Grand Revision - Full Syllabus

Grade 12 Maths Higher — Grand Revision - Full Syllabus: 25 practice questions with instant scoring and explanations.

1. A relation R is an equivalence relation if it is:
2. Range of y = sin⁻¹(x) is:
3. For A of order 3 with det(A) = 4, det(adj A) equals:
4. For A of order 3 with det(A) = 5, det(A⁻¹) equals:
5. If y = tan⁻¹(x), then d²y/dx² at x = 0 is:
6. Evaluate ∫ x·cos x dx using integration by parts:
7. If f is continuous on [a, b] and F'(x) = f(x), then ∫ₐᵇ f(x) dx equals:
8. The direction of a⃗ × b⃗ is:
9. The equation of a line through (x₁, y₁, z₁) with direction ratios (a, b, c) is:
10. The feasible region of an LPP is always a:
11. If E and F are independent, P(E|F) equals:
12. For B(n, p), mean μ = np and variance σ² = npq, so σ² < μ when:
13. ∫₀^(π/4) tan²x dx equals:
14. The rate of change of area of a circle of radius r with respect to r is:
15. If f(x) = x³ - 6x² + 9x + 1, the point of inflection is at x =
16. The general solution of x·dy/dx + y = log x is:
17. The probability of drawing an ace from a pack of 52 cards is:
18. If a⃗ and b⃗ are unit vectors with angle π/3 between them, |a⃗ - b⃗| equals:
19. The length of the projection of vector 2î + ĵ + 2k̂ on î + ĵ is:
20. The equation of the line through (1, 0, -2) perpendicular to both x-axis and y-axis is:
21. The maximum of Z = 5x + 3y at (4, 0), (2, 3), (0, 3), (0, 0), (4, 0) corners is:
22. The number of all possible one-one functions from {1,2,3} to {a,b,c,d} is:
23. If y = sin⁻¹(2x/(1 + x²)) for |x| < 1, then dy/dx is:
24. The value of ∫₀¹ (1 - x)ⁿ dx is:
25. If A(2, 3, 5), B(-1, 3, 2) are two points, the direction cosines of AB are: