Maths-
General
Easy
Question
In ![straight triangle A B C comma left parenthesis a plus b plus c right parenthesis open parentheses tan invisible function application A over 2 plus tan invisible function application B over 2 close parentheses equals](data:image/png;base64,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)
Hint:
To simplify the given equation we will use a+ b+ c = 2s, tan
=
and tan
=
then using other trigonometric identities we will simplify the equation.
The correct answer is: ![2 ccot invisible function application c over 2](data:image/png;base64,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)
As, a+ b+ c = 2s, tan
=
, tan
=![square root of fraction numerator left parenthesis s minus a right parenthesis left parenthesis s minus c right parenthesis over denominator s left parenthesis s minus b right parenthesis end fraction end root](data:image/png;base64,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)
we have, (a +b +c) (tan
+tan
)
![equals 2 s open curly brackets square root of fraction numerator left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis over denominator s left parenthesis s minus a right parenthesis end fraction end root plus square root of fraction numerator left parenthesis s minus c right parenthesis left parenthesis s minus a right parenthesis over denominator s left parenthesis s minus b right parenthesis end fraction end root close curly brackets
equals 2 s square root of fraction numerator left parenthesis s minus c right parenthesis over denominator s end fraction end root open curly brackets square root of fraction numerator left parenthesis s minus b right parenthesis over denominator left parenthesis s minus a right parenthesis end fraction end root plus square root of fraction numerator left parenthesis s minus a right parenthesis over denominator left parenthesis s minus b right parenthesis end fraction end root close curly brackets
equals 2 s square root of fraction numerator left parenthesis s minus c right parenthesis over denominator s end fraction end root open curly brackets fraction numerator square root of s minus b end root square root of s minus b end root plus square root of s minus a end root square root of s minus a end root over denominator square root of s minus a end root square root of s minus b end root end fraction close curly brackets
equals 2 s square root of fraction numerator left parenthesis s minus c right parenthesis over denominator s end fraction end root open curly brackets fraction numerator s minus b plus s minus a over denominator square root of s minus a end root square root of s minus b end root end fraction close curly brackets
equals 2 square root of fraction numerator s squared left parenthesis s minus c right parenthesis over denominator s end fraction end root open curly brackets fraction numerator 2 s minus left parenthesis a plus b right parenthesis over denominator square root of s minus a end root square root of s minus b end root end fraction close curly brackets
equals 2 square root of s left parenthesis s minus c right parenthesis end root open curly brackets fraction numerator c over denominator square root of s minus a end root square root of s minus b end root end fraction close curly brackets
