1
WB JEE 2025
MCQ (More than One Correct Answer)
+2
-0
Change Language

Let $f:[0,1] \rightarrow \mathbb{R}$ and $g:[0,1] \rightarrow \mathbb{R}$ be defined as follows :

$\left.\begin{array}{rl}f(x) & =1 \text { if } x \text { is rational } \\ & =0 \text { if } x \text { is irrational }\end{array}\right]$ and

$\left.\begin{array}{rl}g(x) & =0 \text { if } x \text { is rational } \\ & =1 \text { if } x \text { is irrational }\end{array}\right]$ then

A
$f$ and $g$ are continuous at the point $x=\frac{1}{2}$.
B
$f+g$ is continuous at the point $x=\frac{2}{3}$ but $f$ and $g$ are discontinuous at $x=\frac{2}{3}$.
C
$f(x) \cdot g(x)>0$ for some points $x \in(0,1)$.
D
$f+g$ is not differentiable at the point $x=\frac{3}{4}$.
2
WB JEE 2025
MCQ (Single Correct Answer)
+1
-0.25
Change Language
The velocity-time graph for a body of mass 10 kg is shown in the figure. Work done on the body in the first two seconds of motion is : WB JEE 2025 Physics - Work Power & Energy Question 1 English
A
-9300 J
B
12000 J
C
-4500 J
D
-12000 J
3
WB JEE 2025
MCQ (Single Correct Answer)
+1
-0.25
Change Language
For a domestic AC supply of 220 V at 50 cycles per sec, the potential difference between the terminals of a two-pin electric outlet in a room is given by
A
$\mathrm{V}(\mathrm{t})=220 \sqrt{2} \operatorname{Cos}(100 \pi \mathrm{t})$
B
$V(t)=220 \operatorname{Sin}(50 t)$
C
$\mathrm{V}(\mathrm{t})=220 \operatorname{Cos}(100 \pi \mathrm{t})$
D
$\mathrm{V}(\mathrm{t})=220 \sqrt{2} \operatorname{Cos}(50 \mathrm{t})$
4
WB JEE 2025
MCQ (Single Correct Answer)
+1
-0.25
Change Language

A radioactive nucleus decays as follows :

$$ X \xrightarrow{\alpha} X_1 \xrightarrow{\beta} X_2 \xrightarrow{\alpha} X_3 \xrightarrow{\gamma} X_4 $$

If the mass number and atomic number of ' $X_4$ ' are 172 and 69 respectively, then the atomic number and mass number of ' $X$ ' are

A
72,180
B
69,170
C
68,172
D
70,172
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