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Gaurav BhatiaEduRev Mathematics |
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Gaurav Bhatia
EduRev Mathematics
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Discussed Questions
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Gaurav Bhatia upvoted • 2 weeks ago |
The area o f the region bounded by the curve y(x2 + 2 ) = 3x and 4y = x2 is given by- a)
dxdy - b)
dydx - c)
dydx - d)
dxdy
Correct answer is option 'C'. Can you explain this answer?
The area o f the region bounded by the curve y(x2 + 2 ) = 3x and 4y = x2 is given by
a)
dxdyb)
dydxc)
dydxd)
dxdy
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Veda Institute answered |
The required area
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Gaurav Bhatia upvoted • 4 weeks ago |
The number of ways in which the- letters of the word ARTICLE can be rearranged so that the even places are always occupied by consonants is- a)576
- b)4C3 x (4!)
- c)2(4!)
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
The number of ways in which the- letters of the word ARTICLE can be rearranged so that the even places are always occupied by consonants is
a)
576
b)
4C3 x (4!)
c)
2(4!)
d)
none of these
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Veda Institute answered |
The number of ways to fill the three even places by 4 constonants = 4P3.
After filling the even places, remaining places can be filled in 4P4 ways.
So, the required number of words = 4P3 x 4P4.
After filling the even places, remaining places can be filled in 4P4 ways.
So, the required number of words = 4P3 x 4P4.
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Gaurav Bhatia upvoted • Feb 16, 2025 |
Let {X,Y,Z) be a basis of 
Consider the following statements P and Q
P : {X + Y,Y + Z, X - Z) is a basis of 
Q : {X + Y + Z,X + 2Y - Z, X - 3Z} is a basis of 
Which of the above statements hold true? - a)only P
- b)only Q
- c)both P and Q
- d)neither P nor Q
Correct answer is option 'B'. Can you explain this answer?
Let {X,Y,Z) be a basis of Consider the following statements P and Q
P : {X + Y,Y + Z, X - Z) is a basis of
Q : {X + Y + Z,X + 2Y - Z, X - 3Z} is a basis of
Consider the following statements P and QP : {X + Y,Y + Z, X - Z) is a basis of
Q : {X + Y + Z,X + 2Y - Z, X - 3Z} is a basis of
Which of the above statements hold true?
a)
only P
b)
only Q
c)
both P and Q
d)
neither P nor Q
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Scholars Academy answered |
- For a set of vectors to be a basis of R3, they must be linearly independent.
- Statement P: Vectors {X+Y, Y+Z, X-Z} are not guaranteed to be linearly independent. Linear combinations might lead to dependence.
- Statement Q: Vectors {X+Y+Z, X+2Y-Z, X-3Z} can be shown to be linearly independent using row reduction or determinant methods.
- Thus, only Q forms a basis of R3.
- Correct answer: B.
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Gaurav Bhatia upvoted • Feb 08, 2025 |
If C is a non-singular matrix and B 
then- a)B2 = 1
- b)B2 = 0
- c)B3 = 1
- d)B3 = 0
Correct answer is option 'D'. Can you explain this answer?
If C is a non-singular matrix and B then
thena)
B2 = 1
b)
B2 = 0
c)
B3 = 1
d)
B3 = 0
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Veda Institute answered |
We are given that C is a non-singular matrix and
B =
or B is similar to 
The eigen values of 
are all zeroes.
B =
or B is similar to The eigen values of are all zeroes. Hence, Bk = 0
For k = 3
B3 = 0
For k = 3
B3 = 0
In a certain test, αi, students gave wrong answers to at least i questions, where i = 1,2,3.4...k. No student gave more than k wrong answers the total number of wrong answers given is :Correct answer is option ''. Can you explain this answer?
