NCERT Solutions for Class 11 Maths Chapter 5 Exercise 5.3

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Class 11 Maths NCERT Solutions Chapter 5 Complex Numbers and Quadratic Equations Exercise 5.3 is based on Quadratic Equations.

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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.

      Solve the differential equation \( y + \frac{d}{dx}(xy) = x(\sin x + \log x) \).


        • 3.

          If \(y = \sqrt{\log \left\{ \sin \left( \dfrac{x^2}{3} + 1 \right) \right\}}\), then show that

          \[ \frac{dy}{dx} = \frac{x \cot \left( \dfrac{x^2}{3} + 1 \right)}{3y}. \]


            • 4.

              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

              • 5.

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

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


                  • 6.

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

                      CBSE CLASS XII Previous Year Papers

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