NCERT Solutions for Class 11 Maths Chapter 2 Exercise 2.3

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Class 11 Maths NCERT Solutions Chapter 2 Relations and Functions Exercise 2.3 is based on the following concepts: 

  1. Some functions and their graphs (Identity function, Constant function, Polynomial function, Rational functions, Modulus function, Signum function, Greatest integer function)
  2. Algebra of real functions (Addition of Two Real Functions, Subtraction of a real function from another, Multiplication by a scalar, Multiplication of two real functions, Quotient of two real functions)

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CBSE CLASS XII Related Questions

  • 1.
    Find:

    The principal value of \[ \sec^{-1}(\sqrt{2})+2\csc^{-1}(-2) \] is:

      • \(-\frac{\pi}{2}\)
      • \(-\frac{\pi}{4}\)
      • \(\frac{\pi}{4}\)
      • \(\frac{\pi}{2}\)

    • 2.

      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 :


        • 3.
          If \( xy = e^{x - y} \), then find \( \frac{dy}{dx} \).


            • 4.

              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. 


                • 5.
                  Find:

                  If \[ (3\hat{i}-2\hat{j}+5\hat{k})\times(4\hat{i}+p\hat{j}+q\hat{k})=\vec{0} \] then find the values of \(p\) and \(q\).

                    • \(p = -\frac{2}{3}, \, q = \frac{5}{3}\)
                    • \(p = -\frac{8}{3}, \, q = \frac{20}{3}\)
                    • \(p = \frac{20}{3}, \, q = -\frac{8}{3}\)
                    • \(p = 0, \, q = 0\)

                  • 6.
                    Find:

                    The shortest distance between the lines: \[ \vec{r}=(4+\lambda)\hat{i}+(2\lambda-1)\hat{j}-3\lambda\hat{k} \] and \[ \vec{r}=(1+2\mu)\hat{i}+(4\mu-1)\hat{j}+(2-5\mu)\hat{k} \]

                      CBSE CLASS XII Previous Year Papers

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