Commerce (English Medium) Class 12 - CBSE Question Bank Solutions

If `tan^(-1)((x-2)/(x-4)) +tan^(-1)((x+2)/(x+4))=pi/4` ,find the value of x

Determine whether the following relation is reflexive, symmetric and transitive:

Relation R in the set A = {1, 2, 3, ..., 13, 14} defined as R = {(x, y) : 3x − y = 0}.

The Volume of cube is increasing at the rate of 9 cm 3/s. How fast is its surfacee area increasing when the length of an edge is 10 cm?

Determine whether the following relation is reflexive, symmetric and transitive:

Relation R in the set N of natural numbers defined as R = {(x, y) : y = x + 5 and x < 4}.

Determine whether the following relation is reflexive, symmetric and transitive:

Relation R in the set A = {1, 2, 3, 4, 5, 6} as R = {(x, y) : y is divisible by x}.

Determine whether the following relation is reflexive, symmetric and transitive:

Relation R in the set Z of all integers defined as R = {(x, y) : x − y is an integer}.

Determine whether the following relation is reflexive, symmetric and transitive:

Relation R in the set A of human beings in a town at a particular time given by R = {(x, y) : x is exactly 7 cm taller than y}.

Show that the relation R in the set R of real numbers, defined as R = {(a, b) : a ≤ b²} is neither reflexive nor symmetric nor transitive.

Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} as R = {(a, b) : b = a + 1} is reflexive, symmetric, or transitive.

Show that the relation R in R defined as R = {(a, b) : a ≤ b}, is reflexive and transitive but not symmetric.

Check whether the relation R in R defined by R = {(a, b) : a ≤ b³} is reflexive, symmetric or transitive.

Show that the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is symmetric but neither reflexive nor transitive.

Show that the relation R in the set A of all the books in a library of a college, given by R = {(x, y) : x and y have the same number of pages} is an equivalence relation.

Show that the relation R in the set A = {1, 2, 3, 4, 5} given by R = {(a, b) : |a − b| is even}, is an equivalence relation. Show that all the elements of {1, 3, 5} are related to each other and all the elements of {2, 4} are related to each other. But no element of {1, 3, 5} is related to any element of {2, 4}.

Show that the relation R in the set A = {x ∈ Z : 0 ≤ x ≤ 12} given by R = {(a, b) : |a − b| is a multiple of 4} is an equivalence relation. Find the set of all elements related to 1.

Show that the relation R in the set A = {x ∈ Z : 0 ≤ x ≤ 12} given by R = {(a, b) : a = b} is an equivalence relation. Find the set of all elements related to 1.

Given an example of a relation. Which is Symmetric but neither reflexive nor transitive.

Given an example of a relation. Which is Transitive but neither reflexive nor symmetric.

Given an example of a relation. Which is  Reflexive and symmetric but not transitive.

Given an example of a relation. Which is Reflexive and transitive but not symmetric.