NCERT Solutions for Class 12 Maths Chapter 12 Miscellaneous Exercise

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Class 12 Maths NCERT Solutions Chapter 12 Linear Programming Miscellaneous Exercises are provided in the article. Class 12 Chapter 12 Linear Programming Exercises include questions on following concepts: 

  • Linear Programming Problem and its Mathematical Formulation
  • Different Types of Linear Programming Problems

Download PDF NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming Miscellaneous Exercises 

Check out the solutions of Class 12 Maths NCERT solutions chapter 12 Linear Programming Miscellaneous Exercises 

Read More: NCERT Solutions For Class 12 Mathematics Chapter 12 Linear Programming

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CBSE CLASS XII Related Questions

  • 1.
    Evaluate : \[ I = \int_0^{\frac{\pi}{4}} \frac{dx}{\cos^3 x \sqrt{2 \sin 2x}} \]


      • 2.
        If $M$ and $N$ are square matrices of order 3 such that $\det(M) = m$ and $MN = mI$, then $\det(N)$ is equal to :

          • $-1$
          • 1
          • $-m^2$
          • $m^2$

        • 3.
          If \( \overrightarrow{a} + \overrightarrow{b} + \overrightarrow{c} = 0 \), \( |\overrightarrow{a}| = \sqrt{37} \), \( |\overrightarrow{b}| = 3 \), and \( |\overrightarrow{c}| = 4 \), then the angle between \( \overrightarrow{b} \) and \( \overrightarrow{c} \) is:

            • \( \frac{\pi}{6} \)
            • \( \frac{\pi}{4} \)
            • \( \frac{\pi}{3} \)
            • \( \frac{\pi}{2} \)

          • 4.
            Let \( 2x + 5y - 1 = 0 \) and \( 3x + 2y - 7 = 0 \) represent the equations of two lines on which the ants are moving on the ground. Using matrix method, find a point common to the paths of the ants.


              • 5.

                Draw a rough sketch for the curve $y = 2 + |x + 1|$. Using integration, find the area of the region bounded by the curve $y = 2 + |x + 1|$, $x = -4$, $x = 3$, and $y = 0$.


                  • 6.
                    The integrating factor of the differential equation \( (x + 2y^3) \frac{dy}{dx} = 2y \) is:

                      • \( e^{y^2} \)
                      • \( \frac{1}{\sqrt{y}} \)
                      • \( e^{-\frac{1}{y^2}} \)
                      • \( e^{y^2} \)
                    CBSE CLASS XII Previous Year Papers

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