|
|
Bhavya ReddyEduRev Mathematics |
|
Bhavya Reddy
EduRev Mathematics
|
Content, tests & courses saved by you for accessing later. (visible to you only)
Discussed Questions
|
Bhavya Reddy upvoted • 3 weeks ago |
For a partial differential equation, in a function φ (x, y) and two variables x, y, what is the form obtained after separation of variables is applied?- a)Φ (x, y) = X(x) + Y(y)
- b)Φ (x, y) = X(x) - Y(y)
- c)Φ (x, y) = X(x) / Y(y)
- d)Φ (x, y) = X(x)Y(y)
Correct answer is option 'D'. Can you explain this answer?
For a partial differential equation, in a function φ (x, y) and two variables x, y, what is the form obtained after separation of variables is applied?
a)
Φ (x, y) = X(x) + Y(y)
b)
Φ (x, y) = X(x) - Y(y)
c)
Φ (x, y) = X(x) / Y(y)
d)
Φ (x, y) = X(x)Y(y)
|
Veda Institute answered |
The method of separation of variables relies upon the assumption that a function of the form,
Φ (x, y) = X(x)Y(y)
will be a solution to a linear homogeneous partial differential equation in x and y. This is called a product solution and provided the boundary conditions are also linear and homogeneous this will also satisfy the boundary conditions.
Φ (x, y) = X(x)Y(y)
will be a solution to a linear homogeneous partial differential equation in x and y. This is called a product solution and provided the boundary conditions are also linear and homogeneous this will also satisfy the boundary conditions.
In the conjugate gradient method prove that if v(k)=0 for some k then Ax^((k))=b.?
|
|
Bhavya Reddy answered • 3 weeks ago |
Understanding the Conjugate Gradient Method
The conjugate gradient method is an iterative algorithm used for solving systems of linear equations, particularly when the matrix is symmetric and positive definite. A key aspect of this method is its relationship with the residual vector and how it converges to the solution.
Key Concepts
- Residual Vector (v(k)): The... more
The conjugate gradient method is an iterative algorithm used for solving systems of linear equations, particularly when the matrix is symmetric and positive definite. A key aspect of this method is its relationship with the residual vector and how it converges to the solution.
Key Concepts
- Residual Vector (v(k)): The... more
|
|
Bhavya Reddy upvoted • Feb 09, 2025 |
Which of the following group is cyclic ?- a)S3
- b)Z5
- c)D4
- d)K4
Correct answer is option 'B'. Can you explain this answer?
Which of the following group is cyclic ?
a)
S3
b)
Z5
c)
D4
d)
K4
|
|
Veda Institute answered |
Concept used:
A group is cyclic iff there exists an element of order whose order is equal to the order of the group
Calculations:
o(S3) = 3!
contains 6 elements of the Symmetric group S(3), of degree 3, written in cycles are : {(1), (12), (13), (23), (123), (321)}.
o(1) = 1
o(12), o(23) and o(13) = 2
o(123), and o(321) = 3
no element having order equal to order of group
∴ option 1 is incorrect.
o(D4) = 8
D4 = {1, r, r2, r3 , s, sr, sr2, sr3}
o(s), o(sr), o(sr2), o(sr3) = 2
o(1) = 1, o(r) = 2 , o(r2) = 3, o(r3) = 4
no element having order equal to order of the group
∴ option 3 is incorrect.
o(K4) = 4
K4 = {e, a, b, ab}
o(e) = 1 , o(a) = 2, o(b) = 2, o(ab) = 2
No element having order equal to the order of group
∴ option 4 is incorrect.
o(Z5) = 5
Z5 = {0, 1, 2, 3, 4}
o(0) = 1 o(1) = 5, o(2) = 5 , o(3) = 5 , o(4) = 5
all elements having order = order of the group
all are the generator of the group.
∴ option 2 is correct.
