NCERT Solutions Class 11 Maths Chapter 1 Sets Exercise 1.6 Solutions 

CBSE CLASS XII Related Questions

  • 1.

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


      • 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.

            Evaluate :

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


              • 4.

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


                  • 5.

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

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

                    • 6.

                      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

                      \[ 2x + y \geq 8 \]

                      \[ x + 2y \geq 10 \]

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

                        CBSE CLASS XII Previous Year Papers

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