Yotta Paper 2
20 questions · 75 min · Difficulty 55 · by Yotta
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Questions in this paper
- Question 1Which of these statements is true?
- Question 2Which of these statements is true for positive integers n: 1. n is prime if n=6k+1 or n=6k-1 for some integer k 2. n is prime only if…
- Question 3Which of these statements is true about x=21222324252627: 1. x can be written as p^2+q^2 where p and q are 2 distinct positive integers 2…
- Question 4f(x) is a function defined for all real x. Here are 3 statements: J: f(3)=1, and f(5)=-2 K: f(x)=0 has exactly 3 solutions in the interval…
- Question 5Find the sum of the x-coordinates of the points of intersections of y=(√ x-3)(√ x+3) and |x|=(y+20)/(3).
- Question 6f(x) is a polynomial function defined for all real x. Statement P: f'(5)=0 Statement Q: There is a turning point at x=5 Which option is…
- Question 7A,B and C are three points on a regular n-sided polygon, where n≥3. Let O be the centre of the circle that has A,B and C on its…
- Question 8Find a counterexample, if it exists, to the statement: ∫_0^1 f(x) d x is equal to the area enclosed by f(x), the x-axis, x=0 and x=1 if…
- Question 9It is given that ∫ u(d v)/(d x) d x=uv-∫ v(d u)/(d x) d x. Here is an attempt to prove 0=1: 1. Let u=frac1x and (d v)/(d x)=1 2. (d u)/(d…
- Question 10Find the full range of values of the real number k such that ln(x)^2+ln(frac1x^6)+k=0 has exactly 2 real solutions.
- Question 11A *repunit* is an integer consisting of only ones. Examples: 1111 or 1 or 11111111. Complete the sentence: A repunit with n digits (n>0) is…
- Question 12f(x)=5x^2-x^3-7x+3, and 0≤ x≤4. Find the maximum value of f(x) in this range.
- Question 13A word is *good* if and only if it consists of no letters other than A, B, C, D. Examples: AABDC or CCCB or AB or ABDBCDA. How many…
- Question 14Which of these numbers is the smallest?
- Question 15Which of these statements is true for two positive integers, p and q, where p is prime? 1. The highest common factor of p and q is 1 if q…
- Question 16Of the following 7 statements about numbered lamps in a factory, exactly one of them is true. Which one is the true statement? [n is a…
- Question 17For how many of these functions is f'(x) strictly increasing for all real x? 1. ln(x) 2. sin(x) 3. -ln(x) 4. x^2 5. x^3
- Question 18All 720 permutations of the word “NUMBER” are generated, and arranged in alphabetical order. In what position is the word “NUMBER”?
- Question 19A *squarefree* integer is a positive integer which isn't divisible by the square of a prime. Which of these statements about squarefree…
- Question 20Solve these simultaneous equations to find the real numbers x,y and z. Hence find x+y^2+z^3. x^2+6y+10&=0 3y^2+6z+5&=-1 40x-5z^2&=70