1
WB JEE 2025
MCQ (Single Correct Answer)
+1
-0.25
Change Language

Suppose $\alpha, \beta, \gamma$ are the roots of the equation $x^3+q x+r=0($ with $r \neq 0)$ and they are in A.P. Then the rank of the matrix $\left(\begin{array}{lll}\alpha & \beta & \gamma \\ \beta & \gamma & \alpha \\ \gamma & \alpha & \beta\end{array}\right)$ is

A
3
B
2
C
0
D
1
2
WB JEE 2025
MCQ (Single Correct Answer)
+1
-0.25
Change Language

Let $f_n(x)=\tan \frac{x}{2}(1+\sec x)(1+\sec 2 x) \ldots\left(1+\sec 2^n x\right)$, then

A
$f_5\left(\frac{\pi}{16}\right)=1$
B
$f_4\left(\frac{\pi}{16}\right)=1$
C
$f_3\left(\frac{\pi}{16}\right)=1$
D
$f_2\left(\frac{\pi}{16}\right)=1$
3
WB JEE 2025
MCQ (Single Correct Answer)
+1
-0.25
Change Language

The value of the expression ${ }^{47} C_4+\sum\limits_{j=1}^5{ }^{52-j} C_3$ is

A
${ }^{52} C_3$
B
${ }^{51} C_4$
C
${ }^{52} C_4$
D
${ }^{51} C_3$
4
WB JEE 2025
MCQ (Single Correct Answer)
+1
-0.25
Change Language

If $\operatorname{adj} B=A,|P|=|Q|=1$, then $\operatorname{adj}\left(Q^{-1} B P^{-1}\right)=$

A
$P Q$
B
$Q A P$
C
$P A Q$
D
$P A^{-1} Q$
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