1

A function f:R₊ →R where R, is the set of all nonnegative real numbers) defined by f(x) = 4x + 3 is:

1. one-one but not onto 
2. onto but not one-one
3. both one-one and onto
4. neither one-one nor onto

2

Assertion(A): The domain of the function sec^-1 2x is

（-∞, _ 1/2] U [1/2∞）

Reason(R): sec^-1 (-2) = - π/4

1. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A)
2. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A)
3. Assertion (A) is true and Reason (R) is false
4. Assertion (A) is false and Reason (R) is true

3

Let f: R - {4/3} → R be a function defined as f (x) = 4x/ 3x + 4, Show that f is a one-one function. Also, check whether f is an onto function or not.

4

Let A = (x €Z: 0 ≤ x ≤ 12}. Show that R = {(a, b) : a, b, €, A, la - bl is divisible by 4} is an equivalence relation.

Find the set of all elements related to 1. Also write the equivalence class [2].

5

Evaluate: sin^-1 (sin 3π/4) + cos^-1 (cos 3π/4) + tan^-1 (1)

6

A relation Ron set A = {1, 2, 3, 4, 5) is defined as R = f(x, y) : X²- Y²) < 8} . Check whether the relation R is reflexive, symmetric and transitive.

7

Find the value of : tan^-1 (- 1/√3) + Cot^-1 (1/√3)+ tan^-1 [Sin -(π/4)].

8. 

Find the domain of the function f(x) = sin^-1 x2 - 4).

9.

Let N be the set of natural numbers and R be the relation on N x N defined by (a, b) R (c, d) if ad = bc

for all a, b, c, d e N. Show that Ris an equivalence relation.

10.

Read the following passage and answer the following questions.

Sherlin and Danju are playing Ludo at home during Covid-19. While rolling the dice, Sherlin's sister Raji observed and noted the possible outcomes of the throw every time belonging to the set (1,2,3,4,5,6). Let A be the set of players while B be the set of all.

(i) Raji wants to know the number of functions from A to B. Find the number of all possible functions.

(ii) Raji wants to know the number of relations possible from A to B. Find the number of possible relations.