Vaishnavi Verma

EduRev Mathematics

Vaishnavi Verma
EduRev Mathematics
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Vaishnavi Verma upvoted   •  4 weeks ago

Let T :R3---> R3: be a linear transformation defined by T(x, y, z) = (2x, 2x - 5y, 2y + z). Then T-1 is
  • a)
  • b)
  • c)
  • d)
    None of these
Correct answer is option 'A'. Can you explain this answer?

Veda Institute answered
Let T be a linear transformation defined by T(x, y, z) = (2x, 2x -5y,2y + z)
We need to find T-1
Let (x, y, z) ∈ ker T,
Then T(x,y,z) = (0,0,0)
Using definition of T, we get
(2x, 2x - 5y, 2y + z) - (0, 0, 0) Implies, 2x = 0, 2x- 5y = 0 and 2y + z = 0
Solving for x, y and z, we get
x = 0, y = 0 and z =0
Hence, ker T = {(0, 0, 0)}
and thus T is one-one.
Since R3 is a three dimensional (finite dimensional) vector space and T is a linear transformation from R3 to R3.
Hence, T is onto.
Therefore, T-1 exist.
Let (a, b, c) be the image of (x, y, z) under T-1 then T-1(x, y, z) = (a, b, c) Implies, T(a, b, c) = (x,y, z)
Using the definition of linear transformation T,
we get
(2a, 2a - 5b, 2b + c) = (x, y, z) Comparing the components of the co-ordinates,
we get 2a= x ,2a-5b = y and 2b + c = z
Solving for a, b and c we get,

Therefore 

Vaishnavi Verma upvoted   •  Feb 11, 2025

Consider the differential equation y" + 4y = 8cos2x , with y(0) = 0 and then y( π ) is equal to _________ .
    Correct answer is '0'. Can you explain this answer?

    Veda Institute answered
    We have
    (D2 +4) y = 8 cos 2x 
    A . E.
    ⇒ y(x) = C1 cos 2x + C2 sin 2x + 2x sin 2x
    y(0) = 0 ⇒ C1 = 0
    y'(0) = 0 ⇒ 2C2 = 0 ⇒ C2 = 0
    ⇒ y(x) = 2x sin 2x
    ⇒ 
    and y (π) = 0

    Vaishnavi Verma upvoted   •  Feb 06, 2025

    The area of a quadrilateral, whose vertices are given by (x1,  y1), (x2, y2), (x3, y3) and (x4, y4) respectively, is
    • a)
    • b)
    • c)
    • d)
    Correct answer is option 'B'. Can you explain this answer?

    Veda Institute answered
    Comments on the Area of a Δand a quadrilateral
    The above formula for the area of a triangle or a quadrilateral and are easy to remember.
    Write the coordinates as shown below:

    Note that the first written coordinate is repeated in the last. Multiply diagonally along arrows. Attach a positive sign if the arrow goes from left to right and a negative sign if the arrow goes from right to left.

    Vaishnavi Verma upvoted   •  Jan 30, 2025

    The value of  where F = (x2 - y2)i + xyj and curve C is the arc of curve y = x3 from (0, 0) to (2, 8) is.... (Correction upto two decimal places)
      Correct answer is '39.238'. Can you explain this answer?

      Veda Institute answered
      The curve C is the curve y=x3 from (0,0) to (2,8) Let x = t, Then y = t3. if  is the position vector of any point (x,y) on c, then 
      Also interms of t ,  
      At the point (0,0), t = x=0. At the point (2,8), t=2.
       
       
       

      The solution eurves of the given differential equation xdx - dy = 0 are given by a family of
      • a)
        Parabolas
      • b)
        Hyperbolas
      • c)
        Circles
      • d)
        Ellipses
      Correct answer is option 'A'. Can you explain this answer?

