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Gaurav RaoEduRev Mathematics |
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Gaurav Rao
EduRev Mathematics
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Discussed Questions
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Gaurav Rao upvoted • 3 weeks ago |
Which one of the following is a linear transformation?- a)T : R2 ---> R2 defined by T(x, y) = (xy, x)
- b)T : R2 ---> R3 defined by T(x, y) = (x + 3, 2y, x+y)
- c)T : R3 ---> R2 defined by T(x, y, z) = (Ix| , y + z)
- d)None of these
Correct answer is option 'D'. Can you explain this answer?
Which one of the following is a linear transformation?
a)
T : R2 ---> R2 defined by T(x, y) = (xy, x)
b)
T : R2 ---> R3 defined by T(x, y) = (x + 3, 2y, x+y)
c)
T : R3 ---> R2 defined by T(x, y, z) = (Ix| , y + z)
d)
None of these
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Veda Institute answered |
Let (1,2) and (3,4) be two vectors of R2.
Then T[(1, 2) + (3,4)] = T(4, 6)]
= (4 x 6, 4) = (24, 6)
and T(l, 2) = (1 x 2,1) = (2, 1)
T(3, 4) = (3 x 4,.3) = (12, 3) Thus,T(l, 2) + T(3, 4) = (2, 1) + (12, 3) = (14, 4)
Therefore, T[(1, 2) + (3 ,4)] ≠ T(1 ,2) + T(3,4)
Hence, T is non linear.
To show that a given map T is a linear transformation we must show that
T(αx + βy) = αT(x) + βT(y)
where x,y are vectors and a, P are scalars while to show that the given map is non-linear conveniently we try to find a related contrast example.
Then T[(1, 2) + (3,4)] = T(4, 6)]
= (4 x 6, 4) = (24, 6)
and T(l, 2) = (1 x 2,1) = (2, 1)
T(3, 4) = (3 x 4,.3) = (12, 3) Thus,T(l, 2) + T(3, 4) = (2, 1) + (12, 3) = (14, 4)
Therefore, T[(1, 2) + (3 ,4)] ≠ T(1 ,2) + T(3,4)
Hence, T is non linear.
To show that a given map T is a linear transformation we must show that
T(αx + βy) = αT(x) + βT(y)
where x,y are vectors and a, P are scalars while to show that the given map is non-linear conveniently we try to find a related contrast example.
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Gaurav Rao upvoted • Feb 24, 2025 |
The directional derivative of f(x, y, z) = x2 + y2 + z2 at the point (1, 1, 1) in the direction
- a)zero
- b)1
- c)
- d)
Correct answer is option 'A'. Can you explain this answer?
The directional derivative of f(x, y, z) = x2 + y2 + z2 at the point (1, 1, 1) in the direction
a)
zero
b)
1
c)
d)
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Veda Institute answered |
We have,
Thus, directional derivative of f in the direction of
the point P(1, 1, 1),
Thus, directional derivative of f in the direction of
the point P(1, 1, 1),|
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Gaurav Rao 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
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Gaurav Rao upvoted • Feb 04, 2025 |
The c-discriminant of the equations
(y - c)2 = x(x - a)2 is- a)x(x - a2) = 0
- b) x - a2 = 0
- c)x = a
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
The c-discriminant of the equations
(y - c)2 = x(x - a)2 is
(y - c)2 = x(x - a)2 is
a)
x(x - a2) = 0
b)
x - a2 = 0
c)
x = a
d)
None of these
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Veda Institute answered |
Given, differential equation is
(y - c)2 = x(x - a)2
(y - c)2 = x(x - a)2
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Gaurav Rao upvoted • Jan 30, 2025 |
For an incompressible flow, the x and y components of the velocity vector are 
= 3(y | z), where x, y and z are in metre, all velocities are in m/s. Then, the z component of the velocity vector 
of the flow for the boundary condition 
at z = 0, is - a)5z
- b)-5z
- c)2x + 3z
- d)-2x - 3z
Correct answer is option 'B'. Can you explain this answer?
