Full Syllabus Mixed Practice - Set 2

Grade 12 Maths Higher — Full Syllabus Mixed Practice - Set 2: 25 practice questions with instant scoring and explanations.

1. If R is defined on ℕ by aRb iff a + b is even, then R is:
2. The principal value of tan⁻¹(-1) is:
3. If A is skew-symmetric and n odd, then det(A) is:
4. The derivative of log(sin x) is:
5. The maximum value of f(x) = sin x + cos x is:
6. Evaluate ∫ x·e^x dx using integration by parts:
7. Evaluate the definite integral ∫₋₁¹ x³ dx:
8. If a⃗·b⃗ = |a⃗||b⃗|, the angle between them is:
9. The distance between the parallel lines r⃗ = î + t(ĵ + k̂) and r⃗ = 2î + s(ĵ + k̂) is:
10. The minimum of Z = 2x + 3y subject to x + y ≥ 8, 3x + 5y ≤ 15, x, y ≥ 0 is:
11. If P(A) = 0.3, P(B) = 0.5, P(A ∪ B) = 0.7, then P(A ∩ B) is:
12. If f(x) = (x² - 4)/(x - 2), then limₓ→₂ f(x) equals:
13. The point of local maximum of f(x) = -x² + 4x is at x =
14. The absolute maximum of f(x) = x²(1-x) on [0, 1] is at x =
15. ∫ 1/(x·log x) dx =
16. The area under y = e^x from x = 0 to x = 1 is:
17. If y = x^x, then dy/dx is:
18. The solution of dy/dx = x + y is (linear DE, μ = e^(-x)):
19. The inverse of a 2×2 matrix [[1, 2], [3, 4]] is:
20. For a continuous RV X on [0, 2] with pdf f(x) = x/2, E(X) equals:
21. The equation of the plane passing through (1, 0, 0), (0, 1, 0), (0, 0, 1) is:
22. If A and B are independent, P(A) = 0.5, P(B) = 0.6, then P(A ∪ B) is:
23. Evaluate the integral ∫ cos²x dx:
24. The order and degree of (dy/dx)² + y = sin x are respectively:
25. The principal value of sec⁻¹(-2) is: