PUC Science कक्षा ११ - Karnataka Board PUC Question Bank Solutions

Write the relation as the sets of ordered pairs:

(iii) A relation R on the set [0, 1, 2, ....., 10] defined by 2x + 3y = 12.

Write the relation as the sets of ordered pairs:

(iv) A relation R from a set A = [5, 6, 7, 8] to the set B = [10, 12, 15, 16,18] defined by (x, y) ∈ R ⇔ x divides y.

Let R be a relation in N defined by (x, y) ∈ R ⇔ x + 2y =8. Express R and R⁻¹ as sets of ordered pairs.

 Let A = {1, 2, 3} and\[R = \left\{ \left( a, b \right) : \left| a^2 - b^2 \right| \leq 5, a, b \in A \right\}\].Then write R as set of ordered pairs.

If R = {(2, 1), (4, 7), (1, −2), ...}, then write the linear relation between the components of the ordered pairs of the relation R.

Write the following relations as sets of ordered pairs and find which of them are functions:

(a) {(x, y) : y = 3x, x ∈ {1, 2, 3}, y ∈ [3,6, 9, 12]}

Write the following relations as sets of ordered pairs and find which of them are functions: 

(b) {(x, y) : y > x + 1, x = 1, 2 and y = 2, 4, 6}

Write the following relations as sets of ordered pairs and find which of them are functions:

Express the function f : X → R given by f(x) = x³ + 1 as set of ordered pairs, where X = {−1, 0, 3, 9, 7}

Find the 11th term from the beginning and the 11th term from the end in the expansion of  \[\left( 2x - \frac{1}{x^2} \right)^{25}\] .

Find the 7th term in the expansion of \[\left( 3 x^2 - \frac{1}{x^3} \right)^{10}\] .

Find the 5th term from the end in the expansion of \[\left( 3x - \frac{1}{x^2} \right)^{10}\]

Find the 8th term in the expansion of  \[\left( x^{3/2} y^{1/2} - x^{1/2} y^{3/2} \right)^{10}\]

Find the 7th term in the expansion of \[\left( \frac{4x}{5} + \frac{5}{2x} \right)^8\]

Find the 4th term from the beginning and 4th term from the end in the expansion of \[\left( x + \frac{2}{x} \right)^9\] .

Find the 4th term from the end in the expansion of \[\left( \frac{4x}{5} - \frac{5}{2x} \right)^8\] .

Find the 7th term from the end in the expansion of \[\left( 2 x^2 - \frac{3}{2x} \right)^8\] .

Find the sixth term in the expansion  \[\left( y^\frac{1}{2} + x^\frac{1}{3} \right)^n\] , if the binomial coefficient of the third term from the end is 45.

Find n in the binomial \[\left( \sqrt[3]{2} + \frac{1}{\sqrt[3]{3}} \right)^n\] , if the ratio of 7^th term from the beginning to the 7^th term from the end is  \[\frac{1}{6}\]

if the seventh term from the beginning and end in the binomial expansion of  \[\left( \sqrt[3]{2} + \frac{1}{\sqrt[3]{3}} \right)^n\] are equal, find n.