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Sumit SenguptaEduRev Mathematics |
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Sumit Sengupta
EduRev Mathematics
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Discussed Questions
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Sumit Sengupta upvoted • 4 days ago |
The number of different pairs of words 
that can be made with the letters of the wrord STATICS is- a)828
- b)1260
- c)396
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
The number of different pairs of words that can be made with the letters of the wrord STATICS is
that can be made with the letters of the wrord STATICS isa)
828
b)
1260
c)
396
d)
none of these
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Veda Institute answered |
From every arrangement of 7 letters we get a pair by putting a sign after the four letters from the left.
∴ the required number of pairs = 7!/2!2!
∴ the required number of pairs = 7!/2!2!
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Sumit Sengupta upvoted • 3 weeks ago |
Let S3 be the group of all permutation with 3 symbols then the number of elements in S3 that satisfy the equation x2 = e (where e is identity) is (Answer should be integer) __________.Correct answer is '4'. Can you explain this answer?
Let S3 be the group of all permutation with 3 symbols then the number of elements in S3 that satisfy the equation x2 = e (where e is identity) is (Answer should be integer) __________.
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Veda Institute answered |
If x2 = e then either o(x) is lor 2.
We know that the number of elements of order 2 in S3 = 3.
Thus the mumber ofelements in S3 that satisfy the equation.x2 = e is 4.
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Sumit Sengupta upvoted • Feb 23, 2025 |
For a positive integer n, let Pn denote the space of all polynomials P(x) with coefficients in R such that degree P(x) ≤ n and let Bn denote the standard basis of Pn given by Bn= 
If T : P3 ---> P4 is the linear transformation defined by 
and A = (aij) is the 5 x 4 matrix of T with respect to the standard bases B3 and B4 then- a)a32 = 3/2 and a33 = 7/3
- b)a32 = 3/2 and a33 = 0
- c)a32 = 0 and a33 = 7/3
- d)a32 = 0 and a33 = 0
Correct answer is option 'B'. Can you explain this answer?
For a positive integer n, let Pn denote the space of all polynomials P(x) with coefficients in R such that degree P(x) ≤ n and let Bn denote the standard basis of Pn given by Bn=
If T : P3 ---> P4 is the linear transformation defined by and A = (aij) is the 5 x 4 matrix of T with respect to the standard bases B3 and B4 then
If T : P3 ---> P4 is the linear transformation defined by
and A = (aij) is the 5 x 4 matrix of T with respect to the standard bases B3 and B4 thena)
a32 = 3/2 and a33 = 7/3
b)
a32 = 3/2 and a33 = 0
c)
a32 = 0 and a33 = 7/3
d)
a32 = 0 and a33 = 0
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Veda Institute answered |
For a positive integer n, let Pn denote the space of all polynomials P(x) with coefficients in M such that degree P(x) ≤ n and let Bn denote the standard basis of Pn given by Bn = {1, x, x2,....., xn}
If T : P3---->P4 is a linear transformation defined by
T(P(x)) = x2P'(x) +
and A = (aij) is the 5 x 4 matrix of T with respect to the standard bases B3 and B4
Hence, the matrix of T related to the basis
Hence a32 = 3/2 and a33 = 0
If T : P3---->P4 is a linear transformation defined by
T(P(x)) = x2P'(x) +
and A = (aij) is the 5 x 4 matrix of T with respect to the standard bases B3 and B4
Hence, the matrix of T related to the basis
Hence a32 = 3/2 and a33 = 0|
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Sumit Sengupta upvoted • Feb 09, 2025 |
If 
then the trace of A102 is ___________.
Correct answer is '3'. Can you explain this answer?
If then the trace of A102 is ___________.
then the trace of A102 is ___________.|
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Veda Institute answered |
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Sumit Sengupta upvoted • Feb 02, 2025 |
Let S1 = {2 }, S2 = { 4 , 6 } , S3 = { 8 , 1 0 . 1 2 } ,S4 = { 14 , 16 , 18 , 20 } and so on then sum of elements of S10 is __________ .
Correct answer is '1010'. Can you explain this answer?
Let S1 = {2 }, S2 = { 4 , 6 } , S3 = { 8 , 1 0 . 1 2 } ,S4 = { 14 , 16 , 18 , 20 } and so on then sum of elements of S10 is __________ .
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Veda Institute answered |
Hence sum of elements of S10 is equal to 
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Sumit Sengupta asked • Jun 18, 2024 |
In a Binomial Distribution, if ‘n’ is the number of trials and ‘p’ is the probability of success, then the mean value is given by- a) np
- b) n
- c)p
- d) np(1-p)
Correct answer is option 'A'. Can you explain this answer?
