1

JEE Main 2023 (Online) 31st January Evening Shift

Numerical

+4

-1

Out of Syllabus

The sum $1^{2}-2 \cdot 3^{2}+3 \cdot 5^{2}-4 \cdot 7^{2}+5 \cdot 9^{2}-\ldots+15 \cdot 29^{2}$ is _________.

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2

JEE Main 2023 (Online) 31st January Morning Shift

Numerical

+4

-1

Let $$a_{1}, a_{2}, \ldots, a_{n}$$ be in A.P. If $$a_{5}=2 a_{7}$$ and $$a_{11}=18$$, then

$$12\left(\frac{1}{\sqrt{a_{10}}+\sqrt{a_{11}}}+\frac{1}{\sqrt{a_{11}}+\sqrt{a_{12}}}+\ldots+\frac{1}{\sqrt{a_{17}}+\sqrt{a_{18}}}\right)$$ is equal to ____________.

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3

JEE Main 2023 (Online) 30th January Evening Shift

Numerical

+4

-1

Out of Syllabus

The $8^{\text {th }}$ common term of the series

$$ \begin{aligned} & S_1=3+7+11+15+19+\ldots . . \\\\ & S_2=1+6+11+16+21+\ldots . . \end{aligned} $$

is :

$$ \begin{aligned} & S_1=3+7+11+15+19+\ldots . . \\\\ & S_2=1+6+11+16+21+\ldots . . \end{aligned} $$

is :

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4

JEE Main 2023 (Online) 30th January Morning Shift

Numerical

+4

-1

Out of Syllabus

Let $$\sum_\limits{n=0}^{\infty} \frac{\mathrm{n}^{3}((2 \mathrm{n}) !)+(2 \mathrm{n}-1)(\mathrm{n} !)}{(\mathrm{n} !)((2 \mathrm{n}) !)}=\mathrm{ae}+\frac{\mathrm{b}}{\mathrm{e}}+\mathrm{c}$$, where $$\mathrm{a}, \mathrm{b}, \mathrm{c} \in \mathbb{Z}$$ and $$e=\sum_\limits{\mathrm{n}=0}^{\infty} \frac{1}{\mathrm{n} !}$$ Then $$\mathrm{a}^{2}-\mathrm{b}+\mathrm{c}$$ is equal to ____________.

Your input ____

Questions Asked from Sequences and Series (Numerical)

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