In a certain test, αi, students gave wrong answers to at least i questions, where i = 1,2,3.4...k. No student gave more than k wrong answers the total number of wrong answers given is :
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Gaurav Bhatia answered • Feb 07, 2025 |
Total Wrong Answers Calculation
In this problem, we need to analyze the situation where students have given wrong answers to a specific number of questions. The key points are:
- Each student, denoted by αi, has given wrong answers such that:
- α1: at least 1 wrong answer
- α2: at least 2 wrong answers
- α3: at least 3 wrong answers
... more
In this problem, we need to analyze the situation where students have given wrong answers to a specific number of questions. The key points are:
- Each student, denoted by αi, has given wrong answers such that:
- α1: at least 1 wrong answer
- α2: at least 2 wrong answers
- α3: at least 3 wrong answers
... more
The number of elements of order two in the group S4 is equal to?
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Gaurav Bhatia answered • Nov 21, 2024 |
Understanding the Group S4
S4, or the symmetric group on 4 elements, consists of all the permutations of a set with four elements. The order of S4 is 4! (which equals 24). To find the elements of order two, we need to identify the permutations that, when applied twice, return the original arrangement.
Elements of Order Two
In S4, the permutations of order two can be ch... more
S4, or the symmetric group on 4 elements, consists of all the permutations of a set with four elements. The order of S4 is 4! (which equals 24). To find the elements of order two, we need to identify the permutations that, when applied twice, return the original arrangement.
Elements of Order Two
In S4, the permutations of order two can be ch... more
The set of vectors (1,2,1),(0,1,0),(3,4,3) in R^3 is a
1. linearly dependent set
2. linearly independent set
3. a basis for R^3
4. not a basis of R^3?
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Gaurav Bhatia answered • Jul 30, 2024 |
Linear Dependence or Independence
The set of vectors (1,2,1), (0,1,0), (3,4,3) in R^3 can be analyzed for linear dependence or independence.
Definition of Linear Dependence and Independence
- A set of vectors is linearly dependent if there exist scalars, not all zero, such that a linear combination of the vectors equals the zero vector.
- A set of vectors is... more
The set of vectors (1,2,1), (0,1,0), (3,4,3) in R^3 can be analyzed for linear dependence or independence.
Definition of Linear Dependence and Independence
- A set of vectors is linearly dependent if there exist scalars, not all zero, such that a linear combination of the vectors equals the zero vector.
- A set of vectors is... more
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Gaurav Bhatia asked • Jun 24, 2024 |
For which value of the system of linear equation,
have no solution?Correct answer is '-3.5'. Can you explain this answer?
For which value of the system of linear equation,
have no solution?
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Veda Institute answered |
The matrix form of the given system of equations is,
The given system of equations will have a unique solution if and only if the coefficient matrix is non-singular.
Performing 
, we get,
, we get,
Performing 
, we get
, we get
Therefore the coefficient matrix will be non-singular if and only if,
Thus the given system will have a unique solution if 
Showing that given equations are inconsistent in this case. Thus if 
= -3.5 no solution exists.
Hence, the correct answer is −3.5
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Gaurav Bhatia asked • Jun 17, 2024 |
If ‘X’ is a random variable, taking values ‘x’, probability of success and failure being ‘p’ and ‘q’ respectively and ‘n’ trials being conducted, then what is the probability that ‘X’ takes values ‘x’? Use Binomial Distribution- a)P(X = x) = nCx px qx
- b)P(X = x) = nCx px q(n-x)
- c)P(X = x) = xCn qx p(n-x)
- d)P(x = x) = xCn pn qx
Correct answer is option 'B'. Can you explain this answer?
If ‘X’ is a random variable, taking values ‘x’, probability of success and failure being ‘p’ and ‘q’ respectively and ‘n’ trials being conducted, then what is the probability that ‘X’ takes values ‘x’? Use Binomial Distribution
a)
P(X = x) = nCx px qx
b)
P(X = x) = nCx px q(n-x)
c)
P(X = x) = xCn qx p(n-x)
d)
P(x = x) = xCn pn qx
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Veda Institute answered |
It is the formula for Binomial Distribution that is asked here which is given by P(X = x) = nCx px q(n - x).
