1
JEE Main 2023 (Online) 8th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$P=\left[\begin{array}{cc}\frac{\sqrt{3}}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt{3}}{2}\end{array}\right], A=\left[\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right]$$ and $$Q=P A P^{T}$$. If $$P^{T} Q^{2007} P=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]$$, then $$2 a+b-3 c-4 d$$ equal to :

A
2004
B
2006
C
2007
D
2005
2
JEE Main 2023 (Online) 8th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If for $$z=\alpha+i \beta,|z+2|=z+4(1+i)$$, then $$\alpha+\beta$$ and $$\alpha \beta$$ are the roots of the equation :

A
$$x^{2}+2 x-3=0$$
B
$$x^{2}+3 x-4=0$$
C
$$x^{2}+x-12=0$$
D
$$x^{2}+7 x+12=0$$
3
JEE Main 2023 (Online) 8th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

Negation of $$(p \Rightarrow q) \Rightarrow(q \Rightarrow p)$$ is :

A
$$(\sim q) \wedge p$$
B
$$q \wedge(\sim p)$$
C
$$p \vee(\sim q)$$
D
$$(\sim p) \vee q$$
4
JEE Main 2023 (Online) 8th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If the points with position vectors $$\alpha \hat{i}+10 \hat{j}+13 \hat{k}, 6 \hat{i}+11 \hat{j}+11 \hat{k}, \frac{9}{2} \hat{i}+\beta \hat{j}-8 \hat{k}$$ are collinear, then $$(19 \alpha-6 \beta)^{2}$$ is equal to :

A
16
B
49
C
36
D
25
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