If y(x) = v(x) secx is the solution of y"- ( 2 tan x ) y' + 5y = 0 , - π/2 < 0="" />< π/2="" ,="" satisfying="" y(0)="0" and="" y'(0)="√6" ,="" then="" v="" (="" π/="" 6√6="" )="" is="" ...?="" π/2="" ,="" satisfying="" y(0)=... more
|
|
Bhavya Reddy answered • Nov 29, 2024 |
Understanding the Differential Equation
The given differential equation is:
y'' - (2 tan x)y' + 5y = 0
This is a second-order linear homogeneous differential equation. To solve it, we can use the method of substitution.
Substitution of y(x)
Let y(x) = v(x) sec x, where v(x) is a function we need to determine. By substituting y(x) into the differential equatio... more
The given differential equation is:
y'' - (2 tan x)y' + 5y = 0
This is a second-order linear homogeneous differential equation. To solve it, we can use the method of substitution.
Substitution of y(x)
Let y(x) = v(x) sec x, where v(x) is a function we need to determine. By substituting y(x) into the differential equatio... more
Let x, x e^(x) and 1 x e^(x) be solution of a linear second order ordinary differential eqn with constant coefficiental.if y(x) is the solution of the same eqf satisfying y(0)=3 and y'(e)=4 then y(1) is equal to?
|
|
Bhavya Reddy answered • Aug 22, 2024 |
Given Information:
- Let x, x e^(x), and 1 x e^(x) be solutions of a linear second-order ordinary differential equation with constant coefficients.
- Let y(x) be a solution of the same equation satisfying y(0) = 3 and y'(e) = 4.
Find y(1):
To find y(1), we need to determine the specific solution y(x) that satisfies the initial conditions provided.
... more
- Let x, x e^(x), and 1 x e^(x) be solutions of a linear second-order ordinary differential equation with constant coefficients.
- Let y(x) be a solution of the same equation satisfying y(0) = 3 and y'(e) = 4.
Find y(1):
To find y(1), we need to determine the specific solution y(x) that satisfies the initial conditions provided.
... more
|
|
Bhavya Reddy asked • Jun 18, 2024 |
Convert Cartesian coordinates (2, 6, 9) to Cylindrical and Spherical Coordinates.- a) (6.32, 71.565., 6.32) and (11, 71.565., 35.097)
- b) (6.32, 71.565., 9) and (6.32, 71.565., 35.097)
- c) (6.32, 71.565., 6.32) and (6.32, 35.097., 71.565)
- d) (6.32, 71.565., 9) and (11, 35.097., 71.565)
Correct answer is option 'D'. Can you explain this answer?
Convert Cartesian coordinates (2, 6, 9) to Cylindrical and Spherical Coordinates.
a)
(6.32, 71.565., 6.32) and (11, 71.565., 35.097)
b)
(6.32, 71.565., 9) and (6.32, 71.565., 35.097)
c)
(6.32, 71.565., 6.32) and (6.32, 35.097., 71.565)
d)
(6.32, 71.565., 9) and (11, 35.097., 71.565)
|
|
Veda Institute answered |
The Cylindrical coordinates is of the form ( ρ, φ, z) where ρ = 
and 
and z = z where (x, y, z) is the Cartesian coordinates. The Spherical coordinates is of the form (r, θ, φ) where 
and 
.Now, substituting the values for x as 2, y as 6 and z as 9, we get the answer as (6.32, 71.565., 9) and (11, 35.097., 71.565.).
and and z = z where (x, y, z) is the Cartesian coordinates. The Spherical coordinates is of the form (r, θ, φ) where and .Now, substituting the values for x as 2, y as 6 and z as 9, we get the answer as (6.32, 71.565., 9) and (11, 35.097., 71.565.).|
|
Bhavya Reddy asked • Jun 11, 2024 |
Choose the correct statements;- a)Every non-abelian group has a non-trivial abelian sub-group
- b)Every non-trivial abelian group has a cyclic sub-group
- c)The smallest order for a group to have a non-abelian proper sub-group is 12
- d)There exist a group containing elements a and b such that o(a) = 0(b) = 2 and o(ab) = 3
Correct answer is option 'A,B,C,D'. Can you explain this answer?