For an incompressible flow, the x and y components of the velocity vector are = 3(y | z), where x, y and z are in metre, all velocities are in m/s. Then, the z component of the velocity vector of the flow for the boundary condition at z = 0, is
= 3(y | z), where x, y and z are in metre, all velocities are in m/s. Then, the z component of the velocity vector of the flow for the boundary condition at z = 0, is a)
5z
b)
-5z
c)
2x + 3z
d)
-2x - 3z
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Veda Institute answered |
Given
(where, vz = 0 at z = 0 and fluid is incompressible) For incompressible fluid flow, equation of continuity is
or
or
So,
(where, vz = 0 at z = 0 and fluid is incompressible) For incompressible fluid flow, equation of continuity is
or
or
So,
The orthogonal trajectories of the given family of curves y = cx2 are given by- a)x2 + cy2 = constant
- b)x2 + ky2 = constant
- c)kx2 + y2 = constant
- d)x2 - ky2 = constant
Correct answer is option 'B'. Can you explain this answer?
The orthogonal trajectories of the given family of curves y = cx2 are given by
a)
x2 + cy2 = constant
b)
x2 + ky2 = constant
c)
kx2 + y2 = constant
d)
x2 - ky2 = constant
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Gaurav Rao answered • Jan 28, 2025 |
Understanding Orthogonal Trajectories
Orthogonal trajectories are curves that intersect a given family of curves at right angles. In this case, we are examining the family of curves defined by y = cx², where c is a constant.
Step 1: Finding the Family of Curves
- The given family is y = cx², which represents a set of parabolas opening upwards.
- Each curve corresp... more
Orthogonal trajectories are curves that intersect a given family of curves at right angles. In this case, we are examining the family of curves defined by y = cx², where c is a constant.
Step 1: Finding the Family of Curves
- The given family is y = cx², which represents a set of parabolas opening upwards.
- Each curve corresp... more
The point of inflection of the curve y = x3 - 6x2 + 12x - 3 is______________.
Correct answer is '2'. Can you explain this answer?
The point of inflection of the curve y = x3 - 6x2 + 12x - 3 is______________.
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Gaurav Rao answered • Nov 13, 2024 |
Understanding Inflection Points
An inflection point occurs where the curve changes its concavity, meaning that the second derivative of the function changes sign. For the function y = x^3 - 6x^2 + 12x - 3, we need to find the second derivative and its critical points.
Step 1: Finding the First Derivative
- The first derivative, y', is calculated as:
- y' = 3x^2 -... more
An inflection point occurs where the curve changes its concavity, meaning that the second derivative of the function changes sign. For the function y = x^3 - 6x^2 + 12x - 3, we need to find the second derivative and its critical points.
Step 1: Finding the First Derivative
- The first derivative, y', is calculated as:
- y' = 3x^2 -... more
Which of the following group is cyclic
1) Z2 *Z4
2) Z3*Z4
3) Z3*Z6
4) Z2*Z4?
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Gaurav Rao answered • Jul 24, 2024 |
Explanation of Cyclic Group:
Cyclic groups are groups that can be generated by a single element, which is called a generator. In a cyclic group, every element can be expressed as a power of the generator.
Z2 * Z4:
- Z2 is the group of integers modulo 2 under addition, {0, 1}, and Z4 is the group of integers modulo 4 under addition, {0, 1, 2, 3}.
- The group... more
Cyclic groups are groups that can be generated by a single element, which is called a generator. In a cyclic group, every element can be expressed as a power of the generator.
Z2 * Z4:
- Z2 is the group of integers modulo 2 under addition, {0, 1}, and Z4 is the group of integers modulo 4 under addition, {0, 1, 2, 3}.
- The group... more
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Gaurav Rao asked • Jun 24, 2024 |
If 
, then find out the value of 
.Correct answer is '0'. Can you explain this answer?
If , then find out the value of .
, then find out the value of .|
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Veda Institute answered |
The given equation is,
Differentiating equation (1) with respect to x, we get
Now, again differentiating equation (1) with respect to y, we get
Hence, the correct answer is 0.
