HSC Commerce (English Medium) इयत्ता १२ वी - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

The slope of the tangent to the curve x = `1/"t"`, y = `"t" - 1/"t"`, at t = 2 is ______

State whether the following statement is True or False:

The equation of tangent to the curve y = x² + 4x + 1 at (– 1, – 2) is 2x – y = 0 

Find the equations of tangent and normal to the curve y = 3x² – x + 1 at the point (1, 3) on it

Find the equation of tangent to the curve x² + y² = 5, where the tangent is parallel to the line 2x – y + 1 = 0

Find the equation of tangent to the curve y = x² + 4x at the point whose ordinate is – 3

Choose the correct alternative:

The value of `int ("d"x)/sqrt(1 - x)` is

Choose the correct alternative:

`int(("e"^(2x) + "e"^(-2x))/"e"^x) "d"x` =

`int 5^(6x + 9) "d"x` = ______ + c

State whether the following statement is True or False:

If f'(x) = 3x² + 2x, then by definition of integration, we get f(x) = x³ + x² + c 

If f(x) = k, where k is constant, then `int "k"  "d"x` = 0

State whether the following statement is True or False:

y² = 4ax is the standard form of parabola when curve lies on X-axis

State whether the following statement is True or False:

Standard form of parabola is x² = – 4by, when curve lies in the positive Y-axis

Find the area between the parabolas y² = 5x and x² = 5y

Choose the correct alternative:

Solution of the equation `x("d"y)/("d"x)` = y log y is

Choose the correct alternative:

Differential equation of the function c + 4yx = 0 is

Choose the correct alternative:

General solution of `y - x ("d"y)/("d"x)` = 0 is

A solution of differential equation which can be obtained from the general solution by giving particular values to the arbitrary constant is called ______ solution

The function y = e^x is solution  ______ of differential equation

The solution of differential equation `x^2 ("d"^2y)/("d"x^2)` = 1 is ______

State whether the following statement is True or False:

The integrating factor of the differential equation `("d"y)/("d"x) - y` = x is e^–x