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Ojas ShahEduRev Mathematics |
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Ojas Shah
EduRev Mathematics
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Discussed Questions
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Ojas Shah 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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Ojas Shah upvoted • Feb 24, 2025 |
The distance between the parallel planes 2x -2y + z + 3 = 0 and 4x -4y + 2z + 5 = 0 is- a)1/2
- b)1/3
- c)1/6
- d)none of the above
Correct answer is option 'C'. Can you explain this answer?
The distance between the parallel planes 2x -2y + z + 3 = 0 and 4x -4y + 2z + 5 = 0 is
a)
1/2
b)
1/3
c)
1/6
d)
none of the above
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Veda Institute answered |
To find the distance between two parallel planes, we follow the method given below. Method:Find the perpendicular distance of each plane from the origin with proper sign (i.e. do not. lake the mod). Ther. their differeee is the required distance between two parallel planes. Let d. and d, be the distances of the planes
2x -2y + z + 3 =0 ...(i)
and 4x - 4y + 2z + 5 = 0 ...(ii)
from the origin. Then
2x -2y + z + 3 =0 ...(i)
and 4x - 4y + 2z + 5 = 0 ...(ii)
from the origin. Then
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Ojas Shah 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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Ojas Shah upvoted • Feb 04, 2025 |
Let z be any non - zero complex number. Then arg(z) + arg(z¯) is equal to
- a)-π
- b)π
- c)0
- d)π/2
Correct answer is option 'C'. Can you explain this answer?
Let z be any non - zero complex number. Then arg(z) + arg(z¯) is equal to
a)
-π
b)
π
c)
0
d)
π/2
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Veda Institute answered |
Let z = x+iy
zˉ = x−iy
arg(z) = xy,arg(zˉ) = −xy
arg(z) + arg(zˉ) = 0
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Ojas Shah upvoted • Jan 30, 2025 |
If 
are to arbitrary vectors with magnitudes a and b respectively, 
will be equal to- a)
- b)
- c)
- d)
Correct answer is option 'A'. Can you explain this answer?
If are to arbitrary vectors with magnitudes a and b respectively, will be equal to
are to arbitrary vectors with magnitudes a and b respectively, will be equal toa)
b)
c)
d)
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Veda Institute answered |
Cross checking from option (a),
which is correct answer.
which is correct answer.
et A and B be n×n matrices, where n is an integer greater than 1. Is it true thatdet(A + B) = det(A) + det(B)?If so, then give a proof. If not, then give a counterexample.Correct answer is 'det(A+B)≠det(A)+det(B)'. Can you explain this answer?
et A and B be n×n matrices, where n is an integer greater than 1. Is it true that
det(A + B) = det(A) + det(B)?
If so, then give a proof. If not, then give a counterexample.
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Ojas Shah answered • Jan 06, 2025 |
Understanding the Determinant Property
The statement that det(A + B) = det(A) + det(B) is generally not true for n x n matrices A and B where n > 1.
Counterexample
Consider the matrices:
- A = [[1, 0],
[0, 1]]
- B = [[1, 0],
[0, 1]]
These matrices are both the identity matrix of size 2.
Now, let's compute the determinants:
... more
The statement that det(A + B) = det(A) + det(B) is generally not true for n x n matrices A and B where n > 1.
Counterexample
Consider the matrices:
- A = [[1, 0],
[0, 1]]
- B = [[1, 0],
[0, 1]]
These matrices are both the identity matrix of size 2.
Now, let's compute the determinants:
... more
From a group of persons, the number of ways of selecting 5 persons is equal to that of 8 persons. The number of persons in the group is- a)13
- b)40
- c)18
- d)21
Correct answer is option 'A'. Can you explain this answer?
From a group of persons, the number of ways of selecting 5 persons is equal to that of 8 persons. The number of persons in the group is
a)
13
b)
40
c)
18
d)
21
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Ojas Shah answered • Oct 07, 2024 |
Understanding the Problem
In this problem, we need to find the total number of persons in a group where the number of ways to select 5 persons is equal to the number of ways to select 8 persons.
Combination Formula
The number of ways to choose r persons from n persons is given by the combination formula:
- C(n, r) = n! / [r! * (n - r)!]
Where "!" denotes fac... more
In this problem, we need to find the total number of persons in a group where the number of ways to select 5 persons is equal to the number of ways to select 8 persons.
Combination Formula
The number of ways to choose r persons from n persons is given by the combination formula:
- C(n, r) = n! / [r! * (n - r)!]
Where "!" denotes fac... more
The set S of square matrices of same order with respect to matrix addition is a?
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Ojas Shah answered • Jul 04, 2024 |
Set S of Square Matrices with Respect to Matrix Addition
Matrix Addition in Set S:
- The set S consists of square matrices of the same order.
- Matrix addition in set S is defined as adding corresponding elements of two matrices of the same order.
Closure Property:
- The set S is closed under matrix addition.
- When two matrices from set S are added, the result... more
Matrix Addition in Set S:
- The set S consists of square matrices of the same order.
- Matrix addition in set S is defined as adding corresponding elements of two matrices of the same order.
Closure Property:
- The set S is closed under matrix addition.
- When two matrices from set S are added, the result... more
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Ojas Shah asked • Jun 22, 2024 |
Evaluate 
- a)1
- b)2
- c)3
- d)4
Correct answer is option 'A'. Can you explain this answer?
Evaluate
a)
1
b)
2
c)
3
d)
4
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Veda Institute answered |
Adding (i) and (ii), we get
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Ojas Shah asked • Jun 14, 2024 |
Which of the following transformations reduce the differential equation 
into the form 
- a)
- b)
- c)
- d)
Correct answer is option 'B'. Can you explain this answer?
Which of the following transformations reduce the differential equation into the form
into the form a)
b)
c)
d)
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Veda Institute answered |
Given differential equation is:
Here 
which shows that the transformation 
reduces the given differential equation into the form 
.
reduces the given differential equation into the form .|
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Ojas Shah asked • Jun 07, 2024 |
The total number of roots does the following equation posses 
is (Answer should be an integer) ____________.Correct answer is '2'. Can you explain this answer?
The total number of roots does the following equation posses is (Answer should be an integer) ____________.
is (Answer should be an integer) ____________.|
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Veda Institute answered |
curve intersect at two points
∴ two real solution
8) In a production line of a factory, each packet contains four items. Past record shows that 20% of the produced items are defective. A quality manager inspects each item in a packet and approves the packet for shipment if a... more
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Ojas Shah answered • Mar 20, 2024 |
First, we need to calculate the probability of having at most one defective item in a packet.
- Calculating the probability of having exactly one defective item:
- The probability of having exactly one defective item in a packet of four items can be calculated using the binomial probability formula:
- P(X = 1) = C(4, 1) * (0.2)^1 * (0.8)^3
- P(X = 1... more
If twice the square on the diameter of a circle is equal to the sums of the squares on the sides of the inscribed triangle ABC, then sin2A + sin2B + sin2C = .......- a)0
- b)2
- c)3/2
- d)none
Correct answer is option 'B'. Can you explain this answer?
If twice the square on the diameter of a circle is equal to the sums of the squares on the sides of the inscribed triangle ABC, then sin2A + sin2B + sin2C = .......
a)
0
b)
2
c)
3/2
d)
none
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Ojas Shah answered • Nov 30, 2023 |
To solve this problem, we need to use the properties of circles and triangles.
Let's start by considering the circle with diameter AB. The square on the diameter is simply the square of the length of AB, which we'll denote as d.
The sum of the squares on the sides of the inscribed triangle ABC can be written as:
AB^2 + BC^2 + AC^2
Since the triangle is i... more
Let's start by considering the circle with diameter AB. The square on the diameter is simply the square of the length of AB, which we'll denote as d.
The sum of the squares on the sides of the inscribed triangle ABC can be written as:
AB^2 + BC^2 + AC^2
Since the triangle is i... more
The sum of all the numbers of four different digits that can be made by using the digits 0, 1, 2 and 3 is- a)26664
- b)39996
- c)38664
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
The sum of all the numbers of four different digits that can be made by using the digits 0, 1, 2 and 3 is
a)
26664
b)
39996
c)
38664
d)
none of these
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Ojas Shah answered • Nov 30, 2023 |
The Sum of All Four-Digit Numbers Using Digits 0, 1, 2, and 3
To find the sum of all four-digit numbers that can be formed using the digits 0, 1, 2, and 3, we need to consider the possible combinations. The four-digit numbers can be formed by using these digits as thousands, hundreds, tens, and units places.
