1
JEE Main 2022 (Online) 26th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If $$z=x+i y$$ satisfies $$|z|-2=0$$ and $$|z-i|-|z+5 i|=0$$, then :

A
$$x+2 y-4=0$$
B
$$x^{2}+y-4=0$$
C
$$x+2 y+4=0$$
D
$$x^{2}-y+3=0$$
2
JEE Main 2022 (Online) 26th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

$$ \text { Let } A=\left[\begin{array}{l} 1 \\ 1 \\ 1 \end{array}\right] \text { and } B=\left[\begin{array}{ccc} 9^{2} & -10^{2} & 11^{2} \\ 12^{2} & 13^{2} & -14^{2} \\ -15^{2} & 16^{2} & 17^{2} \end{array}\right] \text {, then the value of } A^{\prime} B A \text { is: } $$

A
1224
B
1042
C
540
D
539
3
JEE Main 2022 (Online) 26th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

$$\sum\limits_{\matrix{ {i,j = 0} \cr {i \ne j} \cr } }^n {{}^n{C_i}\,{}^n{C_j}} $$ is equal to

A
$$2^{2 n}-{ }^{2 n} C_{n}$$
B
$${2^{2n - 1}} - {}^{2n - 1}{C_{n - 1}}$$
C
$$2^{2 n}-\frac{1}{2}{ }^{2 n} C_{n}$$
D
$${2^{2n - 1}} + {}^{2n - 1}{C_n}$$
4
JEE Main 2022 (Online) 26th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$\mathrm{P}$$ and $$\mathrm{Q}$$ be any points on the curves $$(x-1)^{2}+(y+1)^{2}=1$$ and $$y=x^{2}$$, respectively. The distance between $$P$$ and $$Q$$ is minimum for some value of the abscissa of $$P$$ in the interval :

A
$$\left(0, \frac{1}{4}\right)$$
B
$$\left(\frac{1}{2}, \frac{3}{4}\right)$$
C
$$\left(\frac{1}{4}, \frac{1}{2}\right)$$
D
$$\left(\frac{3}{4}, 1\right)$$
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