HSC Arts Class 11 - Tamil Nadu Board of Secondary Education Question Bank Solutions for Mathematics

Integrate the following functions with respect to x:

(x + 5)⁶ 

Integrate the following functions with respect to x:

`1/(2 - 3x)^4`

Integrate the following functions with respect to x:

`sqrt(3x + 2)`

Integrate the following functions with respect to x:

sin 3x

Integrate the following functions with respect to x:

cos(5 – 11x)

Integrate the following functions with respect to x:

cosec² (5x – 7)

Integrate the following functions with respect to x:

`"e"^(3x - 6)`

Integrate the following functions with respect to x:

`"e"^(8 - 7x)`

Integrate the following functions with respect to x:

`1/(6 - 4x)`

Integrate the following functions with respect to x:

`sec^2  x/5`

Integrate the following functions with respect to x:

cosec(5x + 3) cot(5x + 3)

Integrate the following functions with respect to x:

30 sec(2 – 15x) tan(2 – 15x)

Integrate the following functions with respect to x:

`1/sqrt(1 - (4x)^2`

Integrate the following functions with respect to x:

`1/sqrt(1 - 81x^2)`

Integrate the following functions with respect to x:

`1/sqrt(1 + 36x^2)`

Choose the correct alternative:

If `int f"'"(x)"e"^(x^2) "d"x = (x - 1)"e"^(x^2) + "c"`, then`f(x)` is

Construct a quadratic equation with roots 7 and −3

A quadratic polynomial has one of its zeros `1 + sqrt(5)` and it satisfies p(1) = 2. Find the quadratic polynomial

If α and β are the roots of the quadratic equation `x^2 + sqrt(2)x + 3` = 0, form a quadratic polynomial with zeroes `1/α, 1/β`

If one root of k(x − 1)² = 5x − 7 is double the other root, show that k = 2 or −25