Step 1: Find all the possible combinations
... more
To find the sum of all four-digit numbers that can be formed using the digits 0, 1, 2, and 3, we need to consider the possible combinations. The four-digit numbers can be formed by using these digits as thousands, hundreds, tens, and units places.
Step 1: Find all the possible combinations
... more
xx1 + yy1 = a2 is the equation of the- a)Tangent to the circle x2+ y2=a2 at point (x1,y1)
- b)chord of contact of tangents drawn from the external point (x1, y1) to the circle x2+ y2 = a2
- c)polar of the point (x1, y1) w.r.t the circle x2 + y2 = a2
- d)all of the above
Correct answer is option 'D'. Can you explain this answer?
xx1 + yy1 = a2 is the equation of the
a)
Tangent to the circle x2+ y2=a2 at point (x1,y1)
b)
chord of contact of tangents drawn from the external point (x1, y1) to the circle x2+ y2 = a2
c)
polar of the point (x1, y1) w.r.t the circle x2 + y2 = a2
d)
all of the above
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Ojas Shah answered • Nov 30, 2023 |
Explanation:
To understand why the correct answer is option 'D', let's break down each option and see why it is true.
a) Tangent to the circle x^2 + y^2 = a^2 at point (x1, y1):
The equation xx1 + yy1 = a^2 represents a line passing through the point (x1, y1). If this line is a tangent to the circle x^2 + y^2 = a^2, it means that the line intersects the circle at exactly... more
To understand why the correct answer is option 'D', let's break down each option and see why it is true.
a) Tangent to the circle x^2 + y^2 = a^2 at point (x1, y1):
The equation xx1 + yy1 = a^2 represents a line passing through the point (x1, y1). If this line is a tangent to the circle x^2 + y^2 = a^2, it means that the line intersects the circle at exactly... more
If f(x) = x5 - 20x3 + 240 x, then f(x) is
- a)monotonically decreasing everywhere
- b)monotonically decreasing on (0, ∞)
- c)monotonically increasing everywhere
- d)monotonically increasing only in (-∞, 0)
Correct answer is option 'C'. Can you explain this answer?
If f(x) = x5 - 20x3 + 240 x, then f(x) is
a)
monotonically decreasing everywhere
b)
monotonically decreasing on (0, ∞)
c)
monotonically increasing everywhere
d)
monotonically increasing only in (-∞, 0)
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Ojas Shah answered • Nov 09, 2023 |
To determine whether f(x) is monotonically decreasing or increasing, we need to find the derivative of f(x) and analyze its sign.
Given: f(x) = x^5 - 20x^3 + 240x
Taking the derivative of f(x) with respect to x:
f'(x) = 5x^4 - 60x^2 + 240
To find the critical points, we set f'(x) equal to zero and solve for x:
5x^4 - 60x^2 + 240 = 0
We can fact... more
Given: f(x) = x^5 - 20x^3 + 240x
Taking the derivative of f(x) with respect to x:
f'(x) = 5x^4 - 60x^2 + 240
To find the critical points, we set f'(x) equal to zero and solve for x:
5x^4 - 60x^2 + 240 = 0
We can fact... more
Consider the group homomorphism phi:M2(R)--->R,given by phi(A)=trc(A). The ker of phi is isomorphic to which of the map?
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Ojas Shah answered • Oct 25, 2023 |
Group homomorphism phi:M2(R)--->R
The group homomorphism phi:M2(R)--->R is defined by phi(A)=trc(A), where M2(R) is the group of 2x2 matrices with real entries, R is the group of real numbers, and trc(A) denotes the trace of matrix A.
Definition of Trace
The trace of a matrix A = [a11 a12; a21 a22] is defined as the sum of its diagonal elements, i.e.,... more
The group homomorphism phi:M2(R)--->R is defined by phi(A)=trc(A), where M2(R) is the group of 2x2 matrices with real entries, R is the group of real numbers, and trc(A) denotes the trace of matrix A.
Definition of Trace
The trace of a matrix A = [a11 a12; a21 a22] is defined as the sum of its diagonal elements, i.e.,... more
The volume of the region in the first octant (x>=0,y>=0,z>=0) bounded by the cylinder x^2 y^2=4 and the plane z=2 and z y=4 equals?
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Ojas Shah answered • Oct 13, 2023 |
Problem:
Find the volume of the region in the first octant (x>=0, y>=0, z>=0) bounded by the cylinder x^2 y^2=4, the plane z=2, and the plane y=4.
