NCERT Solutions for Class 11 Maths Chapter 11 Miscellaneous Exercises

CBSE CLASS XII Related Questions

  • 1.
    If $f: \mathbb{R} \to \mathbb{R}$ is defined as $f(x) = 2x - \sin x$, then $f$ is:

      • a decreasing function
      • an increasing function
      • maximum at $x = \frac{\pi}{2}$
      • maximum at $x = 0$

    • 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.

        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 $y = 0$.


          • 4.

            If \[ A = \begin{bmatrix} 1 & 2 & 0 \\ -2 & -1 & -2 \\ 0 & -1 & 1 \end{bmatrix} \] then find \( A^{-1} \). Hence, solve the system of linear equations: \[ x - 2y = 10, \] \[ 2x - y - z = 8, \] \[ -2y + z = 7. \]


              • 5.
                Evaluate: $ \tan^{-1} \left[ 2 \sin \left( 2 \cos^{-1} \frac{\sqrt{3}}{2} \right) \right]$


                  • 6.
                    Evaluate: \[ \int_0^{\frac{\pi}{2}} \frac{5 \sin x + 3 \cos x}{\sin x + \cos x} \, dx \]

                      CBSE CLASS XII Previous Year Papers

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