CUET UG 2025 — Mathematics Calculus
The function f(x)=kx3+6kx2+18x+17 is increasing on R(set of real numbers) if:
Held on 14 May 2025 · Verified 13 Jul 2026.
k∈(0,3)
k∈(0,23)
k∈(21,23)
k∈(21,25)
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The derivative of x³ + 2x² - 5x + 1 is:
The value of the definite integral $I = \int_{1}^{2} \frac{1}{x(1 + x^2)}dx$ is:
If $y = ax^2 + bx$ has minima at $x = 2$ and the minimum value is -12, then which of the following are correct? (A) $a = 3$ (B) $a = -3$ (C) $b = 12$ (D) $b = -12$ Choose the correct answer from the options given below:
Curd is at 80° F, five minutes later it came down at 60°F. After another 5 minutes, its temperature became 50° F. Given that the rate of change of temperature is proportional to (T - S), where S is temperature of the surroundings and T is temperature of the curd at any time t. Then the temperature of the surroundings is :
The area bounded by the curve $y = 4 + 3x - x^2$ and $x$-axis is equal to
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