Full Syllabus Mixed Practice - Set 1

Grade 12 Maths Higher — Full Syllabus Mixed Practice - Set 1: 25 practice questions with instant scoring and explanations.

1. If A = {1, 2, 3}, the number of equivalence relations containing (1, 2) is:
2. The principal value of sin⁻¹(sin(5π/6)) is:
3. If A is a 3×3 matrix with |A| = 5, then |2A| is:
4. The function f(x) = |x| is not differentiable at:
5. The derivative of sin⁻¹(x) with respect to x is:
6. ∫(2x)/(1 + x²) dx =
7. ∫₀^(π/2) sin²x dx =
8. If a⃗ = 2î + ĵ and b⃗ = î - ĵ, then a⃗ + b⃗ is:
9. The direction ratios of the line joining (1, 2, 3) and (4, 5, 6) are:
10. The maximum of Z = 3x + 2y over feasible region bounded by x + y ≤ 4, x, y ≥ 0 is:
11. If P(A) = 0.6, P(B) = 0.4 and P(A ∩ B) = 0.24, then A and B are:
12. The continuity of f(x) = x²·sin(1/x) at x = 0 (defining f(0) = 0) is:
13. The tangent to y = x² at x = 1 has slope:
14. The critical points of f(x) = x³ - 3x are:
15. Evaluate the integral ∫ sec²x dx:
16. The area bounded by y = x, x = 0, x = 2, and x-axis is:
17. If f(x) = e^(x²), then f'(x) is:
18. The value of ∫₀¹ x² dx is:
19. If [A B] = [[1, 2]] + [[3, 4]], then [A B] is:
20. The general solution of dy/dx = sec²x is:
21. The value of cos⁻¹(-1/2) is:
22. If A² = A, then A is called:
23. The direction cosines of a line making equal angles with the coordinate axes are:
24. If P(A) = 1/4, P(B|A) = 1/3, then P(A ∩ B) is:
25. ∫(dx/(1 + x²)) from 0 to 1 equals: