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Subodh SahooI am a student of sambalpur university ,odisha. |
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Subodh Sahoo
EduRev UPSC
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Discussed Questions
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Aakash Singh upvoted • 8 hours ago |
Let V be the vector space of polynomial functions of degree three or less. Let the ordered basis for V consisting of the functions of the four functions xj : j = 0, 1, 2, 3 and let D be the differentiation operator. Then the matrix of D in the above ordered basis is- a)
- b)
- c)
- d)
Correct answer is option 'A'. Can you explain this answer?
Let V be the vector space of polynomial functions of degree three or less. Let the ordered basis for V consisting of the functions of the four functions xj : j = 0, 1, 2, 3 and let D be the differentiation operator. Then the matrix of D in the above ordered basis is
a)
b)
c)
d)
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Veda Institute answered |
Let V be the vector space of polynomial functions of degree three or less. Let the ordered basis for V consisting of the functions
xj : j = 0 ,1 ,2 , 3
and let D be the differentiation operator. We need to find the matrix of differentiation operator D in the basis xj, j = 0,1, 2, 3, that is {1, x, x2, x3}.
Therefore, D(1) = d/dx(1) = 0
= 0.1 + 0.x + 0.x2 + 0.x3
D(x) = d/dx (x) = 1 = 1.1 + 0 . x + 0 .x2 + 0.x3 ax
D(x2) =d/dx(x2) = 2x = 0.1 + 2.x + 0.x2 + 0.x3 ax
D(x3) = d/dx (x3) = 3x2 = 0.1 + 0.x + 3.x2 + 0.x4
Thus, the matrix of differentiation operator
is
xj : j = 0 ,1 ,2 , 3
and let D be the differentiation operator. We need to find the matrix of differentiation operator D in the basis xj, j = 0,1, 2, 3, that is {1, x, x2, x3}.
Therefore, D(1) = d/dx(1) = 0
= 0.1 + 0.x + 0.x2 + 0.x3
D(x) = d/dx (x) = 1 = 1.1 + 0 . x + 0 .x2 + 0.x3 ax
D(x2) =d/dx(x2) = 2x = 0.1 + 2.x + 0.x2 + 0.x3 ax
D(x3) = d/dx (x3) = 3x2 = 0.1 + 0.x + 3.x2 + 0.x4
Thus, the matrix of differentiation operator
is
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Aakash Singh upvoted • 3 weeks ago |
Let V be a 3 dimensional vector space with A and B its subspaces of dimensions 2 and 1 , respectively. If 
, then- a)V = A -B
- b)V = A +B
- c)dim(A + B) ≤ 3
- d)dim( A ∩ B) ≠ 0
Correct answer is option 'B'. Can you explain this answer?
Let V be a 3 dimensional vector space with A and B its subspaces of dimensions 2 and 1 , respectively. If , then
, thena)
V = A -B
b)
V = A +B
c)
dim(A + B) ≤ 3
d)
dim( A ∩ B) ≠ 0
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Veda Institute answered |
We know
dim A + dim B = dim (A + B) + dim (A ∩ B ) .............. (1)
Here A ∩) B = { 0 } => dim (A ∩ B ) = 0
then by equation (1), dim (A + B ) = 3 => option (C) and (D) are incorrect.
Now (A + B) be a subspace of V and has same dimension as V.
=> V = A + B
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Aakash Singh upvoted • Feb 23, 2025 |
The intrinsic equation of the curve p = r sin α is given by: - a)
- b)
- c)
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
The intrinsic equation of the curve p = r sin α is given by:
a)
b)
c)
d)
None of these
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Veda Institute answered |
Given curve is p = r sin α ....(i)
Hence
or,
Hence
or,
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Aakash Singh upvoted • Feb 09, 2025 |
Find the work done in moving a particle once around a circle C in the xy plane, if the circle has a centre (0, 0) and radius 1 and if the force field 
is given by
- a)0
- b)π
- c)2π
- d)4π
Correct answer is option 'C'. Can you explain this answer?