Choose the correct statements;
a)
Every non-abelian group has a non-trivial abelian sub-group
b)
Every non-trivial abelian group has a cyclic sub-group
c)
The smallest order for a group to have a non-abelian proper sub-group is 12
d)
There exist a group containing elements a and b such that o(a) = 0(b) = 2 and o(ab) = 3
|
|
Veda Institute answered |
For option (a):
Let G be a nonabelian group.
Then G is not cyclic and let x∈G such that x≠e.
Also let H = (x), then H is cyclic subgroup of G.
⇒ option (a) is correct.
For option (b)
Let G be a non-trival abelian group.
If G is cyclic, then nothing to prove.
If G is non cyclic then g≠ (x) ∀∈G. Let a∈G and consider H = ��. then H is a cyclic subgroup of G.
For option (c)
Let the smallest order for a group to have a non abelian proper subgroup is n.
Clearly n≠1, 2, 3, 4, 5 because if o(G) ≤5 then G is abelian.
If o(G) = 6 then every proper subgroup of G is cyclic. So, o(G) ≠ 6.
If o(G) = 7, 11 then G is cyclic. So. o(G) ≠ 7.11.
If o(G) =8, 9, 10, then every proper subgroup of G is cyclic.
If o(G) = 12 then let G=S3 ×ℤ2
⇒ G has a proper subgroup which is non abelian.
For option (d)
Let G=S3
Let a = (1 2) and b = (2 3)
Clearly o(a) = o(b) =2
But o(ab) = 3
⇒ Statement is true
Consider the system of linear equation
x + y + z = 3, x - y - z = 4, x - 5 y + kz = 6
Then, the value of k for which this system has an infinite number of solution is- a)k = - 5
- b)k = 0
- c)k = 1
- d)k = 3
Correct answer is option 'A'. Can you explain this answer?
Consider the system of linear equation
x + y + z = 3, x - y - z = 4, x - 5 y + kz = 6
Then, the value of k for which this system has an infinite number of solution is
x + y + z = 3, x - y - z = 4, x - 5 y + kz = 6
Then, the value of k for which this system has an infinite number of solution is
a)
k = - 5
b)
k = 0
c)
k = 1
d)
k = 3
|
|
Bhavya Reddy answered • Feb 13, 2024 |
To find the value of k for which the system of linear equations has an infinite number of solutions, we need to examine the coefficient matrix and the augmented matrix of the system.
1. Coefficient Matrix:
The coefficient matrix is obtained by extracting the coefficients of x, y, and z from the system of equations. In this case, the coefficient matrix is:
|1 1 1|
... more
1. Coefficient Matrix:
The coefficient matrix is obtained by extracting the coefficients of x, y, and z from the system of equations. In this case, the coefficient matrix is:
|1 1 1|
... more
The coefficients of 9th, 10th and 11th terms in the expansion (1 + x)n are in A. P., then n =- a)7
- b)7 or 14
- c)14
- d)21
Correct answer is option 'C'. Can you explain this answer?
The coefficients of 9th, 10th and 11th terms in the expansion (1 + x)n are in A. P., then n =
a)
7
b)
7 or 14
c)
14
d)
21
|
|
Bhavya Reddy answered • Feb 13, 2024 |
Explanation:
To find the coefficients of the 9th, 10th, and 11th terms in the expansion of (1 + x)^n, we can use the binomial theorem. The binomial theorem states that for any positive integer n:
(1 + x)^n = C(n,0) + C(n,1)x + C(n,2)x^2 + ... + C(n,n)x^n
Where C(n,r) represents the binomial coefficient, which is given by the formula:
C(n,r) = n! /... more
To find the coefficients of the 9th, 10th, and 11th terms in the expansion of (1 + x)^n, we can use the binomial theorem. The binomial theorem states that for any positive integer n:
(1 + x)^n = C(n,0) + C(n,1)x + C(n,2)x^2 + ... + C(n,n)x^n
Where C(n,r) represents the binomial coefficient, which is given by the formula:
C(n,r) = n! /... more
|
|
Bhavya Reddy asked • Feb 08, 2024 |
A set of linear equations is given in the form Ax = b, where A is a 2 × 4 matrix with real number entries and b ≠ 0. Will it be possible to solve for x and obtain a unique solution by multiplying both left and right sides of the equation by AT (the super script T denotes the transpose) and inverting the matrix AT A? - a)Yes, it is always possible to get a unique solution for any 2 × 4 matrix A.