      Vaishnavi Verma answered  •  Jan 11, 2025
      Understanding the Differential Equation
      The given differential equation is xdx - dy = 0. This can be rewritten as:
      - dy = xdx
      By rearranging this, we have:
      - dy = xdx
      This indicates a relationship between x and y.
      Finding the General Solution
      To solve the equation, we can integrate both sides:
      - ∫ dy = ∫ xdx
      This yields:
      - y = (1/2)x
      ... more

      Even numbers are formed with three digits such that if 5 is one of the digit then 7 is the next digit. The number of such numbers is (repetition is allowed).
      • a)
        360
      • b)
        365
      • c)
        325
      • d)
        none
      Correct answer is option 'B'. Can you explain this answer?

      Vaishnavi Verma answered  •  Sep 30, 2024
      Understanding the Problem
      To find the number of three-digit even numbers under the given conditions, we need to consider the following:
      1. Three-Digit Even Numbers: The last digit must be even (0, 2, 4, 6, or 8).
      2. Condition with Digit 5: If 5 appears in the number, then the next digit must be 7.
      Analyzing the Digits
      - Hundreds Place: Th
      ... more

      The equation of the straight line passing through (4, 5) and parallel to the line 2x - 3y = 5 is given by
      • a)
        2 x - 3 y = 7
      • b)
        2 x - 3 y = -7
      • c)
        3 x - 2 y = 7
      • d)
        3 x - 2 y = -7
      Correct answer is option 'B'. Can you explain this answer?

      Vaishnavi Verma answered  •  Jun 26, 2024
      Given Information:
      - Point (4, 5) passes through the line
      - The line is parallel to 2x - 3y = 5

      Explanation:

      Finding the Gradient:
      - To find the gradient of the given line 2x - 3y = 5, rearrange it into the slope-intercept form, y = mx + c.
      - 2x - 3y = 5
      - -3y = -2x + 5
      - y = (2/3)x - 5/3
      - The gradient of this line is
      ... more
      Vaishnavi Verma asked   •  Jun 14, 2024

      Let A be an n-by-n matrix with coefficients in F, having rows{a1, ..., an). Then which one of the statement is true for the matrix A?
      • a)
         A’ be a matrix obtained from A by an elementary row operation (interchanging two rows). Then D(A’) = –D(A)
      • b)
         A’ be a matrix obtained from A by an elementary row operation (replacing the row ai by ai + λaj , with λ ∈ F, i ≠ j).  Then D(A’) = D(A)
      • c)
         A’ be a matrix obtained from A by an elementary row operation (replacing ai by µaj , for µ ≠ 0 in F).  Then D(A’) = µD(A). 
      • d)
         All the three options are correct.
      Correct answer is option 'D'. Can you explain this answer?

      Veda Institute answered
      By a well known result we know that if A be an n × n matrix with coefficients in F, having rows {a1, a2, ....., an }, then the following statements are true. 
       (a) if A’ be a matrix obtained from A by an elementary row operation (interchanging two rows). Then 
       D(A’) = – D(A) 
       (b) if A’ be a matrix obtained from a by an elementary row operation (replacing the row ai by λaj , with λ ∈ F, i ≠ j). Then 
      D(A’) = D(A) 
      (c) if A’ be a matrix obtained from A by an elementary row operation (replacing ai by µai , for µ ≠ 0 in F). Then 
       D(A’) = µD(A)
      i.e. all the three options are correct. 

      If each of the pairs of straight lines x2 - 2pxy - y2 = 0 and x2 - 2qxy- y2 = 0 bisects the angles between the other pair, then
      • a)
        pq=1
      • b)
        pq=-1
      • c)
        p2=-q2
      • d)
        p2q2 = -1
      Correct answer is option 'B'. Can you explain this answer?

      Vaishnavi Verma answered  •  Mar 19, 2024



      Explanation:



      1. Given equations:
        The given pair of equations are x^2 - 2pxy - y^2 = 0 and x^2 - 2qxy - y^2 = 0.



      2. Angle bisectors:
        To bisect the angles between the pair of lines, the lines themselves must be the angle bisectors of the other pair.



      3. ... more



      4. Applying the condition:
        By applying the angle bisector condition to the given pairs of lines, we get:
        For x^2 - 2pxy - y^2 = 0:
        (1)^2 = (-2p)^2 - 1*(-1) => 1 = 4p^2 + 1 => 4p^2 = 0 => p^2 = 1/4
        For x^2 - 2qxy - y^2 = 0:
        (1)^2 = (-2q)^2 - 1*(-1) => 1 = 4q^2 + 1 => 4q^2 = 0 => q^2 = 1/4



      5. Comparing p^2 and q^2:
        From the above calculations, we can see that p^2 = q^2 = 1/4. Therefore, pq = (1/2)(1/2) = 1/4.



      6. Conclusion:
        Hence, the correct answer is pq = 1, which is represented by option 'B'.




      ?

      Vaishnavi Verma answered  •  Jan 24, 2024
      IIT JAM Mathematics is a highly competitive exam conducted by the Indian Institutes of Technology (IITs) for admission to their M.Sc. programs in Mathematics. To prepare for this exam, it is important to have access to solved question papers and past year papers. These papers provide valuable insights into the exam pattern, types of questions asked, and help in identifying important topics.
      <
      ... more

      Find the volume of the solid which is in the first octant bounded by the cylinder x^2+y^2=a^2 and y^2+z^2=a^2?

      Vaishnavi Verma answered  •  Dec 24, 2023
      Problem:
      Find the volume of the solid which is in the first octant bounded by the cylinder x^2 y^2=a^2 and y^2 z^2=a^2

      Solution:
      To find the volume of the solid bounded by the given surfaces, we need to set up a triple integral in Cartesian coordinates.

      Step 1: Identifying the Boundaries
      In the first octant, the boundaries for x, y, and z a
      ... more

      Please delete my account.If not possible,then atleast stop sending me ur marketing mails.Dont send messages or calls to my number also.I am not at all interested in your courses.pls for the love of god?

      Vaishnavi Verma answered  •  Nov 30, 2023
      Request to Delete Account and Stop Marketing Communication

      I understand that you would like to delete your account and stop receiving marketing emails from us. I apologize for any inconvenience caused and assure you that we will comply with your request. Please find below the details on how we can proceed with your request:

      Account Deletion:
      To delete your
      ... more

      Let v be the vector space of 2x2 matrices over R and let. M=[1 2;3 4] Let T be the linear operator on V defined by T(A)=MA. Then the trace of T is?

      Vaishnavi Verma answered  •  Nov 06, 2023
      Trace of a Linear Operator

      The trace of a linear operator is defined as the sum of the diagonal elements of the matrix representation of the operator. In this case, we are given a linear operator T on the vector space V of 2x2 matrices over the real numbers.

      Matrix Representation of T

      To find the matrix representation of T, we need to determine how T
      ... more

      If inn(G) denote the inner automophism on G and Dn denote the dihedral group of order 2n.choose the correct option a) inn(D6) contains only two element of order three b) inn(D6) contains only two element of order 6 C) inn(D4)... more

      Vaishnavi Verma answered  •  Oct 25, 2023
      Inner Automorphisms and Dihedral Groups

      Definition: An automorphism of a group G is an isomorphism from G to itself. The set of all automorphisms of G, denoted Aut(G), forms a group under composition of functions.

      Definition: An inner automorphism of a group G is an automorphism of the form φ_g(x) = gxg^(-1), where g is an element of G. The set of all inn
      ... more

      What is the probability that an urn containing 5 balls contains only white balls if the first two balls drawn from it was found to be white
      • a)
        1/20
      • b)
        1/10
      • c)
        1/2
      • d)
        1/4
      Correct answer is option 'C'. Can you explain this answer?

      Vaishnavi Verma answered  •  Sep 29, 2023
      To solve this problem, we can use the concept of conditional probability. Let's break down the problem step by step.

      Step 1: Determine the total number of possible outcomes
      The urn contains 5 balls, and each ball can either be white or not white (let's assume there are no other colors). Since there are two possibilities for each ball, the total number of possible outcomes is 2^5 =
      ... more
      Vaishnavi Verma asked   •  Aug 17, 2023

      Can I choose the specialization within the M.Sc. Physics program at the time of admission?

