mean and variance differ by:

d³y/dx³ + 5(d²y/dx²)² + 4(dy/dx)⁴ + 6 = 0 is:

According to L’Hospital’s rule,
lim(x→0) x³/sin x is equal to:

What does ‘C’ represent in the expression?

Write the general term of the expansion.

Express the above information in the form of the differential equation.

If the demand function P = 85 − 4Q − Q², find the consumer’s surplus at demand 4 units and price 64 units. Also make a revenue function for demand equation P = 20 + 5Q − Q². Obtain the standard quadratic equation for marginal revenue. Q represents the number of units demanded and P represents the price.

Write a difference between derivative and antiderivative?

The number of ways that 7 beads of different colours can be strung together so as to form a necklace is:

State the Trapezoidal rule theorem. Also estimate the value of ∫₁⁵ x⁴ dx using Trapezoidal rule with 4 sub-intervals.

Solve the differential equation

How many terms are there in the expression?