Practice IIT JAM Mathematics Test Series for Free only On ** www.examflame.com** and take your preparation to the another level. In the Series of Tests for IIT JAM 2023 this is the test of Sequences of Real Numbers of the

**Chapter Real Analysis.**These Questions are prepared as per the Latest Syllabus of IIT JAM Mathematics 2023 . Practicing mock tests/Test series, you will get an idea about how and which type of Question will ask in the Examination. It also boost your confidence level. Also Solve

**IIT JAM Mathematics Previous Year Question Paper**. And Don’t Forget to Shore with Your Friends.

**IIT JAM Mathematics Test Series 2023 : Real Analysis – Sequences of Real Numbers**

**Q1. The sequence an = (A ^{2}n^{2} + n +1)^{1/2} -n is**

(a) convergent for all real values of A

(b) divergent for all real values of A

(c) convergent for exactly one real value of A

(d) Convergent for exactly two real values of A

**Q2. The least upper bound of the sequence <1- ^{1}/_{n}> is**

(a) 0

(b) -1

(c) 1

(d) None of these

**Q3. Let {a _{n}} and {b_{n}} be sequences of real numbers defined as a_{1} =1 and for n ≥1, a_{n+1} = a_{n}+(-1)^{n}2^{-n}, b_{n} = (2a_{n+1} – a_{n})/a_{n}. Then**

(a) {a_{n}} converges to zero and {b_{n}} is a Cauchy sequence

(b) {a_{n}} converges to non-zero and {b_{n}} is a Cauchy sequence

(c) {a_{n}} converges to zero and {b_{n}} is not a convergent sequence

(d) {a_{n}} converges to non-zero and {b_{n}} is not a convergent sequence

**Q4. Which of the following séquence <a _{n}> is monotonic:**

(a) <a_{n}> = 1- (-1)^{n}/n

(b) a_{n+2} = ** ^{1}/_{2}(a_{n}+a_{n+1})** where a

_{1}<a

_{2}and a

_{1}, a

_{2}are given.

(c) a

_{n+1}=

**[(ab**∀n , where a>0, 0<a

^{2}+ a_{n}^{2})/_{(a+1)}]^{1/2}_{1}<b and a

_{1}= a

(d) None of these

**Q5. Let {x _{n}} be a real sequence. If sequence of even terms of {x_{n}} converges to 1 and sequence of odd terms converges to -1. Then the sequence {x_{n}} will**

(a) Converge to 0

(b) Converge to 1

(c) Converge to -I

(d) None of these

**Q6. Consider he interval (1, -1) and a sequence {a _{n}}^{∞}_{n=1} of elements in it. Then**

(a) Every limit point of {a_{n}} is in (-1,1)

(b) Every limit point of {a_{n}} is in [-1,1]

(c) The limit points of {a_{n}} can only be in {-1,0,1}

(d) The limit points of {a_{n}} cannot be in {-1,0,1}

**Q7. Consider the sequence 4,0,4.1,0,4.11,0, 4.111,0,… Then**

(a) converges to 4^{1}/_{9}

(b) is divergent

(c) is unbounded

(d) is not convergent and has supremum = 4^{1}/_{9}

**Q8. Let p(x) be a polynomial in the real variable x of degree 5. Then limit n→∞ of the function ^{p(n)}/2^{n} is**

(a) 5

(b) 1

(c) 0

(d) ∞

**Q9. If 0<c<d, then the sequence a _{n} = (c^{n} +d^{n})^{1/n}**

(a) is bounded and monotonically decreasing

(b) is bounded and monotonically increasing

(c) is monotonically increasing but unbounded for 1<c<d

(d) is monotonically decreasing, but unbounded for 1<c<d

**Q10. The limit superior and the limit inferior of the following sequence <(-1) ^{n}(1+^{1}/_{n})> are**

(a) 1, -1

(b) 2, -1

(c) 2, 1

(d) 1, 1

**Q11. Let {a _{n}}, {b_{n}}and {c_{n}}be sequences of real numbers such that b_{n}=a_{2n} and c_{n} = a_{2n+1} . Then an is convergent**

(a) implies {b_{n}} is convergent but , {c_{n}} need not be convergent

(b) implies {c_{n}} is convergent but , {b_{n}} need not be convergent

(c) implies both {b_{n}} and {c_{n}} are convergent

(d) if both {b_{n}} and {c_{n}} are convergent

**Q12. For each positive integer n, let an be the number of points of intersection of the graph y = sinx with the line y = ^{x}/_{n}. The sequence {a_{n}} is**

(a) decreasing

(b) constant

(c) converging to zero

(d) diverging to infinity

**Q13. Let <x _{n}> be a convergent sequence and <y_{n}> be a monotonic sequence. Then <x_{n}.y_{n}>**

(a) Always converges

(b) Converges if <x_{n}> is monotonic

(c) Converges if <x_{n}y_{n}> is monotonic

(d) Converges if <y_{n}> is bounded

**Q14. Let {x _{n}} be an unbounded sequence of non- zero real numbers. Then**

(a) {x_{n}} must have a convergent subsequence

(b) {x_{n}} cannot have a convergent subsequence

(c) {^{1}/x_{n}} must have a convergent subsequence

(d) {^{1}/x_{n}}cannot have a convergent Subsequence.

**Q15. x _{n+1} = ^{-3}/_{4} x_{n} , x_{0}=1 . The sequence {x_{n}}**

(a) diverges

(b) x_{n} is monotonically increasing and converges to 0

(c) x_{n} is monotonically decreasing and converges to 0

(d) none of the above

NOTE : – If you need anything else more like e-books, video lectures, syllabus etc regarding your Preparation / Examination then do 📌 mention in the Comment Section below |

Hope you like the test given above for **IIT JAM Mathematics 2023** of Topic Sequences of Real Numbers of the Chapter **Real Analysis** . To get more Information about any exam, Previous Question Papers , Study Material, Book PDF, Notes etc for free, do share the post with your friends and Follow and Join us on other Platforms links are given below to get more interesting information, materials like this.

*Answer Key*

*Answer Key*

01. | (d) | 06. | (b) | 11. | (c) |

02. | (c) | 07. | (d) | 12. | (d) |

03. | (b) | 08. | (c) | 13. | (d) |

04. | (c) | 09. | (a) | 14. | (c) |

05. | (d) | 10. | (a) | 15. | (d) |

**Important Searches & Tags**

- IIT JAM Mock Test Papers download
- IIT JAM test series
- Free Mock Test mathematics Mock Test
- IIT JAM Test series mathematics
- Eduncle IIT JAM Test Series
- Free Mock Test for IIT JAM Mathematics
- IIT JAM Mathematics Mock Test 2022
- IIT JAM Mock Test
- IIT JAM free Mock Test 2022
- IIT JAM Mathematics topic wise questions PDF
- IIT JAM 2022 mock Test
- Best Test Series for IIT JAM Mathematics
- Free Online Test Series for IIT JAM Mathematics
- IIT JAM mock Test 2022
- IIT JAM free Mock Test 2022
- Unacademy IIT JAM Mathematics test series
- DIPS academy Test series
- Career Endeavour Test Series IIT-JAM
- Career Endeavour Test Series pdf