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

Choose the correct alternative:

If pv = 81, then `"dp"/"dv"` at v = 9 is

Choose the correct alternative:

It is given that f'(a) exists, then `lim_(x -> "a") (xf("a") - "a"f(x))/(x - "a")` is

Choose the correct alternative:

If f(x) = `{{:(x + 1,  "when"   x < 2),(2x - 1,  "when"  x ≥ 2):}` , then f'(2) is

Choose the correct alternative:

If g(x) = (x² + 2x + 1) f(x) and f(0) = 5 and `lim_(x -> 0) (f(x) - 5)/x` = 4, then g'(0) is

Choose the correct alternative:

If f(x) = `{{:(x + 2, - 1 < x < 3),(5, x = 3),(8 - x, x > 3):}` , then at x = 3, f'(x) is

Integrate the following with respect to x:

x¹¹ 

Integrate the following with respect to x:

`1/x^7`

Integrate the following with respect to x:

`root(3)(x^4)`

Integrate the following with respect to x:

`(x^5)^(1/8)`

Integrate the following with respect to x:

`1/(sin^2x)`

Integrate the following with respect to x:

`tanx/cosx`

Integrate the following with respect to x:

`cosx/(sin^2x)`

Integrate the following with respect to x:

`1/(cos^2x)`

Integrate the following with respect to x:

12³ 

Integrate the following with respect to x:

`(x^24)/(x^25)`

Integrate the following with respect to x:

e^x

Integrate the following with respect to x:

(1 + x²)^–1 

Integrate the following with respect to x:

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

Choose the correct alternative:

If `int f(x) "d"x = g(x) + "c",` then `int f(x)g"'"(x) "d"x`

If two coins are tossed simultaneously, then find the probability of getting one head and one tail