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Real Analysis
5.Let S = {a, b, c, d} and T = {f, b, d, g}. Then the intersection of set S and T is
a.{b, d, f}
b.{b, d}
c.{b, d,c}
d.{b, d, g}
6.The … are those real numbers, which can be expressed as the ratio of two integers
a.natural numbers
b.irrational numbers
c.rational numbers
d.integers
a.{b, d, f}
b.{b, d}
c.{b, d,c}
d.{b, d, g}
6.The … are those real numbers, which can be expressed as the ratio of two integers
a.natural numbers
b.irrational numbers
c.rational numbers
d.integers
Real Analysis
1.The real number a is less than the real number b if …
a.a -b is a negative number
b.b – a is a positive number
c.b – a is a negative number
d.a – b is a positive number
2.Let M = {a,b}, Then \\[2^{M}\\] is\n
a.{{a, b}, {a}, {b}, ∅}
b.{{a, b}, {a}, {b}}
c.{{a, b}, {b}, ∅}
d.{{a}, {b}, ∅}
a.a -b is a negative number
b.b – a is a positive number
c.b – a is a negative number
d.a – b is a positive number
2.Let M = {a,b}, Then \\[2^{M}\\] is\n
a.{{a, b}, {a}, {b}, ∅}
b.{{a, b}, {a}, {b}}
c.{{a, b}, {b}, ∅}
d.{{a}, {b}, ∅}
Real Analysis
Prove that lim (Xn)=0 if and only if lim(|Xn|)= 0. Give an example to show that the convergence of (|Xn|)= 0 need not imply the convergence of (Xn)= 0.
Real Analysis
Suppose {p} is a cauchy sequence in a metric space X and some subsequence {p} converges to a point a belongs to X . Prove that the full sequence {p} converges to a .
Real Analysis
Show that limit n approaches to infinity (xe^-nx)=0 for x € real number , x>0
Real Analysis
Q. ∫_(-∞)^∞▒e^(〖-x〗^2 ) dx=?
a. π/2
b. π
c. √π
d. 2√π
a. π/2
b. π
c. √π
d. 2√π
Real Analysis
Q. Choose the correct answer.
Q. The series ∑_(n=1)^∞▒〖(-1)〗^(n+1) n/(n^2+π) is
a. conditionally convergent for n>√π
b. absolutely convergent for n>π^2
c. divergent for n>0
d. none of the above
Q. The series ∑_(n=1)^∞▒〖(-1)〗^(n+1) n/(n^2+π) is
a. conditionally convergent for n>√π
b. absolutely convergent for n>π^2
c. divergent for n>0
d. none of the above
Real Analysis
Q. Choose the correct answer.
Q. Which of the following is the sum of infinite series ∑_(n=0)^∞▒〖(-1)〗^n 3^n r^n?
a. 1/(1+3r) for -1/3<r<1/3
b. . 1/(1-3r) for -1/3<r<1/3
. 3/(1-3r) for -1/3<r<1/3
d. ∞
Q. Which of the following is the sum of infinite series ∑_(n=0)^∞▒〖(-1)〗^n 3^n r^n?
a. 1/(1+3r) for -1/3<r<1/3
b. . 1/(1-3r) for -1/3<r<1/3
. 3/(1-3r) for -1/3<r<1/3
d. ∞
Real Analysis
Q. Choose the correct answer.
Q. If a_n=∑_(l=1)^n▒〖(□(1/l))〗, then which of the following statement si true about the sequence {a_n} ?
a. Chauchy sequence.
b. Convergent sequence
c. Not a Cauchy sequence
d. Every subsequence of {a_n} is convergent.
Q. If a_n=∑_(l=1)^n▒〖(□(1/l))〗, then which of the following statement si true about the sequence {a_n} ?
a. Chauchy sequence.
b. Convergent sequence
c. Not a Cauchy sequence
d. Every subsequence of {a_n} is convergent.
Real Analysis
Q. Choose the correct answer.
Q. Which of the following statement is true for sequence {(〖-1)〗^(n-1)}?
a. The sequence is bounded
b. The sequence is increasing
c. The sequence is decreasing
d. The sequence is neither increasing nor decreasing
Q. Which of the following statement is true for sequence {(〖-1)〗^(n-1)}?
a. The sequence is bounded
b. The sequence is increasing
c. The sequence is decreasing
d. The sequence is neither increasing nor decreasing
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#340153 on Dec 2023
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