equals 2 c. square root of fraction numerator s left parenthesis s minus c right parenthesis over denominator square root of s minus a end root square root of s minus b end root end fraction end root
equals 2 c. c o t C over 2 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space open square brackets square root of fraction numerator s left parenthesis s minus c right parenthesis over denominator square root of s minus a end root square root of s minus b end root end fraction end root equals c o t C over 2 close square 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)
Related Questions to study
Maths-
Let f : [-10, 10] →R, where f(x) = sin x +
be an odd function. Then set of values of parameter a is/are
Let f : [-10, 10] →R, where f(x) = sin x +
be an odd function. Then set of values of parameter a is/are
Maths-General
physics-
Light wave enters from medium 1 to medium 2. Its velocity in 2nd medium is double from 1st. For total internal reflection the angle of incidence must be greater than
Light wave enters from medium 1 to medium 2. Its velocity in 2nd medium is double from 1st. For total internal reflection the angle of incidence must be greater than
physics-General
maths-
If the function
f(x) dt → 5 as |x| → I, then the value of ‘a’ so that the equation 2x +
f(t) dt = a has at least two roots of opposite signs in (-1, 1) is
If the function
f(x) dt → 5 as |x| → I, then the value of ‘a’ so that the equation 2x +
f(t) dt = a has at least two roots of opposite signs in (-1, 1) is
maths-General
Maths-
In ![straight triangle A B C comma fraction numerator a left parenthesis cos invisible function application B plus cos invisible function application C right parenthesis over denominator 2 left parenthesis b plus c right parenthesis end fraction equals](data:image/png;base64,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)
In ![straight triangle A B C comma fraction numerator a left parenthesis cos invisible function application B plus cos invisible function application C right parenthesis over denominator 2 left parenthesis b plus c right parenthesis end fraction equals](data:image/png;base64,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)
Maths-General
chemistry-
On Bohr’s stationary orbits -
On Bohr’s stationary orbits -
chemistry-General
chemistry-
For a valid Bohr orbit, its cicumfrence should be -
For a valid Bohr orbit, its cicumfrence should be -
chemistry-General
chemistry-
Arrange the following particles in increasing order of values of e/m ratio: Electron (e), proton (p), neutron (n) and α-particle (α) -
Arrange the following particles in increasing order of values of e/m ratio: Electron (e), proton (p), neutron (n) and α-particle (α) -
chemistry-General
Maths-