Find the work done in moving a particle once around a circle C in the xy plane, if the circle has a centre (0, 0) and radius 1 and if the force field is given by
is given bya)
0
b)
π
c)
2π
d)
4π
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Veda Institute answered |
Equation of the circle is x2 + y2=1
Let x = cosθ, y = sinθ
then dx = -sinθdθ, dy = cosθdθ
and z = 0 ⇒ dz = 0
So total work done is
Let x = cosθ, y = sinθ
then dx = -sinθdθ, dy = cosθdθ
and z = 0 ⇒ dz = 0
So total work done is
at the point (1,-2,-1) is
If f and g be continuous real valued functions on the metric space M. Let A be the set of all x ∈ M s.t. f(x) < g(x)- a) A is closed
- b) A is open
- c) Neither open nor closed
- d) None of these
Correct answer is option 'B'. Can you explain this answer?
If f and g be continuous real valued functions on the metric space M. Let A be the set of all x ∈ M s.t. f(x) < g(x)
a)
A is closed
b)
A is open
c)
Neither open nor closed
d)
None of these
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Aakash Singh answered • Feb 01, 2025 |
Understanding the Set A
The set A is defined as all points x in the metric space M where f(x) < g(x).="" to="" analyze="" the="" properties="" of="" this="" set,="" we="" consider="" the="" functions="" f="" and="" />
Continuity of Functions
- Since f and g are continuous functions, the difference h(x) = g(x) - f(x) is also continuous.
- The continuity of h means ... more
The set A is defined as all points x in the metric space M where f(x) < g(x).="" to="" analyze="" the="" properties="" of="" this="" set,="" we="" consider="" the="" functions="" f="" and="" />
Continuity of Functions
- Since f and g are continuous functions, the difference h(x) = g(x) - f(x) is also continuous.
- The continuity of h means ... more
The p-discriminant does not contain one of the following.- a)The envelope
- b)The tac-locus
- c)The cusp-locus
- d)the node-locus
Correct answer is option 'D'. Can you explain this answer?
The p-discriminant does not contain one of the following.
a)
The envelope
b)
The tac-locus
c)
The cusp-locus
d)
the node-locus
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Aakash Singh answered • Nov 19, 2024 |
Understanding p-Discriminant and Its Components
The p-discriminant is a concept used in the study of polynomial equations, particularly in relation to their singularities and the geometry of their solutions. It helps identify various loci associated with different types of singular points.
Components of the p-Discriminant
- Envelope: Refers to a curve that is ta... more
The p-discriminant is a concept used in the study of polynomial equations, particularly in relation to their singularities and the geometry of their solutions. It helps identify various loci associated with different types of singular points.
Components of the p-Discriminant
- Envelope: Refers to a curve that is ta... more
For a, b ε Z, define a relation a R b if ab > 0. Then the relation R is- a)symmetric, reflexive and transitive
- b)symmetric and reflexive but NOT transitive
- c)symmetric and transitive but NOT reflexive
- d)reflexive and transitive nut NOT symmetric
Correct answer is option 'A'. Can you explain this answer?
For a, b ε Z, define a relation a R b if ab > 0. Then the relation R is
a)
symmetric, reflexive and transitive
b)
symmetric and reflexive but NOT transitive
c)
symmetric and transitive but NOT reflexive
d)
reflexive and transitive nut NOT symmetric
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Aakash Singh answered • Jul 19, 2024 |
Reflexive Property:
For a relation to be reflexive, every element in the set must be related to itself. In this case, since a * a = a^2 is always greater than 0 for any non-zero integer a, the relation is reflexive.
Symmetric Property:
For a relation to be symmetric, if a is related to b, then b must be related to a. In this case, if a * b > 0, then b * a > 0 as ... more
For a relation to be reflexive, every element in the set must be related to itself. In this case, since a * a = a^2 is always greater than 0 for any non-zero integer a, the relation is reflexive.
Symmetric Property:
For a relation to be symmetric, if a is related to b, then b must be related to a. In this case, if a * b > 0, then b * a > 0 as ... more
is the normal derivative of u onthe boundary of the unit disc,then what is the value of 
?
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Aakash Singh asked • Jun 17, 2024 |
Solve the logarithmic function of ln 
- a)
- b)
- c)x-
- d)
Correct answer is option 'A'. Can you explain this answer?
Solve the logarithmic function of ln
a)
b)
c)
x-
d)
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Veda Institute answered |
To solve the logarithmic function ln 
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Aakash Singh asked • Jun 09, 2024 |
If R→R is given by f(x) = x3 + x2f'(1) + xf''(2) + f'''(3) for all x in R. then f(2) - f(1) is- a)f(0)
- b)-f(0)
- c)f'(0)
- d)-f'(0)
Correct answer is option 'B'. Can you explain this answer?
If R→R is given by f(x) = x3 + x2f'(1) + xf''(2) + f'''(3) for all x in R. then f(2) - f(1) is
a)
f(0)
b)
-f(0)
c)
f'(0)
d)
-f'(0)
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Veda Institute answered |
f(x) = x3 + x2f'(1) + xf''(2) + f'''(3)
f(0) = f'''(3)
f(2) = 8 + 4f'(1) + 2f''(2) + f'''(3)
f(1) = 1 + f'(1) + f''(2) + f'''(3)
Then f(2) - f(1) = 7 + 3f'(1) + f''(2)
Now, f'(x) = 3x2 + 2x f;(1) + f''(2)
f''(x) = 6x + 2f'(1)
f'''(x) = 6 
f'''(3) = 6 ...(1)
f''(2) = 12 + 2f'(1) .....(2)
f'(1) = 3 + 2f'(1) + f''(2)
⇒ -f'(1) = 3 + 12 + 2f'(1)
⇒ -15 = 3f'(1)
⇒ f'(1) = -5 and f''(2) = 2
So, f(2) -f(1) = 7 + 3*(-5) + 2
= 7 - 15 + 2
= -6 = -f(0)
If (1 + ax)n = 1 + 8x + 24x2 + ….., then the values of a and n are equal to - a)2, 4
- b)2, 3
- c)3, 6
- d)1, 2
Correct answer is option 'A'. Can you explain this answer?
If (1 + ax)n = 1 + 8x + 24x2 + ….., then the values of a and n are equal to
a)
2, 4
b)
2, 3
c)
3, 6
d)
1, 2
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Aakash Singh answered • Apr 25, 2024 |
Explanation:
Given Equation:
(1 + ax)^n = 1 + 8x + 24x^2 + ...
Expanding the equation:
Using binomial theorem, we can expand the given equation as follows:
(1 + ax)^n = 1 + n(ax) + n(n-1)(ax)^2/2! + ...
Comparing coefficients:
- Constant term: 1 = 1
- Coefficient of x: 8x = n(ax)
- Coefficient of x^2: 24x^2 ... more
Given Equation:
(1 + ax)^n = 1 + 8x + 24x^2 + ...
Expanding the equation:
Using binomial theorem, we can expand the given equation as follows:
(1 + ax)^n = 1 + n(ax) + n(n-1)(ax)^2/2! + ...
Comparing coefficients:
- Constant term: 1 = 1
- Coefficient of x: 8x = n(ax)
- Coefficient of x^2: 24x^2 ... more
Consider the system x + y + z = 0; x - y - z = 0, then the system of equations have- a)no solution
- b)infinite solution
- c)unique solution
- d)None of the above
Correct answer is option 'B'. Can you explain this answer?
Consider the system x + y + z = 0; x - y - z = 0, then the system of equations have
a)
no solution
b)
infinite solution
c)
unique solution
d)
None of the above
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Aakash Singh answered • Feb 11, 2024 |
Given information:
The given system of equations is:
1) x + y + z = 0
2) x - y - z = 0
To determine:
The type of solution for the given system of equations.
Solution:
To determine the type of solution for the given system of equations, we can use the method of elimination or substitution.