- b)No, it is not possible to get a unique solution for any 2 × 4 matrix A.
- c)Yes, can obtain a unique solution provided the matrix AT A is well conditioned
- d)Yes, can obtain a unique solution provided the matrix A is well conditioned.
Correct answer is option 'B'. Can you explain this answer?
A set of linear equations is given in the form Ax = b, where A is a 2 × 4 matrix with real number entries and b ≠ 0. Will it be possible to solve for x and obtain a unique solution by multiplying both left and right sides of the equation by AT (the super script T denotes the transpose) and inverting the matrix AT A?
a)
Yes, it is always possible to get a unique solution for any 2 × 4 matrix A.
b)
No, it is not possible to get a unique solution for any 2 × 4 matrix A.
c)
Yes, can obtain a unique solution provided the matrix AT A is well conditioned
d)
Yes, can obtain a unique solution provided the matrix A is well conditioned.
|
Veer Yadav answered |
Understanding the Problem
In the equation Ax = b, where A is a 2 × 4 matrix and b is a non-zero vector, the goal is to determine if a unique solution can be found by manipulating the equation.
Matrix Dimensions and Solutions
- A 2 × 4 matrix A has more columns than rows.
- This implies that the system has more variables than equations.
Implic... more
- Because there are 4 variables (columns) and only 2 equations (rows), the system is underdetermined.
- An underdetermined system typically has infinitely many solutions or no solution.
Multiplying by the Transpose
- When we multiply both sides of the equation by A^T, we get A^T * A * x = A^T * b.
- A^T * A is a 4 × 4 matrix. However, since A has more columns than rows, A^T * A is not guaranteed to be invertible.
Conditions for Unique Solutions
- For A^T * A to be invertible, matrix A must have full row rank (which is not possible here as it cannot have rank 2 with 4 columns).
- Thus, A^T * A will be a singular matrix in most cases.
Conclusion
- Since the system is underdetermined, and A^T * A is not guaranteed to be invertible, it is not possible to obtain a unique solution for any 2 × 4 matrix A.
- Therefore, option B is the correct answer: No, it is not possible to get a unique solution for any 2 × 4 matrix A.
In the equation Ax = b, where A is a 2 × 4 matrix and b is a non-zero vector, the goal is to determine if a unique solution can be found by manipulating the equation.
Matrix Dimensions and Solutions
- A 2 × 4 matrix A has more columns than rows.
- This implies that the system has more variables than equations.
Implic... more
- Because there are 4 variables (columns) and only 2 equations (rows), the system is underdetermined.
- An underdetermined system typically has infinitely many solutions or no solution.
Multiplying by the Transpose
- When we multiply both sides of the equation by A^T, we get A^T * A * x = A^T * b.
- A^T * A is a 4 × 4 matrix. However, since A has more columns than rows, A^T * A is not guaranteed to be invertible.
Conditions for Unique Solutions
- For A^T * A to be invertible, matrix A must have full row rank (which is not possible here as it cannot have rank 2 with 4 columns).
- Thus, A^T * A will be a singular matrix in most cases.
Conclusion
- Since the system is underdetermined, and A^T * A is not guaranteed to be invertible, it is not possible to obtain a unique solution for any 2 × 4 matrix A.
- Therefore, option B is the correct answer: No, it is not possible to get a unique solution for any 2 × 4 matrix A.
Order of the element 14+8 in the factor group Z14/8 is ?
|
|
Bhavya Reddy answered • Jan 10, 2024 |
Order of the element 14+8 in the factor group Z14/8 is 2
Explanation:
The factor group or quotient group Z14/8 is the group obtained by dividing the group Z14 (integers modulo 14 under addition) by the subgroup generated by the element 8.
To find the order of the element 14+8 in Z14/8, we need to find the smallest positive integer n such that (14+8)^n ≡ 0 (... more
Explanation:
The factor group or quotient group Z14/8 is the group obtained by dividing the group Z14 (integers modulo 14 under addition) by the subgroup generated by the element 8.
