NCERT Solutions Class 11 Maths Chapter 1 Sets Exercise 1.4 Solutions 

CBSE CLASS XII Related Questions

  • 1.
    Find the foot of the perpendicular drawn from point $(2, -1, 5)$ to the line \[ \frac{x - 11}{10} = \frac{y + 2}{-4} = \frac{z + 8}{-11} \] Also, find the length of the perpendicular.


      • 2.

        Draw a rough sketch for the curve $y = 2 + |x + 1|$. Using integration, find the area of the region bounded by the curve $y = 2 + |x + 1|$, $x = -4$, $x = 3$, and $y = 0$.


          • 3.
            If \( x = a \left( \cos \theta + \log \tan \frac{\theta}{2} \right) \) and \( y = \sin \theta \), then find \( \frac{d^2y}{dx^2} \) at \( \theta = \frac{\pi}{4} \).


              • 4.
                If \( \int \frac{1}{2x^2} \, dx = k \cdot 2x + C \), then \( k \) is equal to:

                  • \( -1 \)
                  • \( \log 2 \)
                  • \( -\log 2 \)
                  • \( 1/2 \)

                • 5.
                  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.


                    • 6.
                      The integrating factor of the differential equation \( (x + 2y^3) \frac{dy}{dx} = 2y \) is:

                        • \( e^{y^2} \)
                        • \( \frac{1}{\sqrt{y}} \)
                        • \( e^{-\frac{1}{y^2}} \)
                        • \( e^{y^2} \)
                      CBSE CLASS XII Previous Year Papers

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