In a Binomial Distribution, if ‘n’ is the number of trials and ‘p’ is the probability of success, then the mean value is given by
a)
np
b)
n
c)
p
d)
np(1-p)
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Veda Institute answered |
For a discrete probability function, the mean value or the expected value is given by
Mean(μ) = 
For Binomial Distribution P(x)= nCx px q(n-x), substitute in above equation and solve to get
µ = np.
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Sumit Sengupta asked • Jun 11, 2024 |
Let A be the n * n matrix (n ≥ 2) whose (i. j)th entry is i+j for all i.j = 1.2....n. The rank of A is (Answer should be integer) ___________.Correct answer is '2'. Can you explain this answer?
Let A be the n * n matrix (n ≥ 2) whose (i. j)th entry is i+j for all i.j = 1.2....n. The rank of A is (Answer should be integer) ___________.
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Veda Institute answered |
Given
Apply Rn-i+1 → Rn-i+1 - Rn-i 
We have
⇒ Rank(A) = 2
Find a unit normal vector to the surface x^2 y^2-2z 3=0 at 1,2,-1.?
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Sumit Sengupta answered • May 28, 2024 |
Unit Normal Vector to the Surface
To find a unit normal vector to the surface x^2 y^2 - 2z - 3 = 0 at the point (1, 2, -1), we can follow these steps:
1. Calculate the Gradient of the Surface
The gradient of the surface is given by the vector:
grad(f) =... more
To find a unit normal vector to the surface x^2 y^2 - 2z - 3 = 0 at the point (1, 2, -1), we can follow these steps:
1. Calculate the Gradient of the Surface
The gradient of the surface is given by the vector:
grad(f) =
Find the order of the difference equation Δ3yn – Δ2yn – Δyn = 3- a)4
- b)3
- c)2
- d)5
Correct answer is option 'B'. Can you explain this answer?
Find the order of the difference equation Δ3yn – Δ2yn – Δyn = 3
a)
4
b)
3
c)
2
d)
5
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Sumit Sengupta answered • May 28, 2024 |
Order of the Difference Equation
To find the order of the given difference equation, we need to look at the highest difference operator present in the equation.
Given Difference Equation:
Δ3yn - Δ2yn - Δyn = 3
Finding the Order:
- The highest difference operator present in the equation is the third-order difference operato... more
To find the order of the given difference equation, we need to look at the highest difference operator present in the equation.
Given Difference Equation:
Δ3yn - Δ2yn - Δyn = 3
Finding the Order:
- The highest difference operator present in the equation is the third-order difference operato... more
Two Unite sets have m and n elements. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. The values of m and n are- a)7,6
- b)6 ,3
- c)5,1
- d)8,7
Correct answer is option 'B'. Can you explain this answer?
Two Unite sets have m and n elements. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. The values of m and n are
a)
7,6
b)
6 ,3
c)
5,1
d)
8,7
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Sumit Sengupta answered • May 28, 2024 |
Given Information:
- Two sets have m and n elements
- The total number of subsets of the first set is 56 more than the total number of subsets of the second set
Solution:
Number of Subsets of a Set:
- The number of subsets of a set with 'n' elements is given by 2^n
- Therefore, the number of subsets of the first set with 'm' elements i... more
- Two sets have m and n elements
- The total number of subsets of the first set is 56 more than the total number of subsets of the second set
Solution:
Number of Subsets of a Set:
- The number of subsets of a set with 'n' elements is given by 2^n
- Therefore, the number of subsets of the first set with 'm' elements i... more
Consider the following linear transformation from the vector space R2 into the vector space R3.
T(x, y ) = (- x - y ,3x + 8y, 9x - 11y)
Then, the rank and nullity of T are respectively.- a)2 and 0
- b)1 and 0
- c)1 and 1
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
Consider the following linear transformation from the vector space R2 into the vector space R3.
T(x, y ) = (- x - y ,3x + 8y, 9x - 11y)
Then, the rank and nullity of T are respectively.
T(x, y ) = (- x - y ,3x + 8y, 9x - 11y)
Then, the rank and nullity of T are respectively.
a)
2 and 0
b)
1 and 0
c)
1 and 1
d)
None of these
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Sumit Sengupta answered • Feb 14, 2024 |
Rank and Nullity of the Linear Transformation:
Rank of T:
- The rank of a linear transformation is the dimension of the image of the transformation.
- To find the rank of T, we need to determine the dimension of the column space of the transformation matrix.
