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Aisha GuptaEduRev Mathematics |
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Aisha Gupta
EduRev Mathematics
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Discussed Questions
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Aisha Gupta 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)
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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.
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Aisha Gupta 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
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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.
In the matrix equation PX = q, which of the following is necessary condition for the existence of atleast one solution for the unknown vector- a)Augmented matrix [P q] must have the same rank as matrix P
- b)Vector q must have only non — zero elemetns
- c)Matrix P must be singular
- d)Matrix P must be square
Correct answer is option 'A'. Can you explain this answer?
In the matrix equation PX = q, which of the following is necessary condition for the existence of atleast one solution for the unknown vector
a)
Augmented matrix [P q] must have the same rank as matrix P
b)
Vector q must have only non — zero elemetns
c)
Matrix P must be singular
d)
Matrix P must be square
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Aisha Gupta answered • Jan 19, 2025 |
Understanding the Matrix Equation PX = q
In the context of the matrix equation PX = q, where P is a matrix, X is the unknown vector, and q is the result vector, it is crucial to determine conditions for the existence of at least one solution.
Necessary Condition for Solutions
- The key condition for this equation to have at least one solution is that the augmented mat... more
In the context of the matrix equation PX = q, where P is a matrix, X is the unknown vector, and q is the result vector, it is crucial to determine conditions for the existence of at least one solution.
Necessary Condition for Solutions
- The key condition for this equation to have at least one solution is that the augmented mat... more
The value of 1 + 1.1! + 2. 2! + 3.3! + …… + n. n! is - a)(n + 1)! + 1
- b)(n – 1)! + 1
- c)(n + 1)! – 1
- d)(n + 1)!
Correct answer is option 'D'. Can you explain this answer?
The value of 1 + 1.1! + 2. 2! + 3.3! + …… + n. n! is
a)
(n + 1)! + 1
b)
(n – 1)! + 1
c)
(n + 1)! – 1
d)
(n + 1)!
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Aisha Gupta answered • Oct 23, 2024 |
Understanding the Expression
The expression we need to evaluate is:
1 + 1.1! + 2.2! + 3.3! + ... + n.n!
This series can be simplified using properties of factorials.
Breaking Down the Terms
- Each term in the series is of the form k.k! which can be rewritten as:
- k.k! = k!(k) = (k + 1)! - k!
This transformation is crucial for simplifying the serie... more
The expression we need to evaluate is:
1 + 1.1! + 2.2! + 3.3! + ... + n.n!
This series can be simplified using properties of factorials.
Breaking Down the Terms
- Each term in the series is of the form k.k! which can be rewritten as:
- k.k! = k!(k) = (k + 1)! - k!
This transformation is crucial for simplifying the serie... more
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Aisha Gupta asked • Jun 15, 2024 |
Let h be a continuous and differentiable function defined on [0, 2π]. Some function values of h and h’ are given by the chart below: 
If p(x) = sin2(h(2x)),then p’ (π / 2) is not equal to ____- a)3
- b)-2
- c)-1
- d)0
Correct answer is option 'A,C,D'. Can you explain this answer?
Let h be a continuous and differentiable function defined on [0, 2π]. Some function values of h and h’ are given by the chart below:
If p(x) = sin2(h(2x)),then p’ (π / 2) is not equal to ____
a)
3
b)
-2
c)
-1
d)
0
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Veda Institute answered |
The Chain Rule will have to be applied three times in this.
p’(x) = 2(sin (h(2x))) · cos (h(2x)) · h’(2x) · 2
Because 2x = 2(π/2) = p, you can write:
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Aisha Gupta asked • Jun 08, 2024 |
If A = 
, the eigen values of this matrix are -1 and 7, then the value of ab is (Answer should be integer) ________.Correct answer is '15'. Can you explain this answer?
If A = , the eigen values of this matrix are -1 and 7, then the value of ab is (Answer should be integer) ________.
, the eigen values of this matrix are -1 and 7, then the value of ab is (Answer should be integer) ________.|
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Veda Institute answered |
Given A = 
We know that trace of A= sum ofeigen values
⇒ a + 1 = -1 + 7
⇒ a = 5
Also det (A) = a - 4b = product of eigen values
⇒ a - 4b = -7 ⇒ -5 - 4b = -7 i.e.,b = 3
⇒ ab = 15
State and prove the fundamental theorem of calculus?
