NCERT Solutions for Class 11 Maths Chapter 12 Miscellaneous Exercises

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

  • Coordinate Axes and Coordinate Planes in Three Dimensional Space
  • Coordinates of a Point in Space
  • Distance between Two Points
  • Section Formula

Download PDF NCERT Solutions for Class 12 Introduction to Three Dimensional Geometry Miscellaneous Exercises

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CBSE CLASS XII Related Questions

  • 1.
    The area of the shaded region (figure) represented by the curves \( y = x^2 \), \( 0 \leq x \leq 2 \), and the y-axis is given by:
    The area of the shaded region

      • \( \int_0^2 x^2 \, dx \)
      • \( \int_0^2 \sqrt{y} \, dy \)
      • \( \int_0^4 x^2 \, dx \)
      • \( \int_0^4 \sqrt{y} \, dy \)

    • 2.
      $ \int \frac{e^{10 \log x} - e^{8 \log x}}{e^{6 \log x} - e^{5 \log x}} \, dx$ is equal to :

        • $x + C$
        • $\frac{x^2}{2} + C$
        • $\frac{x^4}{4} + C$
        • $\frac{x^3}{3} + C$

      • 3.
        Let $\mathbf{| \mathbf{a} |} = 5$ and $-2 \leq z \leq 1$. Then, the range of $|\mathbf{a}|$ is:

          • $[5, 10]$
          • $[-2, 5]$
          • $[2, 1]$
          • $[-10, 5]$

        • 4.

          Based upon the results of regular medical check-ups in a hospital, it was found that out of 1000 people, 700 were very healthy, 200 maintained average health and 100 had a poor health record.
          Let \( A_1 \): People with good health,
          \( A_2 \): People with average health,
          and \( A_3 \): People with poor health.
          During a pandemic, the data expressed that the chances of people contracting the disease from category \( A_1, A_2 \) and \( A_3 \) are 25%, 35% and 50%, respectively.
          Based upon the above information, answer the following questions:
          (i) A person was tested randomly. What is the probability that he/she has contracted the disease?}
          (ii) Given that the person has not contracted the disease, what is the probability that the person is from category \( A_2 \)?


            • 5.
              Let \( \vec{a} \) be a position vector whose tip is the point (2, -3). If \( \overrightarrow{AB} = \vec{a} \), where coordinates of A are (–4, 5), then the coordinates of B are:

                • (-2, -2)
                • (2, -2)
                • (-2, 2)
                • (2, 2)

              • 6.
                If \( \mathbf{a} \) and \( \mathbf{b} \) are position vectors of two points \( P \) and \( Q \) respectively, then find the position vector of a point \( R \) in \( QP \) produced such that \[ QR = \frac{3}{2} QP. \]

                  CBSE CLASS XII Previous Year Papers

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