Algebra Equations Actual Questions CAT 2025 Slot 3 Quant

For real values of x, the range of the function f(x) = (2x − 3)/(2x² + 4x − 6)

f(x) = (x²+ 3x)(x² + 3x + 2), then the sum of all real roots of the equation √f(x) + 1 = 9701, is

If (x²+ 1/x²) = 25 and x > 0, then the value of (x⁷ + 1/x⁷) is:

In a class of 150 students, 75 students chose physics, 111 students chose mathematics and 40 students chose chemistry. All students chose at least one of the three subjects and at least one student chose all three subjects. The number of students who chose both physics and chemistry is equal to the number of students who chose both chemistry and mathematics, and this is equal to half the number of students who chose both mathematics and physics. What is the maximum possible number of students who chose physics but not mathematics?

In a school with 1500 students , each students chooses one of the streams out of science , arts and commerce by paying a fee of rs 1100 , 1000 and 800 respectively. The total fees paid by all the students is RS. 15,50000.If the number of science students is not more than the number of arts students , then the maximum possible number of science students in school is : [TITA] _______