Maths-
General
Easy
Question
Represent -7 + 3 on number line
Hint:
We have to represent -7+3 on the number line.
The correct answer is: ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAoUAAAC/CAMAAAC/iVYEAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAMAUExURf////39/eDg4N3d3fLy8v7+/qenp6CgoNvb2/z8/PHx8aKiovn5+enp6e7u7vr6+uHh4d/f3+fn56mpqby8vIqKisnJyfX19ff39+Tk5I+Pj8fHx0BAQJ2dneLi4u/v7+jo6PPz86ioqFlZWWVlZb+/v/v7+5mZmTU1NQkJCTAwMJ6entra2rW1tWhoaA0NDT4+PtbW1lpaWhMTE+Pj4xYWFlBQUMzMzGlpaWdnZ9DQ0MjIyDs7OyQkJM3NzVRUVAsLC1FRUd7e3nt7exAQEIGBge3t7cHBwU5OTnx8fOvr67q6uiEhIS4uLru7uysrKx0dHaurq8TExMvLy9XV1YSEhBEREXd3d0ZGRtHR0dLS0jo6OrCwsJWVlVNTUz8/P0pKSmNjY4ODg5ubm35+fiIiIvDw8Obm5vj4+JSUlCgoKB4eHiUlJfT09CkpKR8fHxUVFRQUFAAAADg4OIWFhaOjo9TU1M7Ozn19fa2trYyMjKWlpfb29mZmZrS0tF9fXwoKCgMDAxISEhgYGHFxcbe3t+rq6p+fn4KCgnR0dF1dXVZWVpaWloaGhuzs7EhISEtLS1JSUq+vr3NzcxkZGZqamhsbGxwcHHp6era2tomJiURERA8PDyMjI3BwcBoaGqGhoRcXFzQ0NJycnIeHh1xcXC0tLXZ2doiIiAYGBk1NTcLCwmFhYXl5eT09PQcHB8bGxr6+vsPDw1hYWAUFBb29vaamppiYmNPT09fX15eXl3h4eJOTk8/Pzy8vL+Xl5WxsbDw8PNjY2GpqakdHRycnJywsLLm5ubi4uCYmJpGRkTk5OSoqKkxMTElJSUFBQTc3N1dXV21tbU9PTw4ODmtra7KyssrKyjIyMmBgYNzc3FtbW7Ozs8DAwDY2NtnZ2X9/f3V1dZKSkouLi6ysrGRkZKqqqq6urkNDQ46OjsXFxV5eXmJiYkVFRXJycpCQkLGxsUJCQjExMY2NjQgICDMzM25ubm9vbwEBASAgIICAgAwMDAICAlVVVaSkpAAAACXz8JcAAAEAdFJOU////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////wBT9wclAAAACXBIWXMAABcRAAAXEQHKJvM/AAAMRElEQVR4Xu3dy5HjKhQGYFexJw1CIAuWEAEJaE8kJEBkZMCSqnuQZVuWkIy4frXn/9zTI7/abuv04SFApznGpg2AT+FRIAzhwxqikPNpA+BFGHsQZCyqaQvgU3gQ0xbAp3Alpy2Aj0G1EAAAAOCXoHYHH8cDev3g05RHrx98Gpc4XAwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADQiuPsAvBpPGaHpXPgs7hIg8XaOfBZTDmdUCjDh/GsA5ZVhGfqaG0InRGF8EzS5aOnpGDJooECzyTzkA9mQ25QJMNTcQpDczCmlEUyhOdSVsdpc4Gp5VKyXEpJIRv00cAF2MWF9tWqoTQpuTgPNyZy8s4Io61AGMIz8TxU63nBWnsfbkJrmzR900MKQpW0CPAcyqZaMlQhcopEceJFuSVox5gSIfthoGAsmRKBCE/iqwflSoTxoFNwOTtR4pTqg+PtnHmdTbZa540qJcBRZoyuGmb0oKlkHigY2ay/urRPmAp+sA5nwIWnOOe4NS78WAcUMWQ7OK6sn6JwilsW0lBv2tzBcDB4LGo3bd1hxupMDeJUegejH4zMeuoodDqcN6Qb0sNSmUWBMIQNVMGTUjIp9CXHzXEzjC3koG2JM5m0uHQUyjRGZsGcrrZt5lig4hyghgXnLTUxEv0zii0DUdkx+koLZTxkF7UPaYw4nodbEU7B6vdjjJ9QIkMdFxR81vvsfSpNkHRuB9+YSznNxRiG3OnsynEW5u6OPVODGX3Y0Ecl7YSSjFGpnAef07kDcLqXODvV/U6cHkvbMlkKRMbN4mALJUnkOuhyTXUkWMNkyGmw7tqO4O7Wi0hFsKf/jE3JKh7MfdJUCVEIfebdM8KOESkDJcR8OTBnpnYwl5Eay2W7dFZrtyp9pbeP2icAVULnaatsT3mRiaTTuVguwwjH/+kmnc41v2CpObMa1cUQhdBJpXTNapQLp23Opv6ZcuMYplw5F6f8KFOqJEOWNaIQurBzr8voFoUl9+lzm1fZ8/E6duvDYU6HdeJT3qJeCH3ybXTrPApL+Tx2FPJKQRu0cKsDLdJjbih0mk0fCefWycXUDz0L04uoHdUNZxFbUNmOKIQ+sxmdVAWcRxZ3Q8mNlUEO0vqYl+0T9NRAN2WvzZPo7+NNpZIGp+bJXDmATKXydG2iLKIQOjF/TWp8OXpflCEKlZKWO63Ecu4T+guhG0XUqt53wTOVyZV+QG60WEUhemqgH4XTZkkqPcUahdx09SpqQ02Z+yg8hfr0KYDH4t6CM9HqeBlOOCNtNqsojBtzSQEeolbFTvAIm7x1q2SZvEvLNUVYHjbLdoBd1ODdiUIetF11DVKFMfm0TKH00GV6BGgj/e5YfWqh2HV3dLBp3T3I0nlYNsBRj3pYgh7WUUj1RX8bBjHhbriMiIXXYb9Y+34UhTFVopB5XTlgh47rdxC/WO9RlQJ3TtWikMrpyow97rf7HuFZXJo2fonS+wtoVqPw5HRtefVg/8dickee+VXZoPPN9P4O5gejkLsHa7LGsh7DtH1jhlo3oxThbpG5A/iBKfPsq2b7xdWw8xY89lbvfjEXRvvg8G+4jLqeKyXyuhexxFJvzZA9XtzhSl5n478OV62/iFuOtGyTV0OVGv3lXChX891HMg37p8+Rfqgs2UAN53oVUOjONMUOVCnlZYmSF5LNB4L8asxRC257o9CViZD/z2ea2ZyJ+upuLG8u1DWZVgZZMDbVa4DRdkYhP9DXyN6worZsHpuRu6LwtBhG1+4JuVDl8P7FT5nwenBKSrW8lElOkoz3Vb5kWQdp3Jxf6NaU4+rWcoex8XrD+rJ8yu0iow6zq/sXocXs2pHLbHP/cuA1km//sbeLtLnraVLmNLvec6G9NAxe1AvH1wl2IGVl4KXzuoT0r/pF//RQHlG2Z8otq1vLtfL4xWPvlGfVaTts37lEL9L82HvtT2t/DT0c+LEX5fedNo+gD/jBR9xg3Kv1ev0rUXk8UC4k8f5LaCPHjTqv3TCYcXP+rKwj/Und33zhbDzfUvsmyg+r36WELS9Uv3PxTQUbWh+7+CaCmF3b/EZfba9RvpIfH3i5qeFb+VI23640fp35RN8W9xz6UlQEDnaxtMY7SJGrywXvV8aMTpXxNFT3mzYqduuFfKc+d6xe2PsJqub+oPbXeHe9MDyhXuiNenu9sJjNJ75hO7ueK2N1qvUlhp1IE3tRKHdebu+tLPW3kUXzeZ1VcwvI9/XUpA+2keXrW3cHsO2zHDNj7VAfbSN2pr/v3bcbaTtvZUV2t5FDcxS2v0ZnLuyOwp87drIdFlxYL3z9r24v3+1G4bNyYXueWgrNy8Cr5p6azv7C/lz4e1G4mYC45Fu5vzsKn5YLu0vk9ihELnybBwloIwpfUy88cOxEvSEK21+jLxeePnns5Ls8SEAbf3UvqRdy0x5ZvLuX4UC9sDkKRXsSnwvtf3X3kAtH+yVyZy48MtCp/4xnobmrVjaft7zz3XT/Ev9SvbDY+H1fkgvfw7SfpKo1XN/O1E4I8pc9isKNeuFqxsnNbhTKjw/FNtsrAPwZsa8G8L2+qF74Hgdy4df6uTOwvrmNzD5+8if3A7nw57w5F35+uoh590ASeOwVbeSv3s3IhV+IrZfjmttsI//dKEQu/D7PrxfG7+5GyP9jpuoX+a0GCg+7Bwg66oXl8PMXcz+xrgHPByYs/gH7cw866oVf7idyIRPDv7QgUMexky+X+0akfhfpryfp/xd0HDv5brx7KvoLyBibZ97PsZBj+oeisKNeSHv63TMMj8jfUy+U2Vrb03EkslLdw8L+oI428ok7+72LrH9TLjRmnL09XWsnnTnJ66nT/wEd9UKu0rCzWvundc5UegVJH6J8tDJGRRmchijcz4Wysvj/THB5bzSrdM61Z4fV6eofOzLMvnG+njLZ9Y5yiftHUGt40sb5IR1Y4uyPC/Wx7Go72ZU1u1bLrl9x5pO3fnPnSud9So07hqtgD+/E9hJZCj+0DOVnht6z7VkvT4mQjw/v4CHTCw5dNcqvxKQaly2Zrq5Vpq0yKdXOkrYxR74ThZH2Vjyfd7kmUnlJgdq2R5lxrr4E1I7mRQN5TCI1FN9cBnliuXlg9g031DrpXO1R/lBPjTqvWrK916m5uzhWxFxZ5aR2lI4eSY8t7ZntKBzH1MiN1b6Kcodr7Y3kvL7gxK7Nl17iXKamaU30E7npOd8QfV4x9bXZf6leyMqSJcFvfhDSJbtYr5JlL2S1l4v+spMYq1IPPlmxP62I5/beyOBfeSCL3Z8uegdzHbmw4D1JlHx1b1iPuFlNky6HsKi4MLeVyMpCRNJp773W29X6QHWa/T/j5elx9wjf2yxowVpK5JGqrHb7UDmET7WXX6ne/S/bqYfXenhlts5sN88iVdWyri0HJYMxtKtEdq62UA8TxlEFizby47FX9GAzvsTBEplHY8YXaSNbcyFVC4/HEn3wxuSXJvO/Yzv1MJtjXNbmeaBGbG0dr5n1Wb2JzCmdn0Y/dx0JzKWUKTkwU74/wAw9uOy+Y7mQamGW3ntz1qLG/rS1j7mus1Aq+pV971r0v4FJdh6ClTdXQ5fjKpLXD5hq69NTTmG/APL1QrvcOP4z2101bOe+io1lkjeoUgM2rR1B9GbaciF3h94zXHFBAVbqZxufNLV2uaKUx+I1d7BATznvQZl3j9FtD8Hkjv72pd9MpZTk6AF7P/te8EfqY6K0tKh51fqUtjYyp1L1yHuGG0mFLcVCPS/xUuKJWCYPU+XwEjLTU4jqHaXHQyLb5VccBro/txVTVIjrwR6IQ1dOE8RdWxOci2QH3dCREnV5z7816vTNWLXv7lyLp4YfbS4m8MqSQEVvZyvt26ldUceoTd7cgKCfVR7ePrZ77Ijkjd2RXAX68aVB9QAT5T13L5wDlJt2FksYm4gUpnc7TSUXjP/i4QrbKAueo/AvvvlfxvYWUqNad1BhUdRQmWqntu6fM+XC9k5xeI/dHcKytev6zvKY3t9hyrqY7DfmP/1DmNwZ6fD3jD01ob2nBuD5uLDJL+q5AG/Gg3MfX68JAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABOp9N/JJGUQcZw1vIAAAAASUVORK5CYII=)
Number line is a line where number are plotted with equal intervals.