- The transformation matrix for T is
[ -1 -1 ]
[ 3 8 ]
[ 9 -11 ]
- By perfo... more
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Sumit Sengupta asked • Feb 09, 2024 |
Each of the six players participating in a chess competition will play one match with each other player. Tell us how many matches will be played in the entire competition-- a)30
- b)36
- c)15
- d)12
Correct answer is option 'C'. Can you explain this answer?
Each of the six players participating in a chess competition will play one match with each other player. Tell us how many matches will be played in the entire competition-
a)
30
b)
36
c)
15
d)
12
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Zara Khan answered |
Calculating the number of matches in a chess competition:
- Each player will play one match with each of the other five players.
- Therefore, for each player, there will be 5 matches in total.
Total number of matches:
- Since there are 6 players in the competition, we need to calculate the total number of matches played by all players combi... more
If in the expansion of (1 + x)m(1 - x)n, the coefficient of x and x2 are 3 and -6 respectively, then m is - a)6
- b)9
- c)12
- d)24
Correct answer is option 'C'. Can you explain this answer?
If in the expansion of (1 + x)m(1 - x)n, the coefficient of x and x2 are 3 and -6 respectively, then m is
a)
6
b)
9
c)
12
d)
24
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Sumit Sengupta answered • Nov 26, 2023 |
To find the coefficient of x in the expansion of (1 + x)^m(1 - x)^n, we can use the binomial theorem. According to the binomial theorem, the general term in the expansion of (a + b)^n is given by:
C(n, r) * a^(n-r) * b^r
where C(n, r) represents the number of ways to choose r items from a set of n items, and r ranges from 0 to n.
In this case, we have (1 + x)^m(1 -... more
C(n, r) * a^(n-r) * b^r
where C(n, r) represents the number of ways to choose r items from a set of n items, and r ranges from 0 to n.
In this case, we have (1 + x)^m(1 -... more
You have three coins in your pocket, two fair ones but the third biased with probability of heads p and tails 1 - p. One coin selected at random drops to the floor, landing heads up. How likely is it that it is one of the fair coins?- a)p
- b)1/(1+p)
- c)1/2
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
You have three coins in your pocket, two fair ones but the third biased with probability of heads p and tails 1 - p. One coin selected at random drops to the floor, landing heads up. How likely is it that it is one of the fair coins?
a)
p
b)
1/(1+p)
c)
1/2
d)
None of these
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Sumit Sengupta answered • Nov 26, 2023 |
Problem:
You have three coins in your pocket - two fair coins and one biased coin with a probability of landing heads up (p) and tails up (1-p). One coin is selected at random and dropped to the floor, landing heads up. How likely is it that the selected coin is one of the fair coins?
Solution:
To solve this problem, we can use Bayes' theorem, which allows us to ... more
You have three coins in your pocket - two fair coins and one biased coin with a probability of landing heads up (p) and tails up (1-p). One coin is selected at random and dropped to the floor, landing heads up. How likely is it that the selected coin is one of the fair coins?
Solution:
To solve this problem, we can use Bayes' theorem, which allows us to ... more
The c-discriminant and p-discriminant both contain- a)envelope
- b)tac-locus once
- c)node-locus
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
The c-discriminant and p-discriminant both contain
a)
envelope
b)
tac-locus once
c)
node-locus
d)
None of these
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Sumit Sengupta answered • Nov 26, 2023 |
The c-discriminant and p-discriminant are concepts used in algebraic geometry to study algebraic curves. They are important tools for understanding the properties and behavior of curves.
C-Discriminant:
The c-discriminant, also known as the characteristic discriminant, is a polynomial that characterizes the singularities of a curve. It is defined as the determinant of the Hessian m... more
C-Discriminant:
The c-discriminant, also known as the characteristic discriminant, is a polynomial that characterizes the singularities of a curve. It is defined as the determinant of the Hessian m... more
Log1/e(x) graph with domain, range and 3 properties?
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Sumit Sengupta answered • Sep 09, 2023 |
The graph of the function f(x) = log₁ₑ(x), also written as ln(x), represents the natural logarithm of x. In this response, we will discuss the graph's domain, range, and three important properties.
Domain:
The domain of the natural logarithm function f(x) = ln(x) is the set of all positive real numbers, excluding zero. This is because the natural logarithm is only defined fo... more
Domain:
The domain of the natural logarithm function f(x) = ln(x) is the set of all positive real numbers, excluding zero. This is because the natural logarithm is only defined fo... more
Consider the function f:R toR then which of the following is true? A) f is one one if the graph of f intersects some line parallel to X axis in at least two points. B)f is not surjective if the graph f does not intersects atl... more
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Sumit Sengupta answered • Sep 09, 2023 |
Introduction:
We are given a function f from the set of real numbers to the set of real numbers, i.e., f: R to R. We need to analyze the properties of the function based on its graph intersecting lines parallel to the x-axis.
