SSLC (English Medium) Class 10 - Tamil Nadu Board of Secondary Education Question Bank Solutions

If (sin α + cosec α)² + (cos α + sec α)² = k + tan²α + cot²α, then the value of k is equal to

If sin θ + cos θ = a and sec θ + cosec θ = b , then the value of b(a² – 1) is equal to

If 5x = sec θ and `5/x` = tan θ, then `x^2 - 1/x^2` is equal to 

If x = a tan θ and y = b sec θ then

a cot θ + b cosec θ = p and b cot θ + a cosec θ = q then p² – q² is equal to

Prove that `cot^2 "A" [(sec "A" - 1)/(1 + sin "A")] + sec^2 "A" [(sin"A" - 1)/(1 + sec"A")]` = 0

Prove that `(tan^2 theta - 1)/(tan^2 theta + 1)` = 1 – 2 cos²θ

Prove that `[(1 + sin theta - cos theta)/(1 + sin theta + cos theta)]^2 = (1 - cos theta)/(1 + cos theta)`

If x sin³ θ + y cos³ θ = sin θ cos θ and x sin θ = y cos θ, then prove that x² + y² = 1

If a cos θ – b sin θ = c, then prove that (a sin θ + b cos θ) = `±  sqrt("a"^2 + "b"^2 -"c"^2)`

Let A = {1, 2, 3, 7} and B = {3, 0, –1, 7}, the following is relation from A to B?

R₁ = {(2, 1), (7, 1)}

Let A = {1, 2, 3, 7} and B = {3, 0, –1, 7}, the following is relation from A to B?

R₂ = {(–1, 1)}

Let A = {1, 2, 3, 7} and B = {3, 0, –1, 7}, the following is relation from A to B?

R₃ = {(2, –1), (7, 7), (1, 3)}

Let A = {1, 2, 3, 7} and B = {3, 0, –1, 7}, the following is relation from A to B?

R₄ = {(7, –1), (0, 3), (3, 3), (0, 7)}

Let A = {1, 2, 3, 4, …, 45} and R be the relation defined as “is square of ” on A. Write R as a subset of A × A. Also, find the domain and range of R

A Relation R is given by the set `{(x, y)/y = x + 3, x ∈ {0, 1, 2, 3, 4, 5}}`. Determine its domain and range

Represent the given relation by
(a) an arrow diagram
(b) a graph and
(c) a set in roster form, wherever possible

{(x, y) | x = 2y, x ∈ {2, 3, 4, 5}, y ∈ {1, 2, 3, 4}

Represent the given relation by
(a) an arrow diagram
(b) a graph and
(c) a set in roster form, wherever possible

{(x, y) | y = x + 3, x, y are natural numbers < 10}

A company has four categories of employees given by Assistants (A), Clerks (C), Managers (M), and an Executive Officer (E). The company provides ₹ 10,000, ₹ 25,000, ₹ 50,000, and ₹ 1,00,000 as salaries to the people who work in the categories A, C, M, and E respectively. If A₁, A₂, A₃, A_4, and A₅ were Assistants; C₁, C₂, C₃, C₄ were Clerks; M₁, M₂, M₃ were managers and E₁, E₂ was Executive officers and if the relation R is defined by xRy, where x is the salary given to person y, express the relation R through an ordered pair and an arrow diagram

Multiple Choice Question :

If there are 1024 relation from a set A = {1, 2, 3, 4, 5} to a set B, then the number of elements in B is