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NMTC Inter Level (Final Stage)

Q)

\( N=\sqrt { 1+1/{ 1 }^{ 2 }+1/2^{ 2 } } +\sqrt { 1+1/{ 2 }^{ 2 }+1/3^{ 2 } } +\quad ......+\sqrt { 1+1/{ 2014 }^{ 2 }+1/2015^{ 2 } } \)

Find the integral part of N

Q) Is it possible to write the numbers 1,2,3.....,121 in an 11x11 table so that any two consecutive numbers be written in cells with common side and all perfect squares lie in a straight column?

Note by Rajat Gupta
2 years ago

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1 vote

  Easy Math Editor

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 \( 2 \times 3 \)
2^{34} \( 2^{34} \)
a_{i-1} \( a_{i-1} \)
\frac{2}{3} \( \frac{2}{3} \)
\sqrt{2} \( \sqrt{2} \)
\sum_{i=1}^3 \( \sum_{i=1}^3 \)
\sin \theta \( \sin \theta \)
\boxed{123} \( \boxed{123} \)

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