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Gaurav Rao asked • Jun 17, 2024 |
If ‘p’, ‘q’ and ‘n’ are probability pf success, failure and number of trials respectively in a Binomial Distribution, what is its Standard Deviation ?- a) (np)1⁄2
- b)(pq)1⁄2
- c)(np)2
- d)
Correct answer is option 'D'. Can you explain this answer?
If ‘p’, ‘q’ and ‘n’ are probability pf success, failure and number of trials respectively in a Binomial Distribution, what is its Standard Deviation ?
a)
(np)1⁄2
b)
(pq)1⁄2
c)
(np)2
d)
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Veda Institute answered |
The variance (V) for a Binomial Distribution is given by V = npq
Standard Deviation = 
X1, X2, .... Xn are independent observations on the random variable X with distribution function F(x). Then the distribution function of Y = Max (X1, X2, ..., Xn) is- a)[F(x)]n
- b)1 - [F(x)]n
- c)1 - [1 - F(x)]n
- d)[1-F(x)]n
Correct answer is option 'A'. Can you explain this answer?
X1, X2, .... Xn are independent observations on the random variable X with distribution function F(x). Then the distribution function of Y = Max (X1, X2, ..., Xn) is
a)
[F(x)]n
b)
1 - [F(x)]n
c)
1 - [1 - F(x)]n
d)
[1-F(x)]n
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Gaurav Rao answered • Apr 16, 2024 |
Explanation:
Distribution function of Y:
- The random variable Y represents the maximum of n independent observations.
- The probability that Y is less than or equal to a particular value y is the same as the probability that each of the n observations is less than or equal to y.
- Since the observations are independent, the probability that all n observatio... more
Distribution function of Y:
- The random variable Y represents the maximum of n independent observations.
- The probability that Y is less than or equal to a particular value y is the same as the probability that each of the n observations is less than or equal to y.
- Since the observations are independent, the probability that all n observatio... more
In any group, the number of improper subgroups is
- a)2
- b)3
- c)depends on the group
- d)1
Correct answer is option 'A'. Can you explain this answer?
In any group, the number of improper subgroups is
a)
2
b)
3
c)
depends on the group
d)
1
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Gaurav Rao answered • Feb 06, 2024 |
Number of Improper Subgroups in a Group
In a group, the number of improper subgroups is always 2. This is a fundamental property of group theory.
Definition of an Improper Subgroup:
An improper subgroup of a group G is a subgroup that contains the identity element of the group and the group itself. In other words, it is the entire group G.
Explanation:
... more
In a group, the number of improper subgroups is always 2. This is a fundamental property of group theory.
Definition of an Improper Subgroup:
An improper subgroup of a group G is a subgroup that contains the identity element of the group and the group itself. In other words, it is the entire group G.
Explanation:
The probability that a man who is 85 yrs. old will die before attaining the age of 90 is 1 / 3. A1, A2, A3 and A4 are four persons who are 85 yrs. old. The probability that A1 will die before attaining the age of 90 and will be the first to die is- a)65/81
- b)13/81
- c)65/324
- d)13/108
Correct answer is option 'C'. Can you explain this answer?
The probability that a man who is 85 yrs. old will die before attaining the age of 90 is 1 / 3. A1, A2, A3 and A4 are four persons who are 85 yrs. old. The probability that A1 will die before attaining the age of 90 and will be the first to die is
a)
65/81
b)
13/81
c)
65/324
d)
13/108
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Gaurav Rao answered • Jan 05, 2024 |
Given information:
- The probability that a man who is 85 yrs. old will die before attaining the age of 90 is 1/3.
- A1, A2, A3, and A4 are four persons who are 85 yrs. old.
To find:
The probability that A1 will die before attaining the age of 90 and will be the first to die.
Solution:
Step 1: Probability that A1 dies before 90:... more
- The probability that a man who is 85 yrs. old will die before attaining the age of 90 is 1/3.
