Clavis TMUA Set A Paper 2
20 questions · 75 min · Difficulty 30 · by Clavis
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Questions in this paper
- Question 1The function f is defined for x>0 by f(x)=fracx^2+6√(x)x. Find the value of f'(9).
- Question 2Find the coefficient of x^3 in the expansion of (1-2x)^5(1+x)^2.
- Question 3Consider the following claim: For all real numbers a and b, if a^2>b^2 then a>b. Which of the following is/are a counterexample to the…
- Question 4The sequence u_1,u_2,u_3,… is defined by u_n=n^2+kn, where k is a real constant. Consider the two statements: P: k>-2 Q: the sequence is…
- Question 5Let n be a positive integer, and let P be the statement if n is a multiple of 4, then n is even. Which of the following must be true? - I P…
- Question 6Consider the following statement (*) about a real constant k: (*) There exists a real number x such that, for all real numbers y, x^2+y^2≥…
- Question 7Here is an attempted proof of the following claim. For all real numbers x, if x^3>x then x>1. - (I) Suppose x^3>x. - (II) Dividing both…
- Question 8In this question a and b are real numbers with a a.
- Question 9A positive integer is called *balanced* if and only if it can be written as the sum of two or more consecutive positive integers. For…
- Question 10The curve C has equation y=ax^2+bx+c, where a, b and c are real constants with a≠0. Let d be the x-coordinate of the vertex of C. Which one…
- Question 11Which of the following statements is/are true? - I For every real number x there is a real number y such that y^2=x. - II There is a real…
- Question 12Consider the following statement: For every positive integer n there is a positive integer m such that m^2+n is a perfect square. Which one…
- Question 13Consider the following attempt to solve the equation 2sin xcos x=cos x for 0≤ x≤2π. - (I) Dividing both sides by cos x gives 2sin x=1. -…
- Question 14n is a positive integer. Consider the statement: Q: n is a multiple of 6 and the following three conditions: - I n is a multiple of 2 and n…
- Question 15In this question f and g are polynomials such that f(x)≤ g(x) all real x. Which of the following statements must be true? - I f(g(x))≤…
- Question 16Consider the following statement (*) about a real number x: (*) There exists a real number y such that y^2+xy+x=0. What is the complete set…
- Question 17Place the following three numbers in order of size, starting with the smallest. P=2^(300) Q=3^(200) R=5^(150).
- Question 18The function f is a polynomial defined for all real x. Which one of the following is a necessary condition for f(x)≥ f(0) all real x
- Question 19A function f defined for all real x is called *self-inverse* if and only if f(f(x))=x all real x. Which of the following statements is/are…
- Question 20It is given that f(x)=x^3+px+q, where p and q are real constants, and that the equation f(x)=0 has three distinct real roots. Which of the…