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Gaurav Bhatia asked • Jun 10, 2024 |
Let G be the group with the generators a and b given byG = {(a,b)|σ(a) = 4,σ(b) = 2, ba = a-1b}. Let Z(G) denotes the centre of G. Then G/Z(G) is isomorphic to.- a)
- b)S3
- c)
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
Let G be the group with the generators a and b given byG = {(a,b)|σ(a) = 4,σ(b) = 2, ba = a-1b}. Let Z(G) denotes the centre of G. Then G/Z(G) is isomorphic to.
a)
b)
S3
c)
d)
none of these
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Veda Institute answered |
Clearly G ≈ D4
Also |z(Dn)| = 2 if n is even and |z(Dn)| = 1 if n is odd
Also G is non abelian
⇒ G/Z(G) can not be cyclic =G/Z(G) ≈ 
The distance of the point (2, 3, 4) from the plane 3x - 6y + 2z + 11 =0 is- a)1
- b)43/√7
- c)1/49
- d)-1/49
Correct answer is option 'A'. Can you explain this answer?
The distance of the point (2, 3, 4) from the plane 3x - 6y + 2z + 11 =0 is
a)
1
b)
43/√7
c)
1/49
d)
-1/49
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Gaurav Bhatia answered • Apr 22, 2024 |
Distance of a Point from a Plane
Given:
Point P(2,3,4)
Plane equation: 3x - 6y + 2z + 11 = 0
Formula:
The distance between a point (x,y,z) and a plane Ax + By + Cz + D = 0 is given by:
Distance = |Ax + By + Cz + D| / √(A^2 + B^2 + C^2)
Calculations:
- Substitute the values of the point coordinates and the coeffic... more
Given:
Point P(2,3,4)
Plane equation: 3x - 6y + 2z + 11 = 0
Formula:
The distance between a point (x,y,z) and a plane Ax + By + Cz + D = 0 is given by:
Distance = |Ax + By + Cz + D| / √(A^2 + B^2 + C^2)
Calculations:
- Substitute the values of the point coordinates and the coeffic... more
Let a mapping f : G→ G defined by f (x) = x-1 , then which of the following is / are true ?- a)f is one - one
- b)f is on to
- c)f is homomorphism as well as automorphism
- d)G is a non - abelian group.
Correct answer is option 'A,B,C'. Can you explain this answer?
Let a mapping f : G→ G defined by f (x) = x-1 , then which of the following is / are true ?
a)
f is one - one
b)
f is on to
c)
f is homomorphism as well as automorphism
d)
G is a non - abelian group.
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Gaurav Bhatia answered • Feb 10, 2024 |
Maps a group G to a group G'. Then, for all elements a, b in G, the mapping f satisfies the following properties:
1. f(a * b) = f(a) * f(b) (Closure under group operation)
2. f(e) = e' (Preservation of identity element)
3. f(a^-1) = (f(a))^-1 (Preservation of inverses)
These properties ensure that the mapping f preserves the group structure of G.
1. f(a * b) = f(a) * f(b) (Closure under group operation)
2. f(e) = e' (Preservation of identity element)
3. f(a^-1) = (f(a))^-1 (Preservation of inverses)
These properties ensure that the mapping f preserves the group structure of G.
A person on a trip has a choice between private car and public transport. The probability of using a private car is 0.45. While using the public transport, further choices available are bus and metro, out of which the probability of commuting by a bus is 0.55. In such a situation, the probability (rounded up to two decimals) of using a car, bus and metro, respectively would be- a)0.45, 0.30 and 0.25
- b)0.45, 0.25 and 0.30
- c)0.45, 0.55 and 0.00
- d)0.45, 0.35 and
Correct answer is option 'A'. Can you explain this answer?
A person on a trip has a choice between private car and public transport. The probability of using a private car is 0.45. While using the public transport, further choices available are bus and metro, out of which the probability of commuting by a bus is 0.55. In such a situation, the probability (rounded up to two decimals) of using a car, bus and metro, respectively would be
a)
0.45, 0.30 and 0.25
b)
0.45, 0.25 and 0.30
c)
0.45, 0.55 and 0.00
d)
0.45, 0.35 and
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Gaurav Bhatia answered • Jan 05, 2024 |
Explanation:
To find the probability of using a car, bus, and metro, we need to consider the different scenarios and calculate their probabilities.
