WB JEE 2024 | Straight Lines and Pair of Straight Lines Question 23 | Mathematics

WB JEE 2024

MCQ (More than One Correct Answer)

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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

$$\mathrm{L}$$ touches the curve $$\Gamma$$ at the point where the curve crosses the axis of $$y$$.

$$\mathrm{L}$$ does not touch the curve at the point where the curve crosses the axis of $$\mathbf{y}$$.

$$\Gamma$$ touches the axis of $$x$$ at a point.

$$\Gamma$$ never touches the axis of $$x$$.

WB JEE 2024

MCQ (More than One Correct Answer)

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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

$$\mathrm{y}(\cos \alpha-\sin \alpha)=x(\sin \alpha+\cos \alpha)$$

$$y(\cos \alpha+\sin \alpha)=x(\cos \alpha-\sin \alpha)$$

$$y(\sin \alpha+\cos \alpha)+x(\cos \alpha-\sin \alpha)=\mathrm{a}$$

$$\mathrm{y}(\cos \alpha-\sin \alpha)+x(\cos \alpha+\sin \alpha)=\mathrm{a}$$

WB JEE 2024

MCQ (More than One Correct Answer)

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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

$$(1,6)$$

$$\left(-\frac{1}{8}, 5\right)$$

$$\left(\frac{5}{6}, 6\right)$$

$$\left(-7, \frac{1}{8}\right)$$

WB JEE 2023

MCQ (More than One Correct Answer)

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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

(3, 8)

($$-$$3, 8)

($$-$$3, $$-$$1)

(3, $$-$$1)

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