Beyond Horizon Set 1 Paper 1
19 questions · 71 min · Difficulty 43 · by Beyond Horizon
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1 question has been withdrawn and is left out of practice sessions.
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Questions in this paper
- Question 1For what values of x is f(x) a valid function? f(x)=(1)/(2log(x^2-2x-3))
- Question 2For a real number x, let [x] denote the largest integer less than or equal to x. Find the value of ∫_(-100)^(100)[t^3] dt
- Question 3Two functions are defined as: f(x)&=| x^2-4|, &&x g(x)&=x+2, &&x Which range of values satisfy the inequality f(x)<g(x)?
- Question 4What is the sum of the coefficients in ((2)/(x)+(3)/(x^2)+5x)^3?
- Question 5How many solutions does this equation have in the interval 0≤ x≤ 2π? sin(cos(sin(x)))=cos(sin(cos(x)))
- Question 6How many integer pairs (x,y) satisfy the equation x^2+6x+y^2=4
- Question 7The number of polynomials of the form x^3+ax^2+bx+c which are divisible by x^2+1 and where a, b, and c belong to \1,2,…,10\, is
- Question 8There are seven greeting cards, each of a different colour, and seven envelopes of the same seven colours. The number of ways in which the…
- Question 9Suppose that F(n+1)=(2F(n)+1)/(2) for n=1,2,3,… and F(1)=2. Then F(101) equals
- Question 10Let p(x) be a continuous function which is positive for all x and ∫_2^3p(x) dx=c∫_0^2p((x+4)/(2)) dx. Then
- Question 11How many real solutions does the equation 2sin^3(x)-6sin(x)cos^2(x)+sin(x)=0 have in the interval 0<x<2π?
- Question 12Suppose a<b. The maximum value of the integral ∫_a^b(frac34-x-x^2) dx over all possible values of a and b is
- Question 13The line x=y is tangent at (0,0) to a circle of radius 1. The centre of the circle is
- Question 14The mth term of an arithmetic progression is x and the nth term is y. What is the sum of the first (m+n) terms?
- Question 15The values of m for which mx^2-6mx+5m+1>0 for all real x is
- Question 16The inequality √(x+6)≥ x is satisfied for real x if and only if
- Question 17The difference between the roots of the equation 6x^2+α x+1=0 is frac16. α is a positive number. The value of α is
- Question 18Let x,y,z be positive. The least value of the following expression is fracx(1+y)+y(1+z)+z(1+x)√(xyz)
- Question 19All the letters of the word PESSIMISTIC are to be arranged so that no two S's, no two I's, and S and I do not occur together. The number of…
- Question 20Withdrawn