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Sweta PradhanEduRev Mathematics |
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Sweta Pradhan
EduRev Mathematics
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Content, tests & courses saved by you for accessing later. (visible to you only)
Discussed Questions
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Madhav Mehra upvoted • 3 weeks ago |
Which one of the following is a linear transformation?- a)T : R2 ---> R2 defined by T(x, y) = (xy, x)
- b)T : R2 ---> R3 defined by T(x, y) = (x + 3, 2y, x+y)
- c)T : R3 ---> R2 defined by T(x, y, z) = (Ix| , y + z)
- d)None of these
Correct answer is option 'D'. Can you explain this answer?
Which one of the following is a linear transformation?
a)
T : R2 ---> R2 defined by T(x, y) = (xy, x)
b)
T : R2 ---> R3 defined by T(x, y) = (x + 3, 2y, x+y)
c)
T : R3 ---> R2 defined by T(x, y, z) = (Ix| , y + z)
d)
None of these
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Veda Institute answered |
Let (1,2) and (3,4) be two vectors of R2.
Then T[(1, 2) + (3,4)] = T(4, 6)]
= (4 x 6, 4) = (24, 6)
and T(l, 2) = (1 x 2,1) = (2, 1)
T(3, 4) = (3 x 4,.3) = (12, 3) Thus,T(l, 2) + T(3, 4) = (2, 1) + (12, 3) = (14, 4)
Therefore, T[(1, 2) + (3 ,4)] ≠ T(1 ,2) + T(3,4)
Hence, T is non linear.
To show that a given map T is a linear transformation we must show that
T(αx + βy) = αT(x) + βT(y)
where x,y are vectors and a, P are scalars while to show that the given map is non-linear conveniently we try to find a related contrast example.
Then T[(1, 2) + (3,4)] = T(4, 6)]
= (4 x 6, 4) = (24, 6)
and T(l, 2) = (1 x 2,1) = (2, 1)
T(3, 4) = (3 x 4,.3) = (12, 3) Thus,T(l, 2) + T(3, 4) = (2, 1) + (12, 3) = (14, 4)
Therefore, T[(1, 2) + (3 ,4)] ≠ T(1 ,2) + T(3,4)
Hence, T is non linear.
To show that a given map T is a linear transformation we must show that
T(αx + βy) = αT(x) + βT(y)
where x,y are vectors and a, P are scalars while to show that the given map is non-linear conveniently we try to find a related contrast example.
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Madhav Mehra upvoted • Feb 24, 2025 |
The differential equation 2ydx - (3y - 2x) dy = 0 is- a)exact and homogeneous but not linear
- b)homogeneous and linear but not exact
- c)exact and linear but not homogeneous
- d)exact, homogeneous and linear
Correct answer is option 'A'. Can you explain this answer?
The differential equation 2ydx - (3y - 2x) dy = 0 is
a)
exact and homogeneous but not linear
b)
homogeneous and linear but not exact
c)
exact and linear but not homogeneous
d)
exact, homogeneous and linear
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Veda Institute answered |
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Madhav Mehra upvoted • Feb 09, 2025 |
If r > p > q, the number of different selections of p + q things taking r at a time, where p things are identical and q other things are identical, is- a)p + q - r
- b)q + q - r + 1
- c)r - p - q + 1
- d)non of these
Correct answer is option 'B'. Can you explain this answer?