In ![straight triangle A B C comma open parentheses fraction numerator b minus c over denominator a end fraction close parentheses sin invisible function application open parentheses fraction numerator B plus C over denominator 2 end fraction close parentheses equals](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANYAAAAnCAYAAABzLbaSAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAZpE86XgAABpFJREFUeNrtXX9kXlcYPuITE1EqpqYiRFTVVJiZqJoSM1HzGVURM1Oq+ldUiaiaT42pmYkpMVFVFaKqKvrPTETVjKmKiSkz+yOmykxMRIRv52mfa7d398c5995z7jn3uw+v9ju59zv3vOe+z33f97z3fEL0Fi5K+dbTa1/g9Tdo4BROSnkqpeXp9eO6N6S83xBUQ1SuYEDK71LGFY7dkdLn6Dje5jgGPSGoXSn7Uv6Q8puUB1LeMnhto1Ku8/p22O81KQcdJypvAeXeUDhujMp2nWmveUBQY7zBo/Nw09C1XZaySsMPiHFYymxKny4Qlbd4U8rfUg4rHNuWsuz4eMD42xyXqwQV6PJOpO3jmLY4dDWva07Kdx4Slde4IuW24rGf8/iOlD/pyqwZdl8G6b5sSdmTci/BdQljScpVhwkq0OVcpO2WlA9LNqwjdDPzxs5VEpXX2KR7oIIVTtIcb264FF8bfIrBqJ5I+ULKASn9dGlOZ5x3QsqvDhNUoMs2dThOMphVPFfHsL7S+F6XiMprgM1eaBz/TMqxSNsBMpoJfElXJA+eSznqKEEFuuxS/lF8UuUxrE3Gc0VQBVF5jc8UfXpBZt2JaX8jw7C6CpLU3wsFty8Jdzg+Fwmqj8Yk+BSelPIjv6dsHe6WNEbbROU14NNfUDz2PcZTUUxI+cHAtb0r5VGB889xfK4RVKDLqM5mGEuW+cTqL9GbsElU3gPp1ynFY6dFfFr2kiH/e4qJiryAa/XQQYIKdLkUaftEqGfudFxBPBkHShijTaLyHnBfVLM9CzGMBUbEupaJrOA7Bf36QU33zBZBJelyiQZXtmHhey+XMEabROU9dKoo7jHgnuTnw2wz6R5gARUZwRaTJLMMpIvEhFUTVKDLIFmB885wrP0GDGtEyl9S5kPxKuLi0zS6SQeJ6uVFITg8VeA7slKhqmUvOuUqeSYIwetHNK599tM2rF9UBqyzvw26IzrY0zy+a4GgBG/0IOmA+V0W6utfeTBGN26bfWK97a7mU9YaUfVxsif5b576ubOc/FaKQlTKXvKUqxS5kXxB15Jh1V2PeYkqFxC0d/j/Tg4/9iAN8vsU5lcpeylSrtIYll/91F6fQ+LVwluQbRng5yGN71hksPqpSH7FIKvspWi5Si8ZFlzlNbozSWs/3YTPZ6jnXbqmw41hmQGMYibSNs12FUzQdQMOcdLikFX2UrRcpZcM62fGiDr66NKorjMJIJisWW8M63/teRawXwNu8McJf0P78YzzW5zkMOuhHi5uVTur7KVouUovGdaOyK7iiDOsUzGx9V5jWOUjzXjSjC7s3kXjMaSUL8ZMYFrZSxnlKl2Fv7suquNrc26mNQ2ryHE+6VFXn6VCxd1bTJm8o3w6RYG3NB9E2rLKXsooV+m15MUgEz2bIr4uz5RhNa5gClQTFPj7L+LVIlwUj1I6jqbdVcpeipar9GpWcD6B4BrDquB+wfrRJcVj4ep1Im3npXyTcg4WCcMLdiplL0XLVXrVsOLipMawKrhfkKp9KtQXgft4/Cg/o1JiQ6TvHXAuYngqZS865SrLVEy7MayXul5rDKt6w7qfMxAMqrNXRPZbryhpeRb6rFr2olquEmdY+zW/EfZi4gCM+aGILwtrDKu3PZzciLqbLm9lVhQtYa8I1xZBnSBpbpM04MHMVERUDYhxJlXCCZItkf8NXdeBJJKtamxbBLXOGDsIKbBNQtYSgo9E5RXgRh6KtK0Kvb0W8gI3HZI5z0NMO2K4zylh7/2hKglqRNjZ69EmUXkPVL7beN0aBrwg/tvZaUWYf+XkvDC3+aWoiKCSsGuhD5tE5T2wLnbbcB/TNKQwbgm9d4HyxpO29mi4KarbD2JCZFf7+EZU3uMI3TOTWOPkR2MF064g3BZbuwrZIKg4YGnlJ6H+VrUvRFULbMTc+CYD+3ANpCmgcNbmPng2CCoKuNVYBvrAUn82iaoWQOXGkuEJCQPs+sTwmPD0mK8ZQYUxSqMas9SfbaKqBZDt0dlzXBdb4vW6SWyVdtfgeIb5RByyrEfTBBUATw3Uiw5YHFsVRFUL4FUWUz+UhhrLRbqAiKuwrYDJ7BJuuk4NCQrAcgkSQTZ/HLAqoqoFwH54i/m4oe+/whviKp9eiEdMpNuxCF7l7zmZJChgtYI4pyqiqg0Q+9j6qVQTPwkTbB56skIdmiaoQq++e0hUtQHWKm54eu14Ulxw4DpsEpRJuEBUDRrUhqCsENW/SORQPeicX9IAAAGHdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pIG1hdGh2YXJpYW50PSJub3JtYWwiPiYjeDI1QjM7PC9taT48bWk+QTwvbWk+PG1pPkI8L21pPjxtaT5DPC9taT48bW8+LDwvbW8+PG1mZW5jZWQgc2VwYXJhdG9ycz0ifCI+PG1mcmFjPjxtcm93PjxtaT5iPC9taT48bW8+JiN4MjIxMjs8L21vPjxtaT5jPC9taT48L21yb3c+PG1pPmE8L21pPjwvbWZyYWM+PC9tZmVuY2VkPjxtaT5zaW48L21pPjxtbz4mI3gyMDYxOzwvbW8+PG1mZW5jZWQgc2VwYXJhdG9ycz0ifCI+PG1mcmFjPjxtcm93PjxtaT5CPC9taT48bW8+KzwvbW8+PG1pPkM8L21pPjwvbXJvdz48bW4+MjwvbW4+PC9tZnJhYz48L21mZW5jZWQ+PG1vPj08L21vPjwvbWF0aD7aKQH1AAAAAElFTkSuQmCC)
In ![straight triangle A B C comma open parentheses fraction numerator b minus c over denominator a end fraction close parentheses sin invisible function application open parentheses fraction numerator B plus C over denominator 2 end fraction close parentheses equals](data:image/png;base64,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)
Maths-General
physics-