Method of elimination:... more
The given system of equations is:
1) x + y + z = 0
2) x - y - z = 0
To determine:
The type of solution for the given system of equations.
Solution:
To determine the type of solution for the given system of equations, we can use the method of elimination or substitution.
Method of elimination:
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Aakash Singh asked • Feb 06, 2024 |
- a)0
- b)1
- c)
- d)Does Not Converge
Correct answer is option 'A'. Can you explain this answer?
a)
0
b)
1
c)
d)
Does Not Converge
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Veda Institute answered |
The sum of the digits in the digits unit place of all the numbers formed with the help of 3,4,5,6 taken all at a time is :- a)432
- b)108
- c)36
- d)18
Correct answer is option 'B'. Can you explain this answer?
The sum of the digits in the digits unit place of all the numbers formed with the help of 3,4,5,6 taken all at a time is :
a)
432
b)
108
c)
36
d)
18
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Aakash Singh answered • Dec 08, 2023 |
Question:
The sum of the digits in the digits unit place of all the numbers formed with the help of 3, 4, 5, 6 taken all at a time is:
a) 432
b) 108
c) 36
d) 18
Answer:
To find the sum of the digits in the unit place of all the numbers formed with the help of 3, 4, 5, and 6 taken all at a time, we need to consider all the possible combin... more
The sum of the digits in the digits unit place of all the numbers formed with the help of 3, 4, 5, 6 taken all at a time is:
a) 432
b) 108
c) 36
d) 18
Answer:
To find the sum of the digits in the unit place of all the numbers formed with the help of 3, 4, 5, and 6 taken all at a time, we need to consider all the possible combin... more
The partial diferential equation of the family of surfaces z = (x + y ) + A (x y ) is- a)xp - yq = 0
- b)xp - yq = x - y
- c)xp + yq = x + y
- d)xp + yq = 0
Correct answer is option 'B'. Can you explain this answer?
The partial diferential equation of the family of surfaces z = (x + y ) + A (x y ) is
a)
xp - yq = 0
b)
xp - yq = x - y
c)
xp + yq = x + y
d)
xp + yq = 0
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Aakash Singh answered • Dec 08, 2023 |
Partial Differential Equation of the Family of Surfaces
The given family of surfaces is represented by the equation z = (x^2 - y^2) + A(x - y), where A is a constant.
Step 1: Find the Partial Derivatives
To find the partial derivatives, we differentiate the equation with respect to x and y.
Partial derivative with respect to x:
∂z/∂x = 2x + ... more
The given family of surfaces is represented by the equation z = (x^2 - y^2) + A(x - y), where A is a constant.
Step 1: Find the Partial Derivatives
To find the partial derivatives, we differentiate the equation with respect to x and y.
Partial derivative with respect to x:
∂z/∂x = 2x + ... more
X(t) is a real valued function of a real variable with period T. Its trigonometric Fourier Series expansion contains no terms of frequency ω = 2π (2k ) / T ; k = 1, 2,.... Also, no sine terms are present. Then x(t) satisfies the equation - a)x(t) = -x(t-T)
- b)x(t) = -x(T-t) = -x(-t)
- c)x(t) = x(T-t) = -x (t-T/2)
- d)x(t) = x(t-T) = x(t-T/2)
Correct answer is option 'D'. Can you explain this answer?
X(t) is a real valued function of a real variable with period T. Its trigonometric Fourier Series expansion contains no terms of frequency ω = 2π (2k ) / T ; k = 1, 2,.... Also, no sine terms are present. Then x(t) satisfies the equation
a)
x(t) = -x(t-T)
b)
x(t) = -x(T-t) = -x(-t)
c)
x(t) = x(T-t) = -x (t-T/2)
d)
x(t) = x(t-T) = x(t-T/2)
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Aakash Singh answered • Nov 17, 2023 |
Ω = 0. This means that the expansion does not contain any terms of the form cos(0t) or sin(0t), which correspond to the constant term in the Fourier series. In other words, the function X(t) does not have a DC offset or a constant component in its Fourier series representation.
