HSC Commerce (English Medium) 11th Standard - Maharashtra State Board Question Bank Solutions

Find the value of k: if the slope of the line passing through the points (3, 4), (5, k) is 9.

Find the value of k: the points (1, 3), (4, 1), (3, k) are collinear.

Find the value of k: the point P(1, k) lies on the line passing through the points A(2, 2) and B(3, 3).

Find the slope of the line y – x + 3 = 0.

Does point A(2, 3) lie on the line 3x + 2y – 6 = 0? Give reason.

Obtain the equation of the line containing the point: (2, 4) and perpendicular to the Y−axis.

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)]`