HSC Arts Class 12 - Tamil Nadu Board of Secondary Education Question Bank Solutions

Find an approximate value of `int_1^1.5` x²dx by applying the right–end rule with the partition {1.1, 1.2, 1.3, 1.4, 1.5}

Find an approximate value of `int_1^1.5 (2 - x)` dx by applying the mid-point rule with the partition {1.1, 1.2, 1.3, 1.4, 1.5}

Evaluate the following integrals as the limits of sum:

`int_0^1 (5x + 4)"d"x`

Evaluate the following integrals as the limits of sum:

`int_1^2 (4x^2 - 1)"d"x`

Choose the correct alternative:

The value of `int_0^(2/3) ("d"x)/sqrt(4 - 9x^2)` is

Choose the correct alternative:

The value of `int_(-1)^2 |x|  "d"x` is

For the following equations, determine its order, degree (if exists)

`("d"y)/("d"x) + xy` = cot x

For the following equations, determine its order, degree (if exists)

`(("d"^3y)/("d"x^3))^(2/3) - 3 ("d"^2y)/("d"x^2) + 5("d"y)/("d"x) + 4` = 0

For the following equations, determine its order, degree (if exists)

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

For the following equations, determine its order, degree (if exists)

`sqrt(("d"y)/("d"x)) - 4 ("d"y)/("d"x) - 7x` = 0

For the following equations, determine its order, degree (if exists)

`y(("d"y)/("d"x)) = x/((("d"y)/("d"x)) + (("d"y)/("d"x))^3`

For the following equations, determine its order, degree (if exists)

`x^2 ("d"^2y)/("d"x^2) + [1 + (("d"y)/("d"x))^2]^(1/2)` = 0

For the following equations, determine its order, degree (if exists)

`(("d"^2y)/("d"x^2))^3 = sqrt(1 + (("d"y)/("d"x)))`

For the following equations, determine its order, degree (if exists)

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

For the following equations, determine its order, degree (if exists)

`("d"^2y)/("d"x^2) + 5 ("d"y)/("d"x) + int y "d"x = x^3`

For the following equations, determine its order, degree (if exists)

x = `"e"^(xy((dy)/(dx))`

Choose the correct alternative:

The order and degree of the differential equation `("d"^2y)/("d"x^2) + (("d"y)/("d"x))^(1/3) + x^(1/4)` = 0 are respectively

Choose the correct alternative:

The order and degree of the differential equation `sqrt(sin  ) ("d"x + "d"y) = sqrt(cos  x)  ("d"x - "d"y)` is

Choose the correct alternative:

The order of the differential equation of all circles with centre at (h, k) and radius 'a' is

Choose the correct alternative:

The degree of the differential equation `y(x) = 1 +  ("d"y)/("d"x) + 1/(1.2) (("d"y)/("d"x))^2 + 1/(1*2*3) (("d"y)/("d"x))^3 + ....` is