ICSE Class 11 Mathematics — Flashcards

A: Step 1: Find integers whose square is less than 20. Step 2: 0^2 = 0, 1^2 = 1, 2^2 = 4, 3^2 = 9, and 4^2 = 16 are all less than 20. Step 3: 5^2 = 25 is not less than 20, so stop there. Step 4: Include

A: Step 1: Notice that every element is an even natural number. Step 2: Each term can be written as 2n. Step 3: Since the set is finite, restrict n to the correct values. Answer: {x : x = 2n, n is a natu

A: Step 1: Check each item exactly as written. Step 2: 1 is an element of A, so 1 ∈ A is correct. Step 3: {1} is not listed as an element, so {1} ∈ A is incorrect. Step 4: {3, 4} is listed as one element

A: Step 1: Use the Cartesian product rule: A × B = {(x, y): x ∈ A and y ∈ B}. Step 2: Pair each element of A with each element of B. A × B = {(1, a), (1, b), (2, a), (2, b)}. Answer: {(1, a), (1, b), (2,

A: Step 1: Switch the order of the sets. Step 2: Form ordered pairs with first element from B and second element from A. B × A = {(a, 1), (a, 2), (b, 1), (b, 2)}. Step 3: Compare with A × B. A × B ≠ B ×

A: Step 1: Use the formula n(A × B) = pq. Here, p = 3 and q = 4. Step 2: Multiply. n(A × B) = 3 × 4 = 12. Answer: 12

A: Step 1: Use the degree-radian relation: 180° = π radian. Step 2: 1° = π/180 rad. Step 3: 60° = 60 × π/180 = π/3 rad. Answer: π/3 radian.

A: Step 1: Use 1 rad = (180/π)°. Step 2: (π/6) × (180/π) = 180/6 = 30°. Answer: 30°.

A: Step 1: Arc length formula: l = rθ, and θ must be in radians. Step 2: 15° = 15 × π/180 = π/12 rad. Step 3: l = 5 × (π/12) = 5π/12 cm. Answer: 5π/12 cm.