1
WB JEE 2024
MCQ (Single Correct Answer)
+1
-0.25
Change Language

If $$\left[\begin{array}{ll}2 & 1 \\ 3 & 2\end{array}\right] \cdot A \cdot\left[\begin{array}{cc}-3 & 2 \\ 5 & -3\end{array}\right]=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$$, then $$A=$$

A
$$\left[\begin{array}{ll}1 & 1 \\ 1 & 0\end{array}\right]$$
B
$$\left[\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right]$$
C
$$\left[\begin{array}{ll}1 & 0 \\ 1 & 1\end{array}\right]$$
D
$$\left[\begin{array}{ll}0 & 1 \\ 1 & 1\end{array}\right]$$
2
WB JEE 2024
MCQ (Single Correct Answer)
+1
-0.25
Change Language

$$ \text { Let } f(x)=\left|\begin{array}{ccc} \cos x & x & 1 \\ 2 \sin x & x^3 & 2 x \\ \tan x & x & 1 \end{array}\right| \text {, then } \lim _\limits{x \rightarrow 0} \frac{f(x)}{x^2}= $$

A
2
B
$$-$$2
C
1
D
$$-$$1
3
WB JEE 2024
MCQ (Single Correct Answer)
+1
-0.25
Change Language

In R, a relation p is defined as follows: $$\forall a, b \in \mathbb{R}, a p$$ holds iff $$a^2-4 a b+3 b^2=0$$. Then

A
$$\mathrm{p}$$ is equivalence relation
B
$$\mathrm{p}$$ is only symmetric
C
$$\mathrm{p}$$ is only reflexive
D
p is only transitive
4
WB JEE 2024
MCQ (Single Correct Answer)
+1
-0.25
Change Language

Let $$\mathrm{f}: \mathbb{R} \rightarrow \mathbb{R}$$ be a function defined by $$\mathrm{f}(x)=\frac{\mathrm{e}^{|x|}-\mathrm{e}^{-x}}{\mathrm{e}^x+\mathrm{e}^{-x}}$$, then

A
$$f$$ is both one-one and onto
B
$$f$$ is one-one but not onto
C
$$f$$ is onto but not one-one
D
$$f$$ is neither one-one nor onto
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