      Naina Rana answered
      Choosing a Specialization within the M.Sc. Physics Program at the Time of Admission

      Introduction:
      When applying for an M.Sc. Physics program, students often wonder if they can choose a specialization at the time of admission. The answer to this question may vary depending on the university or institution offering the program. However, in many cases, students do have the opti
      ... more

      Vaishnavi Verma asked   •  Aug 14, 2023

      Can I get the answer key for the IIT JAM Mathematics in the form of a PDF or a downloadable file?

      Oishi Bajaj answered
      Answer:

      Introduction:
      The 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 courses in science and technology. The Mathematics paper of IIT JAM consists of multiple-choice questions and is conducted for a duration of 3 hours.

      Answer key for IIT J
      ... more
      The answer key for the IIT JAM Mathematics paper is a crucial resource for candidates to assess their performance in the exam and calculate their probable scores. It helps candidates to analyze their strengths and weaknesses and identify areas where they need improvement.

      Availability:
      The answer key for the IIT JAM Mathematics paper is usually released by various coaching institutes and educational platforms after the completion of the exam. It is commonly made available in the form of a PDF or downloadable file on their respective websites.

      Benefits of answer key:
      The answer key provides candidates with the correct answers to the questions asked in the exam. It allows them to compare their answers with the provided solutions and calculate their probable scores. Some of the benefits of using the answer key are:

      1. Self-assessment: Candidates can evaluate their performance and gauge their level of preparation by matching their answers with the correct solutions.

      2. Time management: The answer key helps candidates in analyzing the time they have spent on each question and identifying areas where they need to improve their speed.

      3. Understanding mistakes: By comparing their answers with the correct solutions, candidates can identify and understand their mistakes. This helps them avoid similar mistakes in future exams.

      4. Predicting rank: Using the answer key, candidates can estimate their probable rank based on their calculated scores. This gives them an idea about their chances of getting admission to their desired postgraduate courses.

      Downloading the answer key:
      To download the answer key for the IIT JAM Mathematics paper, you can follow these steps:

      1. Visit the website of a reputed coaching institute or educational platform that provides the answer key for IIT JAM Mathematics.

      2. Look for the section or link related to the answer key for the Mathematics paper.

      3. Click on the link or download button to access the answer key.

      4. The answer key will either open as a PDF file in your browser or will be downloaded to your device.

      5. You can then save the PDF file or open it to view the correct answers to the questions asked in the exam.

      Note: It is important to rely on trusted and reputable sources for the answer key to ensure accuracy and reliability of the solutions provided.

      Conclusion:
      The answer key for the IIT JAM Mathematics paper is a valuable resource for candidates to evaluate their performance and calculate their probable scores. It can be downloaded in the form of a PDF or downloadable file from the websites of reputed coaching institutes and educational platforms. By using the answer key effectively, candidates can assess their preparation, identify their mistakes, and improve their chances of getting admission to their desired postgraduate courses.

      Vaishnavi Verma asked   •  Aug 07, 2023

      Are there any books that focus on the most common mistakes made by candidates in the IIT JAM Mathematics Exam and how to avoid them?

      Radha Mehta answered
      There are several books available that focus on the most common mistakes made by candidates in the IIT JAM Mathematics Exam and provide guidance on how to avoid them. These books aim to help aspiring candidates understand the exam pattern, identify common pitfalls, and provide strategies to overcome them. Here are some popular books that you can consider:

      1. "IIT JAM Mathematics Solved
      ... more

      Vaishnavi Verma asked   •  Aug 02, 2023

      What are the best techniques for memorizing formulas and theorems for the IIT JAM Mathematics Exam?

      Nakul Bajaj answered
      Techniques for Memorizing Formulas and Theorems for the IIT JAM Mathematics Exam


      Create a Structured Study Plan

      - Divide the syllabus into smaller sections and allocate specific time for each topic.
      - Prioritize the formulas and theorems based on their importance and frequency of occurrence in previous exams.

      Understand the Concepts
      ... more

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