- A1, A2, A3, and A4 are four persons who are 85 yrs. old.
To find:
The probability that A1 will die before attaining the age of 90 and will be the first to die.
Solution:
Step 1: Probability that A1 dies before 90:... more
The last two digit of the number 9^9^9?
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Gaurav Rao answered • Dec 09, 2023 |
The Last Two Digits of the Number 9^9^9
To determine the last two digits of the number 9^9^9, we need to understand the properties of modular arithmetic and the concept of finding remainders.
Modular Arithmetic:
Modular arithmetic is a system of arithmetic for integers where numbers "wrap around" upon reaching a certain value, called the modulus. In this ca... more
To determine the last two digits of the number 9^9^9, we need to understand the properties of modular arithmetic and the concept of finding remainders.
Modular Arithmetic:
Modular arithmetic is a system of arithmetic for integers where numbers "wrap around" upon reaching a certain value, called the modulus. In this ca... more
If the equation of the curve is x2 + y2 = a2 then- a)Surface area of the solid generated by revolving about x - axis is 4πa2
- b)Surface area of the Solid generated by revolving about y - axis is 4πa2
- c)Surface area of the Solid generated by revolving about x - axis is 2πa2
- d)Surface area of the Solid generated by revolving about y - axis is 2πa2
Correct answer is option 'A,B'. Can you explain this answer?
If the equation of the curve is x2 + y2 = a2 then
a)
Surface area of the solid generated by revolving about x - axis is 4πa2
b)
Surface area of the Solid generated by revolving about y - axis is 4πa2
c)
Surface area of the Solid generated by revolving about x - axis is 2πa2
d)
Surface area of the Solid generated by revolving about y - axis is 2πa2
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Gaurav Rao answered • Nov 15, 2023 |
To find the surface area of the solid generated by revolving the curve about the x-axis, we can use the formula for the surface area of revolution:
S = 2π∫[a, b] y * √(1 + (dy/dx)^2) dx
First, let's solve the equation of the curve x^2 + y^2 = a^2 for y:
y^2 = a^2 - x^2
y = ±√(a^2 - x^2)
Since we are only interested in the positive y-values, we... more
S = 2π∫[a, b] y * √(1 + (dy/dx)^2) dx
First, let's solve the equation of the curve x^2 + y^2 = a^2 for y:
y^2 = a^2 - x^2
y = ±√(a^2 - x^2)
Since we are only interested in the positive y-values, we... more
Let G be a group of order pq where p and q are prime numbers. Such that p > q then, G can have- a)atmost one subgroup of order p.
- b)atleast one subgroup of order q.
- c)atleast one subgroup of order p.
- d)atmost one subgroup of order q.
Correct answer is option 'C'. Can you explain this answer?
Let G be a group of order pq where p and q are prime numbers. Such that p > q then, G can have
a)
atmost one subgroup of order p.
b)
atleast one subgroup of order q.
c)
atleast one subgroup of order p.
d)
atmost one subgroup of order q.
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Gaurav Rao answered • Oct 30, 2023 |
By Cauchy's theorem, since p and q are primes dividing the order of the group G, there exist elements a and b in G of order p and q respectively.
Consider the subgroup H = . Since the order of a is p, the order of H is p. Therefore, H is a cyclic subgroup of G of order p.
Similarly, consider the subgroup K = . Since the order of b is q, the order of K is q. Therefore, K... more
Consider the subgroup H = . Since the order of a is p, the order of H is p. Therefore, H is a cyclic subgroup of G of order p.
Similarly, consider the subgroup K = . Since the order of b is q, the order of K is q. Therefore, K... more
Let us consider a 3×3 matrix A with Eigen values of λ1, λ2, λ3 and the Eigen values of A-1 are?- a)λ1, λ2, λ3
- b)1 / λ1, 1 / λ2, 1 / λ3
- c)-λ1, -λ2, -λ3
- d)λ1, 0, 0
Correct answer is option 'B'. Can you explain this answer?
Let us consider a 3×3 matrix A with Eigen values of λ1, λ2, λ3 and the Eigen values of A-1 are?
a)
λ1, λ2, λ3
b)
1 / λ1, 1 / λ2, 1 / λ3
c)
-λ1, -λ2, -λ3
d)
λ1, 0, 0
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Gaurav Rao answered • Sep 19, 2023 |
X3 matrix A. The three rows of the matrix can represent three different variables or three different equations. The three columns of the matrix can represent three different data points or three different coefficients.
For example, let's say we have the following matrix A:
A = [[1, 2, 3],
[4, 5, 6],
[7, 8, 9]]
In this case, the three rows repres... more
For example, let's say we have the following matrix A:
A = [[1, 2, 3],
[4, 5, 6],
[7, 8, 9]]
In this case, the three rows repres... more
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Gaurav Rao asked • Aug 17, 2023 |
Are there any specific tips for avoiding silly mistakes that may lead to negative marking in the IIT JAM Mathematics Exam?
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Naina Rana answered |
Tips for Avoiding Silly Mistakes in IIT JAM Mathematics Exam
Introduction:
The IIT JAM Mathematics exam is a prestigious and highly competitive examination. To excel in this exam, it is crucial to minimize the chances of making silly mistakes. Silly mistakes can lead to negative marking and hinder your chances of scoring well. Here are some effective tips to avoid suc... more
Introduction:
The IIT JAM Mathematics exam is a prestigious and highly competitive examination. To excel in this exam, it is crucial to minimize the chances of making silly mistakes. Silly mistakes can lead to negative marking and hinder your chances of scoring well. Here are some effective tips to avoid suc... more
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Gaurav Rao asked • Aug 17, 2023 |
Are there any specific steps I need to follow to download the question papers for the IIT JAM Mathematics Paper?
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Naina Rana answered |
How to Download IIT JAM Mathematics Question Papers
Introduction:
IIT JAM (Joint Admission Test for M.Sc.) is a national-level exam conducted by the Indian Institutes of Technology (IITs) for admission to various postgraduate programs in science and technology. If you are preparing for the IIT JAM Mathematics Paper, it is crucial to practice with previous years' quest... more
Introduction:
IIT JAM (Joint Admission Test for M.Sc.) is a national-level exam conducted by the Indian Institutes of Technology (IITs) for admission to various postgraduate programs in science and technology. If you are preparing for the IIT JAM Mathematics Paper, it is crucial to practice with previous years' quest... more
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Gaurav Rao asked • Aug 07, 2023 |
Can you suggest some strategies to prepare specifically to achieve the cutoff in the IIT JAM Mathematics Paper?
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Radha Mehta answered |
Strategies to Achieve the Cutoff in the IIT JAM Mathematics Paper
1. Understand the Exam Pattern:
- Familiarize yourself with the exam pattern, syllabus, and marking scheme of the IIT JAM Mathematics paper.
- The paper consists of multiple-choice questions with negative marking for incorrect answers.
- Allocate time for each section based on the number of qu... more
1. Understand the Exam Pattern:
- Familiarize yourself with the exam pattern, syllabus, and marking scheme of the IIT JAM Mathematics paper.
- The paper consists of multiple-choice questions with negative marking for incorrect answers.
- Allocate time for each section based on the number of qu... more
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Gaurav Rao asked • Aug 03, 2023 |
Can I get a virtual calculator to practice before the IIT JAM Mathematics Exam?
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Hrithik Choudhury answered |
Virtual Calculator for IIT JAM Mathematics Exam Preparation
Preparing for the IIT JAM Mathematics Exam requires thorough practice and familiarity with the calculator that will be used during the exam. The virtual calculator is an essential tool for solving complex mathematical problems efficiently and accurately. Here, we will discuss how you can obtain and utilize a virtual calc... more
Preparing for the IIT JAM Mathematics Exam requires thorough practice and familiarity with the calculator that will be used during the exam. The virtual calculator is an essential tool for solving complex mathematical problems efficiently and accurately. Here, we will discuss how you can obtain and utilize a virtual calc... more
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