HSC Arts इयत्ता ११ - Tamil Nadu Board of Secondary Education Question Bank Solutions

In the set Z of integers, define mRn if m − n is divisible by 7. Prove that R is an equivalence relation

Choose the correct alternative:

The relation R defined on a set A = {0, −1, 1, 2} by xRy if |x² + y²| ≤ 2, then which one of the following is true?

Choose the correct alternative:

Let R be the set of all real numbers. Consider the following subsets of the plane R × R: S = {(x, y) : y = x + 1 and 0 < x < 2} and T = {(x, y) : x − y is an integer} Then which of the following is true?

Choose the correct alternative:

The number of relations on a set containing 3 elements is

Choose the correct alternative:

Let R be the universal relation on a set X with more than one element. Then R is

Choose the correct alternative:

Let X = {1, 2, 3, 4} and R = {(1, 1), (1, 2), (1, 3), (2, 2), (3, 3), (2, 1), (3, 1), (1, 4), (4, 1)}. Then R is

Choose the correct alternative:

The rule f(x) = x² is a bijection if the domain and the co-domain are given by

Choose the correct alternative:

Let f : R → R be defined by f(x) = 1 − |x|. Then the range of f is

Solve for x: |3 − x| < 7

Solve for x: |4x − 5| ≥ −2

Solve for x: `|3 - 3/4x| ≤ 1/4`

Solve for x: |x| − 10 < −3

Solve `1/(|2x - 1|) < 6` and express the solution using the interval notation

Solve −3|x| + 5 ≤ −2 and graph the solution set in a number line

Solve 2|x + 1| − 6 ≤ 7 and graph the solution set in a number line

Solve `1/5|10x - 2| < 1`

Solve |5x − 12| < −2

Choose the correct alternative:
If |x + 2| ≤ 9, then x belongs to

Choose the correct alternative:
If `("k"x)/((x + 2)(x - 1)) = 2/(x + 2) + 1/(x - 1)`, then the value of k is

Choose the correct alternative:
If `(1 - 2x)/(3 + 2x - x^2) = "A"/(3 - x) + "B"/(x + 1)`, then the value of A + B is