HSC Commerce (English Medium) १२ वीं कक्षा - Maharashtra State Board Important Questions

खालील विषयावर सुमारे २०० ते २५० शब्दांत निबंध लिहा:

माझे आवडते शिक्षक

Use quantifiers to convert the following open sentences defined on N, into a true statement.

n² ≥ 1

 If x=a sin 2t(1+cos 2t) and y=b cos 2t(1−cos 2t), find `dy/dx `

The cost C of producing x articles is given as C = x³-16x² + 47x.  For what values of x, with the average cost is decreasing'?  

The price P for demand D is given as P = 183 + 120 D – 3D².
Find D for which the price is increasing.

If the demand function is D = 50 – 3p – p². Find the elasticity of demand at p = 5 comment on the result.

If the elasticity of demand η = 1, then demand is ______.

If f'(x) = 4x³ − 3x²  + 2x + k, f(0) = 1 and f(1) = 4, find f(x).

`int(x + 1/x)^3 dx` = ______.

`int(1 - x)^(-2) dx` = ______.

Solve the following differential equation.

x²y dx − (x³ + y³) dy = 0

The integrating factor of the differential equation `dy/dx - y = x` is e^−x.

State whether the following statement is true or false:

Order and degree of a differential equation are always positive integers.

For the differential equation, find the particular solution (x – y²x) dx – (y + x²y) dy = 0 when x = 2, y = 0

Deepak’s salary was increased from ₹ 4,000 to ₹ 5,000. The sales being the same, due to reduction in the rate of commission from 3% to 2%, his income remained unchanged. Find his sales.

The payment date after adding 3 days of grace period is known as ______.

Broker is an agent who gives a guarantee to seller that the buyer will pay the sale price of goods.

In an ordinary annuity, payments or receipts occur at ______. 

The equations given of the two regression lines are 2x + 3y - 6 = 0 and 5x + 7y - 12 = 0.

Find:

(a) Correlation coefficient

(b) `sigma_x/sigma_y`

For 50 students of a class, the regression equation of marks in statistics (X) on the marks in accountancy (Y) is 3y − 5x + 180 = 0.  The variance of marks in statistics is `(9/16)^"th"` of the variance of marks in accountancy. Find the correlation coefficient between marks in two subjects.