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

$$ \text { If }\left|\begin{array}{lll} x^k & x^{k+2} & x^{k+3} \\ y^k & y^{k+2} & y^{k+3} \\ z^k & z^{k+2} & z^{k+3} \end{array}\right|=(x-y)(y-z)(z-x)\left(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\right) \text {, then } $$

A
k = $$-$$3
B
k = 3
C
k = 1
D
k = $$-$$1
2
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
$$\left[\begin{array}{ll}0 & 1 \\ 1 & 1\end{array}\right]$$
3
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
4
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
EXAM MAP