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Aisha Gupta answered • Apr 10, 2024 |
The Fundamental Theorem of Calculus
The fundamental theorem of calculus states that if a function \(f(x)\) is continuous on the closed interval \([a,b]\) and \(F(x)\) is an antiderivative of \(f(x)\) on \([a,b]\), then
\[ \int_{a}^{b} f(x) \,dx = F(b) - F(a) \]
This means that the definite integral of a function over an interval can be evaluated by finding an antiderivative of the... more
The fundamental theorem of calculus states that if a function \(f(x)\) is continuous on the closed interval \([a,b]\) and \(F(x)\) is an antiderivative of \(f(x)\) on \([a,b]\), then
\[ \int_{a}^{b} f(x) \,dx = F(b) - F(a) \]
This means that the definite integral of a function over an interval can be evaluated by finding an antiderivative of the... more
A bin of personal computer disks contains a large supply of disks from 4 different manufactures. In how many ways someone choose 6 disks from the bin?- a)82
- b)84
- c)24
- d)none
Correct answer is option 'B'. Can you explain this answer?
A bin of personal computer disks contains a large supply of disks from 4 different manufactures. In how many ways someone choose 6 disks from the bin?
a)
82
b)
84
c)
24
d)
none
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Aisha Gupta answered • Apr 10, 2024 |
Explanation:
Total number of ways to choose 6 disks:
- To find the total number of ways someone can choose 6 disks from the bin, we need to consider the disks from 4 different manufacturers.
- Since the disks are from different manufacturers, we can consider each manufacturer separately and then sum up the total number of ways.
Number of ways to cho... more
- Let's consider each manufacturer one by one:
- Manufacturer 1: Number of ways to choose 6 disks = $\binom{a}{6}$
- Manufacturer 2: Number of ways to choose 6 disks = $\binom{b}{6}$
- Manufacturer 3: Number of ways to choose 6 disks = $\binom{c}{6}$
- Manufacturer 4: Number of ways to choose 6 disks = $\binom{d}{6}$
Total number of ways to choose 6 disks:
- Total number of ways = $\binom{a}{6} + \binom{b}{6} + \binom{c}{6} + \binom{d}{6}$
- Since the question does not specify the values of a, b, c, and d, we cannot calculate the exact number of ways.
- However, we know that the sum of the number of ways to choose 6 disks from each manufacturer will give us the total number of ways.
Therefore, the correct answer is option B) 84.
Total number of ways to choose 6 disks:
- To find the total number of ways someone can choose 6 disks from the bin, we need to consider the disks from 4 different manufacturers.
- Since the disks are from different manufacturers, we can consider each manufacturer separately and then sum up the total number of ways.
Number of ways to cho... more
- Let's consider each manufacturer one by one:
- Manufacturer 1: Number of ways to choose 6 disks = $\binom{a}{6}$
- Manufacturer 2: Number of ways to choose 6 disks = $\binom{b}{6}$
- Manufacturer 3: Number of ways to choose 6 disks = $\binom{c}{6}$
- Manufacturer 4: Number of ways to choose 6 disks = $\binom{d}{6}$
Total number of ways to choose 6 disks:
- Total number of ways = $\binom{a}{6} + \binom{b}{6} + \binom{c}{6} + \binom{d}{6}$
- Since the question does not specify the values of a, b, c, and d, we cannot calculate the exact number of ways.
- However, we know that the sum of the number of ways to choose 6 disks from each manufacturer will give us the total number of ways.
Therefore, the correct answer is option B) 84.
A box contains 5 block balls and 3 red balls. A total of three balls are picked from the box one after another, without replacing them back. The probability of getting two black balls and one red ball is- a)3/8
- b)2/15
- c)15/28
- d)1/2
Correct answer is option 'C'. Can you explain this answer?
A box contains 5 block balls and 3 red balls. A total of three balls are picked from the box one after another, without replacing them back. The probability of getting two black balls and one red ball is
a)
3/8
b)
2/15
c)
15/28
d)
1/2
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Aisha Gupta answered • Jan 31, 2024 |
To find the probability of getting two black balls and one red ball, we need to consider the different ways in which this can occur and calculate the probability for each case.
Let's break down the problem into steps:
Step 1: Total number of balls
- The box contains 5 black balls and 3 red balls.
- So, the total number of balls in the box is 8.
Step 2: Pr... more
Let's break down the problem into steps:
Step 1: Total number of balls
- The box contains 5 black balls and 3 red balls.
- So, the total number of balls in the box is 8.
Step 2: Pr... more
The value of ‘C’ in Rolle’s theorem, where -π/2 < C < π/2 and f(x) = cos x is equal to- a)π/4
- b)π/3
- c)π
- d)0
Correct answer is option 'D'. Can you explain this answer?
The value of ‘C’ in Rolle’s theorem, where -π/2 < C < π/2 and f(x) = cos x is equal to
a)
π/4
b)
π/3
c)
π
d)
0
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Aisha Gupta answered • Dec 30, 2023 |
An item is subjective and can vary depending on factors such as its condition, rarity, demand, and market trends. Therefore, the value of an item cannot be determined without specific context.
Solving by variation of parameter for the equation y" + y = sec x, the value of Wronskion is- a)1
- b)2
- c)3
- d)4
Correct answer is option 'A'. Can you explain this answer?
Solving by variation of parameter for the equation y" + y = sec x, the value of Wronskion is
a)
1
b)
2
c)
3
d)
4
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Aisha Gupta answered • Dec 03, 2023 |
To solve the equation y'' + y = cos(x), we can use the method of variation of parameters.
First, we find the complementary solution by solving the homogeneous equation y'' + y = 0. The characteristic equation is r^2 + 1 = 0, which has the roots r = ±i. Therefore, the complementary solution is y_c(x) = c1*cos(x) + c2*sin(x), where c1 and c2 are arbitrary constants.
Next, we n... more
First, we find the complementary solution by solving the homogeneous equation y'' + y = 0. The characteristic equation is r^2 + 1 = 0, which has the roots r = ±i. Therefore, the complementary solution is y_c(x) = c1*cos(x) + c2*sin(x), where c1 and c2 are arbitrary constants.
Next, we n... more
What is the g.l.b and l.u.b of x^2 x^2 9?
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Aisha Gupta answered • Nov 14, 2023 |
Definition of g.l.b and l.u.b:
In mathematics, g.l.b (greatest lower bound) and l.u.b (least upper bound) are concepts used in the theory of sets, particularly in the context of ordered sets. The g.l.b is the greatest element of a set that is less than or equal to all other elements in the set, while the l.u.b is the smallest element that is greater than or equal to all other elements ... more
In mathematics, g.l.b (greatest lower bound) and l.u.b (least upper bound) are concepts used in the theory of sets, particularly in the context of ordered sets. The g.l.b is the greatest element of a set that is less than or equal to all other elements in the set, while the l.u.b is the smallest element that is greater than or equal to all other elements ... more
If the sequence is increasing, then it ____- a)converges to its supremum.
- b)diverges.
- c)may converges to its supremum.
- d)is bounded
Correct answer is option 'A'. Can you explain this answer?
If the sequence is increasing, then it ____
a)
converges to its supremum.
b)
diverges.
c)
may converges to its supremum.
d)
is bounded
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Aisha Gupta answered • Oct 15, 2023 |
Explanation:
An increasing sequence is a sequence of numbers where each term is greater than or equal to the previous term. In other words, if we have a sequence (a1, a2, a3, ...) such that ai ≤ ai+1 for all i, then the sequence is increasing.
Convergence:
Convergence refers to the behavior of a sequence as the number of terms increases. If a sequence converges, ... more
An increasing sequence is a sequence of numbers where each term is greater than or equal to the previous term. In other words, if we have a sequence (a1, a2, a3, ...) such that ai ≤ ai+1 for all i, then the sequence is increasing.
Convergence:
Convergence refers to the behavior of a sequence as the number of terms increases. If a sequence converges, ... more
Let S = T : R3 —> R3 ; T is a linear transformation with T(1,0,1) = (1, 2, 3), T(1,2, 3) = (1,0,1)}. Then S is- a)A singleton set
- b)A finite set containing more than one element
- c)A countable infinite set
- d)An uncountable set
Correct answer is option 'D'. Can you explain this answer?
Let S = T : R3 —> R3 ; T is a linear transformation with T(1,0,1) = (1, 2, 3), T(1,2, 3) = (1,0,1)}. Then S is
a)
A singleton set
b)
A finite set containing more than one element
c)
A countable infinite set
d)
An uncountable set
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Aisha Gupta answered • Oct 15, 2023 |
In this notation, S represents a subspace and T represents a transformation. The subspace S is defined as the range of the transformation T, which means that S is the set of all possible outputs of T.
