1
WB JEE 2024
MCQ (Single Correct Answer)
+2
-0.5
Change Language

Let $$A=\left(\begin{array}{ccc}1 & -1 & 0 \\ 0 & 1 & -1 \\ 1 & 1 & 1\end{array}\right), B=\left(\begin{array}{l}2 \\ 1 \\ 7\end{array}\right)$$

Then for the validity of the result $$\mathrm{AX}=\mathrm{B}, \mathrm{X}$$ is

A
$$\left(\begin{array}{c}-1 \\ 1 \\ 7\end{array}\right)$$
B
$$\left(\begin{array}{l}1 \\ 2 \\ 4\end{array}\right)$$
C
$$\left(\begin{array}{c}3 \\ 1 \\ -1\end{array}\right)$$
D
$$\left(\begin{array}{l}4 \\ 2 \\ 1\end{array}\right)$$
2
WB JEE 2024
MCQ (Single Correct Answer)
+2
-0.5
Change Language

If $$\alpha_1, \alpha_2, \ldots, \alpha_n$$ are in A.P. with common difference $$\theta$$, then the sum of the series $$ \sec \alpha_1 \sec \alpha_2+\sec \alpha_2 \sec \alpha_3+\ldots .+\sec \alpha_{n-1} \sec \alpha_n=k\left(\tan \alpha_n-\tan \alpha_1\right)$$ where $$\mathrm{k}=$$

A
$$\sin \theta$$
B
$$\cos \theta$$
C
$$\sec \theta$$
D
$$\operatorname{cosec} \theta$$
3
WB JEE 2024
MCQ (Single Correct Answer)
+2
-0.5
Change Language

For the real numbers $$x$$ & $$y$$, we write $$x$$ p y iff $$x-y+\sqrt{2}$$ is an irrational number. Then relation p is

A
reflexive
B
symmetric
C
transitive
D
equivalence relation
4
WB JEE 2024
MCQ (Single Correct Answer)
+2
-0.5
Change Language

Let $$A=\left[\begin{array}{ccc}0 & 0 & -1 \\ 0 & -1 & 0 \\ -1 & 0 & 0\end{array}\right]$$, then

A
$$\mathrm{A}$$ is a null matrix
B
$$\mathrm{A}$$ is skew symmetric matrix
C
$$\mathrm{A}^{-1}$$ does not exist
D
$$\mathrm{A}^2=\mathrm{I}$$
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