1
JEE Main 2023 (Online) 1st February Morning Shift
Numerical
+4
-1
Change Language

Let $$f: \mathbb{R} \rightarrow \mathbb{R}$$ be a differentiable function such that $$f^{\prime}(x)+f(x)=\int_\limits{0}^{2} f(t) d t$$. If $$f(0)=e^{-2}$$, then $$2 f(0)-f(2)$$ is equal to ____________.

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2
JEE Main 2023 (Online) 1st February Morning Shift
Numerical
+4
-1
Change Language

The remainder, when $$19^{200}+23^{200}$$ is divided by 49 , is ___________.

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3
JEE Main 2023 (Online) 1st February Morning Shift
Numerical
+4
-1
Change Language

The number of 3-digit numbers, that are divisible by either 2 or 3 but not divisible by 7, is ____________.

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4
JEE Main 2023 (Online) 1st February Morning Shift
Numerical
+4
-1
Change Language

The number of words, with or without meaning, that can be formed using all the letters of the word ASSASSINATION so that the vowels occur together, is ___________.

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