Exams › JEE Advanced › Maths

Find the number of integral values of x satisfying sgn([15/(1+x²)]) = [1 + {2x}], where sgn(y), [y], {y} denote the signum function, greatest integer function, and fractional part function respectively.

1. 5
2. 7
3. 15
4. 16

Correct answer: 7

Solution

For any integer x, {2x}=0, so [1+{2x}]=1. We need sgn([15/(1+x²)])=1, which requires [15/(1+x²)]>=1, i.e., 15/(1+x²)>=1, i.e., x²<=14. Integer x with |x|<=3 (since 3²=9<=14 but 4²=16>14) gives x in {-3,-2,-1,0,1,2,3}: 7 values.

Related JEE Advanced Maths questions

• In a chemistry class, there are 20 students, while a physics class has 30 students. If 10 students are enrolled in both classes, and the two classes are held at separate times, determine the value of k/8, where k represents the total number of students attending either class.
• Given that A represents the divisors of 15, B contains prime numbers less than 10, and C includes even numbers less than 9, how many elements are there in the intersection of (A ∪ C) and B?
• Identify the periodic function among the following:
• The function f(x) = √|x² - 5| x + 6 + √8 + 2|x| - |x|² is defined as a real number for values of x within which range?
• Let f(x) = 4x / (4x² + 2). If the sum of the integrals ∫(1/1997) + ∫(2/1997) +... + ∫(1196/1997) equals 499q, what is the value of q?
• Given that α, β, γ, and θ are the smallest positive angles in increasing order for which their sine values equal a positive constant k, what is the result of 4 sin(α/2) + 3 sin(β/2) + 2 sin(γ/2) + sin(θ/2)?

⚔️ Practice JEE Advanced Maths free + battle 1v1 →