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

Express the following recurring decimals as a rational number:

`3.4bar56`

If the first term of a G.P. is 16 and sum of its terms to infinity is `176/5`, find the common ratio.

Find the area of the triangle whose vertices are: (4, 5), (0, 7), (–1, 1)

Find the area of the triangle whose vertices are: (3, 2), (–1, 5), (–2, –3)

Find the area of the triangle whose vertices are: (0, 5), (0, – 5), (5, 0)

Find the value of k, if the area of the triangle with vertices at A(k, 3), B(–5, 7), C(–1, 4) is 4 square units.

Find the area of the quadrilateral whose vertices are A(–3, 1), B(–2, –2), C(4, 1), D(2, 3).

Find the area of triangles whose vertices are A(−1, 2), B(2, 4), C(0, 0).

Find the area of triangles whose vertices are P(3, 6), Q(−1, 3), R(2, −1)

Find the area of triangles whose vertices are L(1, 1), M(−2, 2), N(5, 4)

Find the value of k, if area of ΔPQR is 4 square units and vertices are P(k, 0), Q(4, 0), R(0, 2).

Find the value of k, if area of ΔLMN is `33/2` square units and vertices are L(3, − 5), M(− 2, k), N(1, 4).

Evaluate the following limits: `lim_(x -> 0) [(sqrt(6 + x + x^2) - sqrt(6))/x]`

Evaluate the following limits: `lim_(y -> 0) [(sqrt(1 - y^2) - sqrt(1 + y^2))/y^2]`

Evaluate the following limits: `lim_(x -> 2)[(sqrt(2 + x) - sqrt(6 - x))/(sqrt(x) - sqrt(2))]`

Evaluate the following limits: `lim_(x -> "a") [(sqrt("a" + 2x) - sqrt(3x))/(sqrt(3"a" + x) - 2sqrt(x))]`

Evaluate the following limits: `lim_(x -> 2)[(x^2 - 4)/(sqrt(x + 2) - sqrt(3x - 2))]`

Evaluate the following limits: `lim_(x -> 1) [(x^2 + xsqrt(x) - 2)/(x - 1)]`

Evaluate the following limits:  `lim_(x -> 0)[(sqrt(1 + x^2) - sqrt(1 + x))/(sqrt(1 + x^3) - sqrt(1 + x))]`

``Evaluate the following limits: `lim_(x -> 4) [(x^2 + x - 20)/(sqrt(3x + 4) - 4)]`