CBSE Class 12 Mathematics Paper 1 Sample 2023

Questions in this quiz

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1. Question 1

   What is the range of the function $f(x) = \sin^{-1}(x)$?

2. Question 2

   If $\tan^{-1}(x) + \tan^{-1}(y) = \pi/4$, and $xy < 1$, then $x + y$ equals:

3. Question 3

   Simplify $\sin^{-1}\left(\sin\left(\frac{5\pi}{6}\right)\right)$.

4. Question 4

   Find the derivative of $f(x) = e^{\sin(x)} \cdot \cos(x)$.

5. Question 5

   A rectangular box with an open top has a fixed base area of 12 m². If the volume is to be maximized for a height $h$, which of the following is the condition at the maximum?

6. Question 6

   The equation of the tangent to the curve $y = x^3 - 3x$ at the point where $x = 1$ is:

7. Question 7

   If $f(x) = x^2$ on $[0, 1]$, what is $\int_0^1 f(x) \, dx$?

8. Question 8

   The area bounded by the curves $y = x^2$ and $y = x$ in the first quadrant is:

9. Question 9

   A fair die is rolled once. The probability of getting a number greater than 4 is:

10. Question 10

    Two events $A$ and $B$ are independent. If $P(A) = 0.4$ and $P(B) = 0.5$, then $P(A \cap B)$ is:

11. Question 11

    Is the function $f(x) = |x|$ differentiable at $x = 0$?

12. Question 12

    If $y = \ln(\sec(x))$, then $\frac{dy}{dx}$ equals:

13. Question 13

    The second derivative test tells us that if $f''(c) < 0$ at a critical point $c$, then $c$ is a local:

14. Question 14

    Compute $\int_1^2 (3x^2 + 2x) \, dx$.

15. Question 15

    In how many ways can a committee of 3 people be chosen from a group of 5, where order does not matter?