NCERT Solutions Class 11 Maths Chapter 1 Sets Exercise 1.1 Solutions 

CBSE CLASS XII Related Questions

  • 1.
    A coin is tossed twice. Let $X$ be a random variable defined as the number of heads minus the number of tails. Obtain the probability distribution of $X$ and also find its mean.


      • 2.


        A carpenter needs to make a wooden cuboidal box, closed from all sides, which has a square base and fixed volume. Since he is short of the paint required to paint the box on completion, he wants the surface area to be minimum.
        On the basis of the above information, answer the following questions :
        Find a relation between \( x \) and \( y \) such that the surface area \( S \) is minimum.


          • 3.
            Evaluate : \[ I = \int_0^{\frac{\pi}{4}} \frac{dx}{\cos^3 x \sqrt{2 \sin 2x}} \]


              • 4.
                The principal value of $\sin^{-1} \left( \sin \left( -\frac{10\pi}{3} \right) \right)$ is :

                  • $-\frac{2\pi}{3}$
                  • $-\frac{\pi}{3}$
                  • $\frac{\pi}{3}$
                  • $\frac{2\pi}{3}$

                • 5.
                  The integrating factor of the differential equation \( (x + 2y^3) \frac{dy}{dx} = 2y \) is:

                    • \( e^{y^2} \)
                    • \( \frac{1}{\sqrt{y}} \)
                    • \( e^{-\frac{1}{y^2}} \)
                    • \( e^{y^2} \)

                  • 6.
                    If \( x = a \left( \cos \theta + \log \tan \frac{\theta}{2} \right) \) and \( y = \sin \theta \), then find \( \frac{d^2y}{dx^2} \) at \( \theta = \frac{\pi}{4} \).

                      CBSE CLASS XII Previous Year Papers

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