HSC Commerce (English Medium) इयत्ता ११ वी - Maharashtra State Board Question Bank Solutions

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

Express the following recurring decimals as a rational number.

`4.bar18`

Without expanding determinant as far as possible, show that

`|(0,a,b),(-a,0, c),(-b, -c, 0)|` = 0

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

Evaluate the following limit:

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

Find the value of `(i^(592) + i^(590) + i^(588) + i^(586) + i^(584))/(i^(582) + i^(580) + i^(578) + i^(576) + i^(574))`

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

Evaluate the following limit:

`lim_(z->2)[(z^2-5z+6)/(z^2 -4)]`

Evaluate the following limit:

`lim_(x->0)[(sqrt(6+x+x^2)-sqrt6)/x]`

Verify whether the following sequence is G.P. If so, find t_n.

`sqrt5 , 1/sqrt5 , 1/(5sqrt5) , 1/(25sqrt5)`, ...

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

Evaluate the following limit :

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

Evaluate the following limits :

`lim_(z->2)[(z^2 - 5z +6)/(z^2- 4)]`