1
WB JEE 2023
MCQ (More than One Correct Answer)
+2
-0
Change Language

A rectangle ABCD has its side parallel to the line y = 2x and vertices A, B, D are on lines y = 1, x = 1 and x = $$-$$1 respectively. The coordinate of C can be

A
(3, 8)
B
($$-$$3, 8)
C
($$-$$3, $$-$$1)
D
(3, $$-$$1)
2
WB JEE 2023
MCQ (More than One Correct Answer)
+2
-0
Change Language

Let $$f(x) = {x^m}$$, m being a non-negative integer. The value of m so that the equality $$f'(a + b) = f'(a) + f'(b)$$ is valid for all a, b > 0 is

A
0
B
1
C
2
D
3
3
WB JEE 2023
MCQ (More than One Correct Answer)
+2
-0
Change Language

Which of the following statements are true?

A
If f(x) be continuous and periodic with periodicity T, then $$I = \int\limits_a^{a + T} {f(x)} ~dx$$ depend on 'a'.
B
If f(x) be continuous and periodic with periodicity T, then $$I = \int\limits_a^{a + T} {f(x)} ~dx$$ does not depend on 'a'.
C
Let $$\mathrm{f(x)} = \left\{ \matrix{ 1,\,\,\,\mathrm{if\,x\,is\,rational} \hfill \cr 0,\,\,\mathrm{if\,x\,is\,irrational} \hfill \cr} \right.$$, then f is periodic of the periodicity T only if T is rational.
D
f defined in (C) is periodic for all T.
4
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
Change Language

A ray of monochromatic light is incident on the plane surface of separation between two media $$\mathrm{X}$$ and $$\mathrm{Y}$$ with angle of incidence '$$\mathrm{i}$$' in medium $\mathrm{X}$ and angle of refraction 'r' in medium Y. The given graph shows the relation between $$\sin \mathrm{i}$$ and $$\sin \mathrm{r}$$. If $$\mathrm{V}_{X}$$ and $$\mathrm{V}_{Y}$$ are the velocities of the ray in media X and Y respectively, then which of the following is true?

WB JEE 2023 Physics - Wave Optics Question 3 English

A
$$\mathrm{V}_{X}=\frac{1}{\sqrt{3}} \mathrm{~V}_{\mathrm{Y}}$$
B
$$\mathrm{V}_{\mathrm{X}}=\sqrt{3} \mathrm{~V}_{\mathrm{Y}}$$
C
Total internal reflection can happen when the light is incident in medium X.
D
$$v_{X}=\sqrt{3} v_{Y}$$, where $$v_{X}$$ and $$v_{Y}$$ are frequencies of the light in medium X and Y respectively.
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