The center of the number line is 0. It extends in both positive and negative directions.
To plot any number we start from zero. If the number is positive, we count the places in right direction. If the number is negative, we count the places in left direction.
Let’s represent the given number.
The number is -7+3
The first term is negative. So, we count 7 places from zero in the left direction. We reach -7 on the number line.
Now, “+3” is added to the number. It means 3 places to the right from the number.
After going to the three places to the right we get -4.
So, the option who has final value -4 is the right option. The right option is as follows:
![It is the correct option of the number line.](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/generalfeedback/1713422/1/1188313/download.png)
When we add something to the given number, we don’t start counting the second number from zero. We count the places from the number itself. Any negative value means we move in left direction. Any positive value means we move in right direction.
Related Questions to study
Maths-
Statement-I: ![integral subscript blank superscript blank fraction numerator 1 over denominator 4 plus 5 s i n x end fraction d x equals 1 third l o g vertical line fraction numerator 2 t a n left parenthesis x divided by 2 right parenthesis plus 1 over denominator 2 t a n left parenthesis x divided by 2 right parenthesis plus 4 end fraction vertical line plus c](data:image/png;base64,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)
Statement-II: If 0<a<b, then ![integral subscript blank superscript blank fraction numerator d x over denominator a plus b s i n x end fraction equals fraction numerator 1 over denominator square root of b squared minus a squared end root end fraction l o g vertical line fraction numerator a t a n left parenthesis x divided by 2 right parenthesis plus b minus square root of b squared minus a squared end root over denominator a t a n left parenthesis x divided by 2 right parenthesis plus b plus square root of b squared minus a squared end root end fraction vertical line plus c](data:image/png;base64,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)
Statement-I: ![integral subscript blank superscript blank fraction numerator 1 over denominator 4 plus 5 s i n x end fraction d x equals 1 third l o g vertical line fraction numerator 2 t a n left parenthesis x divided by 2 right parenthesis plus 1 over denominator 2 t a n left parenthesis x divided by 2 right parenthesis plus 4 end fraction vertical line plus c](data:image/png;base64,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)
Statement-II: If 0<a<b, then ![integral subscript blank superscript blank fraction numerator d x over denominator a plus b s i n x end fraction equals fraction numerator 1 over denominator square root of b squared minus a squared end root end fraction l o g vertical line fraction numerator a t a n left parenthesis x divided by 2 right parenthesis plus b minus square root of b squared minus a squared end root over denominator a t a n left parenthesis x divided by 2 right parenthesis plus b plus square root of b squared minus a squared end root end fraction vertical line plus c](data:image/png;base64,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)
Maths-General
Maths-
Statement-I: ![integral subscript blank superscript blank fraction numerator 1 over denominator 5 plus 4 c o s x end fraction d x equals 2 over 3 t a n to the power of negative 1 end exponent left parenthesis fraction numerator 4 plus 5 t a n left parenthesis x divided by 2 right parenthesis over denominator 3 end fraction right parenthesis plus c](data:image/png;base64,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)
Statement-II: If a>0, a>b, then ![integral subscript blank superscript blank fraction numerator d x over denominator a plus b s i n x end fraction equals fraction numerator 2 over denominator square root of a squared minus b squared end root end fraction t a n to the power of negative 1 end exponent left parenthesis fraction numerator b plus a t a n left parenthesis x divided by 2 right parenthesis over denominator square root of a squared minus b squared end root end fraction right parenthesis plus c](data:image/png;base64,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)
Statement-I: ![integral subscript blank superscript blank fraction numerator 1 over denominator 5 plus 4 c o s x end fraction d x equals 2 over 3 t a n to the power of negative 1 end exponent left parenthesis fraction numerator 4 plus 5 t a n left parenthesis x divided by 2 right parenthesis over denominator 3 end fraction right parenthesis plus c](data:image/png;base64,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)
Statement-II: If a>0, a>b, then ![integral subscript blank superscript blank fraction numerator d x over denominator a plus b s i n x end fraction equals fraction numerator 2 over denominator square root of a squared minus b squared end root end fraction t a n to the power of negative 1 end exponent left parenthesis fraction numerator b plus a t a n left parenthesis x divided by 2 right parenthesis over denominator square root of a squared minus b squared end root end fraction right parenthesis plus c](data:image/png;base64,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)
Maths-General
Maths-
Statement-I: ![integral subscript blank superscript blank fraction numerator 1 over denominator 3 plus 2 c o s x end fraction d x equals fraction numerator 2 over denominator square root of 5 end fraction t a n to the power of negative 1 end exponent left parenthesis fraction numerator 1 over denominator square root of 5 end fraction t a n x over 2 right parenthesis plus c](data:image/png;base64,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)
Statement-II: If a>b then ![integral subscript blank superscript blank fraction numerator d x over denominator a plus b c o s x end fraction equals fraction numerator 2 over denominator square root of a squared minus b squared end root end fraction t a n to the power of negative 1 end exponent left parenthesis square root of fraction numerator a minus b over denominator a plus b end fraction end root t a n x over 2 right parenthesis plus c](data:image/png;base64,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)
Statement-I: ![integral subscript blank superscript blank fraction numerator 1 over denominator 3 plus 2 c o s x end fraction d x equals fraction numerator 2 over denominator square root of 5 end fraction t a n to the power of negative 1 end exponent left parenthesis fraction numerator 1 over denominator square root of 5 end fraction t a n x over 2 right parenthesis plus c](data:image/png;base64,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)
Statement-II: If a>b then ![integral subscript blank superscript blank fraction numerator d x over denominator a plus b c o s x end fraction equals fraction numerator 2 over denominator square root of a squared minus b squared end root end fraction t a n to the power of negative 1 end exponent left parenthesis square root of fraction numerator a minus b over denominator a plus b end fraction end root t a n x over 2 right parenthesis plus c](data:image/png;base64,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)
Maths-General
Maths-
Statement-I: ![integral subscript blank superscript blank fraction numerator 1 over denominator 3 plus 4 c o s x end fraction d x equals fraction numerator 1 over denominator square root of 7 end fraction l o g vertical line fraction numerator square root of 7 plus t a n left parenthesis x divided by 2 right parenthesis over denominator square root of 7 minus t a n left parenthesis x divided by 2 right parenthesis end fraction vertical line plus c](data:image/png;base64,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)
Statement-II: If a<b then ![integral subscript blank superscript blank fraction numerator d x over denominator a plus b c o s x end fraction equals fraction numerator 1 over denominator square root of b squared minus a squared end root end fraction l o g vertical line fraction numerator square root of b plus a end root plus square root of b minus a end root t a n left parenthesis x divided by 2 right parenthesis over denominator square root of b plus a end root minus square root of b minus a end root t a n left parenthesis x divided by 2 right parenthesis end fraction vertical line plus c](data:image/png;base64,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)
Statement-I: ![integral subscript blank superscript blank fraction numerator 1 over denominator 3 plus 4 c o s x end fraction d x equals fraction numerator 1 over denominator square root of 7 end fraction l o g vertical line fraction numerator square root of 7 plus t a n left parenthesis x divided by 2 right parenthesis over denominator square root of 7 minus t a n left parenthesis x divided by 2 right parenthesis end fraction vertical line plus c](data:image/png;base64,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)
Statement-II: If a<b then ![integral subscript blank superscript blank fraction numerator d x over denominator a plus b c o s x end fraction equals fraction numerator 1 over denominator square root of b squared minus a squared end root end fraction l o g vertical line fraction numerator square root of b plus a end root plus square root of b minus a end root t a n left parenthesis x divided by 2 right parenthesis over denominator square root of b plus a end root minus square root of b minus a end root t a n left parenthesis x divided by 2 right parenthesis end fraction vertical line plus c](data:image/png;base64,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)
Maths-General
Maths-
I: ![integral subscript blank superscript blank fraction numerator 1 over denominator 3 plus 4 c o s x end fraction d x equals fraction numerator 1 over denominator square root of 7 end fraction l o g left square bracket fraction numerator square root of 7 plus t a n left parenthesis x divided by 2 right parenthesis over denominator square root of 7 minus t a n left parenthesis x divided by 2 right parenthesis end fraction right square bracket plus c](data:image/png;base64,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)
II:
Which of the following is true
I: ![integral subscript blank superscript blank fraction numerator 1 over denominator 3 plus 4 c o s x end fraction d x equals fraction numerator 1 over denominator square root of 7 end fraction l o g left square bracket fraction numerator square root of 7 plus t a n left parenthesis x divided by 2 right parenthesis over denominator square root of 7 minus t a n left parenthesis x divided by 2 right parenthesis end fraction right square bracket plus c](data:image/png;base64,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)
II:
Which of the following is true
Maths-General
Maths-
I:![not stretchy integral subscript blank superscript blank fraction numerator left parenthesis 1 plus x right parenthesis e to the power of x end exponent over denominator s e c to the power of 2 end exponent left parenthesis x e to the power of x end exponent right parenthesis end fraction d x equals blank l o g blank vertical line t a n fraction numerator x over denominator 2 end fraction vertical line plus s e c x plus C](data:image/png;base64,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)
II:
Which of the following is true
I:![not stretchy integral subscript blank superscript blank fraction numerator left parenthesis 1 plus x right parenthesis e to the power of x end exponent over denominator s e c to the power of 2 end exponent left parenthesis x e to the power of x end exponent right parenthesis end fraction d x equals blank l o g blank vertical line t a n fraction numerator x over denominator 2 end fraction vertical line plus s e c x plus C](data:image/png;base64,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)
II:
Which of the following is true
Maths-General
Maths-
I:![not stretchy integral subscript blank superscript blank fraction numerator 1 over denominator 1 plus c o s 2 x end fraction d x equals fraction numerator 1 over denominator 2 end fraction t a n x plus C](data:image/png;base64,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)
II
Which of the following is true
I:![not stretchy integral subscript blank superscript blank fraction numerator 1 over denominator 1 plus c o s 2 x end fraction d x equals fraction numerator 1 over denominator 2 end fraction t a n x plus C](data:image/png;base64,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)
II
Which of the following is true
Maths-General
Chemistry-
The probability density plots of 1s and 2s orbitals are given in figure
![](data:image/png;base64,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)
The density of dots in region represents the probability density of finding electrons in the region. On the basis of above diagram which of the following statements is incor-rect?
