1
JEE Main 2023 (Online) 29th January Evening Shift
Numerical
+4
-1
Change Language

The total number of 4-digit numbers whose greatest common divisor with 54 is 2, is __________.

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2
JEE Main 2023 (Online) 29th January Evening Shift
Numerical
+4
-1
Change Language

Let $$X=\{11,12,13,....,40,41\}$$ and $$Y=\{61,62,63,....,90,91\}$$ be the two sets of observations. If $$\overline x $$ and $$\overline y $$ are their respective means and $$\sigma^2$$ is the variance of all the observations in $$\mathrm{X\cup Y}$$, then $$\left| {\overline x + \overline y - {\sigma ^2}} \right|$$ is equal to ____________.

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3
JEE Main 2023 (Online) 29th January Evening Shift
Numerical
+4
-1
Out of Syllabus
Change Language

If the equation of the normal to the curve $$y = {{x - a} \over {(x + b)(x - 2)}}$$ at the point (1, $$-$$3) is $$x - 4y = 13$$, then the value of $$a + b$$ is equal to ___________.

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4
JEE Main 2023 (Online) 29th January Evening Shift
Numerical
+4
-1
Change Language

Let $$\alpha = 8 - 14i,A = \left\{ {z \in c:{{\alpha z - \overline \alpha \overline z } \over {{z^2} - {{\left( {\overline z } \right)}^2} - 112i}}=1} \right\}$$ and $$B = \left\{ {z \in c:\left| {z + 3i} \right| = 4} \right\}$$. Then $$\sum\limits_{z \in A \cap B} {({\mathop{\rm Re}\nolimits} z - {\mathop{\rm Im}\nolimits} z)} $$ is equal to ____________.

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