1
WB JEE 2024
MCQ (More than One Correct Answer)
+2
-0
Change Language

Let $$\Gamma$$ be the curve $$\mathrm{y}=\mathrm{be}^{-x / a}$$ & $$\mathrm{L}$$ be the straight line $$\frac{x}{\mathrm{a}}+\frac{\mathrm{y}}{\mathrm{b}}=1$$ where $$\mathrm{a}, \mathrm{b} \in \mathbb{R}$$. Then

A
$$\mathrm{L}$$ touches the curve $$\Gamma$$ at the point where the curve crosses the axis of $$y$$.
B
$$\mathrm{L}$$ does not touch the curve at the point where the curve crosses the axis of $$\mathbf{y}$$.
C
$$\Gamma$$ touches the axis of $$x$$ at a point.
D
$$\Gamma$$ never touches the axis of $$x$$.
2
WB JEE 2024
MCQ (More than One Correct Answer)
+2
-0
Change Language

A square with each side equal to '$$a$$' above the $$x$$-axis and has one vertex at the origin. One of the sides passing through the origin makes an angle $$\alpha$$ $$\left(0<\alpha< \frac{\pi}{4}\right)$$ with the positive direction of the axis. Equation of the diagonals of the square

A
$$\mathrm{y}(\cos \alpha-\sin \alpha)=x(\sin \alpha+\cos \alpha)$$
B
$$y(\cos \alpha+\sin \alpha)=x(\cos \alpha-\sin \alpha)$$
C
$$y(\sin \alpha+\cos \alpha)+x(\cos \alpha-\sin \alpha)=\mathrm{a}$$
D
$$\mathrm{y}(\cos \alpha-\sin \alpha)+x(\cos \alpha+\sin \alpha)=\mathrm{a}$$
3
WB JEE 2024
MCQ (More than One Correct Answer)
+2
-0
Change Language

If $$\mathrm{ABC}$$ is an isosceles triangle and the coordinates of the base points are $$B(1,3)$$ and $$C(-2,7)$$. The coordinates of $$A$$ can be

A
$$(1,6)$$
B
$$\left(-\frac{1}{8}, 5\right)$$
C
$$\left(\frac{5}{6}, 6\right)$$
D
$$\left(-7, \frac{1}{8}\right)$$
4
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)
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