1
JEE Main 2023 (Online) 29th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$f$$ and $$g$$ be the twice differentiable functions on $$\mathbb{R}$$ such that

$$f''(x)=g''(x)+6x$$

$$f'(1)=4g'(1)-3=9$$

$$f(2)=3g(2)=12$$.

Then which of the following is NOT true?

A
$$g(-2)-f(-2)=20$$
B
There exists $$x_0\in(1,3/2)$$ such that $$f(x_0)=g(x_0)$$
C
$$|f'(x)-g'(x)| < 6\Rightarrow -1 < x < 1$$
D
If $$-1 < x < 2$$, then $$|f(x)-g(x)| < 8$$
2
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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3
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 ____________.

Your input ____
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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