1Given two positive integers a = p^3q^4 and b = p^2q^3, where p and q are prime numbers, if HCF(a,b) = p^mq^n and LCM(a,b) = p^rq^s, which of the following statements are correct?
2If p is a prime number, which of the following are characteristics of the quadratic equation whose roots are the factors of p?
3In a triangle ABC, if DE is parallel to BC (where D is on AB and E is on AC), which of the following ratios are mathematically true based on the Basic Proportionality Theorem?
4Given the trigonometric identity sin θ + cos θ = √2, identify the correct derived values.
5A circular wheel of radius 0.25m rolls a distance of 11km. Which of the following are true regarding this scenario?
6According to the empirical relationship between the measures of central tendency, which of the following equations hold true?
7If two coins are tossed simultaneously, what are the correct probabilities for the outcomes?
8Consider a cuboid where the sum of length, breadth, and height is 6√3 cm and the diagonal is 2√3 cm. Which of the following values are correct?
9In an Arithmetic Progression where seats are arranged in concentric circles such that the first row has 30 seats and each subsequent row increases by 10, select the true statements.
10Which of the following are valid geometric properties regarding circles and tangents mentioned in the course material?