Find limit lim x-0 {[cotx-(1/x)]/x}?
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Aakash Singh answered • Oct 30, 2023 |
Limit of the given expression:
To find the limit of the expression lim x→0 {[cot(x) - (1/x)]/x}, we can apply algebraic manipulations and trigonometric identities to simplify the expression.
Step 1: Simplify the expression:
Let's start by simplifying the expression inside the curly brackets.
We know that cot(x) = cos(x)/sin(x), so we can re... more
To find the limit of the expression lim x→0 {[cot(x) - (1/x)]/x}, we can apply algebraic manipulations and trigonometric identities to simplify the expression.
Step 1: Simplify the expression:
Let's start by simplifying the expression inside the curly brackets.
We know that cot(x) = cos(x)/sin(x), so we can re... more
Find out total no of local extremum of the function|x^3 3|x| 2| =?
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Aakash Singh answered • Oct 16, 2023 |
Introduction:
To find the total number of local extrema of the function |x^3 - 3|x| + 2|, we need to analyze the critical points and determine whether they correspond to local maxima or minima.
Steps to Find Local Extrema:
1. Find the derivative of the function.
2. Set the derivative equal to zero to find the critical points.
3. Analyze the sign of the ... more
To find the total number of local extrema of the function |x^3 - 3|x| + 2|, we need to analyze the critical points and determine whether they correspond to local maxima or minima.
Steps to Find Local Extrema:
1. Find the derivative of the function.
2. Set the derivative equal to zero to find the critical points.
3. Analyze the sign of the ... more
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Aakash Singh asked • Aug 17, 2023 |
Is there any provision for rechecking or challenging the marks after the IIT JAM Mathematics Exam results are declared?
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Naina Rana answered |
Yes, there is a provision for rechecking or challenging the marks after the IIT JAM Mathematics Exam results are declared. Candidates who are not satisfied with their marks can apply for a revaluation or request for a challenge. The process for rechecking or challenging the marks is as follows:
Revaluation Process:
1. Candidates who wish to apply for revaluation... more
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Aakash Singh asked • Aug 14, 2023 |
Can I get my IIT JAM Mathematics answer key without my exam center code mentioned on it?
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Oishi Bajaj answered |
Yes, you can get your IIT JAM Mathematics answer key without your exam center code mentioned on it. The exam center code is not a mandatory requirement for accessing the answer key. Here is a detailed explanation on how to obtain the answer key without the exam center code:
Step-by-step process:
1. Visit the official website: Start by visiting the official websi... more
Step-by-step process:
1. Visit the official website: Start by visiting the official websi... more
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Aakash Singh asked • Aug 07, 2023 |
How is the cutoff for the IIT JAM Mathematics Paper determined?
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Radha Mehta answered |
Determining the Cutoff for IIT JAM Mathematics Paper
Introduction
The cutoff for the IIT JAM Mathematics Paper is determined based on various factors. The cutoff marks are the minimum marks required by candidates to qualify for the next stage of the admission process. The cutoff is determined by the conducting authority, which is the Indian Institute of Technology (IIT) for the Joint Admission Test for M.Sc. (JAM) in Mathematics.... more
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Aakash Singh asked • Aug 03, 2023 |
Is there a sectional marking scheme for different topics in the IIT JAM Mathematics Paper?
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Hrithik Choudhury answered |
< b="" />Sectional Marking Scheme for IIT JAM Mathematics Paper< />
The IIT JAM Mathematics paper is divided into three sections, namely Section A, Section B, and Section C. Each section has a specific marking scheme which determines the allocation of marks based on the correct and incorrect answers. Let's take a detailed look at the sectional marking scheme for each section:
... more
The IIT JAM Mathematics paper is divided into three sections, namely Section A, Section B, and Section C. Each section has a specific marking scheme which determines the allocation of marks based on the correct and incorrect answers. Let's take a detailed look at the sectional marking scheme for each section:
... more
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