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

If the quadratic equation $$a x^2+b x+c=0(a>0)$$ has two roots $$\alpha$$ and $$\beta$$ such that $$\alpha<-2$$ and $$\beta>2$$, then

A
$$c<0$$
B
$$\mathrm{a}+\mathrm{b}+\mathrm{c}>0$$
C
$$a - b + c<0$$
D
$$\mathrm{a}-\mathrm{b}+\mathrm{c}>0$$
2
WB JEE 2024
MCQ (More than One Correct Answer)
+2
-0
Change Language

If $$\mathrm{a}_{\mathrm{i}}, \mathrm{b}_{\mathrm{i}}, \mathrm{c}_{\mathrm{i}} \in \mathbb{R}(\mathrm{i}=1,2,3)$$ and $$x \in \mathbb{R}$$ and $$\left|\begin{array}{lll}\mathrm{a}_1+b_1 x & a_1 x+b_1 & c_1 \\ \mathrm{a}_2+b_2 x & a_2 x+b_2 & c_2 \\ \mathrm{a}_3+b_3 x & a_3 x+b_3 & c_3\end{array}\right|=0$$, then

A
$$x=1$$
B
$$x=-1$$
C
$$\left|\begin{array}{ccc}a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3\end{array}\right|=0$$
D
$$x=2$$
3
WB JEE 2024
MCQ (More than One Correct Answer)
+2
-0
Change Language

The function $$\mathrm{f}: \mathbb{R} \rightarrow \mathbb{R}$$ defined by $$\mathrm{f}(x)=\mathrm{e}^x+\mathrm{e}^{-x}$$ is :

A
one-one
B
onto
C
bijective
D
not bijective
4
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
$$\mathrm{y}(\cos \alpha-\sin \alpha)+x(\cos \alpha+\sin \alpha)=\mathrm{a}$$
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