Solution:
To find the volume of the given region, we need to determine the limits of integration for each variable and set up the triple integral.
Limit of Integration:
To dete... more
Find the volume of the region in the first octant (x>=0, y>=0, z>=0) bounded by the cylinder x^2 y^2=4, the plane z=2, and the plane y=4.
Solution:
To find the volume of the given region, we need to determine the limits of integration for each variable and set up the triple integral.
Limit of Integration:
To dete... more
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Ojas Shah asked • Oct 01, 2023 |
From a pack of regular from a playing cards, two cards are drawn at random. What is the probability that both cards will be Kings, if first card in NOT replaced- a)1/26
- b)1/52
- c)1/169
- d)1/221
Correct answer is option 'D'. Can you explain this answer?
From a pack of regular from a playing cards, two cards are drawn at random. What is the probability that both cards will be Kings, if first card in NOT replaced
a)
1/26
b)
1/52
c)
1/169
d)
1/221
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Veda Institute answered |
Here sample space S = 52
∴The probability of drawing both cards are king without replacement
∴The probability of drawing both cards are king without replacement
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Ojas Shah asked • Aug 17, 2023 |
What is the total number of seats for M.Sc. Physics across all IITs?
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Naina Rana answered |
Total Number of Seats for M.Sc. Physics across all IITs
The Indian Institutes of Technology (IITs) are renowned institutions in India that offer a wide range of undergraduate, postgraduate, and doctoral programs in various fields. Among these programs, M.Sc. Physics is one of the sought-after courses for students interested in pursuing a career in the field of physics. The IITs are known for their rigorous academic curriculum and exceptional faculty, making them an ideal choice for students aspiring to excel in physics.... more
Introduction
The Indian Institutes of Technology (IITs) are renowned institutions in India that offer a wide range of undergraduate, postgraduate, and doctoral programs in various fields. Among these programs, M.Sc. Physics is one of the sought-after courses for students interested in pursuing a career in the field of physics. The IITs are known for their rigorous academic curriculum and exceptional faculty, making them an ideal choice for students aspiring to excel in physics.... more
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Ojas Shah asked • Aug 14, 2023 |
Can I get my IIT JAM Mathematics admit card without my exam time mentioned on it?
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Oishi Bajaj answered |
Can I get my IIT JAM Mathematics admit card without my exam time mentioned on it?
Yes, it is possible to get your IIT JAM Mathematics admit card without the exam time mentioned on it. However, it is important to understand the process and requirements for obtaining the admit card.
Process for obtaining the IIT JAM Mathematics admit card
1. Registratio... more
Yes, it is possible to get your IIT JAM Mathematics admit card without the exam time mentioned on it. However, it is important to understand the process and requirements for obtaining the admit card.
Process for obtaining the IIT JAM Mathematics admit card
1. Registratio... more
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Ojas Shah asked • Aug 07, 2023 |
Can you suggest books that provide step-by-step solutions for numerical methods and approximation methods questions in the IIT JAM Mathematics Paper?
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Radha Mehta answered |
Books for Numerical Methods and Approximation Methods in IIT JAM Mathematics Paper
Numerical Methods and Approximation Methods are important topics in the IIT JAM Mathematics Paper. These topics require a strong understanding of various numerical techniques and methods to solve complex problems. Here are some books that provide step-by-step solutions and explanations for numerica... more
Numerical Methods and Approximation Methods are important topics in the IIT JAM Mathematics Paper. These topics require a strong understanding of various numerical techniques and methods to solve complex problems. Here are some books that provide step-by-step solutions and explanations for numerica... more
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Ojas Shah asked • Aug 02, 2023 |
Can you suggest some strategies for effectively attempting the multiple-choice questions in the IIT JAM Mathematics Paper?
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Nakul Bajaj answered |
Strategies for effectively attempting the multiple-choice questions in the IIT JAM Mathematics Paper:
1. Understand the Exam Pattern:
- Familiarize yourself with the exam pattern to understand the structure of the paper.
- Know the number of questions, marking scheme, and time allotted for the exam.
2. Thoroughly Study the Syllabus:
- Go th... more
1. Understand the Exam Pattern:
- Familiarize yourself with the exam pattern to understand the structure of the paper.
- Know the number of questions, marking scheme, and time allotted for the exam.
2. Thoroughly Study the Syllabus:
- Go th... more
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