NCERT Solutions for Class 11 Maths Chapter 2 Exercise 2.1

CBSE CLASS XII Related Questions

  • 1.

    Differential of \( \log \sin x \) with respect to \( \sqrt{\cos x} \) is :

      • \( -2\sqrt{\cos x}\cdot\cot x\cdot\operatorname{cosec} x \)
      • \( \sqrt{\cos x}\cdot\cot x\cdot\operatorname{cosec} x \)
      • \( \frac{2\sqrt{\cos x}}{\sin x} \)
      • \( \frac{1}{\sin x\sqrt{\cos x}} \)

    • 2.

      For the following Linear Programming Problem, shade the feasible region on the graph and find the coordinates of its corner points :

      Minimize \(Z = 18x + 10y\)

      subject to constraints

      \[ \begin{aligned} 4x + y &\ge 20 \\ 2x + 3y &\ge 30 \\ x, y &\ge 0. \end{aligned} \]


        • 3.

          The motion of a particle is described as \( S = 2t^{3} - 6t^{2} + 8 \). Its velocity \( \frac{dS}{dt} \), when the acceleration \( \frac{d^{2}S}{dt^{2}} \) vanishes is :

            • \( -6 \) unit/sec
            • \( 0 \) unit/sec
            • \( 18 \) unit/sec
            • \( 6 \) unit/sec

          • 4.

            For the given Linear Programming Problem, shade the feasible region on the graph and write the coordinates of the corner points.

            Minimize \(Z = 5x + 7y\)

            subject to constraints

            \[ 2x + y \geq 8 \]

            \[ x + 2y \geq 10 \]

            \[ x,\ y \geq 0. \]


              • 5.

                \( \int e^{x}\left( \frac{2+\sin 2x}{1+\cos 2x} \right) dx \) is equal to :

                  • \( \log \cos 2x + C \)
                  • \( \sec^{2} 2x + C \)
                  • \( e^{x}\tan x + C \)
                  • \( e^{x}\cot x + C \)

                • 6.

                  Evaluate :

                  \[ I = \int_{-\pi}^{\pi} \frac{2x\,(1+\sin x)}{1+\cos^2 x}\,dx \]

                    CBSE CLASS XII Previous Year Papers

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