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Sonu Sainii want to be a mathematician |
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Sonu Saini
EduRev Mathematics
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Top Scoring Tests by Sonu
Discussed Questions
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Sonu Saini asked • Nov 16, 2020 |
If {v1, v2, v3} is a linearly independent set of vectors in a vector space over 
then which one of the following sets is also linearly independent?- a){v1 + v2 – v3, 2v1 + v2 + 3v3, 5v1 + 4v2}
- b){v1 – v2, v2 – v3, v3 – v1}
- c){v1 + v2 – v3, v2 + v3 – v1, v3 + v1 – v2, v1 + v2 + v3}
- d){v1 + v2, v2 + 2v3, v3 + 3v1}
Correct answer is option 'D'. Can you explain this answer?
If {v1, v2, v3} is a linearly independent set of vectors in a vector space over then which one of the following sets is also linearly independent?
then which one of the following sets is also linearly independent?a)
{v1 + v2 – v3, 2v1 + v2 + 3v3, 5v1 + 4v2}
b)
{v1 – v2, v2 – v3, v3 – v1}
c)
{v1 + v2 – v3, v2 + v3 – v1, v3 + v1 – v2, v1 + v2 + v3}
d)
{v1 + v2, v2 + 2v3, v3 + 3v1}
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Azaz 919 answered |
A
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Sonu Saini asked • Oct 25, 2020 |
Let S be the set of all rational numbers in (0, 1). Then which of the following statements is/are TRUE ?- a)S is a closed subset of R
- b)S is not a closed subset of R
- c)S is an open subset of R
- d)Every x ∈ (0, 1)\S is a limit point of S.
Correct answer is option 'B,D'. Can you explain this answer?
Let S be the set of all rational numbers in (0, 1). Then which of the following statements is/are TRUE ?
a)
S is a closed subset of R
b)
S is not a closed subset of R
c)
S is an open subset of R
d)
Every x ∈ (0, 1)\S is a limit point of S.
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Rutuja Sengupta answered |
Solution:
Statement a) S is a closed subset of R:
To determine if S is a closed subset of R, we need to consider its complement, which is the set of all irrational numbers and the numbers outside the interval (0, 1).
The set of irrational numbers is not closed since it contains numbers like √2 that are limit points but not contained within the set. Similar... more
Statement a) S is a closed subset of R:
To determine if S is a closed subset of R, we need to consider its complement, which is the set of all irrational numbers and the numbers outside the interval (0, 1).
The set of irrational numbers is not closed since it contains numbers like √2 that are limit points but not contained within the set. Similar... more
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Sonu Saini
asked a question
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Let S be a subset of ¡ such that 2018 is an interior point of S. Which of the following is (are) true?- a)S contains an interval
- b)There is a sequence in S which does not converge to 2018
- c)There is an element
such that y is also an interior point of S - d)There is point
Correct answer is option 'A,B,C'. Can you explain this answer?
Let S be a subset of ¡ such that 2018 is an interior point of S. Which of the following is (are) true?
a)
S contains an interval
b)
There is a sequence in S which does not converge to 2018
c)
There is an element such that y is also an interior point of S
such that y is also an interior point of Sd)
There is point
Then|
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Sonu Saini
asked a question
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Then which one of the followings is NOT TRUE ?- a)Both {an} and {bn} converge, but the limits are not equal.
- b)Both {an} and {bn} converge, but the limits are equal.
- c){bn} is decreasing sequence.
- d){an} is an increasing sequence.
Correct answer is option 'A'. Can you explain this answer?
Then which one of the followings is NOT TRUE ?
a)
Both {an} and {bn} converge, but the limits are not equal.
b)
Both {an} and {bn} converge, but the limits are equal.
c)
{bn} is decreasing sequence.
d)
{an} is an increasing sequence.
for (x, y) ≠ (0, 0). Then
and f are bounded
. Which of the following values of a, b, c do NOT result in the convergence of the series
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Sonu Saini asked • Oct 17, 2020 |
Which of the following conditions implies (imply) the convergence of a sequence {xn} of real numbers?- a)Given ε > 0 there exists an n0 ∈ N such that for all
- b)Given ε > 0 there exists an n0 ∈ N such that for all
- c)Given ε > 0 there exists an n0 ∈ N such that for all
- d)Given ε > 0 there exists an n0 ∈ N such that for all m, n with
Correct answer is option 'C,D'. Can you explain this answer?
Which of the following conditions implies (imply) the convergence of a sequence {xn} of real numbers?
a)
Given ε > 0 there exists an n0 ∈ N such that for all
b)
Given ε > 0 there exists an n0 ∈ N such that for all
c)
Given ε > 0 there exists an n0 ∈ N such that for all
d)
Given ε > 0 there exists an n0 ∈ N such that for all m, n with
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Sakshee Chauhan answered |
C and D
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Sonu Saini asked • Oct 16, 2020 |
Let A6 be the group of even permutations of 6 distinct symbols. Then the number of elements of order 6 in A6 is _______ .
Correct answer is '0'. Can you explain this answer?
Let A6 be the group of even permutations of 6 distinct symbols. Then the number of elements of order 6 in A6 is _______ .
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Srishti Khanna answered |
Explanation:
To find the number of elements of order 6 in A6, we need to consider the cycle decomposition of each element of A6.
What is cycle decomposition?
Cycle decomposition is a way of representing a permutation as a product of disjoint cycles. A cycle is a sequence of elements that are permuted cyclically, i.e., each element is replaced by the n... more
To find the number of elements of order 6 in A6, we need to consider the cycle decomposition of each element of A6.
What is cycle decomposition?
Cycle decomposition is a way of representing a permutation as a product of disjoint cycles. A cycle is a sequence of elements that are permuted cyclically, i.e., each element is replaced by the n... more
then f(3) + f(1) equals:
- a)∞
- b)0
- c)2
- d)1
Correct answer is option 'C'. Can you explain this answer?
a)
∞
b)
0
c)
2
d)
1
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Sonu Saini answered • Aug 05, 2019 |
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