The probability density plots of 1s and 2s orbitals are given in figure
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKgAAAB2CAYAAABcf9jrAAAgAElEQVR4nO2deZBc13Wfv/u2fr1OT88+g31fCYAAdxAiSGqhRJGiZSk2y5alJLbsOJbscjm2/0nJjksVKWVFcZzIiS3FkmWJoTY7MiWS4gbuBLGDAAhiIWbB7Evvr99688cbQCIBkIOZ7pkGq7+qQU/NYN673ff37r3n3HPOFVJKSYMGdYqy0A1o0OCdaAi0QV3TEGiDuqYh0AZ1TUOgDeqahkAb1DUNgTaoaxoCbVDXNATaoK5pCLRBXaMtdAMazBE/QPoSggAZSJCA5yO9AGFooAhQBOLCq6aAEAvd6hnTEOi1RCCRro90fXB8AsvFO5/HG8jiD+fxcxZB0cZ7Yxz3zDiRm5aidiRQ4gZqSxytO4W2LIPamgiFqqsIQ0Xo6kK/sysiGsEidY4fEBRsgnwFf7iAc2IE++QozrlxvNESgesh/YAAkIaC1ARiuIi0PFiURGgKwgkQvkQRCkIVKPEIeleKyMo2jA2d6GvaUNJRlJSJEjcW+h2/hYZA6xTp+siyg/fmJOWXzmHt7cU9N4lvOXimwG4xcFsi+G1R/JYIMmkgDRVUwJMIRChWKcPpvuKj5BzUMQttvIIx4WBMuaguaK1xjHUdxG5djnnjEtSWGMLUQV14E6Uh0DpE2h7Wc2cpfPcAzr4BPM+jsihKZUMae22aoM0EQyXQFdAUpKaEwnzHiwK+RHgBuAGKE4DloQ6WiL42iXkyjzHmoLXGid6zjsQvXYexriNcCiwgDYHWC35AUPGwnjlN8fuHsY8NYWkB1oYm7A0Z/K4YQdpAJnSkpiAuGESS8J+Z9KIgNJAESBH+QDg+St5BmbTRevOYhyaI91eIJGNEbl1O6te3oy/L/NzgmmcaAl1oJAQlG+fwIMVHjmO9dI5SUMFa14SzqQVvaYIgYyJVgfAlyBmKcaYIgVTDV2H7aMNltLN5IocniPVZxLqaid21mvgH16MtSYdCnUcaAl1ggqky+W/to/T465Sm8pS2ZnCua8FdlkTG9XDUC+apiy6MsIFEHa+gn85hvjJK4nyF6JpOkg9eT/SOVSimPj/toSHQBUN6Afah8+S/9gLlV3sprE1i3daJsy5NkNAQF6fvBUIBAlBHLSJHJog9O0TS0Yjfv4nEg9vRF6fnpRkNgS4AQdnBeuo0hW/vI3eoF+vOHqxd3XhLEuEU7tdJlwjC9a7jEzk6ifmzfpLnKiTvXkfyX9+Isba95kZUQ6DzTFCoUPx/x8j/4z4KpSLlu3qwbu1ARrVwKq/H3pg2rNShMrEnBogfnCR13WKaPnsrkW2LairSeRNoULLxR4r4EyWCgo0/WcYfyiMiGtqSZoSpoaajqC0x1PYkIvLe2+TyRwoUf3CY7Lf2UejSKd3VjXNdS7j2q0dhvh0hEGWX6IsjJH42QHJRG82/fRvm7SsRem1EWjMVSC/A65vCPTWG2zuF1zeFdz6Hn7VASvzRIvbx8yhxE/OGZRAEYGiomRja4jT60mb05S3oK1vRulO1aua84U+WKT58iKmvv0xxmUnxY0txV0y/r2tBnABSIuM61q4upKkSPHwavrqHZiGI3r4CajCSVncElRI/Z+H3ZbGPDlF5pRfnxAj+WAkRUVFb4iitcbSOJFII/OFwBNUXpfEnSnijRYKJEkHWQkrQulJEruvCvHkp+tp2tJ503W3FzQRpuRR/eITJ//EchaSk8G/W43XHp/2Y14o6fwElbHpszxCJh07TtL6H5j+5G3NLd9V3n6om0CBrYR8bxnr2LNZzZ5AFG7UjibGpi8iWLvQ17eiL0yiJSOjwfftdBeGe8pSFe24C5/gI9pEh3DdG8UcLaMsyxHavxrx1GcbqdoR5bSwBpONjPX2aib98ilzUp/DJFdPG0EK3bO5IQWjd/7iP9NZlNP/hHRir26p6jzkLVDo+zolhyo+fpPzMGfADIhs7MXcuJ7K1BzUTR0TUMHJmJk/X9N4xXkBQcfGGC9iv9GI9/ybe2QmUtjjxD60n+r6VaEszCLW+Q8cqe/uY+q/PMDU6QeHjy3E2Z94T4gRAAWEHRJ8epOnx8zR/YCPpz92O2p6s2i3mJNCgZFN5uY/c114Iw7u2LyL54HbMHYsRph4unOcaezgdYhbkLMpPnaLwnYO4p8eJfWANqU/fiLGhY953N2aKdz5H9r88zfhPj1D81BqsnV2Xnz2uZRSBknOI/+As6aN5mj99E6nP3lo1y37WAg1yFsUfHSX7P19AKILmP7yD2AfXoaTMqjTsSvjjRfJ/9wqFhw6iLcvQ9Ls7ie1aUXdWv3Q8cn/zIpP/6wUKt7RReHBVGNTxXkQItP4CiW+epKVikPnSvUR2LK6KSNUvfOELX7iqvwgk3nCB/Df3UfjOfiJbumn5Tx/GvGlpuL6sMUrMILK1B31lC87RIaynTiGDAH15C0p0/rbg3hE/oPJKL/m/30u+RaX4iZUEiTppWy0QEKQN0BWU18YR4xbm9sUoCWPOM+hVS9w7n6PwrVcpPHSA6M4VNH9uF5FNnSix+bOulUSE2J1rSH9uF2pnkvzXX6H4/cME+UpdTJ9+rkL58ZMUcwUqOzvxOmML3aTaIgEE9rY2ije3YR3ox9pzBun4c770VQnUnypTePggua/vJbZ7NenP78JY17EgOS4iqmPeuozmP7oTY0MH+b99idJPTyBtb97b8nYqL5+j/MJZrE1pKjvaEH6w0E2qPYEkSOg417dRjEPp8ZPhgDFHZixQaXuUfnKC4sOHid21muY/vhOtK7UgMYIXEKpCZHMX6c/twljfQeEf9lN5pXfB2gPTwcZPn6FolXG2tCIjal2M6vOB8CTu4jiVG9uonBql9MjxOV9zZgKVksqBAQrfPYC+oYP053ehtsTnfPNqYWzsIvnr25FBQP5br+KPFBZMFOWnT2Ed6sdek8JZkUTMsyNeCIEQAkVRLn4PMC872lIiDRVnTZpyxKf82OsEJWdOfTEjgbr9WYo/OAxuQOpTO6rujJ0rQhWYty4nft9GnGPD5P72JaTjzn9DvADrsZOUckXcTS3ImAbzNLurqkoikaClpYWOjg46Ojpob28nnU5jmiaqOj+ZmyKQ+N0xKuuacE6PU3nhTaQ3+7XojHwz1pNvYD1zOvRxbl8MdegcV2IG8XvW454ap/DQQWIfWBtG2sxXSm0gcU6P4R0ewu4xcdbWNl5SSokQglgsRmtbG6lUCsMwUFU1HDkJB64gCPB9H8uyyE5NMT4+juM4KEqNXF4SZFTDW5OmcmCS4j8dxbxt2az74V0F6hwbpvToSdTWBImPbZ4XV9Js0ZdmiN+zHmvPGYo/OIK+vAW1LTEv95auT2VvH3bBwtvehp+JhCkaNcKMRmlrayOTyRCLxdD1d3ZjxeNxkokEzZkMY2NjTE1O4nnexSVAtfG641SWxnD2nycYK6PEImHU1lXyzgL1A6znz+L1T5H85Fb05Zm6r0oR2dxF4r5NlJ86hXt6HDUTm5f0Wen42IcGseICb1ly+nOqjUATySRdXV1kMhkMY2buPSEEZjSKGY0SjUYxTZOxsTEqllV9kQaSoCWcRYL9vdjHhlA7EohZ+Kmv3HNS4g4VqLzch9aVIv7RjXUvTgC1LUH83vUQBFgvvBku0muNlASTZbzeKexuE787FmZdVv02klQqxdKlS2lvb5+xON9OPB6np6eHrs5OTNOsiQEVmCp+dwI3oWIfGSQoz64frjyCBhL3xDDe+SzmzuXoy1tm29a3UPEkp3Iur47YHJ9ySBsKW1oN1jUbrGzS5+61UgTa0gz6mjbsAwMEJafm26/Sl7jnJggmSng3p/