1
GATE EE 2024
MCQ (More than One Correct Answer)
+2
-0

Let $f(t)$ be a real-valued function whose second derivative is positive for $- \infty < t < \infty$. Which of the following statements is/are always true?

A

$f(t)$ has at least one local minimum.

B

$f(t)$ cannot have two distinct local minima.

C

$f(t)$ has at least one local maximum.

D

The minimum value of $f(t)$ cannot be negative.

2
GATE EE 2024
MCQ (More than One Correct Answer)
+2
-0

Consider the function $f(t) = (\text{max}(0,t))^2$ for $- \infty < t < \infty$, where $\text{max}(a,b)$ denotes the maximum of $a$ and $b$. Which of the following statements is/are true?

A

$f(t)$ is not differentiable.

B

$f(t)$ is differentiable and its derivative is continuous.

C

$f(t)$ is differentiable but its derivative is not continuous.

D

$f(t)$ and its derivative are differentiable.

3
GATE EE 2023
MCQ (More than One Correct Answer)
+2
-0

Consider the following equation in a 2-D real-space.

$$|{x_1}{|^p} + |{x_2}{|^p} = 1$$ for $$p > 0$$

Which of the following statement(s) is/are true.

A
When p = 2, the area enclosed by the curve is $$\pi$$.
B
When p tends to $$\infty$$, the area enclosed by the curve tends to 4.
C
When p tends to 0, the area enclosed by the curve is 1.
D
When p = 1, the area enclosed by the curve is 2.
4
GATE EE 2022
MCQ (Single Correct Answer)
+2
-0.67

Let $$f(x) = \int\limits_0^x {{e^t}(t - 1)(t - 2)dt} $$. Then f(x) decreases in the interval.

A
x $$\in$$ (1, 2)
B
x $$\in$$ (2, 3)
C
x $$\in$$ (0, 1)
D
x $$\in$$ (0.5, 1)
GATE EE Subjects
EXAM MAP