To find the order of the element 14+8 in Z14/8, we need to find the smallest positive integer n such that (14+8)^n ≡ 0 (... more
If the volume of the solid in R3 bounded by the surfaces x=-1,x=1,y=-1,y=1,z=2,and y2+z2=2?
|
|
Bhavya Reddy answered • Dec 15, 2023 |
Volume of the Solid Bounded by the Given Surfaces
To find the volume of the solid bounded by the surfaces x = -1, x = 1, y = -1, y = 1, z = 2, and y^2 + z^2 = 2 in R3, we will use the method of triple integration. This involves integrating the volume element over the given region of interest.
Region of Interest
The region of interest is the area enclo... more
To find the volume of the solid bounded by the surfaces x = -1, x = 1, y = -1, y = 1, z = 2, and y^2 + z^2 = 2 in R3, we will use the method of triple integration. This involves integrating the volume element over the given region of interest.
Region of Interest
The region of interest is the area enclo... more
|
|
Bhavya Reddy asked • Sep 30, 2023 |
A lot has 10% defective items. Ten items are chosen randomly from this lot. The probability that exactly 2 of the chosen items are defective is - a)0.0036
- b)0.1937
- c)0.2234
- d)0.3874
Correct answer is option 'B'. Can you explain this answer?
A lot has 10% defective items. Ten items are chosen randomly from this lot. The probability that exactly 2 of the chosen items are defective is
a)
0.0036
b)
0.1937
c)
0.2234
d)
0.3874
|
|
Veda Institute answered |
Let A be the event that items are defective and B be the event that items are non-defective.
∴ P(A) = 0.1 and P(B) = 0.9
∴ Probability that exactly two of those items are defective
∴ P(A) = 0.1 and P(B) = 0.9
∴ Probability that exactly two of those items are defective
Which of the following statements is correct?
- a)(A + B)T = AT + BT
- b)(AB)T = ATB
- c)(KA)T = KTAT
- d)none of the above
Correct answer is option 'A'. Can you explain this answer?
Which of the following statements is correct?
a)
(A + B)T = AT + BT
b)
(AB)T = ATB
c)
(KA)T = KTAT
d)
none of the above
|
|
Bhavya Reddy answered • Sep 15, 2023 |
Statement: (A B)T = AT BT
To determine whether this statement is correct or not, let's break it down and analyze each part separately.
Part 1: (A B)T
- (A B) represents the product of two matrices A and B.
- The order of the product matrix (A B) is determined by the number of rows of A and the number of columns of B.
- The transpose operation (T) ... more
To determine whether this statement is correct or not, let's break it down and analyze each part separately.
Part 1: (A B)T
- (A B) represents the product of two matrices A and B.
- The order of the product matrix (A B) is determined by the number of rows of A and the number of columns of B.
- The transpose operation (T) ... more
Square matrix A of order n over R has rank n. Which one of the following statement is not correct?- a)AT has rank n
- b)A has n linearly independent columns
- c)A is non — singular
- d)A is singular
Correct answer is option 'D'. Can you explain this answer?
Square matrix A of order n over R has rank n. Which one of the following statement is not correct?
a)
AT has rank n
b)
A has n linearly independent columns
c)
A is non — singular
d)
A is singular
|
|
Bhavya Reddy answered • Sep 15, 2023 |
The correct answer is:
c) A is non-singular
If the rank of a square matrix A of order n is equal to n, it means that A is full rank and has n linearly independent rows (or columns). This implies that A is invertible or non-singular. Therefore, statement c) is not correct.
c) A is non-singular
If the rank of a square matrix A of order n is equal to n, it means that A is full rank and has n linearly independent rows (or columns). This implies that A is invertible or non-singular. Therefore, statement c) is not correct.
The set of negative integers have the least upper bound
- a)1
- b)-1
- c)2
- d)0
Correct answer is option 'D'. Can you explain this answer?
The set of negative integers have the least upper bound
a)
1
b)
-1
c)
2
d)
0
|
|
Bhavya Reddy answered • Sep 15, 2023 |
The least upper bound of a set:
The least upper bound (also known as the supremum) of a set is the smallest number that is greater than or equal to all the numbers in the set. In other words, it is the smallest upper bound of the set.
