NCERT Solutions Class 11 Maths Chapter 1 Sets Exercise 1.5 Solutions 

CBSE CLASS XII Related Questions

  • 1.

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


      • 2.

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


          • 3.

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

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

            • 4.

              Evaluate :

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


                • 5.

                  For events A and B, if \(P(B)=\frac{3}{5}\), \(P(A/B)=\frac{1}{2}\) and \(P(A\cup B)=\frac{4}{5}\), then \(P(A)\) is :

                    • \(\frac{1}{2}\)
                    • \(\frac{3}{5}\)
                    • \(\frac{1}{5}\)
                    • \(\frac{3}{10}\)

                  • 6.

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

                      • \( -2\sqrt{\cos x}\cdot\cot x\cdot\operatorname{cosec} x \)
                      • \( \sqrt{\cos x}\cdot\cot x\cdot\operatorname{cosec} x \)
                      • \( \frac{2\sqrt{\cos x}}{\sin x} \)
                      • \( \frac{1}{\sin x\sqrt{\cos x}} \)
                    CBSE CLASS XII Previous Year Papers

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