tmua.me Medium Set C Paper 2
20 questions · 75 min · Difficulty 50 · by tmua.me
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Questions in this paper
- Question 1Consider the following claim about a real number x: If x>1, then 2^x>x^2. Which of the following values of x is a counterexample to this…
- Question 2The positive real numbers a and b satisfy a^2+ab=12, b^2+ab=18. What is the value of a+b?
- Question 3For which values of the real constant k do the graphs y=(x^2-4)/(x-2) (x≠2) y=kx have no point in common?
- Question 4A data set consists of five distinct real numbers. Consider the statements - P: The mean equals the median. - Q: The sum of the smallest…
- Question 5A rectangle has width w, height h and diagonal length d. Consider the statement If d>10, then w>6 or h>8. Which of the following is its…
- Question 6The function f is defined for all real x by f(x)=ab^x+c, where a and c are real constants and b>0. It is given that f(0)=5, f(1)=7…
- Question 7In trapezium ABCD, the sides AB and DC are parallel, and AD is perpendicular to them. Also, AB=9 and DC=4. A circle lies inside the…
- Question 8A non-empty collection of circles is drawn in a plane. Consider the statement: For every straight line through the origin, there is at…
- Question 9For 1≤ x≤2, the curve C has equation y=(x^3+1)/(x^2). A horizontal line y=k has the following property: within the strip 1≤ x≤2, the total…
- Question 10Let a and b be positive integers. Consider the statements - P: The highest common factor of a and b is 1. - Q: a^2+ab+b^2 is prime. Which…
- Question 11All the positive integers whose usual base-ten representations contain only the digits 0 and 1 are listed in increasing order: 1, 10, 11…
- Question 12Bag A contains three red balls and two blue balls. Bag B contains two red balls and one blue ball. One ball is chosen at random from bag A…
- Question 13Let a and b be real numbers satisfying a+b=2. A student gives the following proof that a^4+b^4≥2. 1. Since (a-b)^2≥0, the identity…
- Question 14The quadratic equation x^2+ax+b=0 has two distinct real roots, where a and b are real constants. Consider the statements - P: |a|+|b|<1. -…
- Question 15Find the sum of all the distinct solutions θ of √(1+sinθ)+√(1-sinθ) =√2 (sinθ+cosθ) for which 0≤θ<2π.
- Question 16Let x and y be positive real numbers. Consider the conditions P:& x=y, [3pt] Q:& log_2(x+y)=1+(log_2x+log_2y)/(2). Which statement…
- Question 17The 2n distinct positive real numbers a_1<a_2<…<a_(2n) are divided into n pairs. The sum of the numbers in each pair is found, and these n…
- Question 18A non-empty list of real numbers is used to form two new lists. In the first new list, each number x is replaced by (x-2)^2. In the second…
- Question 19The positive integers a and b have highest common factor 1. Both ab and a+b are perfect squares. Which of the following statements must be…
- Question 20A tank is a right circular cone with its vertex at the bottom. Its vertical height is 10 cm and its top radius is 6 cm. Initially it…