If r > p > q, the number of different selections of p + q things taking r at a time, where p things are identical and q other things are identical, is
a)
p + q - r
b)
q + q - r + 1
c)
r - p - q + 1
d)
non of these
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Veda Institute answered |
The number of selections of p things from p identical things and r - p things from q identical things = 1 x 1
Similarly in all other cases,
∴ the total number of ways
= p - (r - q )+ 1 or q - (r - p) + 1
= p + q - r + l
Similarly in all other cases,
∴ the total number of ways
= p - (r - q )+ 1 or q - (r - p) + 1
= p + q - r + l
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Madhav Mehra upvoted • Feb 04, 2025 |
The c-discriminant of the equations
(y - c)2 = x(x - a)2 is- a)x(x - a2) = 0
- b) x - a2 = 0
- c)x = a
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
The c-discriminant of the equations
(y - c)2 = x(x - a)2 is
(y - c)2 = x(x - a)2 is
a)
x(x - a2) = 0
b)
x - a2 = 0
c)
x = a
d)
None of these
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Veda Institute answered |
Given, differential equation is
(y - c)2 = x(x - a)2
(y - c)2 = x(x - a)2
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Madhav Mehra upvoted • Jan 30, 2025 |
For an incompressible flow, the x and y components of the velocity vector are 
= 3(y | z), where x, y and z are in metre, all velocities are in m/s. Then, the z component of the velocity vector 
of the flow for the boundary condition 
at z = 0, is - a)5z
- b)-5z
- c)2x + 3z
- d)-2x - 3z
Correct answer is option 'B'. Can you explain this answer?
For an incompressible flow, the x and y components of the velocity vector are = 3(y | z), where x, y and z are in metre, all velocities are in m/s. Then, the z component of the velocity vector of the flow for the boundary condition at z = 0, is
= 3(y | z), where x, y and z are in metre, all velocities are in m/s. Then, the z component of the velocity vector of the flow for the boundary condition at z = 0, is a)
5z
b)
-5z
c)
2x + 3z
d)
-2x - 3z
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Veda Institute answered |
Given
(where, vz = 0 at z = 0 and fluid is incompressible) For incompressible fluid flow, equation of continuity is
or
or
So,
(where, vz = 0 at z = 0 and fluid is incompressible) For incompressible fluid flow, equation of continuity is
or
or
So,
What is Eigen value?Correct answer is 'A scalar associated with a given linear transformation'. Can you explain this answer?
What is Eigen value?
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Madhav Mehra answered • Dec 25, 2024 |
What is an Eigenvalue?
An eigenvalue is a fundamental concept in linear algebra, particularly in the study of linear transformations. It provides insight into the behavior of these transformations.
Definition
- An eigenvalue is defined as a scalar associated with a linear transformation represented by a square matrix.
- When a linear transformation is appli... more
An eigenvalue is a fundamental concept in linear algebra, particularly in the study of linear transformations. It provides insight into the behavior of these transformations.
Definition
- An eigenvalue is defined as a scalar associated with a linear transformation represented by a square matrix.
- When a linear transformation is appli... more
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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Madhav Mehra answered • Sep 24, 2024 |
Understanding S3 and Permutations
S3, the symmetric group of degree 3, consists of all possible permutations of three symbols (for example, {1, 2, 3}). The group has a total of 3! (factorial of 3) = 6 elements.
Elements of S3
The elements in S3 can be listed as follows:
- (1) : Identity (e)
- (12) : Swap 1 and 2
- (13) : Swap 1 and 3
- (23) : Swap 2... more
S3, the symmetric group of degree 3, consists of all possible permutations of three symbols (for example, {1, 2, 3}). The group has a total of 3! (factorial of 3) = 6 elements.
Elements of S3
The elements in S3 can be listed as follows:
- (1) : Identity (e)
- (12) : Swap 1 and 2
- (13) : Swap 1 and 3
- (23) : Swap 2... more
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Madhav Mehra asked • Jun 12, 2024 |
Number of homomorphism from ℤ8 ⊕ ℤ2, onto ℤ4 ⊕ ℤ4, (Answer Should be integer) _______.Correct answer is '0'. Can you explain this answer?
Number of homomorphism from ℤ8 ⊕ ℤ2, onto ℤ4 ⊕ ℤ4, (Answer Should be integer) _______.
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Kabir Shah answered |
Explanation:
Homomorphism:
Homomorphism is a structure-preserving map between two algebraic structures of the same type. In this case, we are looking for homomorphisms between two direct sum groups.
Direct Sum:
The direct sum of two groups A and B, denoted as A ⊕ B, is the set of all pairs (a, b) where a belongs to group A and b belongs to... more
Homomorphism:
Homomorphism is a structure-preserving map between two algebraic structures of the same type. In this case, we are looking for homomorphisms between two direct sum groups.
Direct Sum:
The direct sum of two groups A and B, denoted as A ⊕ B, is the set of all pairs (a, b) where a belongs to group A and b belongs to... more
A letter is knwon to have come from either TATANAGAR' or CALCUTTA. On the envelope, Just two consecutive letters, TA, are visible. The probability that the letter has come from CALCUTTA is.- a)4/11
- b)1/3
- c)5/12
- d)none
Correct answer is option 'A'. Can you explain this answer?
A letter is knwon to have come from either TATANAGAR' or CALCUTTA. On the envelope, Just two consecutive letters, TA, are visible. The probability that the letter has come from CALCUTTA is.
a)
4/11
b)
1/3
c)
5/12
d)
none
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Madhav Mehra answered • Mar 14, 2024 |
Understanding the Problem:
Given that a letter is known to have come from either TATANAGAR or CALCUTTA, with only the consecutive letters "TA" visible on the envelope. We need to find the probability that the letter has come from CALCUTTA.
Solving the Problem:
- There are two possibilities for the location of the letter: TATANAGAR or CALCUTTA.
- We kno... more
Bag A contain 10 bulbs in which 3 bulbs are defective. 2 bulbs are drawn. What is the probability of the both bullps being non-defective?- a)1/15
- b)7/15
- c)7/90
- d)8/15
Correct answer is option 'B'. Can you explain this answer?
Bag A contain 10 bulbs in which 3 bulbs are defective. 2 bulbs are drawn. What is the probability of the both bullps being non-defective?
a)
1/15
b)
7/15
c)
7/90
d)
8/15
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Madhav Mehra answered • Mar 14, 2024 |
Solution:
Given:
- Total number of bulbs in Bag A = 10
- Number of defective bulbs = 3
- Number of non-defective bulbs = 10 - 3 = 7
Calculation:
Step 1: Calculate the probability of drawing a non-defective bulb on the first draw
- Probability of drawing a non-defective bulb on the first draw = Number of non-defe... more
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Madhav Mehra asked • Oct 02, 2023 |
f(x), shown in the figure is represented by f(x) = 
+ bn sin(nx)}. The value of a0 is
- a)0
- b)π/2
- c)π
- d)2π
Correct answer is option 'A'. Can you explain this answer?
f(x), shown in the figure is represented by f(x) = + bn sin(nx)}. The value of a0 is
+ bn sin(nx)}. The value of a0 isa)
0
b)
π/2
c)
π
d)
2π
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Veda Institute answered |
From the figure, we say that, f(x) is odd function.
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Madhav Mehra asked • Sep 29, 2023 |
Let X be a randon variable following normal distribution with mean +1 and variance 4. Let Y be another normal variable with mean –1 and variance unknown. If P(X ≤ –1) = P(Y ≥ 2) the standard deviation of Y is- a)3
- b)2
- c)√2
- d)1
Correct answer is option 'A'. Can you explain this answer?
Let X be a randon variable following normal distribution with mean +1 and variance 4. Let Y be another normal variable with mean –1 and variance unknown. If P(X ≤ –1) = P(Y ≥ 2) the standard deviation of Y is
a)
3
b)
2
c)
√2
d)
1
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Chirag Verma answered |
given
Convert into standard and normal variates,
...(i)Now since us know that in standard normal distribution,
What is the number of proper subsets of a given finite set with n elements?- a)2n - l
- b)2n - 2
- c)2n - 1
- d)2n - 2
Correct answer is option 'C'. Can you explain this answer?
What is the number of proper subsets of a given finite set with n elements?
a)
2n - l
b)
2n - 2
c)
2
n
- 1d)
2n - 2
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Madhav Mehra answered • Aug 26, 2023 |
Number of Proper Subsets of a Finite Set with n Elements
To find the number of proper subsets of a given finite set with n elements, we need to understand the concept of subsets and proper subsets.
Subsets:
A subset of a set is a collection of elements that are all contained within the original set. For example, if we have a set A = {1, 2, 3}, then the subsets of A are:<... more
To find the number of proper subsets of a given finite set with n elements, we need to understand the concept of subsets and proper subsets.
Subsets:
A subset of a set is a collection of elements that are all contained within the original set. For example, if we have a set A = {1, 2, 3}, then the subsets of A are:<... more
If, A = {1,2,3,4} and
R = {(1, 1), (1, 3), (2, 2), (3, 1) (3, 4), (4, 3) (4, 4) is a relation on A x A, then which one of the following is correct?
- a)R is reflexive
- b)R is symmetric and transitive
- c)R is reflexive and symmetric
- d)R is neither reflexive nor transitive
Correct answer is option 'C'. Can you explain this answer?
If, A = {1,2,3,4} and
R = {(1, 1), (1, 3), (2, 2), (3, 1) (3, 4), (4, 3) (4, 4) is a relation on A x A, then which one of the following is correct?
R = {(1, 1), (1, 3), (2, 2), (3, 1) (3, 4), (4, 3) (4, 4) is a relation on A x A, then which one of the following is correct?
a)
R is reflexive
b)
R is symmetric and transitive
c)
R is reflexive and symmetric
d)
R is neither reflexive nor transitive
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Madhav Mehra answered • Aug 26, 2023 |
R is transitive, but not reflexive.
Explanation:
Reflexive property:
A relation R on a set A is said to be reflexive if every element of A is related to itself. In other words, for every element a in A, (a, a) must be in R.
In the given relation R = {(1, 1), (1, 3), (2, 2), (3, 1) (3, 4), (4, 3) (4, 4)}, we can see that (2, 2) is missing. ... more
Explanation:
Reflexive property:
A relation R on a set A is said to be reflexive if every element of A is related to itself. In other words, for every element a in A, (a, a) must be in R.
In the given relation R = {(1, 1), (1, 3), (2, 2), (3, 1) (3, 4), (4, 3) (4, 4)}, we can see that (2, 2) is missing. ... more
Which one of the following is the empty set?- a){x : x is a real number and x2 - 1 = 0}
- b){x : x is a real number and x2 + 1 = 0 }
- c){x : x is a real number and x2- 9 = 0}
- d){x : x is a real number and x2 = x + 2}
Correct answer is option 'B'. Can you explain this answer?
Which one of the following is the empty set?
a)
{x : x is a real number and x2 - 1 = 0}
b)
{x : x is a real number and x2 + 1 = 0 }
c)
{x : x is a real number and x
2
- 9 = 0}d)
{x : x is a real number and x2 = x + 2}
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Madhav Mehra answered • Aug 26, 2023 |
The empty set is a set that does not contain any elements. In other words, it is a set with no members.
To determine which of the given options represents the empty set, we need to analyze the conditions specified in each option and check if there are any real numbers that satisfy those conditions.
Option a: {x : x is a real number and x^2 - 1 = 0}
- This option repres... more
To determine which of the given options represents the empty set, we need to analyze the conditions specified in each option and check if there are any real numbers that satisfy those conditions.
Option a: {x : x is a real number and x^2 - 1 = 0}
- This option repres... more
The lines joining ihe origin to the points of intersection of 2x2 + 3xy - 4x + 1 = 0 and 3x + y - 1 = 0 are given by- a)x2+y2-5xy=0
- b)x2-y2-5xy=0
- c)x2+y2+5xy=0
- d)x2-y2+5xy=0
Correct answer is option 'B'. Can you explain this answer?
The lines joining ihe origin to the points of intersection of 2x2 + 3xy - 4x + 1 = 0 and 3x + y - 1 = 0 are given by
a)
x2+y2-5xy=0
b)
x2-y2-5xy=0
c)
x2+y2+5xy=0
d)
x2-y2+5xy=0
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Madhav Mehra answered • Aug 26, 2023 |
Given Equations:
- 2x^2 + 3xy - 4x + 1 = 0
- 3x - y - 1 = 0
Step 1: Find the points of intersection
To find the points of intersection, we need to solve the given system of equations simultaneously.
Step 2: Solve the system of equations
Using substitution method, we can solve the given system of equations as follows:
From eq... more
- 2x^2 + 3xy - 4x + 1 = 0
- 3x - y - 1 = 0
Step 1: Find the points of intersection
To find the points of intersection, we need to solve the given system of equations simultaneously.
