HSC Science Class 12 - Tamil Nadu Board of Secondary Education Question Bank Solutions for Mathematics

Choose the correct alternative:

If w(x, y, z) = x²(y – z) + y²(z – x)+ z²(x – y) then `(del"w")/(delz) + (del"w")/(dely) + (del"w")/(delz)` is 

Choose the correct alternative:

If f(x, y, z) = xy + yz + zx, then f_x – f_z is equal to

Evaluate the following:

`int_0^(pi/2) sin^10 x  "d"x`

Evaluate the following:

`int_0^(pi/2) cos^7 x  "d"x`

Evaluate the following:

`int_0^(pi/4) sin^6 2x  "d"x`

Evaluate the following:

`int_0^(pi/6) sin^5 3x  "d"x`

Evaluate the following:

`int_0^(pi/2) sin^2x cos^4 x  "d"x`

Evaluate the following:

`int_0^(2pi) sin^7  x/4  "d"x`

Evaluate the following:

`int_0^(pi/2) sin^3theta cos^5theta  "d"theta`

Evaluate the following:

`int_1^0 x^2 (1 - x)^3  "d"x`

Choose the correct alternative:

The value of `int_0^(pi/6) cos^3 3x  "d"x` is

Choose the correct alternative:

If `f(x) = int_1^x "e"^(sin u)/u  "d"u, x > 1` and `int_1^3 "e"^(sin x^2)/x  "d"x = 1/2 [f("a") - f(1)]`. then one of the possible value of a is

Choose the correct alternative:

The value of `int_0^1 (sin^-1x)^2  "d"x` is

Choose the correct alternative:

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

If F is the constant force generated by the motor of an automobile of mass M, its velocity V is given by `"M""dv"/"dt"` = F – kV, where k is a constant. Express V in terms of t given that V = 0 when t = 0

The velocity v, of a parachute falling vertically satisfies the equation `"v" (dv)/(dx) = "g"(1 - v^2/k^2)` where g and k are constants. If v and are both initially zero, find v in terms of x

Find the equation of the curve whose slope is `(y - 1)/(x^2 + x)` and which passes through the point (1, 0)

Solve the following differential equation:

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

Solve the following differential equation:

`y"d"x + (1 + x^2)tan^-1x  "d"y`= 0

Solve the following differential equation:

`sin  ("d"y)/("d"x)` = a, y(0) = 1