In other words, S is the set of all vectors in R3 that can be obtained by applying the transformation T to some vector in R3.
For example, if T is a linear transformation that r... more
In other words, S is the set of all vectors in R3 that can be obtained by applying the transformation T to some vector in R3.
For example, if T is a linear transformation that r... more
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Aisha Gupta asked • Aug 17, 2023 |
How many marks are deducted for incorrect answers in the MCQs of the IIT JAM Mathematics Paper?
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Naina Rana answered |
Marking Scheme for MCQs in IIT JAM Mathematics Paper
The Indian Institute of Technology Joint Admission Test for M.Sc. (IIT JAM) is a national level entrance exam conducted for admission to various postgraduate programs in the field of science, including Mathematics. The Mathematics paper of the IIT JAM exam consists of multiple-choice questions (MCQs) that test the candidates' k... more
The Indian Institute of Technology Joint Admission Test for M.Sc. (IIT JAM) is a national level entrance exam conducted for admission to various postgraduate programs in the field of science, including Mathematics. The Mathematics paper of the IIT JAM exam consists of multiple-choice questions (MCQs) that test the candidates' k... more
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Aisha Gupta asked • Aug 14, 2023 |
Can I get access to the final answer key for the IIT JAM Mathematics Exam before the result declaration?
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Oishi Bajaj answered |
Access to the final answer key for the IIT JAM Mathematics Exam
To maintain the integrity and fairness of the examination process, the final answer key for the IIT JAM Mathematics Exam is typically not released before the result declaration. The final answer key is prepared by expert committees appointed by the conducting authority, and it undergoes a thorough scrutiny process to... more
To maintain the integrity and fairness of the examination process, the final answer key for the IIT JAM Mathematics Exam is typically not released before the result declaration. The final answer key is prepared by expert committees appointed by the conducting authority, and it undergoes a thorough scrutiny process to... more
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Aisha Gupta asked • Aug 07, 2023 |
What are the best books for improving my problem-solving skills in mathematical statistics and probability for the IIT JAM Mathematics Paper?
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Radha Mehta answered |
Recommended Books for Improving Problem-Solving Skills in Mathematical Statistics and Probability for IIT JAM Mathematics Paper
1. Mathematical Statistics
- Mathematical Statistics by John E. Freund and Benjamin M. Perles: This book covers various topics in mathematical statistics, including probability theory, distribution theory, estimation theory, hypothesis testing, and more. It provides a comprehensive understanding of the subject and includes numerous examples and exercises to enhance problem-solving skills.
- Introduction to Mathematical Statistics by Robert V. Hogg, Joseph W. McKean, and Allen T. Craig: This book is widely used for introductory courses in mathematical statistics. It covers all the essential topics and concepts necessary for IIT JAM Mathematics Paper. It includes numerous solved examples and exercises to help students develop a strong problem-solving ability.
- An Introduction to Probability Theory and Mathematical Statistics by V.K. Rohatgi and A.K. Md. Ehsanes Saleh: This book provides a rigorous introduction to probability theory and mathematical statistics. It covers a wide range of topics and includes numerous exercises with solutions to enhance problem-solving skills.
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Aisha Gupta asked • Aug 03, 2023 |
Are there any specific rules regarding rough work during the IIT JAM Mathematics Paper?
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Hrithik Choudhury answered |
Rules for Rough Work during the IIT JAM Mathematics Paper
During the IIT JAM Mathematics Paper, there are certain rules and guidelines that candidates must follow regarding rough work. These rules help maintain fairness, clarity, and integrity during the examination. It is important for candidates to be aware of these rules and adhere to them to avoid any penalties or inconvenience. Below are the specific rules regarding rough work during the IIT JAM Mathematics Paper:
... more|
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Aisha Gupta asked • Aug 02, 2023 |
What is the minimum qualifying marks required in the IIT JAM Mathematics Exam?
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Nakul Bajaj answered |
The Minimum Qualifying Marks in IIT JAM Mathematics Exam
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, including Mathematics. To be eligible for admission, candidates must meet the minimum qualifying marks set by the organizing institute. Let's ... more
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, including Mathematics. To be eligible for admission, candidates must meet the minimum qualifying marks set by the organizing institute. Let's ... more
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