Bazapb70EQkEwm6enpobm5ec6jnmEYdHZ1EUjJwMAAgT93p/pbkBA0GdjdUeyTI0hrdkbrFQUqfYl7ahxUQWRrz5z9nW4geX3K5Wd9Fq8MV9g7YnNu3EGPKFzXbrAxY3Dnoii7F5ksTuqzWa5cRIkbmDcuofh/D+P1ZdE6k7Ud/f0At3cK1/fw22JIU0VY1e1wwzBoa2ujtbX1su/FC2Cw5HEy6zJu+biBJKYJehIa65oN0oZyyZ/puk57ezvlcpnx8fHqxqZKSRDXcRbF8M7mZz2TXVGggeXg9k6itiYw1rbPup0Qptq8MFjhr47keayvTNkOQk+AqeAC+0dt9o/YPNZb5lfWJvj3m5tY3qShzlJUIqJjbOgC5Qj2gX7MHYtq63nwA7yhPE4EZEJD1MC1lEqlyLS0XFacJTfg6fMVHjlX5vkhi768hx1ImgyVdWmdu5dEuXdZjI0tBsbbBprotLFVyOexbbtq7RUynOa9njjyeIlgtAir2656oLuiQP3hAt5gHm1RGq27aU6NfXm4wpcPZHmi38KTXCqW6aSsESvgG8eL5OyAP78pw+LkLCOUBKiZGEraxDk1hgxA1NDbJAOJP17EM8S077OaSQoSTdNIpVJEo9FLfm/7kodPFfmrI3lOTDi4v1BwZMzymbB8Do3ZHBiz+dPtaW5oNy/ReDweJ5VKMTY2VrV2IyXSVPDaowSOjzeUny4JeXUdcUUjyR8rEeQrqO2JOUWvl9yAr58o8ESfdfHDuyICCo7Pd04UeXLAouDMfigSMR21LYF3Pgeyxt7yQBLkbPyIQmBWd2tTSolpmsTj8cuuO49OOHz5QI6j4w52EO4LXLi9BHwg70oeOVvmG8cLDBQvjVWIRCIkU1XO+5KAqhAkDSQSf6IU5p1dJVcUaJC1AFDT5qzXb76U7B2xOThm43oz7DUh8BX43ukS/Zf5MGeKMDWUJhN/rFT7bc9AguOF++569QUaMU0ipnmJQAeKHt8/XeT1rBum0l+pmwS4wEOnijw/VLmkeYqiYBgGmlaDmFpNEBgKsuzOalftigK9YHWJOZQ58SUcHrcZKflXFTflS3h93GbSnsMIqqmIqI4s2rUXqBcgvQAZUZBq9f2fuqZdVjwDRY8nB6wZG5S5csDrUw4l99LPVdM0dF2vrstJEg5umiCwvVld+8oCdf3QqptDVLSUMF4JKLjv9HhfHt8HZy47MdPlrqUfIGcxtVwN0vWRQYBUFRCz2jC58rWlRFGUy25NllzJ+eK0t2CGNx2vBOQu8+ALIWqzXz9dSU/OMuTwXdQnEHP8uMNiGfNfaEjwC7cU83XvGt3nCkssiSS4ynsuSPGSOUwqVxaoAiDnPORHNYE+Cx+qYG6uV3nxmRC13wFTRHifGvW8DILL9oOuCOLa9Kg3o3tLoqq4xNV08be1CsmTzDr79ooCFZFw7Snt2YetKQJWN+m0Ra/ecGhJqCTnUk7FD5C2h4hqCFHjvXhdu1gLnkAiqzjJCyHwfR//Mjs97VGVHe3GjP3rEVVhRZNGa/TSqdz3fVyvytkI06UjhQ9CV2c1Tlyx55RUGH0SFJ1Z7zBoQnBLZ4RVTVdhaMmwUXcvidEZn/2aSDoeQaGC2lz7fCChivC0jIqPcIOqLkKFENi2jXMZJ/qylM7HV8ZJGe9+QxW4odvk+rbIJTOTlBLXdfFct+qBIyIA4QZhQuMsrn1FgaqZOMLQCCbKs566hIDFSZ2PrYixqlmf0XUUBbriKp9cFacrNnu3h7RcgikLtavG25wQGmQxA8UOEHb1BWpZFlalcskUHNUEuxdF+Y31SRIaV/x8hZR0xFV+e1OKGzouDZd0XZdyqURQbWNSSrA9FE+G8RCzWLNdUaBaZxKtLYE3mMOfLM26jYqAB9ck+J3NKZYmVLQLa8O3fQkJBpINaZ3/vbuVDS3GnNagQcHGGymgL8vUPm9KESjNUTQ3QFS8qj4QQghc16VYKOC6ly63WqMqv7+lic9vTbMkrhKTkogEQ4IpJfFAckOnyRdvznDv8thl7YFKpUIul6tam6cbjnAC1IkKQlVQ2xOzCnu84hClNMdQlzZTebkX99Q4WufsdxriusKvrknQFFF46FSJ/cM2tvdz+1NBkDYVdi+O8vFVcT6wJIY2B1FJLwzewAuIbO6i1ktQoQj0jhSGI1BKbtUPmJRSks1mSafTtLa9Nd1GEE71n90cjo4Hxmz6ih62D2lDYV1aZ0ubwZbWCE3GpQ3zPI/s1BTlcrm6bRagVHy0wRKKqaF1N83KULryHKop6CtaKP/sDZzXhsLyenOgK67xK6sTbGuLcHzC4WzBY9zyUYWgI6awNq2zsSXC8pQ2J3ECyJJDZV8fIm6gr+8I1w21RFXQFqXRPVCmnKrXlBdCUKlUGBsbIxqLEY+/NWFREbA4obE4obGz2yRrB3gSoqqgPaZivoMwstkso6Oj1Z/eFYFS8tAHyijN8XCKn8XMckWBCkVgrOtATZlUDp4nka+gzjGuMq4rXN8WYUtrhKITUHIlioCELojpStVmYj9nYb/aj7Gpc36MJE1BX9mCmjBRB0ooORcZr37QyOTkJKqmsWTJEkzz8n3RYqq0mDMzLqempjjf349lWVVr50UUECUXY6CMcXP3rKLppy9zpd8IjJUtGJs7cU+OUtlzpmp+PlVAU0ShO6HSGVdJGNUTp7RcKi/34k+Vie5cMT85VIpA7U6hdqcwBkpow6Xpc4iqi+d5jI+NMdDfT7lUmrXf0vd9Jicn6e/vJ5fPV7mVIcKXqOMWkQmHyMZORKzaAgVEzCB623KEoVJ65DhBzqr7IgTOqTGKDx3EWNUWZnXOU1ExxdTR13VgTrpo/cWaGGaKouB5HqOjo/T19TE5MXFZw+mdsCyLkZER+np7yWWzVW8jAAKUnIN2OoeiqkS29My6NNK7Ls4iNy3FvHUZ9oEBynvOIN2FLy1zJYKpMtZTp7CPDhJ/YFNoOc4Xukr0piWYqhF2TKk2efkXHPfj4+Oc6+2lv6+PsbExSqXSZZ35ELqR8vk8Q4OD9J47R39fH4VC4eL1qo1UBOpwmeipAvqaNrRlmVnHdLzr8KI2RYl/eAPO4SGK3ztEZFMn+orW6kZEVAMpqewfoPSTE0S2LSK6e828FjQTmoKxpQd9WTP6mSG03iLu2nTNDuGSUlIqFimXSpgTEyQSCaKx2MXc+At4noddqVAqly+6qmqVagyEO8tegHauQHTKI/bL6+ZUtn1G819kx2ISn9xK9q+fo/jDozT9u9vqrla82ztF8UdHkbZH+nd3orXG5v0hUptMjNuWET0zgn1iCndlbWtXXRCaZVmUy+WLa1JVVVEU5WLRhgv/90I5nJoiBOpEBePEFHpznNiH1oYxsrNkRuOuUBWid6wievsKSj85TvH7h+uiitwF/PEShW/vxz50nsQnthJ938oFS5GO37Oe+KoOjKMTqKMWskbHs/wiF8SnqurF0fOC2+jCz2pWSeStDUEC2tk80YFKePjF0gxiDg/pjC0IrTNJ8sHrkYC1ty/0ky5qChfA6UtzZWqOlHgDOZxjQzhnJ3H7p0h8/DqSv7xl/tvyC+jLW4jdv4nEt/fiPT9MaXc3fkcsPAb7vYwAvAD9bI740Smati0l/sDmuV/2qkqA+wGB5eKeHmfiC48STJZJfvpGEvdtQm2d32p37tkJ8n+/l9KPjxG9fTnpP7gDrTMV5k8tcIEJabkUf3yMia88RXZjguKvrQnLf9e5B2QuSFWgn8qRevgMLdEUmb/4MPrqtjmXAb+6v1YVlESEyNYe2r7yMbSlzWS/+izZr+7BPTtRlYq674ic9nPu72fqPz9B6UdHSPzyFjJ/dg/68pbQGVwH1U+EqRO7cxXJnSuJ7Z/AfHEkzMdZ+KbVDKXoEn12kGS/Tey+jegrWhaoRv2FP2yKYlzXjRBQfvxkWGYvkIiYjhI3