Question

Q1 Choose the correct option in the following questions:

(i) if A = (1, 2, 3, 4, 5) then which of these is true: (a) (b)(2, 3) \in A

(c)3 A (ii) if A(x, y, z, t) then these is not true: (a)x E A (b)(y,z) A

(d)5 € A

(c)t A

(d)w E A

(a) 1,2,3,4)

(iii) Roaster form of {x:xEN,x≤5] is (b)(5,6,7......)

( iv) If A = (1, 2, 4) and B (2,3,5) then An Bis

(d)(5)

(a)

(b)(1,4)

(c)(3)

(d)(2)

(v)

For any set A. (A) is

(a)A

(b)

(c)

(d)A

(vi) Hn(A) = 3 then number of subsets of A are: ()3 b)8

( (c)6 (vii) Hn(A) = 4 then number of proper subsets of A are:

(d)4

(2)16

(b)15

(d)1

(a)(3,7)

(x)

(а)ф

(b)15

(b)[3.7)

(b)U

(c)14 (viii) Ifn(A) = 4 then number of improper subsets of A are:

(d)1

(c)[3, 7)

(d) (3,7)

(c)14

(ix ) Interval form of the set (x:xER,

3 < x <=7 rfloor!

(c)Any non-empty set

(d)Singleton set.

(xi) fA = (1, 2) and B (5,7), then which of the following is a relation from A to B

(a)((1, 5), (7, 2)] (b)\{(1, 5), (1, 7)\} (c) ((

(xii) (a)64

If nof relations from A to B are:

(b)256

(xiii) if n(A)=3 and n(B) 7 then n(Ax B) is (a)37 equal to

(b)73 (c)3 x 7 (d)3+7 (xiv) If number of elements in the set A are n then number of relations defined on A are:

5,2), (7,1))

(d)((1,2), (5,7))

(c)128

(d)512

(a)n²

(b)2

(xv)

if f(x) = 2x ^ 2 - 3x + 4, t 9

f(-1)is equal to:

(a

(c)n2

(c)0

( xvi) if f(x) = 2x and g(x)=3x-5 then (f+g)(x) (a)5x-5 (b)x+5

is: (c)x-5

(xvii) Domain of the function f(x) = x ^ 2 + 2 is (a)R.

(b)(2, on)

(d)2

(d)1

(d)6x210x

(c) * \mathbb{R} - \{2\}

(d)[0, ∞)

Answer 1

Here are the correct options for each question:

(i) if A = (1, 2, 3, 4, 5) then which of these is true:
**Answer:** (a) (b)(2, 3) \in A **(False, because (2, 3) is a tuple and not an element of A)**
**(c)3 A** **(Incorrect, notation unclear)**
**(d)5 € A** (True, because 5 is in A).

(ii) if A = (x, y, z, t) then which of these is not true:
**Answer:**
(a)x E A (True)
(b)(y,z) A **(False, because (y,z) is not an element of A)**
(c)t A (True)
(d)w E A (False, because w is not in A).

So, the answer is **(b)**.

(iii) Roaster form of {x:xEN,x≤5] is
**Answer:** (a) **(1, 2, 3, 4, 5)**

(iv) If A = (1, 2, 4) and B (2,3,5) then An Bis
**Answer:** (d) **(2)**

(v) For any set A, (A) is
**Answer:** (a) **A**

(vi) If n(A) = 3 then number of subsets of A are:
**Answer:** (b) **8** (as the number of subsets of a set with n elements is \(2^n\)).

(vii) If n(A) = 4 then number of proper subsets of A are:
**Answer:** (b) **15** (as the number of proper subsets of a set with n elements is \(2^n - 1\)).

(viii) If n(A) = 4 then the number of improper subsets of A are:
**Answer:** (d) **1** (Only the set itself is the improper subset).

(ix) Interval form of the set (x:xER, 3 < x <=7) is
**Answer:** (b) **(3, 7]**.

(xi) If A = (1, 2) and B = (5, 7), then which of the following is a relation from A to B
**Answer:** (b) **{(1, 5), (1, 7)}** (because both items are valid pairs).

(xii) If number of relations from A to B are:
**Answer:** (b) **256** (the number of relations is \(2^{m \times n}\), where m and n are the number of elements in A and B respectively).

(xiii) if n(A)=3 and n(B)=7 then n(A x B) is equal to
**Answer:** (c) **3 x 7**.

(xiv) If number of elements in the set A are n then number of relations defined on A are:
**Answer:** (b) **2^n**.

(xv) if f(x) = 2x^2 - 3x + 4, f(-1) is equal to:
**Answer:**
Calculate f(-1):
f(-1) = 2(-1)^2 - 3(-1) + 4 = 2(1) + 3 + 4 = 9

**So, the answer is:** (d) **9**.

(xvi) if f(x) = 2x and g(x)=3x-5 then (f+g)(x) is:
**Answer:** (a) **5x - 5**. (because f(x) + g(x) = 2x + (3x - 5))

(xvii) Domain of the function f(x) = x^2 + 2 is
**Answer:** (a) **R** (the domain of a polynomial function is all real numbers).