لمّاح✨ PMAU

Question 1: If p denotes "I study hard" and q denotes "I pass the exam", then q → p denotes A. I study hard if and only if I pass the exam. B. If I study hard, then I pass the exam. C. I pass the exam and I study hard. ✅ D. If I pass the exam, then I study hard. Question 2: The degree of the Boolean function f(w, x, y, z) = w x̄ + y z̄ is 4. ✅ True False Question 3: In Boolean Algebra, the value of (a + b̄)·(complement of ab), when a = 1 and b = 0, is A. 0 B. 2 ✅ C. 1 D. operation is not possible Question 4: The decimal expansion of the number with octal expansion (157)₈ is ✅ A. 111 B. 125 C. 157 D. 103 Question 5: If A = {1, 2, 3, 4, 5} and B = {2, 4, 6, 8}, then A ∩ B = {2, 4, 6}. True ✅ False Question 6: Let A be the set of positive multiples of 3 less than 30, then the cardinality of A is: A. 10 B. 27 ✅ C. 9 D. 30 Question 7: In Insertion sort, to sort the elements 9, 4, 12, 1, 6 we must begin with the ……. element from the list. A. First ✅ B. Second C. Third D. Fourth Question 8: The sentence "x + 4 = 9" is a proposition. True ✅ False Question 9: Using Bubble sort, the list 3, 8, 2 becomes 2, 3, 8 after the first pass. True ✅ False Question 10: The proposition ¬(p ∨ q) is logically equivalent to A. ¬p ∨ q B. ¬p ∨ ¬q ✅ C. ¬p ∧ ¬q D. p ∨ q Question 11: Let f be the function from {p, q, r, s, t} to {−5, 3, 8, 0, 12} defined by f(p) = −5, f(q) = 3, f(r) = 8, f(s) = −5 and f(t) = 12, then the range of f is: ✅ A. {−5, 3, 8, 12} B. {−5, 3, 8, 0, 12} C. {−5, 8, 0, 12} D. {p, q, r, s, t} Question 12: The sum of two congruences 17 ≡ 3 (mod 7) and 23 ≡ 2 (mod 5) is: ✅ A. congruence sum is not possible B. 40 ≡ 6 (mod 7) C. 40 ≡ 5 (mod 5) D. 391 ≡ 6 (mod 7) Question 13: Let f(0) = 0 and f(n) = f(n − 1) + n² for n ≥ 1. What is f(5)? A. 30 ✅ B. 55 C. 91 D. 50 Question 14: The product of two positive integers is 2160 and their lcm is 360. What is their gcd? A. 4 B. 8 ✅ C. 6 D. 12 Question 15: The inverse of 5 modulo 11 is 9. ✅ True False

The answer is True.

The answer is C. 6

The answer is B. 55

The answer is A. congruence sum is not possible

The answer is C. ¬p ∧ ¬q

The answer is False.

The answer is False.

The answer is B. Second

C. 9 ✅

Tuesday, 27 Oct 2026 🟣 3rd Session (7:00 – 8:00 PM) MATH150: Discrete Mathematics ❌❌ https://t.me/+U-PPf1ZbA-4yYmM0

Question 1: For f(x) = √(5 − x), the domain is x ≥ 5 True False ✅ Question 2: If f(x) = e^(sin x), then f′(x) = cos(x)·e^(sin x) True ✅ False Question 3: If f(x) = x³ − 3x² + 2, then the critical values of x are: A. x = 0 only B. x = 1 and x = 2 C. x = 2 only D. x = 0 and x = 2 ✅ Question 4: If A = x² and dx/dt = 3, then dA/dt at x = 10 is A. 60 ✅ B. 100 C. 30 D. 300 Question 5: If f(x) = −3 for x < 0 and 2 for x > 0, then the limit of f(x) as x → 0⁺ is A. 2 ✅ B. −3 C. 0 D. 3 Question 6: Which of the following conditions must be satisfied for f to be continuous at x = a? A. f′(a) = 0 B. f(a) defined only C. lim (x→a) f(x) = f(a) ✅ D. lim (x→a) f(x) exists only Question 7: lim (x→a) (f(x) + g(x)) = lim (x→a) f(x) + lim (x→a) g(x) True ✅ False Question 8: If xy² + 2xy = 8, then at the point (1, 2) the value of dy/dx is: A. 0 B. −1/2 C. −5/2 D. −4/3 ✅ Question 9: The function f(x) = (x² − 1)/(x − 1) is continuous at x = 1 True False ✅ Question 10: Which of the following functions is not continuous at x = 0? A. f(x) = x + 1 B. f(x) = |x| C. f(x) = x² D. f(x) = 1/x ✅ Question 11: The limit as x → ∞ of (x⁵ − 2x + 11)/(3 − 2x⁵) is A. −∞ B. ∞ C. −1/2 ✅ D. 0 Question 12: The function f(x) = x² − 2x + 1 has absolute maximum 1 and absolute minimum 1 on [0, 3] True False ✅ Question 13: The limit as x → 0 of sin(5x)/x is A. 1 B. Does not exist C. 0 D. 5 ✅ Question 14: If f(x) = 3x² − 4x + 5, then f′(x) is A. 6x − 4 ✅ B. 6x² − 4 C. 3x − 4 D. 6x + 5 Question 15: If f(x) = x² and g(x) = x + 1, what is f∘g(x)? A. x² + 1 B. 2x + 1 C. (x + 1)² ✅ D. x² + x + 1

C