EFp10weCnIVzaozCPx4g/7UXkCWH1G/eQvLB6+uqVikQ+gGjOiIZQR4fwz8ygrc8SdBcv4XXZo0iwA2IPTNI8vkRkrvX0vTZW1HisysW9nbmdk6SH+CPl7D29lL4h334I0X0Va3EP7qRyOYu1NZ4uJMzy+Jd0vEJ8hX88SLWnjOUn3gDbyiPubWHxMe3ENm+CCVp1u3IJCsexX86yuR/e4b8UpPCJ1bgddSmbtOCMF0gzTg0Qer7Z2le2knzf7iLyKbO6t2iGifNSS/AHy1Q/skJCt89gHtuEmNdB9H3ryF29xqMFS3TOzrTGWUXBXXhG3nxRUoZlk0puziHByk/+Qbln76OP1kisn0xqc/cSPSWZaGbax6q1s0VWXHJf3Mv43+1h8LtHRT+1cprot0zQSoC/VyB1MNnSFd0mv9oN7G71lTVtVa9szqlJKh4BCMFys+fxXrsJPZrQ0jHQ1uUxljfgb66DX1JM2pHEiVlhlUmpETaHv6khTecxzs3ifPGKM7xEWTWQsQNzBuWEPvoRiLXdaO2xuevKG2V8IfzZL/2IlM/OkhxZweFT6wEXamZE7/mTCfBqUNlkv/4Bk2jPs2f30Xi41uqfqhaTY7jDgoVvIEcXt8U9vER3NNjeCNFZM5C+jJMj1CV6VPXwjRD6flhaRRdRcnE0LqSGOs60de0oS9Oo/U01d1hXTMmkDinxsj9zYtknzhOcXc35fcvIkhHqluwaz5QBHgSra9A4kdvkhp0SD+4g8SndtQkcqy258VLGZ4NPx6eYOwXbIKpMv5kGVlywtx7AcLQUFImaksMJWWG32diqJkYImrU7RrzqvADnNdHyX3jFbKPvkbpfV2UPrj42jOchMA4mSX+SC+J8w7Nv34DiV/ZVrNK1rUV6OUIJIHrh/UCLwTJKkqY9VeNsz3rmUDi9WfJfXMvUw/tx9rYRP7X1uC3mqHhVMeDqRSAqhB9eYT4P58j4Ws0/+7txO/bVNNt7/kXaAO8wRyFb+0j9/1DlDIqpXuXYG/KgKHW37pUgBQCNesQ2zOI+Xg/qcVtNP3GDcQ+sqHmATkNgS4Q/miB4j8fo/jdAxR8i/L2Niq3tOO3R+vjROSLx4RIjNezRF8aIXZkitS2pSR+dRvmLcvmJRi8IdAFJCg7VF7tp/TDI+RfPovVqlG5tRN7Wyt+OhIeobgQvaMKCCTa+RLRF0eIHBwnHomSvGcD8fs3oy/LVO247XejIdCFJpC4A1msx09S/JdjFM4MU1ndhHNjO/aWFoKWCPhhjGVNxaoIpB4KU+8tETkwhnFglNioS3LnKmIf2UB018qqnGB8NTQEWidIx8fe10fph0fDUdW1sFYncdY34y1J4ndEw+K4MF1ivApGlSJC40eCknfQB8to5/IYr00SG7SJdzQTuWsViQc2oy/NzPFms6Mh0DpD2h7Wi29iPfEG9oHzWNkCVquBuzKFtyiO3x7Fz5gESR206ZHsYqG0d+rKt+3i2T5q1kGdqKCOlNHeLBA5VyRWUYgsyRC5aQmxu9YQ2dxVy7f7rjQEWodIP0CWHZzXR7FePod7bBinL0ulVKJigNdu4nfFCTIRgiaDIGFAVAsL6GrKW0dGPwA3COtGlT2UgouStVHGLdTBEsaki6noRJri6KtaMa9fROSGJeiL0uFO3wKeZg0NgdY3fli5OSja2IcHsV/twzk2jD9cwC/auCLAMcAzBYGpEsQ0pKmBPj1aBiAcH2H5KGUP1Q7QbDBsiaaqKOkY2tJmzK09mDctQVsexkyIaZHXAw2BXoO4vZM4x4ZxT47inp3E688STJXBCcINkDDqJjRmFAGaiohrKK0J9CXNaKvaMNa1YWycn8IWc6Eh0GuRQCIDGTr1p7+k54cV/Yp2WG47ICw/Y2qImIEwtZ/HP0x/CUWp+23khkDfa1zciZo+F0BUuWj+PNMQaIO65r0ROdvgPUtDoA3qmoZAG9Q1DYE2qGsaAm1Q1zQE2qCuaQi0QV2zcAJteF8bzID5yeOVkkB6VCb7OHYmi0gvY8falnm59XsXifQtSueP89K+NxguCmLty9hww3ZWN+tzPimlXpgXgQalcfpO7WPPY4/ww9fiXH/vpxsCnStult4DT/KDhx7l6GiOifEJck6Cnhs+zKc+80luX50JT5+7xpm3tyCDAoNnjnPoaIbO3TWugveeJyDbf5IDe48ykLmB99/eQaR4jiNP/zPf/Lsvkzc6af+d93N9T/xa3oYH5kmgSryVJZt3c/sNe/iXE6P4jfXnHHEo2ILEsjv47btvY4WuIGSZnZtamDj0ezz2/Iu88Us72NwTp74KtV898zOCCgFCQVF0tMuezC3x7ALjg8NkKz4yEKhGhGRHF21J82JmQ4MLCNKLVrOtPU5b9IIEUzQt3s4dGyK8MCrwL6YsueSGBxnLlnGC8NjJaKadltYMca3+A53qYpUS2Dn69j/Gc6+7aFENxcnSd3KMjo8+yH07VpKZ3RlQ72EiJJMRkm/5mY9XyTM2YdCzdRsrWtIY0qdw9in2vDLChKsTMyoMHT5JsG4Xdz7wYa5L1X8hl7rwg1oTZ3n6u9/hqNjIzvd/lPsf+BCbMwrScxvLgZniTDB17lWezd/C+z94I8s7EyCLHPnWV3jsdYeO7R/hY/ffz+517aQCC9u/Njx9dTGC+n6Rkf43OVx8lOdXRbltbTe33P9RhhJdxOriEap3fAqDZzn40mn8+z7Ph69fRIcJ+BVy2SynTj7D80tX0pPawopdHyIlYmiRukk7ekfqovvjmTXsumsr7qt/x59+9rf4gy9+gycnU7Sk4kSvrVKgC4DELw5y/PA+9lZu4c9+/zZWZAwUQCit3PLAA6wWR/j2n/8ev/MHf87fHCxgJzrojNb/+hPmUKP+apGBxfnDz/LkkQKZLXdw//XtF34Dmknzih3cvLmHpDPE8Zce56c/289ofDmbV3eRvMw55w0AAqQ1xmt797C/P81t99/Nlvbo9LQoQQTIti1s37aelRmX4RMv89Mf/IRDYxrda9exOG3U/Sg6bz0vECjiwusvfioeVmGYk29M0nPTx/itP/ki//0vPsNW9STPPrmX85Pl+WriNUaAVxjg1CuP88yBCktvvomNnVFcq0Rucpih8Ry2k+fY3uO4mc3c+2//mC9+6U/4zA7oe+VpXgxtI6MAAAGoSURBVDp6Hs+v/7Ob5k2gUjq4rofnuniu8/NiGICTG+DVHz7EU30uZtcaNtz5G3zkpkV0t8TQlMYcf1msQQ499j3+8quPMpVpotz/Gi8/9wxPP/ko3/vGX/PtJ04zUSzx5o//Dz995RRjRjertt3LvXdu5/plcQzdqP2xiFVgfoykfD8nDzzGI88dZah/Cn/PP/HdTRF2bVtHd1xBUXxygy/z6Bf/I3s3rWV5ymEkeS+f+sgHWNVR33nbC0JliIM//lu+/OVv81RvmdjRVzGERE4/8kbL7fzml1LEkxq6OsKeb36FV196ls1LTPKjPWy9933cc9ti9Hqf35mvrE63TG5qhPPnR5nIeeipFroWd9HWnCKqCXw7S//Jk4xVVIx4nLguCbQMnV2tpKLaNbGYn1d8i6nBNzl1doicJxC+TzhZh8UatFg3qzeuoLtJYfLMCfonKgSRBImoQiBjpNvaaW+J1YcL511opB03qGsa5nGDuqYh0AZ1TUOgDeqahkAb1DUNgTaoaxoCbVDXNATaoK5pCLRBXdMQaIO6piHQBnVNQ6AN6pr/D74uhby8MX41AAAAAElFTkSuQmCC)
The density of dots in region represents the probability density of finding electrons in the region. On the basis of above diagram which of the following statements is incor-rect?
