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Vector Algebra

At Saralstudy, we are providing you with the solution of Class 12th mathematics Vector Algebra according to the latest NCERT (CBSE) Book guidelines prepared by expert teachers. Here we are trying to give you a detailed answer to the questions of the entire topic of this chapter so that you can get more marks in your examinations by preparing the answers based on this lesson. We are trying our best to give you detailed answers to all the questions of all the topics of Class 12th mathematics Vector Algebra so that you can prepare for the exam according to your own pace and your speed.

Exercise 1

Popular Questions of Class 12th mathematics

 

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Let A = R – {3} and B = R – {1}. Consider the function  f : A → B defined by

. Is f one-one and onto? Justify your answer. 

 

  • Q:- Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} as
    R = {(a, b): b = a + 1} is reflexive, symmetric or transitive.
  • Q:-

    Check the injectivity and surjectivity of the following functions:

    (i) f : N → N given by f(x) = x2

    (ii) f : Z → Z given by f(x) = x2

    (iii) f : R → R given by f(x) = x2

    (iv) f : N → N given by f(x) = x3

    (v) f : Z → Z given by f(x) = x

  • Q:-

    A stone is dropped into a quiet lake and waves move in circles at the speed of 5 cm/s. At the instant when the radius of the circular wave is 8 cm, how fast is the enclosed area increasing?

  • Q:- Show that the relation R in the set R of real numbers, defined as R = {(a, b): a ≤ b2} is neither reflexive nor symmetric nor transitive.
  • Q:- If a matrix has 24 elements, what are the possible order it can have? What, if it has 13 elements?
  • Q:- Given an example of a relation. Which is
    (i) Symmetric but neither reflexive nor transitive.
    (ii) Transitive but neither reflexive nor symmetric.
    (iii) Reflexive and symmetric but not transitive.
    (iv) Reflexive and transitive but not symmetric.
    (v) Symmetric and transitive but not reflexive.
  • Q:- If a matrix has 18 elements, what are the possible orders it can have? What, if it has 5 elements?
  • Q:-

    Find the direction cosines of a line which makes equal angles with the coordinate axes.