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

Choose the correct alternative:

If y = `1/("a" - z)`, then `("d"z)/("d"y)` is

Choose the correct alternative:

If y = cos (sin x²), then `("d"y)/("d"x)` at x = `sqrt(pi/2)` is

Choose the correct alternative:
If f(x) = x tan^-1x then f'(1) is

Choose the correct alternative:

`"d"/("d"x) ("e"^(x + 5log x))` is

Choose the correct alternative:

If the derivative of (ax – 5)e^3x at x = 0 is – 13, then the value of a is

Choose the correct alternative:

x = `(1 - "t"^2)/(1 + "t"^2)`, y = `(2"t")/(1 + "t"^2)` then `("d"y)/("d"x)` is

Choose the correct alternative:

If x = a sin θ and y = b cos θ, then `("d"^2y)/("d"x^2)` is

Choose the correct alternative:

The differential coefficient of `log_10 x` with respect to `log_x 10` is

Choose the correct alternative:

If y = `(1 - x)^2/x^2`, then `("d"y)/("d"x)` is

Choose the correct alternative:

If f(x) = `{{:(x - 5,  "if"  x ≤ 1),(4x^2 - 9,  "if"  1 < x < 2),(3x + 4,  "if"  x ≥ 2):}` , then the right hand derivative of f(x) at x = 2 is

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)`