HSC Commerce (English Medium) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions

If A = {2, 3, 4, 5, 6, 7, 8}, determine the truth value of the following statement.

∃ x ∈ A, such that 3x + 2 > 9

If A = {2, 3, 4, 5, 6, 7, 8}, determine the truth value of the following statement.

∀ x ∈ A, x² < 18.

If A = {2, 3, 4, 5, 6, 7, 8}, determine the truth value of the following statement.

∃ x ∈ A, such that x + 3 < 11.

If A = {2, 3, 4, 5, 6, 7, 8}, determine the truth value of the following statement.

∀ x ∈ A, x² + 2 ≥ 5.

Find `"dy"/"dx"` if, y = log(log x)

Find `"dy"/"dx"` if, y = log(10x⁴ + 5x³ - 3x² + 2)

Find `"dy"/"dx"` if, y = log(ax² + bx + c) 

Find `"dy"/"dx"` if, y = `"e"^(5"x"^2 - 2"x" + 4)`

Find `"dy"/"dx"` if, y = `"a"^((1 + log "x"))`

Find `"dy"/"dx"` if, y = `5^(("x" + log"x"))`

Find the differential equation whose general solution is

x³ + y³ = 35ax.

Form the differential equation from the relation x² + 4y² = 4b²

Solve the following differential equation.

`dy/dx = x^2 y + y`

Solve the following differential equation.

`(dθ)/dt  = − k (θ − θ_0)`

Solve the following differential equation.

`y^3 - dy/dx = x dy/dx`

For each of the following differential equations find the particular solution.

(x − y² x) dx − (y + x² y) dy = 0, when x = 2, y = 0

For the following differential equation find the particular solution.

`(x + 1) dy/dx − 1 = 2e^(−y)`,

when y = 0, x = 1

Choose the correct alternative.

If y = (5x³ - 4x² - 8x)⁹, then `"dy"/"dx"` =

Choose the correct alternative.

If y = `sqrt("x" + 1/"x")`, then `"dy"/"dx" = ?`

If y = 2x² + 2² + a², then `"dy"/"dx" = ?`