Scenario 1: Using a private car
Given that the probability of using a private car is 0.45, the probability of using a car is 0.45.
Scenario 2: Using public transport
If the person decides ... more
To find the probability of using a car, bus, and metro, we need to consider the different scenarios and calculate their probabilities.
Scenario 1: Using a private car
Given that the probability of using a private car is 0.45, the probability of using a car is 0.45.
Scenario 2: Using public transport
If the person decides ... more
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Gaurav Bhatia asked • Dec 27, 2023 |
If ai > 0 for i = 1, 2, 3,..,n and a1, a2, a3, ...an = 1 then the greatest value of (1 + a1)(1 + a2)... (1 + an) is:- a)22n
- b)2n
- c)1
- d)2n/2
Correct answer is option 'B'. Can you explain this answer?
If ai > 0 for i = 1, 2, 3,..,n and a1, a2, a3, ...an = 1 then the greatest value of (1 + a1)(1 + a2)... (1 + an) is:
a)
22n
b)
2n
c)
1
d)
2n/2
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Pranav Sharma answered |
If AI (artificial intelligence) continues to advance and improve, it could have a significant impact on various aspects of society. Here are a few potential outcomes:
1. Automation and job displacement: AI has the potential to automate many tasks currently performed by humans, leading to job displacement in certain industries. This could result in economic and societal changes as people... more
1. Automation and job displacement: AI has the potential to automate many tasks currently performed by humans, leading to job displacement in certain industries. This could result in economic and societal changes as people... more
There are 25 calculators in a box. Two of them are defective. Suppose 5 calculators are randomly picked for inspection (i.e., each has the same chance of being selected), what is the probability that only one of the defective calculators will be included in the inspection?- a)1/2
- b)1/3
- c)1/4
- d)1/5
Correct answer is option 'B'. Can you explain this answer?
There are 25 calculators in a box. Two of them are defective. Suppose 5 calculators are randomly picked for inspection (i.e., each has the same chance of being selected), what is the probability that only one of the defective calculators will be included in the inspection?
a)
1/2
b)
1/3
c)
1/4
d)
1/5
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Gaurav Bhatia answered • Nov 19, 2023 |
To solve this problem, we need to use the concept of probability.
Step 1: Calculate the total number of ways to select 5 calculators out of 25
The total number of ways to select 5 calculators out of 25 is given by the combination formula:
C(25, 5) = 25! / (5! * (25-5)!) = 53130
So, there are 53130 different ways to select 5 calculators from the box.... more
Step 1: Calculate the total number of ways to select 5 calculators out of 25
The total number of ways to select 5 calculators out of 25 is given by the combination formula:
C(25, 5) = 25! / (5! * (25-5)!) = 53130
So, there are 53130 different ways to select 5 calculators from the box.
The system of linear equations(4d - 1) x + y + z = 0, - y + z = 0, (4d - 1 )z = 0 has a non-trivial solution, if the value of d is ___ .
Correct answer is '0.25'. Can you explain this answer?
The system of linear equations
(4d - 1) x + y + z = 0, - y + z = 0, (4d - 1 )z = 0 has a non-trivial solution, if the value of d is ___ .
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Gaurav Bhatia answered • Nov 18, 2023 |
Given equations:
(4d - 1)x + y + z = 0 ...(1)
-y + z = 0 ...(2)
(4d - 1)z = 0 ...(3)
Non-trivial solution:
A non-trivial solution means that the variables (x, y, z) cannot all be zero. In other words, there exists at least one solution where at least one of the variables is non-zero.
Analysis of equations:
L... more
(4d - 1)x + y + z = 0 ...(1)
-y + z = 0 ...(2)
(4d - 1)z = 0 ...(3)
Non-trivial solution:
A non-trivial solution means that the variables (x, y, z) cannot all be zero. In other words, there exists at least one solution where at least one of the variables is non-zero.
