NCERT Solutions for Class 12 Chapter 9 Differential Equations Exercise 9.1 Solutions

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Class 12 Maths NCERT Solutions Chapter 9 Differential Equations Exercise 9.1 is provided in the article. Class 12 Chapter 9 Differential Equations Exercises include questions on Order and Degree of Differential Equations, Formation of Differential Equation, Methods of Solving First Order, First Degree Differential Equations.

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CBSE CLASS XII Related Questions

  • 1.
    Let $\mathbf{| \mathbf{a} |} = 5$ and $-2 \leq z \leq 1$. Then, the range of $|\mathbf{a}|$ is:

      • $[5, 10]$
      • $[-2, 5]$
      • $[2, 1]$
      • $[-10, 5]$

    • 2.

      Based upon the results of regular medical check-ups in a hospital, it was found that out of 1000 people, 700 were very healthy, 200 maintained average health and 100 had a poor health record.
      Let \( A_1 \): People with good health,
      \( A_2 \): People with average health,
      and \( A_3 \): People with poor health.
      During a pandemic, the data expressed that the chances of people contracting the disease from category \( A_1, A_2 \) and \( A_3 \) are 25%, 35% and 50%, respectively.
      Based upon the above information, answer the following questions:
      (i) A person was tested randomly. What is the probability that he/she has contracted the disease?}
      (ii) Given that the person has not contracted the disease, what is the probability that the person is from category \( A_2 \)?


        • 3.
          The area of the shaded region (figure) represented by the curves \( y = x^2 \), \( 0 \leq x \leq 2 \), and the y-axis is given by:
          The area of the shaded region

            • \( \int_0^2 x^2 \, dx \)
            • \( \int_0^2 \sqrt{y} \, dy \)
            • \( \int_0^4 x^2 \, dx \)
            • \( \int_0^4 \sqrt{y} \, dy \)

          • 4.
            Using integration, find the area of the region bounded by the line \[ y = 5x + 2, \] the \( x \)-axis, and the ordinates \( x = -2 \) and \( x = 2 \).


              • 5.
                Let \[ A = \begin{pmatrix} 1 & 4 \\ -2 & 1 \end{pmatrix} \quad \text{and} \quad C = \begin{pmatrix} 3 & 4 & 2 \\ 12 & 16 & 8 \\ -6 & -8 & -4 \end{pmatrix}. \] Then, find the matrix $B$ if $AB = C$.


                  • 6.
                    If \( f(x) = \begin{cases} \frac{\sin^2 ax}{x^2}, & \text{if } x \neq 0 \\ 1, & \text{if } x = 0 \end{cases} \) is continuous at \( x = 0 \), then the value of 'a' is :

                      • 1
                      • -1
                      • 0
                      • \( \pm 1 \)
                    CBSE CLASS XII Previous Year Papers

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