NCERT Solutions Class 11 Maths Chapter 1 Sets Exercise 1.3 Solutions 

CBSE CLASS XII Related Questions

  • 1.

    Evaluate:
    \[ \int_{0}^{1} \frac{x \tan^{-1}x}{(1+x^2)^{3/2}}\,dx \]


      • 2.

        A carpenter needs to design a wooden box in the shape of a cuboid such that the sum of its length and breadth is 3 cm more than its height. Twice of its length, thrice of its breadth and its height add up to 10 cm. Its breadth added to 7 times its height is 1 cm less than 3 times its length. 


          • 3.

            At a birthday party, children are being served orange juice in conical cups, as shown in the figure. 


            Each cup is 15 cm deep and has a radius 5 cm. The juice is being poured into this cup at a rate of 0·1 cm3/s.
            On the basis of the above information, answer the following questions :


              • 4.
                A relation $R$ on set $A=\{1,2,3\}$ defined as $R=\{(1,2),(2,1),(2,2)\}$ is

                  • Reflexive only
                  • Reflexive and Transitive
                  • Symmetric and Transitive
                  • Symmetric only

                • 5.

                  An NGO organises a charity event in which they decide to distribute woollen caps to protect children from winter. The caps to be distributed are in three separate boxes, Box I has 30 red caps, Box II has 20 red and 10 green caps, and Box III has 30 green caps. The probability that a Box i is selected and a cap picked out is i/6, where i = 1, 2, 3.  
                  Based on the above information, answer the following questions :


                    • 6.
                      Find the vector and cartesian equations of the line passing through the point of intersection of the lines \( \vec{r} = (\hat{i} + \hat{j} - \hat{k}) + \lambda(3\hat{i} - \hat{j}) \) and \( \vec{r} = (4\hat{i} - \hat{k}) + \mu(2\hat{i} + 3\hat{k}) \) and parallel to the line \( \frac{x - 1}{-2} = \frac{7 - y}{-3} = z \).

                        CBSE CLASS XII Previous Year Papers

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