NCERT Solutions for Class 11 Maths Chapter 12 Exercise 12.1

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Class 11 Maths NCERT Solutions Chapter 12 Introduction to Three Dimensional Geometry Exercise 12.1 is based on the following concepts:

  • Coordinate Axes and Coordinate Planes in Three Dimensional Space
  • Coordinates of a Point in Space

Download PDF NCERT Solutions for Class 12 Introduction to Three Dimensional Geometry Exercise 12.1

Check out the solutions of Class 11 Maths NCERT Solutions Chapter 12 Introduction to Three Dimensional Geometry Exercise 12.1

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CBSE CLASS XII Related Questions

  • 1.
    If \[ \frac{d}{dx}(F(x))=\frac{1}{e^x+1}, \] then find \(F(x)\), given that \[ F(0)=\log\left(\frac{1}{2}\right). \]


      • 2.
        Assertion (A) : In an experiment of throwing an unbiased die, the probability of getting a prime number given that number appearing on the die being odd is \( \frac{2}{3} \).
        Reason (R) : For any two events \( A \) and \( B \), \( P(A|B) = \frac{P(A \cup B)}{P(B)} \).

          • Both Assertion (A) and Reason (R) are true and the Reason (R) is the correct explanation of the Assertion (A).
          • Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
          • Assertion (A) is true and Reason (R) is false.
          • Assertion (A) is false and Reason (R) is true.

        • 3.

          Find the domain of \[ q(x)=\cos^{-1}(4x^2-3). \] Hence, find the value of \(x\) for which \[ q(x)=0. \] Also, write the range of \[ 3q(x)-\pi. \] 


            • 4.
              Evaluate: \[ \cos\left[\sin^{-1}(-1)-\tan^{-1}(-\sqrt{3})\right]. \]


                • 5.
                  The least value of \[ f(x)=e^{-x} \] in the interval \[ [0,3] \] is:

                    • \( e^{-3} \)
                    • \( -1 \)
                    • \( 1 \)
                    • \( -e^3 \)

                  • 6.
                    In a school, the probability of holding a debate competition is \( \frac{1}{3} \) and that of a quiz competition is \( \frac{2}{3} \). In the two participating teams, A has 4 girls and 6 boys and B has 7 girls and 3 boys. If a debate competition is held, the students are selected from team A and for the quiz competition they are selected from team B. If only two students are to be chosen from the teams, then find the probability that one will be a girl and the other a boy.

                      CBSE CLASS XII Previous Year Papers

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