Question

19.Every convergent sequence has …………….. one limit.

(A) at least

(B) at most

(C) exactly

(D) none of these

20.If the sequence is decreasing, then it …………….

(A) converges to its infimum.

(B) diverges.

(C) may converges to its infimum

(D) is bounded.

QUE…… MATCH THE PAIR 2.5X8 = 20 MARKS

A GROUP B GROUP

1. lurking variables. A. Polynomials

2. Algebraic consist of variables B. 6x3+4x3+3x+1

3. Cubic Polynomial C. 75.5

4. Sub-normal series of a group D.G=G0⊇G1⊇G2⊇… ⊇Gn=(e)

5. average of first 150 natural no E. potentially affect the outcomes

6. Basic definitions and results F. hk = kh for all h E H and k E K.

7. Isomorphism Theorems G a * (b * c) = (a * b) * c

8. G

( ) = G ,G

(2) = G

( )

I

, .,G

( ) = G

( - )

H. G( ) = {e}.​

Answer 1

Every convergent Sequence has ___limit

Answer 2

19. Every convergent sequence has exactly one limit (option c)

20. if the sequence is decreasing, then it may converge to its infinimum (option c)

Match the pair-

1. lurking variables- E

2. Algebraic consisting of variables- A

3. Cubic polynomial- B

4. Sub-normal series of a group- D

5. Average of first 150 natural numbers- C

6. Basic definitions and results- G

7. Isomorphism theorems- F

• 19. A convergent sequence has a unique limit. That is, it has only one limit. Hence, option (C) is correct
• 20. The monotone convergence theorem states that if a sequence is decreasing AND is bounded below by an infinimum, then it will converge to the infinimum. Since our statement only provides for one of these two conditions for convergence, then the sequence MAY converge to the infinimum. Hence, option (C) is correct.
• Match the pair-

1. Lurking variables are variables that may potentially affect the outcomes- E
2. An algebraic expression consisting of variables is called a polynomial- A
3. An example of a cubic polynomial is 6x³+4x²+3x+1- B
4. A sub-normal series of a group can be defined as G=G0⊇G1⊇G2⊇… ⊇Gn=(e)- D
5. The average of the first 150 natural numbers is 75.5
6. A basic definition and result is the associative property- G
7. one of the isomorphism theorems states that hk = kh for all h E H and k E K- F

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