Chemistry-General
Physics-
In the set up shown in Fig the two slits,
and
are not equidistant from the slit S. The central fringe at O is then
![](data:image/png;base64,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)
In the set up shown in Fig the two slits,
and
are not equidistant from the slit S. The central fringe at O is then
![](data:image/png;base64,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)
Physics-General
Physics-
In a Young’s double slit experimental arrangement shown here, if a mica sheet of thickness t and refractive index
is placed in front of the slit
then the path difference ![left parenthesis S subscript 1 end subscript P minus S subscript 2 end subscript P right parenthesis](data:image/png;base64,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)
![](data:image/png;base64,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)
In a Young’s double slit experimental arrangement shown here, if a mica sheet of thickness t and refractive index
is placed in front of the slit
then the path difference ![left parenthesis S subscript 1 end subscript P minus S subscript 2 end subscript P right parenthesis](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJYAAACRCAYAAAAhBEFaAAATGElEQVR4nO3de1BU5/3H8ffeZHeBBXZhucotcvGKF5J6aTbiJJKmVlRKrKZNM1JNk5hMmrQ6sRNn2tQLuTTFWGMSnSQ0JtHY6cS0QtTBakOIDcV4i2ZRAaEKCrhcFgR2l/7hj/3FyEVxj3vhec3sjAfZs9/jfHyes895znNkPT09PQiCi8ndXYDgm0SwBEmIYAmSEMESJCGCJUhCBEuQhAiWIAkRLEESIliCJESwBEmIYAmSEMESJCGCJUhCBEuQhNLdBQjXunDhAkePHnVuf+973yM4ONiNFQ2NS4P1u9/9jsLCQud2YGAge/fudeVH+Ly2tjbOnj3r3J44caIbqxk6lwbrzJkzjB8/nsTERABeeuklV+5e8CIu7wr9/f29sukWXEucvAuSEMESJCGCJUhCBEuQhAiWIAkRLEESIliCJESwBEmIYAmSEMESJCGCJUhCBEuQhAiWIAkRLEESIliCJESwBEmIYAmSEMESJNHv1GSHw0FxcTHPPvss1dXVPPLII6xatQqj0djvzjQaDe+8845zW0xRHr76bbH++9//UlRUxDPPPIPFYsFoNNLY2Djgzt544w0sFovzVVVV5fKCBe/Qb4vV09ODUqmko6ODpqYmVq1aNejOrFYrZ8+epb6+noCAAFJTU0WrNUz122KFhYUxffp0Dh06xGuvvUZlZeWgO9u/fz9PPPEEDzzwAIsXL+att95yabGC9+g3WBqNhrlz5/Kb3/yGI0eOUFxcTEtLCyUlJXz++ed9vufzzz+nvLyc7u5uKisr2bBhQ7+/K/i2PoN1+fJlNm3aRGtrK1FRUYSHh2O1WrFarWi1WkpKSvrc2fTp00lLS0OlUpGQkMBDDz3EP/7xD2prayU9CMHz9HmOJZPJOH36NPPnz6enp4e0tDQyMzMxGAxERESwb9++PneWkZFBTEwM9fX1BAYGkpKSwsWLFwkKCqK1tRWbzUZISIikByR4hj6DpdPpWLlyJfX19QAYjUaMRiNy+cDDXv7+/tetNWAwGLDZbOzevZs9e/awbNkyJkyY4KLyBU/VZ1Lkcjnh4eFMmDCBCRMmEBERgVwup66uji1btnDw4EHKy8uve9/jjz9OaGio8zVq1CgAlEolmZmZmEwm1qxZw3/+8x9pj0pwO5krn/718MMPo9frSUlJAeC3v/0tTU1N1/xORUUFBoOB4OBg7HY7KpXKVR/vEyoqKq451ViwYAHh4eFurGhobvslnaSkJPR6PSdOnGDVqlXU1NTQ1dV1u8sQJOa2a4Xjx49n5MiRPP744xw+fNhdZQgSceuKfk899RTJycl0dnZis9no7OzE39/fnSUJLuL2pSLvv/9+AOrr6/n000+Jj48nPT0drVbr5sqEW+Ex02bUajUymYy3336boqIicd7l5dzeYvUKCgpi3rx5REVFodfrUSgU7i5JuAUe02LB1cVwZ86cyYQJE+jq6mLt2rV9jpcJns+jggWgUChQKBSo1Wqio6PJzs5mx44d7i5LuEkeF6xeMpmMn//85/z973/nwoUL7i5HuEkec47Vn7FjxzJ27FhsNhtms5menh6SkpIYMWKEu0sTBuCxLdZ32e12ysrKWLlyJXv37qWzs9PdJQkD8PgWq5efnx8LFy4kJiaGyspKmpubB7yxQ3AvrwkWXA3XrFmzsNlsABw6dAi5XE5aWproGj2M13SF36ZUKlEqlTQ1NbFlyxY++ugjHA6Hu8sSvsWrWqzvMplMBAQEUFhYSFtbGzqdzt0lCf/Hq4Pl7+/P3XffTXx8PBqNBovFwtmzZ5k8ebK7Sxv2vLIr/K6RI0eiUqmora3l17/+NR9++KG7Sxr2fCJYvcaOHcvWrVvZs2cPBQUF7i5nWPPqrvC7ZDIZCQkJbNq0iY6ODlpbW+nu7kan06FU+tShejyfarF6qdVqQkJC+Oabb8jPz6e4uJi2tjZ3lzWs+PR/4/T0dCwWC9u2bUOn03HXXXcNegub4Bo+HSyAe++9l7CwMMLCwpDJZJjNZpKTk91dls/z+WABpKWlOf/8/vvvEx8fz49+9CMMBoMbq/Jtw65fyMjI4N///jebNm1ydyk+bVi0WN9mMpmIjo6+7kZawbWGXbBkMhmjRo3C4XDQ0NDAX/7yFyIiIpg/fz5qtdrd5fmMYdcV9pLL5RgMBqZOncobb7zBunXraG5udndZPmPYtVjfJpPJmDZtGu+//z41NTUoFAq6urqc8+6FoRvWweoVFRVFVFQUANu3b0epVHLvvfcSFBTk5sq817DtCvsTGRnJn/70JwoKCsT051swYIt14cIFSkpKsFgsjBs3jokTJw56gnvixAkaGhpcWuTtZDKZeO+99ygsLOTKlSuoVCp6enpE13iT+g1WS0sLn3zyCV988QVxcXEcO3aMsLAw7rjjjn53Nn/+fI4ePercXrlypWurvU3i4uL45S9/CVz9j3L48GEyMzMJCwtzc2Xeo99gNTY2YjabycrKIisri9LS0kHXbM/MzMRut/PPf/6TMWPG8NBDD7m84NtNJpPx5ZdfUltby89+9jOio6PdXZJX6DdYgYGBaLVaPvzwQ+Lj45k2bdqgOysqKiIvL4+vvvoKg8FAc3Mzzz33nEsLvt2SkpJ48sknOX78ON3d3e4ux2v0e/IeEhLC8uXLMZlMPPHEE+zZs2fQnX366accOXIEm81GfX09GzZsoKCgwKuX41apVIwaNYr777+f6Ohozp07x+7du3HhCps+qd9gKRQKjEYjubm5zJo1i5MnT1JcXMzrr79OTk4Op06duu49o0ePvuYrekxMDKdPn3aG8vjx4/ztb3+jqqoKu90uweFIR61Wo1Kp6OzsZP369Tf0CJjhrM9g1dbWsmDBAqqqqqiurqaiogK1Ws2MGTN47LHHmDJlCq2trde975FHHuHRRx/FaDSSnZ3NJ598wu9//3uWLFkC/P8TxUwmE5s3b6arq4vGxkbKy8tpb2/3iq4mKSmJgwcP0tzczM6dOwFE69WHPldNbm9vZ+vWrWzcuBGAxx57jGXLlqHVarl8+TJPPfUUGzduvKUBxN6nXBw9epTc3Fw0Gg0LFy5k6dKldHZ2YrVaUalUBAQEePQ1vN4HUyUkJBAQEHDL+/OVVZNvajnuS5cu8ec//xmTyUR6evp19/F9/fXX1NXVObdVKhV33333oPt1OBxcvHiRlpYWkpOT2bdvH0VFRfj5+WEymcjMzMRms3HhwgX0er1HrVNaW1vLK6+8wh133MHcuXOJjo6+pTEvXwnWTV3SqampITo6mo6ODhoaGq4L1vr16ykrK3P+3Gw239D0FLlcTkREBBEREcDVWZ+JiYmcPHnS2c00Nzfz7rvvYjAYGDNmDOnp6fj5+eFwOFCpVMhksps5FJeJiYnh6aefpqCggNLSUrKyssRgKjcZrMmTJw96M+js2bOveYDAUCUmJpKYmOjcViqVTJo0iYqKCqqrqxk3bhyNjY0UFhbS3d1NSkoK991335A/71bExcWxfPly7HY7CoWCsrIyRo8e7VEt6+3mNRehg4KC+OEPfwjg/EZpt9sxGAycP3+eiooK7rvvPhobG/nrX/+Kv78/48ePJyUlBT8/P8nr6334lM1m4+DBgxQWFrJs2TKv7MZcwSsvQvdOazEajfz4xz9m6dKlLFiwALi6Ik1ERATnzp2juLiY8+fPA7B7926OHDkieW1KpZK5c+ficDjYvn275J/nqbymxRqIRqNBo9EAV9dzyMzMZNq0adhsNoKDg+no6ODMmTN88MEHVFVVUVRUhFKppKWlBZ1O5/IWbdSoUSxfvpyOjg4cDgeNjY3D7jqjV7ZYA5HJZPj5+REWFkZkZCQajQa1Wk1ubi75+fns3LkTrVZLa2srr776KuPHj+dXv/oV1dXVLq3DYDAQExOD3W7no48+4umnnx5W8+x9Llh9kclkaLVa9Ho94eHhyGQyQkNDWbt2Lfv27SMzM9PZauXk5JCbm8ubb77pXFS3p6dnyIOgKpWKhQsX0t3dzS9+8YtrhmN8mU90hbciNjaW2NhY5/aGDRv47LPPqK6upqmpidDQUP71r39x5swZ7rzzTlJSUtBoNNhsthteD8JgMPDiiy/S0NBASEgIVqsVhUKBn5+f24ZJpDbsg/VdkZGR5OTkOLd7z9Pq6up4/vnnef7550lPT6e8vNz5KOLw8HD0ev2A+/X393cOP+zevZumpiYyMjKIj4/3ydv+RbAGoVQq+xy/q6mpYefOnURGRjJnzhxmzZpFRUUF9fX16PV64uLi+h3HSkpKYuPGjVRXV/Pcc885v3j4EhGsIcrOziYrKwuz2exsrcxmM/v37wdg3rx5TJ8+nZaWFmpqahg5cqRzouS4ceNYs2YNpaWlyOVyOjs76e7udsm1Rk8hgnULlEolY8aMcW5///vfJyEhgdraWmfYLl68yI4dO+ju7uauu+5iwYIFWK1WdDodc+bMAa5eH3z99ddZunSpz6zj5RtH4SGCgoIICgq6JmyRkZFkZWXR0NDgXJf+6NGjbNu2DaPRyPTp05k0aRLBwcHk5+fzwAMPuKt8lxLBklhgYCDp6enX/Cw1NZXc3FyOHz/OiBEj0Ov1ZGVlsWLFCvbv349eryc0NNRNFbuG730d8QIhISFMmjSJnJwcpk6d6lzi8sEHH8Rms3Hq1KlB72l85513iIuLc75KS0s9asKhCJYbqdVq5xM1dDodS5Ys4cknn2TGjBkDXmayWq1cvnyZVatWUVlZybp163jppZc8agauCJYHkclkztdAmpqaaG5uJjQ0FLlcTkBAgMd9oxTB8kKtra20t7fT2trKl19+yVtvvcXixYs96hul51Qi3LC6ujpKSko4efIku3btYvHixcycOdOjRvBFsLyM3W7n0qVLTJkyhby8PI8dtfeciAs3pL29nYaGBuLi4jw2VCBaLK8zYsQIZs6ciUqlcncpAxLB8jJ+fn6MHTvW3WUMSnSFgiREsARJiGAJkhDBEiQhgiVIQnwr9CJdXV0cOHCAyspKIiIimDp1qnOOl6cRLZYXOXnyJJs3b3Ze0vnqq6/cXVK/RIvlRY4dO0ZPTw+rV6/m3LlzzjUsTp06xZtvvklLSwv+/v7k5+dz7NgxduzYgZ+fH7GxsWRlZdHc3MyLL77IlStXCA8PZ82aNQBcvnyZDz74gPLycgBeeeUVgoKCaGpqIi8vj6SkJL744gsyMjKYO3cugYGBg9YqWiwPo9PpSE1Ndb6+fdlm8uTJNDU18eijj9LY2EhCQgIWi4U1a9aQnp5OTk4O8+bNA67eRVRYWEhkZCRTpkyhvb2dvLw8Zs+eTXZ2NsHBwWzdupWOjg4+/vhjOjo6yMnJYcqUKbz88ssAtLW1sX37dhwOB9OmTaOsrAyz2XxDx+HyFuu9995zTl4Tbl5oaOg1K1R/+98yJSWFt99+m7KyMp599lnmzJnDnXfeiV6vZ9asWc71xXqNGTOGRYsWodVqKS0tZc+ePRQXFyOXy7ly5Qomk4nZs2dz4MAB9u7dS3BwsPOhCS+88AIARqORRYsW0dXVhdlspr6+/oaOw6XB2rx58zWzGH31Ll8pDfSAKIVCQUJCArGxsQQEBPDZZ59x+vRptFptn+9Rq9VotVrg6on/xIkTyc/Pd97vqFKpuHjxIhEREbz88sv84Ac/ALhm+o1KpSIwMJDm5mZkMhkOh+OGjsOlXaFWq3XeqRIUFHTdin/CrcnPz2fXrl10dHRw/vx5WltbiY2Npbi4mLq6Otra2rBarX2+NzU1FbPZTFVVFQqFAqVSiUqlIjQ0FJlMxtdff01nZycKhcIlF7jFybsX+clPfsLMmTMBSE5OZsWKFcyYMYPVq1ezbNkyLBYLwcHBlJaWEhAQcE3XGB4ezsaNG53LKwUGBrJ8+XIefvhhcnNzWbduHffccw9w9WbbdevWoVKpiIuLA662YmFhYTc8BfqmFrcdzIkTJ4iKinKubicMX0PuCktKSnj33Xf5+OOPncv95OXlcfjwYaxWK9u2baOtrY22tjYOHTpES0uLy4oWPN+QglVTU8P69eupqKigpKSEgwcPXvP3NpuNiooKbDYbDQ0NFBQU3PC3CcE3DOkc68iRIzQ0NPCHP/yBurq6655PGBQUhMViQaPR8Oqrr3LgwAEsFguLFi1yrlcg+LYhtViTJ09mxIgRLFmyhMrKSsaNG3fd72zZsgWFQkFaWhpxcXHcc889JCUl3XLBgncYUrCioqLYsmUL2dnZvPDCC6xevbrPZ+v0ri0VHx9PRkaGc/13wfcNebghKSmJxMREdDodu3bt4ptvvnFlXYKXG1KL9cc//pGdO3dit9uxWq3U19cP+BSGzs5OLl265HWPkhOGbkjBeuaZZ1ixYgWpqamsXbuWBx98kNGjRxMWFua8aNo7sGYwGEhOTuanP/0pr732musqFzyaSwdIBaGXmDYjSEIES5CECJYgCREsQRIiWIIkRLAESYhgCZIQwRIkIYIlSEIES5CECJYgCREsQRIiWIIk/gfE3UHXrOXD8wAAAABJRU5ErkJggg==)
Physics-General
Physics-
Following figure shows sources
and
that emits light of wavelength
in all directions. The sources are exactly in phase and are separated by a distance equal to
If we start at the indicated start point and travel along path 1 and 2, the interference produce a maxima all along
![](data:image/png;base64,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)
Following figure shows sources
and
that emits light of wavelength
in all directions. The sources are exactly in phase and are separated by a distance equal to
If we start at the indicated start point and travel along path 1 and 2, the interference produce a maxima all along
![](data:image/png;base64,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)
Physics-General
Physics-
Two coherent sources separated by distance d are radiating in phase having wavelength
. A detector moves in a big circle around the two sources in the plane of the two sources. The angular position of n = 4 interference maxima is given as
![](data:image/png;base64,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)
Two coherent sources separated by distance d are radiating in phase having wavelength
. A detector moves in a big circle around the two sources in the plane of the two sources. The angular position of n = 4 interference maxima is given as
![](data:image/png;base64,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)
Physics-General
Physics-
A beam with wavelength
falls on a stack of partially reflecting planes with separation d. The angle
that the beam should make with the planes so that the beams reflected from successive planes may interfere constructively is (where n =1, 2, ……)
![](data:image/png;base64,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)
A beam with wavelength
falls on a stack of partially reflecting planes with separation d. The angle
that the beam should make with the planes so that the beams reflected from successive planes may interfere constructively is (where n =1, 2, ……)
![](data:image/png;base64,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)
Physics-General
Physics-
Two point sources X and Y emit waves of same frequency and speed but Y lags in phase behind X by 2
l radian. If there is a maximum in direction D the distance XO using n as an integer is given by
![](data:image/png;base64,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)
Two point sources X and Y emit waves of same frequency and speed but Y lags in phase behind X by 2
l radian. If there is a maximum in direction D the distance XO using n as an integer is given by
![](data:image/png;base64,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)
Physics-General
Physics-
Two ideal slits S1 and S2 are at a distance d apart, and illuminated by light of wavelength
