HSC Commerce: Marketing and Salesmanship ११ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Obtain the equation of the line containing the point: (2, 5) and perpendicular to the X−axis.

Find the equation of the line: containing the point T(7, 3) and having inclination 90°.

Find the equation of the line: containing the origin and having inclination 90°.

if f(x) = `{(4x - 2"," x ≤ - 3),(5"," -3 < x < 3),(x^2"," x ≥ 3):},`the find f(– 3)

if f(x) = `{(4x - 2"," x ≤ - 3),(5"," -3 < x < 3),(x^2"," x ≥ 3):},`the find f(1)

if f(x) = `{(4x - 2"," x ≤ - 3),(5"," -3 < x < 3),(x^2"," x ≥ 3):},`the find f(5)

Evaluate the Following limits :

`lim_(x->7)[((root3x - root3(7))(root3x + root3(7)))/(x - 7)]`

Evaluate the Following limit :

`lim_(x->7) [((root(3)(x) - root(3)(7))(root(3)(x) + root(3)(7)))/(x -7)]`

Evaluate the following limit :

`lim_("x"-> 5)[("x"^3-125)/("x"^5 - 3125) ]`

Show that `(-1 + sqrt3 "i")^3` is a real number.

If for a sequence, `t_n = (5^(n- 3))/(2^(n - 3))`, show that the sequence is a G.P. 

Find its first term and the common ratio.

Evaluate the following limit :

`lim_(x ->7) [((root(3)(x) - root(3)(7))(root(3)(x) + root(3)(7)))/(x - 7)]`

Evaluate the following limit:

`lim_(x->3)[sqrt(x + 6)/x]`

Evaluate the following limit:

`lim_(x->5) [(x^3 - 125)/(x^5 - 3125)]`

Evaluate the following limit:

`lim_(x->7)[((root (3)(x) - root(3)(7))(root(3)(x) + root(3)(7)))/(x - 7)]`

For the G.P. if a = `2/3` t₆ = 162, find r.

Evaluate the following limit:

`lim_(x->0)[(sqrt(6 + x + x^2) - sqrt(6))/x]`

Evaluate the following limit:

`lim_(x->3) [sqrt (x + 6)/ x]`

Evaluate the following limit:

`lim_(x->5) [(x^3 - 125)/(x^5 - 3125)]`

If w is a complex cube-root of unity, then prove the following

(w² + w − 1)³ = −8