1
GATE ECE 2025
MCQ (Single Correct Answer)
+1
-0.33

A pot contains two red balls and two blue balls. Two balls are drawn from this pot randomly without replacement.

What is the probability that the two balls drawn have different colours?

A
$\frac{2}{3}$
B
$\frac{1}{3}$
C
$\frac{1}{2}$
D
1
2
GATE ECE 2025
MCQ (More than One Correct Answer)
+1
-0

Consider the function $f: \mathbb{R} \rightarrow \mathbb{R}$ defined as

$$ f(x)=2 x^3-3 x^2-12 x+1 $$

Which of the following statements is/are correct?

(Here, $\mathbb{R}$ is the set of real numbers.)

A
$f$ has no global maximizer
B
$f$ has no global minimizer
C
$x=-1$ is a local minimizer of $f$
D
$x=2$ is a local maximizer of $f$
3
GATE ECE 2025
Numerical
+1
-0

The function $y(t)$ satisfies

$$ t^2 y^{\prime \prime}(t)-2 t y^{\prime}(t)+2 y(t)=0 $$

where $y^{\prime}(t)$ and $y^{\prime \prime}(t)$ denote the first and second derivatives of $y(t)$, respectively. Given $y^{\prime}(0)=1$ and $y^{\prime}(1)=-1$, the maximum value of $y(t)$ over $[0,1]$ is ___________ (rounded off to two decimal places).

Your input ____
4
GATE ECE 2025
MCQ (Single Correct Answer)
+2
-0.67

Consider a non-negative function $f(x)$ which is continuous and bounded over the interval $[2,8]$. Let $M$ and $m$ denote, respectively, the maximum and the minimum values of $f(x)$ over the interval.

Among the combinations of $\alpha$ and $\beta$ given below, choose the one(s) for which the inequality

$$ \beta \leq \int_2^8 f(x) d x \leq \alpha $$

is guaranteed to hold.

A
$\beta=5 \mathrm{~m}, \alpha=7 \mathrm{M}$
B
$\beta=6 \mathrm{~m}, \alpha=5 \mathrm{M}$
C
$\beta=7 \mathrm{~m}, \alpha=6 \mathrm{M}$
D
$\beta=7 \mathrm{~m}, \alpha=5 \mathrm{M}$
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