HSC Science (General) इयत्ता १२ वी - Maharashtra State Board Question Bank Solutions

The function f (x) = x³ – 3x² + 3x – 100, x∈ R is _______.

(A) increasing

(B) decreasing

(C) increasing and decreasing

(D) neither increasing nor decreasing

If the vectors `2hati-qhatj+3hatk and 4hati-5hatj+6hatk` are collinear, then value of q is

(A) 5

(B) 10

(C) 5/2

(D) 5/4

 Show that the points A (-7 , 4 , -2),B (-2 , 1 , 0)and C (3 ,-2 ,2) are collinear.

The lines `(x - 2)/(1) = (y - 3)/(1) = (z - 4)/(-k) and (x - 1)/k = (y - 4)/(2) = (z - 5)/(1)` are coplnar if ______.

The edge of a cube is decreasing at the rate of`( 0.6"cm")/sec`. Find the rate at which its volume is decreasing, when the edge of the cube is 2 cm.

Test whether the following functions are increasing or decreasing : f(x) = x³ – 6x² + 12x – 16, x ∈ R.

Test whether the following functions are increasing or decreasing : f(x) = 2 – 3x + 3x² – x³, x ∈ R.

Test whether the following functions are increasing or decreasing: f(x) = `x-(1)/x`, x ∈ R, x ≠ 0.

Find the values of x for which the following functions are strictly increasing : f(x) = 2x³ – 3x² – 12x + 6

Find the values of x for which the following functions are strictly increasing:

f(x) = 3 + 3x – 3x² + x³

Find the values of x for which the following func- tions are strictly increasing : f(x) = x³ – 6x² – 36x + 7

Find the values of x for which the following functions are strictly decreasing:

f(x) = 2x³ – 3x² – 12x + 6

Find the values of x for which the following functions are strictly decreasing : f(x) = `x + (25)/x`

Find the values of x for which the following functions are strictly decreasing : f(x) = x³ – 9x² + 24x + 12

Find the values of x for which the function f(x) = x³ – 12x² – 144x + 13 (a) increasing (b) decreasing

Find the values of x for which f(x) = `x/(x^2 + 1)` is (a) strictly increasing (b) decreasing.

show that f(x) = `3x + (1)/(3x)` is increasing in `(1/3, 1)` and decreasing in `(1/9, 1/3)`.

Show that f(x) = x – cos x is increasing for all x.

Show that y = `log (1 + x) – (2x)/(2 + x), x > - 1` is an increasing function on its domain.

Prove that y = `(4sinθ)/(2 + cosθ) - θ` is an increasing function if `θ ∈[0, pi/2]`