The set of negative integers:
The set of negative integers consists of all numbers less than zero and can be represented as {-1, -... more
The least upper bound (also known as the supremum) of a set is the smallest number that is greater than or equal to all the numbers in the set. In other words, it is the smallest upper bound of the set.
The set of negative integers:
The set of negative integers consists of all numbers less than zero and can be represented as {-1, -... more
|
|
Bhavya Reddy asked • Aug 17, 2023 |
Can I get access to the question papers for the IIT JAM Mathematics Exam without my exam center code mentioned on it?
|
Naina Rana answered |
Accessing IIT JAM Mathematics Exam Question Papers without Exam Center Code
To access the question papers for the IIT JAM Mathematics Exam without the exam center code mentioned on it, you can follow the steps below:
Step 1: Visit the Official Website
- Go to the official website of IIT JAM (Joint Admission Test for M.Sc.) which is conducted by the Indian I... more
To access the question papers for the IIT JAM Mathematics Exam without the exam center code mentioned on it, you can follow the steps below:
Step 1: Visit the Official Website
- Go to the official website of IIT JAM (Joint Admission Test for M.Sc.) which is conducted by the Indian I... more
|
|
Bhavya Reddy asked • Aug 14, 2023 |
Is the admit card for the IIT JAM Mathematics based on the final registration or preliminary registration?
|
Oishi Bajaj answered |
Admit Card for IIT JAM Mathematics
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 admit card is an essential document that candidates must possess to appear for the examination. It ser... 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 admit card is an essential document that candidates must possess to appear for the examination. It ser... more
|
|
Bhavya Reddy asked • Aug 07, 2023 |
Is there any difference in the cutoff marks for different categories in the IIT JAM Mathematics Exam?
|
Radha Mehta answered |
Introduction:
The IIT JAM (Joint Admission Test for Masters) is a national level entrance exam conducted by the Indian Institutes of Technology (IITs) for admission to various postgraduate courses. The IIT JAM Mathematics exam is one of the popular exams among aspiring mathematicians. The cutoff marks for different categories play a crucial role in determining the eligibility of candid... more
The IIT JAM (Joint Admission Test for Masters) is a national level entrance exam conducted by the Indian Institutes of Technology (IITs) for admission to various postgraduate courses. The IIT JAM Mathematics exam is one of the popular exams among aspiring mathematicians. The cutoff marks for different categories play a crucial role in determining the eligibility of candid... more
|
|
Bhavya Reddy asked • Aug 03, 2023 |
How many marks are awarded for correct answers in the IIT JAM Mathematics Exam?
|
Hrithik Choudhury answered |
Marking Scheme for IIT JAM Mathematics Exam
The IIT JAM (Joint Admission Test for M.Sc.) Mathematics Exam is conducted by the Indian Institute of Technology (IIT) for admission into various postgraduate programs in Mathematics. The marking scheme for the IIT JAM Mathematics Exam is as follows:
Total Marks: The total marks for the IIT JAM Mathematics Exam is 100.... more
The IIT JAM (Joint Admission Test for M.Sc.) Mathematics Exam is conducted by the Indian Institute of Technology (IIT) for admission into various postgraduate programs in Mathematics. The marking scheme for the IIT JAM Mathematics Exam is as follows:
Total Marks: The total marks for the IIT JAM Mathematics Exam is 100.... more
|
|
Bhavya Reddy asked • Aug 02, 2023 |
Can I get admission to integrated Ph.D. programs through the IIT JAM Mathematics Exam?
|
|
Nakul Bajaj answered |
Introduction:
Yes, you can get admission to integrated Ph.D. programs through the IIT JAM Mathematics Exam.
What is IIT JAM Mathematics Exam?
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, including integrated Ph.D. courses.
... more
Yes, you can get admission to integrated Ph.D. programs through the IIT JAM Mathematics Exam.
What is IIT JAM Mathematics Exam?
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, including integrated Ph.D. courses.
Fetching relevant content for you
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up
within 7 days!
within 7 days!
Takes less than 10 seconds to signup