HSC Commerce Class 12 - Tamil Nadu Board of Secondary Education Question Bank Solutions for Business Mathematics and Statistics

Solve the following:

A bank pays interest by continuous compounding, that is by treating the interest rate as the instantaneous rate of change of principal. A man invests ₹ 1,00,000 in the bank deposit which accrues interest, 8% per year compounded continuously. How much will he get after 10 years? (e^0.8 = 2.2255)

Choose the correct alternative:

If y = ex + c – c³ then its differential equation is

Choose the correct alternative:

The integrating factor of the differential equation `("d"y)/("d"x) + "P"x` = Q is

Choose the correct alternative:

The differential equation of y = mx + c is (m and c are arbitrary constants)

Choose the correct alternative:

Solution of `("d"x)/("d"y) + "P"x = 0`

Choose the correct alternative:

If sec² x is an integrating factor of the differential equation `("d"y)/("d"x) + "P"y` = Q then P = 

Choose the correct alternative:

The solution of the differential equation `("d"y)/("d"x) + "P"y` = Q where P and Q are the function of x is

Choose the correct alternative:

The differential equation of x² + y² = a²

Choose the correct alternative:

A homogeneous differential equation of the form `("d"y)/("d"x) = f(y/x)` can be solved by making substitution

Choose the correct alternative:

A homogeneous differential equation of the form `("d"x)/("d"y) = f(x/y)` can be solved by making substitution

Choose the correct alternative:

The variable separable form of `("d"y)/("d"x) = (y(x - y))/(x(x + y))` by taking y = vx and `("d"y)/("d"x) = "v" + x "dv"/("d"x)` is

Choose the correct alternative:

Which of the following is the homogeneous differential equation?

Choose the correct alternative:

The solution of the differential equation `("d"y)/("d"x) = y/x + (f(y/x))/(f"'"(y/x))` is

Form the differential equation having for its general solution y = ax² + bx

Solve (x² + y²) dx + 2xy dy = 0

Solve `x ("d"y)/(d"x) + 2y = x^4`

A manufacturing company has found that the cost C of operating and maintaining the equipment is related to the length ’m’ of intervals between overhauls by the equation `"m"^2 "dC"/"dm" + 2"mC"` = 2 and c = 4 and when  = 2. Find the relationship between C and m

Solve (D² – 3D + 2)y = e^4x given y = 0 when x = 0 and x = 1

Solve `("d"y)/("d"x) + y cos x + x = 2 cos x`

Solve x²ydx – (x³ + y³) dy = 0