1
JEE Main 2022 (Online) 27th July Evening Shift
Numerical
+4
-1
Out of Syllabus
Change Language

$$ \frac{2^{3}-1^{3}}{1 \times 7}+\frac{4^{3}-3^{3}+2^{3}-1^{3}}{2 \times 11}+\frac{6^{3}-5^{3}+4^{3}-3^{3}+2^{3}-1^{3}}{3 \times 15}+\cdots+ \frac{30^{3}-29^{3}+28^{3}-27^{3}+\ldots+2^{3}-1^{3}}{15 \times 63}$$ is equal to _____________.

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2
JEE Main 2022 (Online) 26th July Evening Shift
Numerical
+4
-1
Out of Syllabus
Change Language

If $$\sum\limits_{k=1}^{10} \frac{k}{k^{4}+k^{2}+1}=\frac{m}{n}$$, where m and n are co-prime, then $$m+n$$ is equal to _____________.

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3
JEE Main 2022 (Online) 26th July Evening Shift
Numerical
+4
-1
Change Language

Different A.P.'s are constructed with the first term 100, the last term 199, and integral common differences. The sum of the common differences of all such A.P.'s having at least 3 terms and at most 33 terms is ___________.

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4
JEE Main 2022 (Online) 26th July Morning Shift
Numerical
+4
-1
Out of Syllabus
Change Language

The series of positive multiples of 3 is divided into sets : $$\{3\},\{6,9,12\},\{15,18,21,24,27\}, \ldots$$ Then the sum of the elements in the $$11^{\text {th }}$$ set is equal to ____________.

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