A) f is one-one if the graph of f intersects some line parallel to the x-axis in at least two points:
To determine if the function is one-o... more
We are given a function f from the set of real numbers to the set of real numbers, i.e., f: R to R. We need to analyze the properties of the function based on its graph intersecting lines parallel to the x-axis.
A) f is one-one if the graph of f intersects some line parallel to the x-axis in at least two points:
To determine if the function is one-o... more
A cyclic group can be generated by a/an ________ element.- a)singular
- b)non-singular
- c)inverse
- d)multiplicative
Correct answer is option 'A'. Can you explain this answer?
A cyclic group can be generated by a/an ________ element.
a)
singular
b)
non-singular
c)
inverse
d)
multiplicative
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Sumit Sengupta answered • Sep 09, 2023 |
Introduction:
A cyclic group is a type of mathematical group that is generated by a single element. In other words, all the elements in a cyclic group can be obtained by repeatedly applying the group operation to the generator element. This generator element is known as a cyclic generator.
Explanation:
A cyclic group can be generated by a singular element. Let's ... more
A cyclic group is a type of mathematical group that is generated by a single element. In other words, all the elements in a cyclic group can be obtained by repeatedly applying the group operation to the generator element. This generator element is known as a cyclic generator.
Explanation:
A cyclic group can be generated by a singular element. Let's ... more
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Sumit Sengupta asked • Aug 17, 2023 |
Can I get more practice on MCQs and NAT questions to improve my accuracy in the IIT JAM Mathematics Paper?
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Naina Rana answered |
Practice for MCQs and NAT questions in IIT JAM Mathematics Paper
To improve your accuracy in the IIT JAM Mathematics Paper, it is crucial to practice a wide range of Multiple Choice Questions (MCQs) and Numerical Answer Type (NAT) questions. Here are some strategies and resources you can use to enhance your problem-solving skills:
1. Previous Year Question Papers:
... more|
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Sumit Sengupta asked • Aug 17, 2023 |
Can I get access to the question papers for the IIT JAM Mathematics Exam without my parent's name mentioned on it?
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Naina Rana answered |
Access to IIT JAM Mathematics Question Papers without Parent's Name
Introduction:
The IIT JAM (Joint Admission Test for M.Sc.) is a highly competitive entrance exam for students seeking admission into various postgraduate programs offered by the Indian Institutes of Technology (IITs). As an aspiring candidate, you may be looking for previous years' question papers to practic... more
Introduction:
The IIT JAM (Joint Admission Test for M.Sc.) is a highly competitive entrance exam for students seeking admission into various postgraduate programs offered by the Indian Institutes of Technology (IITs). As an aspiring candidate, you may be looking for previous years' question papers to practic... more
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Sumit Sengupta asked • Aug 14, 2023 |
Are there any mobile applications where I can download my admit card for the IIT JAM Mathematics Exam?
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Oishi Bajaj answered |
Mobile Applications for Downloading IIT JAM Mathematics Admit Cards
There are several mobile applications available that allow candidates to download their admit cards for the IIT JAM Mathematics exam. These applications provide a convenient and accessible way for candidates to access their admit cards and stay updated about the exam details. Below are some popular mobile applica... more
There are several mobile applications available that allow candidates to download their admit cards for the IIT JAM Mathematics exam. These applications provide a convenient and accessible way for candidates to access their admit cards and stay updated about the exam details. Below are some popular mobile applica... more
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Sumit Sengupta asked • Aug 07, 2023 |
Are there any scholarships or financial assistance opportunities available for candidates who achieve high marks above the cutoff in the IIT JAM Mathematics Exam?
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Radha Mehta answered |
Scholarships and Financial Assistance for IIT JAM Mathematics Exam
1. IIT JAM Scholarships:
- IITs (Indian Institutes of Technology) offer scholarships and financial assistance to students who qualify the IIT JAM Mathematics Exam with high marks.
- These scholarships are primarily awarded based on merit and academic performance.
2. Institute-specifi... more
- Each IIT has its own scholarship programs for meritorious students.
- These scholarships are offered to students who have achieved exceptional scores in the IIT JAM Mathematics Exam.
- The specific details and eligibility criteria for these scholarships can be obtained from the respective IIT's official website.
3. National Scholarships:
- The Government of India provides various national scholarships to deserving students, including those who excel in the IIT JAM Mathematics Exam.
