Clavis TMUA Set C Paper 2
20 questions · 75 min · Difficulty 31 · by Clavis
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Questions in this paper
- Question 1Find the value of ∫_0^1(2x-1)^3 dx.
- Question 2Given that y=fracx^2+1√(x) x>0 find the value of (dy)/(dx) when x=1.
- Question 3The numbers a, b and c are real, and ab=ac. Which of the following statements must be true? - I a=0 - II b=c - III a=0 or b=c
- Question 4Let a and b be positive integers, and consider the two statements: P: ab is divisible by 6 Q: a is divisible by 6 or b is divisible by 6…
- Question 5Which of the following statements is/are true? - I Every integer greater than 2 can be written as the sum of two prime numbers. - II Every…
- Question 6Which one of the following is smallest in value?
- Question 7Here is an attempted proof of the following claim. If a and b are real numbers with a^2=b^2, then a=b. - (I) Suppose a^2=b^2. - (II) Then…
- Question 8Eight chairs are arranged in a circle, and some of them are occupied. A chair is called *crowded* if both of the chairs next to it are…
- Question 9The function f is defined on the positive integers by f(1)=3 and, for n≥1, f(n+1)=3f(n)+1 if f(n) is odd f(n+1)=frac12f(n) if f(n) is even…
- Question 10The trapezium rule is used to estimate ∫_a^b f(x) dx, where a<b. Which one of the following conditions guarantees that the estimate is an…
- Question 11Let x be a real number. Which one of the following statements is a sufficient condition for exactly three of the other four statements?
- Question 12Consider the following statement: For every real number x there is a real number y such that xy>1. Which one of the following is the…
- Question 13Consider the following attempt to solve the equation log_2x+log_2(x-2)=3. - (I) Combining the logarithms gives log_2(x(x-2))=3. - (II)…
- Question 14In this question f is a polynomial. Consider the following three conditions: - I ∫_0^a f(x) dx=0 for every real number a - II f(x)=0 for…
- Question 15Class X contains m students, and their mean mark in a test is 60. Class Y contains n students, and their mean mark in the same test is 70…
- Question 16A bag contains 5 red counters and 3 blue counters. Three counters are drawn at random, without replacement. Consider the following three…
- Question 17Let n be a positive integer. Which one of the following is a necessary but not sufficient condition for n to be a perfect square?
- Question 18The real numbers a, b and c satisfy a bc
- Question 19For a positive integer n, let d(n) denote the number of positive divisors of n. For example d(6)=4, since 6 has divisors 1, 2, 3 and 6…
- Question 20In this question n is a positive integer and N=n^4+4. Which of the following statements is/are true? - I N is composite for every integer…