TMUAmockz Set 1 Paper 2
20 questions · 75 min · Difficulty 62 · by TMUAmockz
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Questions in this paper
- Question 1Let p and q be real constants with p≠ q. Two curves are defined by C_1:y=(x-p)^2(x-q) C_2:y=(x-q)^2(x-p) Consider the following four…
- Question 2The distinct points P and Q with coordinates (p^2,2p) and (q^2,2q) respectively lie on the curve C with equation y^2=4x. Consider the…
- Question 3The equation ax^2+bx+c=0, where a,b,c are real and a≠0, is said to have property R if it has two distinct real roots. Consider the…
- Question 4A data set consists of seven values: 4, 1, 15, x, 1, 10, 1 where x is a real number. The mean, median and mode of this data set form a…
- Question 5Real numbers p,q,r satisfy p 2q^2 only if q (r-q)^2+(q-p)^2
- Question 6Let x be an integer. Consider the expression (5x)/(12)+frac x8. Which of the following statements about x are true whenever this expression…
- Question 7A line ℓ with gradient m is tangent to the curve y=x^2 and passes through the point (10,36). Which of the following is a necessary and…
- Question 8Let p and q be distinct positive real numbers, and define I=∫_0^1x^pd x and J=∫_0^1x^(1/q)d x. Which of the following is a necessary and…
- Question 9Let a,b be real constants. Let n be the number of real solutions to the equation x^2-a|x|+b=0. Which of the following statements are true?…
- Question 10Given that f"(x)>0 for all x with 0≤ x≤1, which of the following statements must be true? - I. f(dfrac12)<dfracf(0)+f(1)2 - II. ∫_0^1f(x)d…
- Question 11The first term of an infinite geometric progression is cos x and the common ratio is also cos x. For how many values of x in the interval…
- Question 12A student claims that log_3(x-4)+log_3(22-x)<4 holds for all integers x with 4<x<22. Is the student correct? If not, state the integer…
- Question 13An ant sits on the surface of a regular tetrahedron with edges of length 1. It crawls along the surface from the midpoint of one edge to…
- Question 14The function f(x)=x^3+ax^2-a^2x+b has a local maximum at x=a/3 and three distinct real roots. What conditions must a and b satisfy?
- Question 15A curve C has equation y=px^2+qx+r, where p≠0. The curve C is reflected in the x-axis to give a curve C'. The curve C is then translated 3…
- Question 16The expansion of (x^a+x^(-b))^n, where a,b,n are positive integers, contains a constant term. Which of the following is/are necessary and…
- Question 17Two parabolas have equations f(x)=x^2+px+q and g(x)=x^2+rx+s, where p,q,r and s are integers each chosen independently and uniformly at…
- Question 18Three circles with radii p,q and r, where p<q<r, are mutually externally tangent. Let P,Q,R denote their respective centres. Which of the…
- Question 19Given that p and q are real constants, which of the following is a necessary but not sufficient condition for the equation…
- Question 20A sequence a_n is defined by a_(n+1)=(a_n+1)/(1-a_n) and it is given that a_(13)=√3. Find the value of Σ_(n=0)^(30)a_n.