Step 2: Solve the system of equations
Using substitution method, we can solve the given system of equations as follows:
From eq... more
Let < an > and < bn> be two sequences of real numbers such that an = bn - bn + 1 for n = 1, 2 , 3 , 4 , . . . if Sbn is convergent, then which is always true?- a)San may not be convergent
- b)San is convergent and San = b1
- c)San is convergent and San = 0
- d)San is convergent and San = a1 - b1
- e)
Correct answer is option 'B'. Can you explain this answer?
Let < an > and < bn> be two sequences of real numbers such that an = bn - bn + 1 for n = 1, 2 , 3 , 4 , . . . if Sbn is convergent, then which is always true?
a)
San may not be convergent
b)
San is convergent and San = b1
c)
San is convergent and San = 0
d)
San is convergent and San = a1 - b1
e)
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Madhav Mehra answered • Aug 26, 2023 |
Me know if there's anything else I can help you with!
For a linear transformation T : R10 → R6, the kernal has dimension 5. Then, the dimension of the range of T is- a)5
- b)6
- c)4
- d)2
Correct answer is option 'A'. Can you explain this answer?
For a linear transformation T : R10 → R6, the kernal has dimension 5. Then, the dimension of the range of T is
a)
5
b)
6
c)
4
d)
2
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Madhav Mehra answered • Aug 26, 2023 |
To fully define the linear transformation T : R10, we need to specify its action on each element of R10. In other words, for every vector x = (x1, x2, ..., x10) in R10, we need to determine the corresponding image vector T(x) under the transformation T.
One possible way to define T is by specifying its action on the standard basis vectors of R10. The standard basis vectors of R10 are gi... more
One possible way to define T is by specifying its action on the standard basis vectors of R10. The standard basis vectors of R10 are gi... more
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Madhav Mehra asked • Aug 17, 2023 |
Can I get the question papers for the IIT JAM Mathematics Exam without my admit card number mentioned on it?
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Naina Rana answered |
Introduction
The IIT JAM Mathematics Exam is a prestigious examination conducted by the Indian Institutes of Technology (IITs) for admission to various postgraduate programs in mathematics. As an aspiring candidate, it is crucial to have access to the question papers to prepare effectively for the exam. However, it is important to note that the question papers are typically relea... more
The IIT JAM Mathematics Exam is a prestigious examination conducted by the Indian Institutes of Technology (IITs) for admission to various postgraduate programs in mathematics. As an aspiring candidate, it is crucial to have access to the question papers to prepare effectively for the exam. However, it is important to note that the question papers are typically relea... more
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Madhav Mehra asked • Aug 14, 2023 |
Can I get a soft copy of my IIT JAM Mathematics admit card that I can save for future reference?
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Oishi Bajaj answered |
Steps to Get a Soft Copy of IIT JAM Mathematics Admit Card:
To obtain a soft copy of your IIT JAM Mathematics admit card that you can save for future reference, follow the step-by-step procedure outlined below:
Step 1: Visit the Official Website
Go to the official website of IIT JAM (Joint Admission Test for M.Sc.) conducted by the Indian Institutes of Tech... more
To obtain a soft copy of your IIT JAM Mathematics admit card that you can save for future reference, follow the step-by-step procedure outlined below:
Step 1: Visit the Official Website
Go to the official website of IIT JAM (Joint Admission Test for M.Sc.) conducted by the Indian Institutes of Tech... more
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Madhav Mehra asked • Aug 03, 2023 |
Are there any special considerations for differently-abled candidates in the marking scheme of the IIT JAM Mathematics Paper?
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Hrithik Choudhury answered |
Special Considerations for Differently-abled Candidates in the Marking Scheme of IIT JAM Mathematics Paper
Introduction:
The IIT JAM (Joint Admission Test for M.Sc.) is a national-level entrance exam conducted by the Indian Institutes of Technology (IITs) for admission to various postgraduate programs in science and technology. The exam aims to assess the knowledge an... more
Introduction:
The IIT JAM (Joint Admission Test for M.Sc.) is a national-level entrance exam conducted by the Indian Institutes of Technology (IITs) for admission to various postgraduate programs in science and technology. The exam aims to assess the knowledge an... more
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