An antenna behaves as resonant circuit only when its length is
An antenna behaves as resonant circuit only when its length is
physics-General
Maths-
If ![A equals 60 to the power of ring operator text then the value of end text open parentheses 1 plus a over c plus b over c close parentheses open parentheses 1 plus c over b minus a over b close parentheses equals](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZYAAAAmCAYAAADnRb1XAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAY00gKyAAACKVJREFUeNrtnXGEVVkcx4+MMTJirKwxVqyVrGRJMkZWJFkjWZJkJUPSHytZsjKStaQ/kpEYK0nGkDVWMv+sJMkaMpIkkayVjFgZY+R5vD1f73d3bmfOfXPvfffce86d74cf8+7c+97vft9953fO7/zuuUoRQtJyWts1ylAIE6IntQ9Df0KIA/Zoe6qth1JYWda2IcP+0PGZtm+pfSVk0Z8Q4oCN2t5o+4ZSWPlKGqmsbBdd+6l9JaTRnxDiiF+0XacMiRzSNp3z2AnRl9pXw1r6E0IcsFnbB21DnvmFtNNFbQvaGqqdKtpSkS8XtJ0Xf95p+6jtgbbBFMdin0XRORTtI9DTv6ztrXwHM9oGArseOulPCHEEGszbHvp1T3qbA9Ko3JGRQxXgs19rOxfz50qGUcwNbeMBaR8FlXltv2rbpK1X20/aRgO8HpL0J4Q44oVqTx77xFFpOOLc0vZdRf680va1sW2T9ITTMKLtZSDaR1yShrwO10OS/oQQB2zV9t5Dv5BmGja2PVTVpMLQO162bO/LEFgAUjjbAtA+Ouf3qrq0l4vrwdSfEOKIE9qmPPTLLO3F30sV+bJbGjYTNHT3M7zPlOjtu/Zgl7ZHNbseTP1JwjB1UewS5SA5QTrhlId+mT15pDLmK/IFaZiblu1nVba8/Zjo7bv2ACmmmZpdD6b+xBJUHqt2tcOg9CwYXEge7qnq5i06gSqkvthrNOC/V+TLhKWni4nsZypdVVjEAW2zAWgPdiq/5iSKuB5M/YnBknFBR+V0hOTpCfpYhon7DiZVO+WBPPpUhY0Ceu6YvN8nr4dkW9a0Sr/R8/ZV+wiU86IiDHewo1DhjIwUQr0e+lWJc1pnSvgM5CvvSOOP+ve7avUyA/jicJPUnNikbCsjsLQ8vrh99s13H9FDQ4lss4OPaZYp2So9xKcl+39efjfj0lvF5GsV5cb43IMSXJqiQx4/zCIAn7UHX6j2BHlTRmdjFV/P3V4PSUUYhXNEtW+0cbk+z0kJJFtjAeSYWj0xdl8u3ohRlTwxaKbCHqt0qbB/PW4YffYt1MDyt1pdIpvH99tyHVd9nnW4wa0RqPY+srlL/Z0wIFH4T4e9IPyon6TY77Cy14tfVe2Jw6TgsiSWdn6l5XHD6LNvoQaWVsG+twLXxrfrfD1pv26ugUlptI8rd0tVT3YIDHEwCbXfsn2vKm7CsmWYTWxMJP6l2um6hzIUNsH5/CP73FSfTqjF3+uwpGE6vVfZvsVBRYlZ0z5iSTlgFDknPZ1Xyp5jbnURJLP4HB/NvhCfXhgj3TSaMrAwsDCwOAD15/fk78+lAczSKLdS/nBRVZGmagRpoF7LdmxbKGlUgPzpbKyxPSENeJzdck5o1DfIEP2K5b0QVLC+0JYO71WFb3GwNMVFYxtGjeeMbVNqJZ2Ez31eYGDJ6nN0DK7X7fJ6u7we5oiFgYWBpas2ME8b/z+YT3li9HhtvdciQC8UcyuoIFmWHiY++5ixX7PDezRKEtW8UWuD5bNnLCOwd5b32pvivarwLc6QpUOB/b/scEzSeeQNLFl9jka3o5YRzB8MLAwsDCzVaXJBeqtxUFJ32tFJzEsap0caphFJqZxOGVg+lhRY+lLsvyQjvDiLXaSByvbNBHdT75K/UaU3l1PDvIElj8+LltFtb8JxVQSWbnp+rZzmky9ZrvM6aB+y/oWxTdnv1kSjcteBQIvKvhw2HujzNvZ6ISEV1ldiKkylbDDXOncXgaUo30xOqpWiCcyHnbXsM65WykxbBQeWIn8YjS4aI45YOGJhKqyLgPWow0Euyo5nVXKdesNIbxyw7LNfFXu3cbeNN+aCNhb8GWX6ZjIgAT5acM8sCECwOWyMmIoMLHl89n3EwsDCwLKuUmHonV7t8P9pVfzyCkh3HUkYOcXTLt9r+82yH6qEjhboTyMh0KVtCOHPWM4vruWBbzYwN3FJ2RfcS9tYm9ualnOZKMhndDTMKjCUy88wsDCwMLCUqwkqs3DPSqfnHo+tEXjygJ7kQ3nvaDS0W3zZZ+yLfP8Z2Q/HnVdrV1Jl5WlCoErbeOO536/VSmk0qr5uFRRYyvDNBj4T81g/Wv73MtbwI6WJZSXeqdXpTdMXfG/HY37dkQ5GET7vkmOiSrUd8nok54+IgYWBhYElJ/hhr/XUMzQWrxycyGYZjSxJTxaNzp6EtMwNaeSWJQ3TX7AvqNZaUN3Ni6Bheyzn8tzSe84bWMrwzUaP6G0rC0ejPS+jqTnpFESPRu3kS7QUBo7D6gnDBfs8KkGvIccc6uJHlHdSmJQTWKh9/ToXhNSeJiUolUZA2qdZyyw0fxq8BAlZf41HnYlGxyFojzTts5r5Y+pPCHEEquIGKEMpfKY+XbbdZ+2RXp2umT+m/oQQR2BpowOe+4i5xsvSECOVMVNhg9yNL6g6nQ1Ee9xIjgIizCmiYAVzvygwGgzYH1N/QogjUPLs83PA0ZCjgAKrY+CRE6iYxMoZowH6clJ9+ohjn7VHwROqDc9J4ETK7kqFo5gi/DH1J4Q44gfVfuaHr+Aeo4ma+DJtBBKftUeFrPksHwTTxYD9mfa8E0VIbcAiqQue+hatiDBQE19w/LYAtE960mJfRYGlKH9M/QkhDkG1zbCHfuEen0c18QX3ab0MRHvcr/XAsh1+3g/UnyT9CSGOwDzBDQ/9wmTrTE18