Exams › JEE Main › Maths

Let {x} and [x] denote the fractional and integral parts of a real number x. Match each condition in Column-I with the correct solution set in Column-II. Column-I: (A) [x²] >= 4 (B) [x]² - 5[x] + 6 = 0 (C) x = {x} (D) [x] < -5 Column-II: (p) x in [2, 4) (q) x in (-inf, -2] U [2, inf) (r) x in (-inf, -5) (s) x in {-2} (t) x in [0, 1)

1. A-q, B-p, C-t, D-r
2. A-p, B-q, C-t, D-r
3. A-q, B-p, C-t, D-s
4. A-r, B-p, C-t, D-q

Correct answer: A-q, B-p, C-t, D-r

Solution

(A) [x²] >= 4 means x² >= 4, so x <= -2 or x >= 2 -> (q). (B) ([x]-2)([x]-3)=0 => [x]=2 or 3 => x in [2,3) U [3,4) = [2,4) -> (p). (C) x = {x} means integral part 0, so x in [0,1) -> (t). (D) [x] < -5 means [x] is an integer <= -6, i.e. x < -5 -> (r).

Related JEE Main Maths questions

• Given f(x)=(x(x-p))/(q-p)+(x(x-q))/(p-q), where p≠ q, determine the value of f(p)+f(q).
• A real-valued function f(x) obeys the relation f(x-y)=f(x)f(y)-f(a-x)f(a+y), where a is a fixed constant, and f(0)=1. Then the value of f(2a-x) is
• The set of all real values of x for which the function f(x)=(3)/(4-x²)+log₁₀(x³-x) is defined is:
• A relation R is defined on the set of integers Z by the condition that (x,y) belongs to R exactly when x² + y² = 9. Which statement below is false?
• If f(x)=√(1+x²), then which of the following statements is true?
• For the function f(x)=√(x-√(1-x²)), what is its domain?

⚔️ Practice JEE Main Maths free + battle 1v1 →