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JEE Main Ultimate Online Test Series - 2027
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1
JEE Main 2024 (Online) 1st February Morning Shift
Numerical
+4
-1
Let $3,7,11,15, \ldots, 403$ and $2,5,8,11, \ldots, 404$ be two arithmetic progressions. Then the sum, of the common terms in them, is equal to ___________.
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2
JEE Main 2024 (Online) 30th January Evening Shift
Numerical
+4
-1
Let $$S_n$$ be the sum to $$n$$-terms of an arithmetic progression $$3,7,11$$, If $$40<\left(\frac{6}{n(n+1)} \sum_\limits{k=1}^n S_k\right)<42$$, then $$n$$ equals ________.
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3
JEE Main 2024 (Online) 30th January Morning Shift
Numerical
+4
-1
Let $$\alpha=1^2+4^2+8^2+13^2+19^2+26^2+\ldots$$ upto 10 terms and $$\beta=\sum_\limits{n=1}^{10} n^4$$. If $$4 \alpha-\beta=55 k+40$$, then $$\mathrm{k}$$ is equal to __________.
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4
JEE Main 2024 (Online) 27th January Morning Shift
Numerical
+4
-1
If $8=3+\frac{1}{4}(3+p)+\frac{1}{4^2}(3+2 p)+\frac{1}{4^3}(3+3 p)+\cdots \cdots \infty$, then the value of $p$ is ____________.
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