CBSE Class 12 Mathematics Sample Paper 2023

Questions in this quiz

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1. Question 1

   Let $f(x) = \frac{x^2 - 9}{x - 3}$ for $x \neq 3$. What is $\lim_{x \to 3} f(x)$?

2. Question 2

   The function $f(x) = |x|$ is continuous at $x = 0$ but not differentiable there. Why is differentiability not satisfied?

3. Question 3

   If $f(x) = x^3 - 3x + 2$, what is $f'(x)$?

4. Question 4

   Which of the following is the antiderivative of $f(x) = 5x^4$?

5. Question 5

   Evaluate $\int_0^1 (2x + 1) \, dx$.

6. Question 6

   The area bounded by $y = x^2$, the $x$-axis, and the lines $x = 0$ and $x = 2$ is found by evaluating which integral?

7. Question 7

   What is the order and degree of the differential equation $\frac{d^2y}{dx^2} + 3\frac{dy}{dx} + 2y = 0$?

8. Question 8

   If $A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}$ and $B = \begin{pmatrix} 2 & 0 \\ 1 & 3 \end{pmatrix}$, what is $A + B$?

9. Question 9

   What is the determinant of $A = \begin{pmatrix} 2 & 3 \\ 1 & 4 \end{pmatrix}$?

10. Question 10

    If a matrix $A$ is singular, then its determinant is zero. This means $A$ has no inverse.

11. Question 11

    What is the rank of the matrix $\begin{pmatrix} 1 & 2 \\ 2 & 4 \end{pmatrix}$?

12. Question 12

    If $A = \begin{pmatrix} 1 & 1 \\ 0 & 1 \end{pmatrix}$, find $A^2 = A \times A$.

13. Question 13

    Using the first principles definition, what is the derivative of $f(x) = 2x + 3$ at $x = 1$?