passing through an ideal source slit S placed on the line through S2 as shown. The distance between the planes of slits and the source slit is D. A screen is held at a distance D from the plane of the slits. The minimum value of d for which there is darkness at O is
![](data:image/png;base64,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)
Two ideal slits S1 and S2 are at a distance d apart, and illuminated by light of wavelength
passing through an ideal source slit S placed on the line through S2 as shown. The distance between the planes of slits and the source slit is D. A screen is held at a distance D from the plane of the slits. The minimum value of d for which there is darkness at O is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJ8AAACVCAYAAABGgCiGAAANkUlEQVR4nO3dfUxTVx8H8C8UWl5KaYUORgF1IbgJTBhKeNmgmxAci8wFtyl7kckmZiHGaaIze0Ezt2RZZG4zajI2A4hzMFimsqCGKQuOjc2JIFJwskqhGiGMl2JbKL3PH4T70EdEprec8vD7JCb23N5zfhe+nHt723vrxHEcB0IYcGZdAJm7KHyEGQofYYbCR5ih8BFmKHyEGQofYYbCR5ih8BFmKHyEGQofYYbCR6bU2dkJi8Vil74pfGRKn3/+Ofr7++3SN4WPTKm2thZGo9EufbsI2dmpU6dQVlZm0yYSiXDw4EEhh2HujTfeuK3ttddeQ3x8PINqZi9BZ76mpibcvHkTixYt4v99/fXXQg7hEA4fPmyzjVqtFm1tbazLmnUEnfkAIDg4GMuWLRO6W4ciEolstrGpqYlhNbMXHfMRZih8hBkKH2GGwkeYofARZih8hBkKH2GGwkeYofARZih8hBkKH2GGwkeYofARZih8hBkKH2GGwkeYofARZih8hBkKH2GGwmdHRqMR+/fvh1QqhVQqxZEjR2C1WlmX5TAEv4BoLrBardBqtfzjvr6+SZ939epVVFZWoq6uDmKxGOfPn0d3dzf8/PxmqlSHRuG7B4mJifjmm29s2lQq1aTPHRkZwT///IOYmBgsWrRoJsqbNSh896CqqmpazwsICEBqaiqKi4uh1WqRlpYGX19fO1c3e9Axnx3NmzcPmzZtQnp6Oo4dO4ZLly6hvb0dpaWloO/eoZnvnkzndhnNzc24ePEiMjMzERgYCKlUipGREXAch8bGRjz//PMzWbJDopnvHkzndhleXl4oKirCihUr8N5772Hp0qWIjo7G/PnzERgYyKhyx0Iz3z2Yzu0yVCoVDhw4gFu3bsHV1RX+/v6QyWQzWabDo/DZiUgkwsKFC29rP3v2LM6cOQOTyYTNmzczqMxxUPhmmFqthlqtZl2GQ6BjPsIMhY8wQ+EjzFD4CDMUPsIMhY8wQ+EjzFD4CDMUPsIMhY8wQ+EjzFD4CDMUPsIMhY8wQ+EjzFD4CDMUPsLMpJ9ktlqtMBgMAMY+Du7p6TmtziQSCYqKilBUVMS30XUL5E4mDV99fT0yMzPh7u4OlUqF7777blohys3NRW5uruBFOprp3i6DTG3S8G3duhV79+7F008/jZqaGjQ1NSEhIWGma3NY/+Z2GXNFf38/fv31VwBje8vg4GCEhoZOuc6k4ZPJZGhqakJsbCySk5OFr3SWm+7tMuaKzs5OFBQUQKPRwMvLC4ODg1AoFNixYweCg4PvuJ4TN8l9G86ePYtjx47BaDTipZdewuOPP37HDsxmM06ePIkLFy7wbYsXL8aKFSvg5eUFq9WKAwcOoKenh1/+xBNPICEhARKJBP39/di7dy+/zN3dHU899RSWLl0KALh48SKOHz+O0dFRAGO3oEhNTeX/qqqqqnD+/HlYLBYAgFKpRGZmJuRyOSwWC8rLy6HRaPj+g4KCsH79egCAXq/HyZMn0dHRwS+Pj49HSkoKAOCvv/5CZWWlzW517dq1CA0NBcdxaGlpQVlZGb/M09MTr7/+Oj92bW0tampq+OUhISFIS0uDQqEAMHbx+dWrV/nly5Ytg1qthoeHBwBg165d/DJnZ2ckJiYiKSkJANDa2ory8nKMjIwAGLtI/cknn0RUVBT/O6yrq8Pw8DAAQC6XIyMjg79gvaKiwuZ6Yx8fH/6Qqbe3F6dOnUJraysKCgpQV1c35YXu27ZtQ3d3Nz799FPI5XJcu3YNe/bsQXR0NNatW3fH9Sad+dRqNaKjo7Fz504UFhZOGT5nZ2coFAqb3Y6Pjw9EIhH/2N/fHxKJhH8sk8ng5OQEYGyKnrium5sbpFIp/9jDwwMqlYoPn7e3N9zd3fnlcrkcKpWKD59CoeDHdnJygo+Pj03/SqWS/79YLIZSqeT7Hu9/Yi3+/v42L7gmjj1+TDyx1oljy2Qym+W+vr5wcXGxeWwymWy2xdn5vycgJq4rEolsjrvd3NygUqn48Hl6etrUKZPJEBAQYBNOsVjML583b55N/xO328XFhf+5Tfy9TebKlStobm5Gfn4+5HI5vx0BAQHo7e2dcl1wE3R2dnKfffYZ19PTw3Ecx7377rtcdnY2R+auuLg4TqfT3XF5cXExt337ds5gMPBtXV1d3M6dO7mjR49O2bfNzKdUKqHT6bB8+XJYLBY8+uij2LNnz9TpnaCwsBCffPKJTZuLiwsaGhqm3cdsEB4eflvb7t27sWrVKgbVsGUwGCCVSvk9GQC0t7ejsbERa9eunXJdm/CJxWLs3r0b77//PjiOg6urq81u5m56enqQkJCAZ599lm/7f/yFaLValJaW8o8PHz48Z0+3PPLII9iwYQM2btwIDw8PdHR0YMeOHcjKykJISMiU6952zCeRSO66n5+KWCye9knp2WziNrq6ujKshK2kpCTk5OQgLCwMJpMJfn5+KCgoQGJi4l3XpXu12NHg4CD/StrPz+//9q6kW7ZswZYtW/71ehQ+OzGbzTh06BBKSkogFovx3HPPIScnZ07sFaaLwmcnBoMBJSUl+PLLL+Hn5weNRoOBgQEK3wT0qRY7cXZ2hoeHB2pqaiAWi5GUlIQHH3yQdVkOhcJnJ1KpFG+//TZ0Oh0++OADXL58mXVJDod2u3bi6uqKlJQUBAUF4YsvvsCff/6J7u5u/P333xgaGsKbb75pc25sLqKZzw4aGhqwdetW/q0ys9kMFxcXREZGIi0tDX/88QfjCh0Dhc8OIiIi0NDQAG9vbzzzzDOIiopCRkYGvL29odVqJ32HZC6i3a4diEQiVFdX39Z+5coV1NbW4pVXXpnzu1yAZr4ZVVFRAYvFghMnTtA3EIFmvhm1fft21iU4FJr5CDMUPsIMhY8wQ+EjzFD4CDMUPsIMhY8wQ+EjzFD4CDMUPsIMhY8wQ+EjzFD4CDMUPsIMhY8wQ+EjzFD4CDMUPsIMhY8wQ+EjzFD4CDMUPsIMhY8wQ+EjzFD4CDMUPsIMhY8wQ+EjzFD4CDMUPsIMhY8wQ+EjzFD4CDMUPsIMhY8wI/g9mTs6OvD7778L3a1DGR0dtdlGvV7PsJrZS9DwRUREQKPRoLW1lW9bv369kEM4hJdfftlmGxcsWIDQ0FCGFc1OThzdk59MIT4+HqWlpQgMDBS8bzrmI8zM2PdwjI6O4vr167BarQgODhakz5aWFuTn50On0wEAvLy88PHHH+Ohhx4SpP9xAwMDMBqN8PHxgYvL1D+yW7duobGxEbGxsYKMbTKZUFZWhpKSEr4tOzsbK1euhJubmyBjAIDVakV3dzckEgnkcrlg/U5lRsKn1+tRVFQEiUSC7Oxswfq9du0alEolsrOz4eXlhfLycuTm5qK4uBg+Pj6CjePp6YkTJ06go6MDa9aswYIFC257jslkwo8//oiqqiq88847go1tNpvR1dWF9PR0JCUlobm5Gfv374dSqURiYiL/5YL3y8nJCWazGQUFBQgPD8fy5cshlUoF6ftO7LrbHRgYwIcffoj4+Hi0trYiKysLMplMsP4vXbqEBx54AOHh4QgLC8PGjRvh7e2NtrY2wcYAxr5LbfXq1QCA6Oho5OXl4fr16wCA4eFhnD59GitXrsSuXbuQk5ODoKAgwcY2Go1oa2tDVFQUwsLCkJGRgbi4OGg0GlgsFsHGcXJyQmBgIFJTU7Fv3z6sXr0aP/30E8xms2Bj/C+7zXwGgwFqtRotLS0wmUw4cuQIKioq7qvP8PBwnDt3DgDAcRz0ej3UajW/+7nTLjElJQX19fX3NTYAjIyMwGg04qOPPkJpaSm++uortLS0YNu2bejv7wcAqNXq+56Nzpw5g8ceewzA2MzX19eHkJAQAGN/CP/bf2trK2JiYu5rzHFWqxUmkwlWqxU///wzhoeHBel3UpydHTp0iFuyZAn31ltvcTdv3hSs3xs3bnAbNmzg6uvr+bbLly9zsbGxXE9Pj2DjjBsYGOD27dvHPfzww1xOTg7X3t7OL7tw4QL34osvcsnJyVx9fT1ntVoFGdNqtXLV1dXcq6++yrcNDg5y6enp3OnTp7nR0VFBxhk3MjLC1dfXc2vWrOFSUlK477//nouMjOR0Op2g44yz+6vdrKwsnDt3DkuWLEFVVZVg03hXVxekUil/XKLVapGfn48XXnhB0OM9YOx47pdffsGNGzdQUVGBgwcPYuHChfzyyMhIHD16FHl5eTh+/Dj6+voEGZfjOGg0Gn7W6+vrQ3FxMebPn4/FixcLdrw3PpZer8dvv/2GtLQ0lJaWYtWqVQgMDIRIJBJsnIlm9Dzf0NAQLBYLvL2977uvyspKfPvtt4iIiIBCoUBdXR1kMhny8vIEf7XW29uLoaEh+Pv7w9XV9a7P7+zsFOS82OjoKDZv3gyz2YyYmBh0dXVBp9Nh3bp1iIuLu+sr7387ll6vh7u7O3x9ffn2H374AcnJyfD09BRsrHGz9iRzQ0MDqqurYTAYAAAKhQKbNm1iXJWwrFYrCgsL0dHRAQBwc3NDWloaIiIiGFcmjFkbPjL70TschBkKH2GGwkeYofARZih8hBkKH2GGwkeYofARZih8hBkKH2GGwkeYofARZih8hBkKH2GGwkeYofARZv4DEHCYmBwpyDsAAAAASUVORK5CYII=)
Physics-General