NCERT Solutions for Class 11 Maths Chapter 16 Exercise 16.1

CBSE CLASS XII Related Questions

  • 1.

    Find:
    Let \(A=[a_{ij}]\) be a \(2\times2\) matrix whose elements are given by \[ a_{ij}=\frac{(2i-j)^2}{3} \] Find the transpose matrix \(A'\).

      • \(\begin{bmatrix} \frac{1}{3} & 3 \\ 0 & \frac{4}{3} \end{bmatrix}\)
      • \(\begin{bmatrix} \frac{1}{3} & 0 \\ 3 & \frac{4}{3} \end{bmatrix}\)
      • \(\begin{bmatrix} \frac{4}{3} & 3 \\ 1 & 0 \end{bmatrix}\)
      • \(\begin{bmatrix} \frac{4}{3} & 0 1 & \frac{3}{3} \end{bmatrix}\)

    • 2.

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


        • 3.
          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 \( \frac{x - 1}{-2} = \frac{7 - y}{-3} = z \).


            • 4.
              Which of the following equations is NOT a Linear Differential Equation?

                • \((1 + x^2) \, dy + 2xy \, dx = \cot x \, dx\)
                • \(y + \frac{d}{dx}(xy) = x(\sin x + \log x)\)
                • \(x(1 + y^2) \, dx - y(1 + x^2) \, dy = 0\)
                • \(y \, dx - (x + 3y^2) \, dy = 0\)

              • 5.
                Find:

                If the function \[ f(x)= \begin{cases} \frac{\sin x}{x}+\cos x, & x\neq0\\ k, & x=0 \end{cases} \] is continuous at \(x=0\), then find the value of \(k\).

                  • \(0\)
                  • \(-2\)
                  • \(-1\)
                  • \(2\)

                • 6.

                  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. 

                    CBSE CLASS XII Previous Year Papers

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