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

Let $$f:\mathbb{R}\to\mathbb{R}$$ be a differentiable function that satisfies the relation $$f(x+y)=f(x)+f(y)-1,\forall x,y\in\mathbb{R}$$. If $$f'(0)=2$$, then $$|f(-2)|$$ is equal to ___________.

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

Five digit numbers are formed using the digits 1, 2, 3, 5, 7 with repetitions and are written in descending order with serial numbers. For example, the number 77777 has serial number 1. Then the serial number of 35337 is ____________.

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3
JEE Main 2023 (Online) 29th January Morning Shift
Numerical
+4
-1
Change Language

Let the co-ordinates of one vertex of $$\Delta ABC$$ be $$A(0,2,\alpha)$$ and the other two vertices lie on the line $${{x + \alpha } \over 5} = {{y - 1} \over 2} = {{z + 4} \over 3}$$. For $$\alpha \in \mathbb{Z}$$, if the area of $$\Delta ABC$$ is 21 sq. units and the line segment $$BC$$ has length $$2\sqrt{21}$$ units, then $$\alpha^2$$ is equal to ___________.

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

Two particles of equal mass '$$m$$' move in a circle of radius '$$r$$' under the action of their mutual gravitational attraction. The speed of each particle will be :

A
$$\sqrt{\frac{G m}{4 r}}$$
B
$$\sqrt{\frac{G m}{2 r}}$$
C
$$\sqrt{\frac{G m}{r}}$$
D
$$\sqrt{\frac{4 G m}{r}}$$
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