NCERT Solutions for Class 11 Maths Chapter 3 Exercise 3.3

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.

          Find the value of \(x\) if \(A = B\), where

          \[ A = \begin{bmatrix} 6 & 3x \\ 8 & -6 \end{bmatrix} \text{ and } B = \begin{bmatrix} 6 & x^2+2 \\ 8 & x^2-5x \end{bmatrix}. \]


            • 4.

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

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

              • 5.

                Solve the differential equation \( (x+y)\,dy + (x-y)\,dx = 0 \), given that \( y(1) = 1 \).


                  • 6.

                    Find the sum of maximum and minimum values of \(f(x) = \sin x\,(1 + \cos x)\) in the interval \([0, \pi]\).

                      CBSE CLASS XII Previous Year Papers

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