1
GATE CE 2025 Set 2
MCQ (More than One Correct Answer)
+2
-0

Consider the function given below and pick one or more CORRECT statement(s) from the following choices.

$$ f(x)=x^3-\frac{15}{2} x^2+18 x+20 $$

A
$f(x)$ has a local minimum at $x=3$
B
$f(x)$ has a local maximum at $x=3$
C
$f(x)$ has a local minimum at $x=2$
D
$f(x)$ has a local maximum at $x=2$
2
GATE CE 2025 Set 1
MCQ (Single Correct Answer)
+2
-0.67

$$ \text { The value of }\mathop {\lim }\limits_{x \to \infty } \left(x-\sqrt{x^2+x}\right) \text { is equal to }$$

A
-1
B
-0.5
C
-2
D
0
3
GATE CE 2025 Set 1
Numerical
+2
-0

The maximum value of the function $h(x)=-x^3+2 x^2$ in the interval $[-1,1.5]$ is equal to _________ . (rounded off to 1 decimal place)

Your input ____
4
GATE CE 2024 Set 2
Numerical
+2
-0

The expression for computing the effective interest rate $(i_{eff})$ using continuous compounding for a nominal interest rate of 5% is

$i_{eff} = \lim\limits_{m \to \infty} \left(1 + \frac{0.05}{m}\right)^m - 1$

The effective interest rate (in percentage) is ___________ (rounded off to 2 decimal places).

Your input ____
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