PUC Science Class 11 - Karnataka Board PUC Question Bank Solutions for Mathematics

Area of the triangle formed by the points \[\left( (a + 3)(a + 4), a + 3 \right), \left( (a + 2)(a + 3), (a + 2) \right) \text { and } \left( (a + 1)(a + 2), (a + 1) \right)\]

The line segment joining the points (−3, −4) and (1, −2) is divided by y-axis in the ratio

The area of a triangle with vertices at (−4, −1), (1, 2) and (4, −3) is

The line segment joining the points (1, 2) and (−2, 1) is divided by the line 3x + 4y = 7 in the ratio ______.

Distance between the lines 5x + 3y − 7 = 0 and 15x + 9y + 14 = 0 is

The value of λ for which the lines 3x + 4y = 5, 5x + 4y = 4 and λx + 4y = 6 meet at a point is

The vertices of a triangle are (6, 0), (0, 6) and (6, 6). The distance between its circumcentre and centroid is

The ratio in which the line 3x + 4y + 2 = 0 divides the distance between the line 3x + 4y + 5 = 0 and 3x + 4y − 5 = 0 is

Solve each of the following system of equations in R.

\[5x - 7 < 3\left( x + 3 \right), 1 - \frac{3x}{2} \geq x - 4\]

Make correct statement by filling in the symbols ⊂ or ⊄ in the blank space:

{2, 3, 4} _____ {1, 2, 3, 4, 5}

{a, e} ⊂ {x : x is a vowel in the English alphabet}

{a, b} ⊄ {b, c, a}

{1, 2, 3} ⊂ {1, 3, 5}

{a} ⊂ {a. b, c}

{a} ∈ (a, b, c)

{x : x is an even natural number less than 6} ⊂ {x : x is a natural number which divides 36}

Let A = {1, 2, {3, 4}, 5}. The following statement is correct or incorrect and why?

{3, 4} ⊂ A

Write down all the subsets of the following set:

{a}

How many elements has P(A), if A = Φ?

Write the following as interval:

{x : x ∈ R, – 4 < x ≤ 6}