- Some of the popular national scholarships include the National Scholarship Scheme for Post-Matric Studies, the Central Sector Scholarship Scheme, and the Prime Minister's Scholarship Scheme.
- Eligibility criteria, application procedures, and other details for these scholarships can be found on the National Scholarships Portal (scholarships.gov.in).
4. State-level Scholarships:
- Many state governments also offer scholarships to students who perform exceptionally well in competitive exams like the IIT JAM Mathematics Exam.
- The eligibility criteria and application procedures for these scholarships vary from state to state.
- Students are advised to visit the official websites of their respective state governments or the state education department to obtain detailed information about available scholarships.
5. Private Scholarships:
- Several private organizations, foundations, and trusts also provide scholarships to students who achieve high marks in the IIT JAM Mathematics Exam.
- These scholarships may have specific eligibility criteria and application procedures.
- It is recommended to search and explore scholarship opportunities offered by private institutions or corporations in the field of mathematics and related disciplines.
Conclusion:
- Candidates who achieve high marks above the cutoff in the IIT JAM Mathematics Exam have various scholarship and financial assistance opportunities available.
- These include scholarships offered by IITs, institute-specific scholarships, national scholarships, state-level scholarships, and scholarships from private organizations.
- It is advisable for candidates to research and explore the different scholarship options and their respective eligibility criteria and application procedures.
1. IIT JAM Scholarships:
- IITs (Indian Institutes of Technology) offer scholarships and financial assistance to students who qualify the IIT JAM Mathematics Exam with high marks.
- These scholarships are primarily awarded based on merit and academic performance.
2. Institute-specifi... more
- Each IIT has its own scholarship programs for meritorious students.
- These scholarships are offered to students who have achieved exceptional scores in the IIT JAM Mathematics Exam.
- The specific details and eligibility criteria for these scholarships can be obtained from the respective IIT's official website.
3. National Scholarships:
- The Government of India provides various national scholarships to deserving students, including those who excel in the IIT JAM Mathematics Exam.
- Some of the popular national scholarships include the National Scholarship Scheme for Post-Matric Studies, the Central Sector Scholarship Scheme, and the Prime Minister's Scholarship Scheme.
- Eligibility criteria, application procedures, and other details for these scholarships can be found on the National Scholarships Portal (scholarships.gov.in).
4. State-level Scholarships:
- Many state governments also offer scholarships to students who perform exceptionally well in competitive exams like the IIT JAM Mathematics Exam.
- The eligibility criteria and application procedures for these scholarships vary from state to state.
- Students are advised to visit the official websites of their respective state governments or the state education department to obtain detailed information about available scholarships.
5. Private Scholarships:
- Several private organizations, foundations, and trusts also provide scholarships to students who achieve high marks in the IIT JAM Mathematics Exam.
- These scholarships may have specific eligibility criteria and application procedures.
- It is recommended to search and explore scholarship opportunities offered by private institutions or corporations in the field of mathematics and related disciplines.
Conclusion:
- Candidates who achieve high marks above the cutoff in the IIT JAM Mathematics Exam have various scholarship and financial assistance opportunities available.
- These include scholarships offered by IITs, institute-specific scholarships, national scholarships, state-level scholarships, and scholarships from private organizations.
- It is advisable for candidates to research and explore the different scholarship options and their respective eligibility criteria and application procedures.
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Sumit Sengupta asked • Aug 03, 2023 |
Are there any special instructions for handling the marking scheme during the IIT JAM Mathematics Exam?
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Hrithik Choudhury answered |
Special Instructions for Handling the Marking Scheme during the IIT JAM Mathematics Exam
Introduction
The IIT JAM (Joint Admission Test for M.Sc.) Mathematics Exam is a highly competitive examination conducted for admission to various postgraduate programs in mathematics offered by the Indian Institutes of Technology (IITs). To perform well in the exam, it is importan... more
Introduction
The IIT JAM (Joint Admission Test for M.Sc.) Mathematics Exam is a highly competitive examination conducted for admission to various postgraduate programs in mathematics offered by the Indian Institutes of Technology (IITs). To perform well in the exam, it is importan... more
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Sumit Sengupta asked • Aug 02, 2023 |
What are some effective time management strategies for the IIT JAM Mathematics Paper?
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Nakul Bajaj answered |
Effective Time Management Strategies for IIT JAM Mathematics Paper
1. Understand the Exam Pattern
- Familiarize yourself with the exam pattern and syllabus of the IIT JAM Mathematics paper.
- Understand the weightage given to different topics and prioritize your preparation accordingly.
2. Create a Study Plan
- Develop a well-structured study plan that covers all the topics systematically.... more
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