HSC Science इयत्ता ११ - Tamil Nadu Board of Secondary Education Question Bank Solutions

Choose the correct alternative:

If f(x) = `{{:(2"a" - x,  "for"  - "a" < x < "a"),(3x - 2"a", "for"  x ≥ "a"):}` , then which one of the following is true?

Choose the correct alternative:

If f(x) = `{{:("a"x^2 - "b"",", - 1 < x < 1),(1/|x|",",  "elsewhere"):}` is differentiable at x = 1, then

Choose the correct alternative:

The number of points in R in which the function f(x) = |x – 1| + |x – 3| + sin x is not differentiable, is

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