Analysis of equations:
L... more
The area of the triangle formed by the complex number z, iz, z + iz in the argand plane is- a)(1/2) |z|2
- b)|z|2
- c)2 |z|2
- d)none
Correct answer is option 'A'. Can you explain this answer?
The area of the triangle formed by the complex number z, iz, z + iz in the argand plane is
a)
(1/2) |z|2
b)
|z|2
c)
2 |z|2
d)
none
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Gaurav Bhatia answered • Oct 31, 2023 |
The area of the triangle formed by the complex numbers z, iz, and z + iz in the Argand plane can be found using the Shoelace formula.
Shoelace Formula:
The Shoelace formula is a method used to calculate the area of a polygon given the coordinates of its vertices in the Cartesian plane. The formula states that the area of a polygon with vertices (x1, y1), (x2, y2), ..., (xn,... more
Shoelace Formula:
The Shoelace formula is a method used to calculate the area of a polygon given the coordinates of its vertices in the Cartesian plane. The formula states that the area of a polygon with vertices (x1, y1), (x2, y2), ..., (xn,... more
?
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Gaurav Bhatia answered • Sep 26, 2023 |
Test for Group Theory
Group Theory is a branch of mathematics that deals with the study of groups, which are mathematical structures consisting of a set of elements and an operation that combines any two elements to form a third element. If you are preparing for the IIT JAM Mathematics exam, it is important to have a thorough understanding of Group Theory as it is a significant topic in the syllabus. To test your knowledge and understanding of Group Theory, you can consider the following test:
... more|
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Gaurav Bhatia asked • Aug 17, 2023 |
Are there any specific topics or sections with higher marking weightage in the IIT JAM Mathematics Exam?
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Naina Rana answered |
Topics with Higher Marking Weightage in IIT JAM Mathematics Exam
When preparing for the IIT JAM Mathematics exam, it is important to allocate your study time wisely and focus on the topics that carry higher marking weightage. While the weightage may vary from year to year, it is generally observed that the following topics have a higher probability of appearing in the exam:
... more|
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Gaurav Bhatia asked • Aug 17, 2023 |
Where can I access the question papers for the IIT JAM Mathematics Paper?
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Naina Rana answered |
Accessing IIT JAM Mathematics Question Papers
To access the question papers for the IIT JAM Mathematics paper, you can follow the steps below:
1. Visit the EduRev website:
- Open your preferred web browser and go to the EduRev website. EduRev is a platform that provides educational resources, including question papers for various exams, including IIT JAM.
... more
To access the question papers for the IIT JAM Mathematics paper, you can follow the steps below:
1. Visit the EduRev website:
- Open your preferred web browser and go to the EduRev website. EduRev is a platform that provides educational resources, including question papers for various exams, including IIT JAM.
... more
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Gaurav Bhatia asked • Aug 07, 2023 |
Are there any cutoff relaxation criteria for candidates belonging to certain categories, such as PwD (Persons with Disabilities) or EWS (Economically Weaker Sections)?
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Radha Mehta answered |
Yes, there are cutoff relaxation criteria for candidates belonging to certain categories such as PwD (Persons with Disabilities) or EWS (Economically Weaker Sections).
PwD (Persons with Disabilities) Category:
For candidates belonging to the PwD category, there are certain relaxations in the cutoff criteria. The relaxations vary depending on the type of disability:
... more|
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Gaurav Bhatia asked • Aug 03, 2023 |
Can I get extra rough sheets if required during the IIT JAM Mathematics Paper?
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Hrithik Choudhury answered |
Can I get extra rough sheets if required during the IIT JAM Mathematics Paper?
Yes, you can get extra rough sheets if required during the IIT JAM Mathematics Paper. The conducting body understands that solving mathematical problems might require additional space for rough work and calculations. Therefore, they provide the candidates with the option to request extra rough sheets if needed. However, it is important to follow certain guidelines and procedures to obtain these sheets.... more
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