Class 12 Mathematics CBSE Board Test 2025-26

1. If \( f(x) = x^3 - 3x + 1 \), find \( f'(x) \).
3x^2 - 3
3x^2 + 3
x^2 - 3
x^2 + 3
2. Evaluate \( \int x e^x dx \).
\( (x-1)e^x + C \)
\( xe^x - e^x + C \)
\( xe^x + C \)
\( e^x + C \)
3. The sum of the first 20 terms of an AP is 210. If the first term is 5, find the common difference.
5
4
3
2
4. Find the inverse of the function \( f(x) = 2x + 3 \).
\( f^{-1}(x) = (x-3)/2 \)
\( f^{-1}(x) = 2x - 3 \)
\( f^{-1}(x) = (x+3)/2 \)
\( f^{-1}(x) = x/2 - 3 \)
5. If \( A = \begin{bmatrix}1 & 2\\3 & 4\end{bmatrix} \), find det(A).
-2
2
-1
1
6. The roots of the equation \( x^2 - 5x + 6 = 0 \) are:
2,3
1,6
-2,3
-1,-6
7. If \( \sin^2 \theta + \cos^2 \theta = 1 \), find \( \sin^4 \theta + \cos^4 \theta \).
1
1/2
0
1/4
8. Find the derivative of \( \ln(x^2 + 1) \).
\( 2x/(x^2+1) \)
\( 1/(x^2+1) \)
\( x/(x^2+1) \)
\( 2/(x^2+1) \)
9. The probability of drawing a red card from a deck of 52 cards is:
1/4
1/2
1/3
2/3
10. If \( \vec{a} = \hat{i} + 2\hat{j} \) and \( \vec{b} = 2\hat{i} - \hat{j} \), find \( \vec{a} \cdot \vec{b} \).
0
1
2
-1