Qcrr50C0x2oUtrkILNI6Hqg/SfoTQhyBMswPyr4Sd5Xs9KiX2Y0vWIlhSXQOQXvMI5lzEb0yuhoM0J9O+hNCHIJyzmse+oU15FCFhZvbMFmL9fRGAvMFSzpdDEh7jMwwWR6tZzgk204E6s9a+hNCHIHl+1HOucMzv6J115rSQx0LzBc8e+mN6rzun2/ao6DgoFp5DhEC6qFA/UmjPyHEISPyo+2hFIUQpWv2UHvv9SeEOAQ3kV2nDIWA9NYpah+M/pn4DwlYfBGtqa1dAAAB33RFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT5BPC9taT48bW8+PTwvbW8+PG1zdXA+PG1uPjYwPC9tbj48bW8+JiN4MjIxODs8L21vPjwvbXN1cD48bXRleHQ+JiN4QTA7dGhlbiB0aGUgdmFsdWUgb2YmI3hBMDs8L210ZXh0PjxtZmVuY2VkIHNlcGFyYXRvcnM9InwiPjxtcm93Pjxtbj4xPC9tbj48bW8+KzwvbW8+PG1mcmFjPjxtaT5hPC9taT48bWk+YzwvbWk+PC9tZnJhYz48bW8+KzwvbW8+PG1mcmFjPjxtaT5iPC9taT48bWk+YzwvbWk+PC9tZnJhYz48L21yb3c+PC9tZmVuY2VkPjxtZmVuY2VkIHNlcGFyYXRvcnM9InwiPjxtcm93Pjxtbj4xPC9tbj48bW8+KzwvbW8+PG1mcmFjPjxtaT5jPC9taT48bWk+YjwvbWk+PC9tZnJhYz48bW8+JiN4MjIxMjs8L21vPjxtZnJhYz48bWk+YTwvbWk+PG1pPmI8L21pPjwvbWZyYWM+PC9tcm93PjwvbWZlbmNlZD48bW8+PTwvbW8+PC9tYXRoPkl7PzwAAAAASUVORK5CYII=)
If ![A equals 60 to the power of ring operator text then the value of end text open parentheses 1 plus a over c plus b over c close parentheses open parentheses 1 plus c over b minus a over b close parentheses equals](data:image/png;base64,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)
Maths-General
physics-
In the adjoining diagram, a wavefront AB, moving in air is incident on a plane glass surface XY. Its position CD after refraction through a glass slab is shown also along with the normals drawn at A and D. The refractive index of glass with respect to air (
) will be equal to
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAARkAAAC9CAYAAACH6glbAAAgAElEQVR4nO3df3RT9f0/8GcVRBf3IawKbnWYNrWbP2BNHFKwYMuvlFkxVTwCoi0CsgSlKXqAUxitzDLTCW1ltFQKbR1SPOBaRSYwpECx/HAklTIURkJV8Fh1p+HYis4fr+8ffJP1R5om6b259yavxzk5G/nxvi9v33nl/eu+bxQRERhjTCRXSR0AYyy8cZJhjImKkwxjTFScZBhjouIkwxgTFScZxpioOMkwxkTFSYYxJipOMowxUXGSYYyJipNMP+Tn56OsrEzqMBiTNU4y/fDAAw+guroamZmZ6OjokDocxmSJk0w/6HQ6HD16FEOGDIFer8f+/fulDokx2bk6Pz8/X+oglC4tLQ033ngjHn/8cfz4448YN26c1CExJhtRvNWDcFpaWmAymTBw4ECUlZUhJiZG6pAYkxx3lwSk0Wjw9ttv46677oJOp8Prr78udUiMSY5bMiLZs2cPTCYTHnroIfz5z3+WOhzGJMMtGZEYDAbY7XZcvHgR48aNw6lTp6QOiTFJcJIR0eDBg7F161Y8/PDD0Ol0qKiokDokxTl8+DCioqJ6fRQWFkodIusDd5dC5Pjx4zCZTNDpdCgrK8PAgQOlDklR4uPj4XA44HA4EBcX1+U5q9WKJUuWSBwh6w23ZELk7rvvxokTJzBo0CDodDo0NDRIHZKiOBwOaLVaT4IBgCeffBLAlVk9Jl+cZEJs/fr1WLp0KaZOncoDwn46fPgwAGDKlCldnncnF41GE/KYmP84yUjgscceg91ux549e/DQQw/h888/lzokWWtsbATQM5ns3bsXALirJHOcZCRy6623oqioCF988QV0Oh3efPNNqUOSLXeLZezYsZ7n3OMxPKQof5xkJGSxWPDQQw+hvLwcCxcuRG5urtQhyZK7xTJu3DjPrNKTTz7JCUYhOMlIZPXq1VCpVMjOzkZ6ejrsdjv+/e9/Y8KECThz5ozU4cmG0+mEw+GAwWAAEXke+/fv5ylspSAWckeOHCGVSkVOp7PHay+++CJdd911VFVVJUFk8lNTU0MAyGq1dnne4XAQAOIqLH/ckpGAxWJBcXExYmNje7z2zDPP4B//+AfWrFkDk8kkQXTycujQIQBdx2MA4NNPP/X8f6fTGdKYWGA4yYTY8uXLERsbi3nz5vX6nnvuuQc2mw0//PCDZ8+aSOUej0lOTu7y/NatWwFcuXyj89oZJkNSN6Uiyb59+2jo0KHU2trq92c2bdpE11xzDRUVFYkYmTw1NDR47RKZTCbuKikIX1YQIkSEkSNHIjc3FzNnzgzos6dPn4bJZMLPf/5zlJWVYciQISJFKR9RUVE+X+dLCZSDk0yIWCwWdHR0YOPGjUGXsXTpUrz22msoKyvD1KlTBYyOMfFwkgmBN998ExaLBc3NzVCpVP0qq7a2FiaTCQsWLMBzzz0nUISMiYeTjMja29sxcuRIFBcXY9q0aYKU+emnn8JsNuPy5csoKyvjgU8mazy7JLKcnBxMmzZNsAQDAL/4xS9QV1eH1NRU6PV6z0wLY3LELRkR1dTUYPXq1WhubhbtGPX19TCbzZg8eTJeeukl0Y7DWLAU2ZJRwl1cWltbPYvuxJSamgqbzYavvvrKs2cNE54S6pxcKbIlExUVJfuL42bOnIm4uDgUFBSE7Jjl5eUwmUxYt24dFi5cGLLjRgIl1Dm54iQjgoqKClRUVEiyUrepqQlmsxlarRZlZWW4/vrrQx5DOJJ7nZMzRXaX5MzpdMJisaCkpESS4ycmJqKxsRE33ngj9Ho99u3bJ0kcjLlxS0Zg06ZNQ1JSkiz2hnnttddgNpuRk5ODFStWSB2Oosm5zsmdIlsybW1tUofgVUlJCTo6OmSRYADgkUcegc1mw5EjR5Ceno5PPvlE6pAUS651TgkUmWTUarXUIfTQ3NwsaTepN7fccgt27dqF0aNHQ6/XY/v27VKHpEhyrHNKocjukhxNnDgR06ZNQ3Z2ttSh9Grv3r0wm8144IEHsGbNGqnDYRFCkS2ZnJwcqUPoYvXq1bj++utlnWCAK7cUsdlsaG1txT333IOTJ09KHZJiyK3OKYkiWzJyGoQ7evQoJk2ahObmZq873cnVunXrkJOTg9LSUs9N0ljv5FTnlIaTTD8lJSVh3rx5Pne6k6v33nsPZrMZI0aMQFlZGQYNGiR1SLIlpzqnNIrsLsnF8uXLERcXp8gEAwCjRo3Ce++9B5VKBb1ej4MHD0odEgtD3JIJ0jvvvINZs2ahubkZQ4cOlTQWIWzZsgVmsxnLly/H0qVLpQ5HduRQ55RKkUlGDkaMGBHUVppydu7cOZjNZqhUKpSVleGmm26SOiQWBri7FASLxYKkpKSwSjDAlVu/7t27F3feeSf0ej3q6uqkDomFAW7JBEjIrTTlbNeuXTCbzZg5cyZeeOEFqcNhCqbIlsycOXMkOW57e7tnj5hwTjAAcN9998Fms+H8+fNITU3FBx98IHVIkpKqzoUDRbZkpBqEmz9/PlQqlegbUcnN2rVrsXz5cpSWlkbsl40HfoPHScZPodhKU84aGxthNpsxevRolJWV4aqrFNkIDhonmeBFVk0JUqi20pSzsWPHwmazAQD0ej0aGxsljogphSKTjEajCenxcnJyMG/ePEycODGkx5Wbq666CuXl5cjOzsbEiROxdu1aqUMKmVDXuXCiyO5SKEm5laacffDBBzCbzRg6dChKS0sRHR0tdUhMphTZkgkV91aakdxN6s1tt92G+vp6xMbGQq/XY9euXVKHxGSKWzI+yGkrTTmrq6uD2WzG3Llz8cc//lHqcJjMKLIlk5GRIfoxSkpK8PXXX3OC8YPRaITNZsOpU6cwZcoUnDt3TuqQBBeKOheuFNmSEXs6sbm5GSNHjsTJkycxYsQI0Y4TjqxWKwoKClBaWorZs2dLHY5geAo7eJxkvFDCVppydvDgQZjNZkyYMAHr1q2TOhxBcJIJniK7S2JSylaacnbvvffCZrOho6PDs2cNi1yKTDKJiYmilHv06FGsXr0aRUVFopQfSQYNGoTNmzdj/vz5GDNmjOJbNGLVuUigyO6SWJS8laacnTx5EiaTCbGxsSgtLcX//d//SR0SCyFFtmTEoPStNOVs5MiRePfddzFs2DDo9Xrs3btX6pBYCHFLBv/bSvPkyZMYNmyY1OGEte3bt8NsNmPRokX4wx/+IHU4LAQU2ZJJTU0VtDz3ql5OMOJ7+OGHYbPZcOzYMdx333346KOPpA7JL0LXuUiiyJaMkNOJFosFHR0d2LhxoyDlMf89//zzKCoqQmlpKR555BGpw/GJp7CD5zPJPPfcc/jlL3+JJ554IpQx9UmoP3ikbKUpZ/v27YPZbEZ6erqsr+rmJBM8n92ltLQ0rF27Fs8880yo4gmZjo6OiNlKU84mTZoEm82GL774AmPHjkVTU5PUITGB+Uwyo0ePxrFjx3Dx4kUYDAZcuHAhVHH5lJKS0u8yLBYLpk2bhmnTpgkQEeuP66+/Hn/961/x6KOPQq/Xo7y8XOqQehCizkUs8tOqVasoJiaGdu/e7e9HZGvr1q00YsQIqcNgXvzzn/+kUaNGUVZWFn399ddSh8ME4HeSISJ6/fXXSa1W05o1a8SKR3Stra00dOhQ2rdvn9ShMB+efvpp+vWvf0379++XOhTWTwHPLp09exZz587Frbfeik2bNiEqKkqsRpYoZs6cibi4OBQUFEgdCuvD1q1bYTabsWzZMixbtkzqcFiQAl4nk5CQgIaGBlxzzTVISkrCqVOnxIjLp9jY2KA+V1FRgZaWFk4wCjFr1izYbDbU19fDaDTi008/lSyWYOscg/9jMt689NJLpFKpaNu2bcK0q/wUTNhOp5NUKhUdOXJEhIiY2FauXEnDhg2jv/3tb5Icv59flYjW7zO3f/9+io2NpRUrVggRj1+C+YPff//9VFBQIEI0LFT+/ve/0y233EJLliwJ+bE5yQSv35cVpKam4ujRo2hqasKDDz6Itra2/hYpON5KMzxMnToVdrsdH330Ee69916cPn1a6pCYHwS5dmno0KHYuXMnEhISkJSUhMOHDwtRbK+MRqPf721ubobFYuE9YsLEkCFDsG3bNmRkZECn02Hz5s0hOW4gdY51I3TT6JVXXqGBAwfShg0bhC46KBMmTKDi4mKpw2AiOHLkCCUmJtL8+fPpu+++C/nxGxoaCECvD4PBEPKY5Ejwq7Afe+wxHDt2DOXl5Xj66aeFLj4gvJVmeEtKSoLdbsfVV18NvV6Pd999N6THT05O7nI9k8PhAF0Z50RDQwP27NmDqKgo0Vv2sidW9vr2229p9uzZlJqaSk6nU6zD9OrIkSOkUqnI4XCE/NhMOFartdeWgcPhIABktVqpqqqKrrvuOnrxxRdDHiMA0mq1PZ7v3NKJZKL/1//pT3+ioUOH0s6dOwUrU61W9/me0aNH08aNGwU7Jgs9rVZLVqvV828AVFNT4/m3wWDo8uX+8MMPKTU1laZPn05ffPGFoLH0VufcicRkMnl93WAw9Ig70oi+adWyZcuwadMmzJ07Fy+88IIgZbpcLp+vB7OVZmFhIaKiohAVFYW0tLT+hsj6KT4+HlVVVViyZInnOYPBgEOHDgEADh8+jD179nTZyvNXv/oV9u/fj1tvvRU6nQ5vvfWWYPH0VucaGxsBABqNxuvrEyZMAAB8/PHHgsWiNCHZGS89PR1Hjx7F3r178dhjj+G///2vaMd65513UFFREdBsUnx8PAB4+tN79uzBtm3bxAqR9aGwsBDx8fFITk7u8ZrT6QRwZcOrhoYGxMXF9XjP6tWrsX79eixYsAArVqwQNdaWlhYAwNixY/16X0QKddPpqaeeIp1ORzabLegyfIV955130tatW/0uS6vVUkNDQ5fnDAZDr81fJi73OEv3vwkRecZfGhoa/Op+tLa20oMPPkgTJ06ks2fP9iuu3uqcVqv1WR9NJpMn7kglyYjUhg0baODAgfTKK68E9fmsrCyvz2dnZ9O8efP8LsdqtXqdZjQYDDz9KJHOA73eHsGMbRQWFpJKpQq6vhF5r3PuhOirrriTkLekGSkkG/ZuaGighIQEWrp0qSDlvfHGGxQXF0dfffWVX+/35xeThZ5Wq/XainQPoAZq06ZNVF5eTocOHaI77riDzGazEGESEVFNTY3PuuKuY95mniKJZHcrSE5OxtGjR3H27Fncf//9+Pzzz4Muy72VptPphN1u9+szO3bsAACMGzfOM+DrfgDA8OHDg46HBcfpdMLhcGD8+PFdnncP8lqt1oDKe+aZZ7B27VpER0dj3LhxsNvt+Pbbb3HXXXfh+PHj/Y7XPQjd23iM2WwGAFRVVfX7WIomdZYjIlqxYgXFxsYGvUHRvHnzKDs7m1599VUaOHAgvfbaa31+RuhfTNZ/7ung7mub3OMagdi1axfdcccdXlu2GzdupAEDBlBJSUm/4nV3hbytxXJ3+7hFLGF3qbtt27aRSqWil156qc/3dq5w7q00f/zxRyK6clX4TTfd5HP3Pncztnv/3l3JuWJIw33+vT0X6FjMPffcQ6+++mqvrzc3N1NycjLNnDmTXC5Xn+V1j8tdh7wlGR6H6SqgJOP+le/8cPc3vV3HEeiXtbm5me6++25asGCB76D//x+8t600z549S7/97W973RJAyF9MJqzOCSXYBPPWW2/R+PHj/Xrvs88+S7GxsX3uXd25XnSv590fkbzwzpuAv1GdM7jXAvt5kn/88UeaM2cOJScn05kzZ3o9BhHRjBkzKDc31+t7Ll26RL/5zW9o3bp1PV4T8heTCcs9mOqrjvVl/fr1ff5QdbZjxw668cYbKT8/v9f38I9P8II6c+7+ZvcvpLc1J8Fas2YNqdVqev3113u8BoA2btxISUlJPss4ceIERUdHe+2XC/GLyeSpqqqKZs2aFdBnLly4QPfffz+lpaXR+fPne7we6iTTPdmi21S5u0vmfsh5XVfQZ677f7TBYBC8D7p7926KiYmhVatWdXl+0aJFfm+lOXv2bNq0aVOP54X4xWTydPLkSdJqtZ5xukAUFBSQWq3u8YOTl5cnVHh+cTgcnh8/b1PgDofD82Mv94uAg/52uccvHA4HmUwm0VoBn3zyCU2ZMoUeeeQRam9vJ6LAttJcs2YNPfXUU6LExuQrMzMz6C1h33nnHUpISKDs7GyBowqcexzUWyJRyo9j0Otknn32WQCAVqvF+PHjMWPGjGCL8unmm2/Gnj17EBMTg9GjR2Px4sUBbaV56dIlDBkyRJTYmHytWrUKb7zxBvLy8gL+7IQJE2Cz2dDW1ubZs0YqWVlZAP63rsstPj4eDodDipAC158M5SvLimHTpk2UkpJC7777rt+fOX36NH3//fciRsXkqrW1lcaPH0+ffPJJ0GWUlpZSXl4eLVu2zOtYjdi8XbpgMpkUNT3er+6Svxd/5eXl9Tntxw9+RNLj8OHDfn/XOv+YW61Wxa3jCirJmEwmz39oX1ehigEApaSkBPy59vZ2GjRokAgRMaE8+uijNH/+fEljcLlcVFJSQjqdjkaOHElr1qwhAJSYmEi1tbUhj8c9wKvU3QECHpMpLCyERqPxbCb0/PPPA0DI919xuVwoLi4O6DPffPMNfvKTn4gUERNCTEyMZHdrbGhowLx583DDDTfg+PHjsFqteP/997F48WIAQG1tLebMmdPnpmlCc18bde7cOZSWlob02IIIJCNZrVavmRQI7ZWmAOj8+fOkVqsD6ifv2rWLRo0aJWJkrL8mTZpEu3btCtnx2tvb6S9/+QuNGjWKbr/9drJarfTZZ5/1eJ/7q2KxWMhoNIYsPqK+t/iUO7+TjK89Vtx9xv72FWtqavzax6WoqMjzv4F0mzIyMujll1/2+/1irP2JRL2dx84bgbv99Kc/pS+//FL0mBobG2nBggV07bXX0owZM+jtt9/2+X53nWtrayONRkP19fWix+jW2+JXpegzyXi7Xsk9m+Qe+O3t9YCDCaJFlJiYSJWVlX2+78MPP6Sf/exn9MMPP/hVrsPhiPh9QITg6zx23wi8vb2drrvuOtFiuXz5Mm3YsIHGjBlDCQkJVFBQQBcuXAi4nPr6etJoNCJE6F2oZ3GFJpvVPJ0TViD87TY9++yzAd1DWYmj+HLU23n0dpHqV199RQMGDAhqpa4vx48fp4ULF5JKpaLp06cLcucMo9EYklXAfV0rqASyiLyhoaHLlHhfGdtut3f5t8Vi8dlteuWVVyg+Pp4+//xzv2PirpIwejuPvT1/1113UUVFRb+P+91331FFRQWNGzeO4uLi6LnnnqOWlpagy+te59ra2ghAj+eF0tvdKZW4Lawskoy7yezue/b15faW1XubXjx27BhdddVVfq9L6N495NZMcHydR18bgb/88suk0+n87tZ2d+LECVq0aBENHjyYjEajYFPO3upcZWVlUEspIo3kScZqtXoqXF97prp5+4N76zadOnWKbrvtNtq8eXOfcXTe89fdxPe1DzDzTojzuGDBAjIajQG1PKuqqig1NZWGDx9OK1euFHz8orfuir9jgpFM0iTjcDi6NP/8narr7Q/eeXqxqKiIrrnmGiouLvYrls5fAq1W66mkSh7Vl4JQ5zE3N5fUajUVFhbSpUuXvL7n/fffp8WLF1N0dDSlp6fT9u3b+/8f0Ive6lwwSykijaRJxmAw9PjF8aff6WsQTKPR0Pz58+nxxx+nxsZGv+IwmUyeLlvn2RBuyQRG6PNot9tp1qxZNGDAAHriiSdo+/bt1N7eTlu2bKHJkydTTEwM5ebm9rq5mZB81bm8vLyQr51REsmSjLdNedyPvqaOfTVP6+vrSa1WU1tbm9+xdL7ncufZEKvVytPYARDrPH722WeUm5tLcXFxBIDS0tJC3rrsq0uk0WgkueRACSRLMr7WTvR3TUAgqzK7byrOXaXgiHUea2pqKC0tjYYNG0ZLliyhf/3rX4LFLCT3jxvrSZIk42uTK/c0dn+6KO5Vmf7+srh/gTs38Q0GA88sBUio83jmzBnKzc2lmJgYmjRpEm3ZskWMcAWXlZXV691NI1nIk0znfrs37mlsX4O//izpDqTb1PlOf3w7i+D19zxu376d0tPTKTo6mhYvXkzvv/++iNEGxp865/5xE2vtjFKFLMn0dcuUvjZO7hK0n6sfs7KyAhqQE3Ij9EgWyHl0OBy0cuVKGj58OKWmplJVVZXI0QXH3zpXW1sb0ksOlEDydTLB8PcPHki3qaGhQZGrKeXG3/NYW1tLRqORBg8eTIsWLaITJ06EILrgBbKs32g0ei6oZEQD/N8UQnnUajUqKyuRkZEBo9Ho872NjY2YMGFCiCILX77O48cff4yqqipUV1cjJiYGmZmZ2L59OwYMCK9qWFlZidjYWBiNRmg0GqnDkZ7UWS4YgYZtNBr77DZ1ng1hwfN2Hnfu3EnTp08nlUpFCxcupOPHj0sUXfACrXOBbkMSzhSZZAJdjyDFHiCR7sKFC1RQUEAJCQk0ZswY2rBhA12+fFnqsIIWzBoYqbbrlJsoIiKpW1OhcODAAWRkZKCtrU3qUMLa7t27UV1djbq6OmRmZiIzMxNjxoyROixJtLS0QKfT4fz581Cr1VKHI5mISTIAkJGR4RmnYcJpbW1FdXU1qquroVKpkJmZiaysLKhUKqlDk1xOTg5aWlpQW1srdSjSkbYhFZxgm6C8jkFYe/fupUcffZQGDBhAc+fOpUOHDkkdkmj6W+ciuauuyJZMVFQUgg27rq4OOTk5OH/+vMBRRYb//Oc/nlbL1VdfjaysLGRmZmLw4MFShyaq/tS5AwcOYM6cORFb54K+Ta1SGY1GJCYmIicnR+pQFKW+vh5ZWVm44YYbcPLkSRQXF8Nms2HRokVhn2D6KyUlBYmJicjPz5c6FElEXEsGuHLPptjYWNTX1yMxMVHAyMLLpUuXUF1djaqqKvzwww+egdzo6GipQws5IerckCFDYLfbI67ORVxLBui6SI/15OsmZ5GYYITgrnOR2IJWZJKx2+39LsPdbYrUJmx3HR0dWL9+Pe6++278/ve/R0JCAi5cuIAtW7Zg8uTJUocnOSHqXFZWFlwuF6qqqro83/3fYUe6MWfpib3jvBIEepMz1j/etuu0WCwSRiQ+RbZkhKJWq1FbWxtx3aZvvvkG5eXlGDt2LLKysjB8+HCcO3cONTU1SEtLkzq8sKbRaJCVleXpNjU1NaGurk7iqMSlyCQjZPPS3W0qLi4WrEy5eu+99/DUU0/hhhtuwL59+5Cbm4szZ84gNzcXMTExUocna0LWuaKiIk9yOXDgAFwul2Bly1FEzi51F84j/99//71nXcvFixc9q3GHDx8udWiK0t8619TUhJaWFqSkpECtVnsuczEajaiqqkJbW1vYXnoQXtfYB6nzbFO4LJiy2Wye5JKamorFixf3ud0FE09iYiJcLhd0Oh1cLpcn2bhbSC6XK2yTDLdkOklNTcUDDzwAi8UieNmh4k4sDofDsxo3Li5O6rAUT8g6V1xc3GMqu76+HikpKYKULzvSjTkHT6yw3bNNSrtRVyhvchaphK5zdrudsrKyPFvNhvNdKBU58CtWl0atVqOoqAhz5swRpXyhvfrqq5g8eTJ+97vf4dprr0VjYyN27tyJ6dOnSx1a2BG6ziUmJqKyshKVlZXQaDRhPfiryO6S2HQ6HTIzM2XZbTp9+rSnS+SOc8aMGVKHxfqpqakp7CYd3DjJeOHebMhut8tmj9Zt27ahuroadrvdcw3R7bffLnVYjPVJkd0lsde0aDQa5OXlSd5tOnv2LJYvX46bb74ZmzdvxuzZs/HZZ5/BarVyggmxSFhHJRZFtmTEml3qTqfTITs7G1lZWaIfq7MdO3aguroaR44c8bRaRo4cGdIYWFehqnPhiJOMD6HsNjmdTs+2Clqt1pNcmDxwkgmeIrtLwXI6nYiKiurxiI+PR3x8fI/3azQaZGdni9ptqqurQ0ZGBvR6PVwuF2pra7F//35OMCxsREySiY+Ph1arRU1NDejKrWBARDAYDHA4HHjyySe9fi4/Px8ul0vQi9g++ugjrFq1ClqtFmvXrkV6ejq+/PJLlJSUQK/XC3YcxmRBgrU5/dbW1hbQ+903f+/t5m3o48bw3i7PD0Y43OQsUgVa59j/KHJMJhBmsxllZWWoqanpdT1JfHw8zp0757OcYG9tcfHiRc+6lujoaM9Yy7XXXhtQOYwpVVgnGafTCa1WC61W22cS8YdOp0NeXp5fFxryTc4Yu0KRYzL+7pO6Y8cOAMCUKVMEOa77koPeloC3traisLAQd9xxB1auXInk5GR8+eWX2LBhAycYhYvEvXkFI21vLTj+hm0wGAgA1dTUCHZsi8VCRqOxy3ORdJOzSKXQr4oshPV+Mu4u0s033yxYmXl5edDpdKirq/OsbXHf5Gz9+vV8DyLGugnrJCMG9wZXU6dORUZGBoqLi5Gamip1WIzJliLHZPzlXmDX2NjY63vMZjO2bdsWULkpKSmYMWMGLl++zAmGsT4oMsmQnxNi7muOXn75Za+vHz58GACC2iqh82bQLPz5W+dYT2E9hQ38b51M92lss9kMp9OJ3bt3B122ezPotrY2IUJlLCyFfZIBruzFMnPmzC7P+VqcFwj3PZsCXaTHWKRQZHcp0AsWZ8yY0eV6JSISbDe5yspKNDU14cCBA4KUx+RJ6r2FlEyRLRm5XXbP3abwJ7c6pyScZASSkZHhmd5m4UeOdU4pOMkIxH3jrtra2rDdEDqSybHOKYUix2TkeKc99+1U3APBLLzIsc4phSJbMnKWkZEBjUaDoqKiLs+H821IGfNFkS0ZOausrERVVRWampq6PM+zTyxScZIRmHvwt3O3yeVy4eDBgxJGxZh0FJlk5D7uYTQakZiYiPz8fABXWjEtLS0SR8X6Q+51Tld9U3EAAAETSURBVM4UOSajhJF+l8uF2NhY1NfX48CBAygpKRHtHt5MfEqoc3KlyJaMXNXV1XnGXjp3mw4ePBjWN1RnzBdOMgIyGo1oampCVFSUJ7kAV5KPy+XiRMMikiKTTKhvGxsIi8WCtrY2qNVqFBcXdxmL4XEZ5ZJznZM7RY7JKEVTUxPmzJnjmc6ur69HSkqKxFExFlqKbMkoRWJiIux2OyorK6HRaHqsnWEsEnBLJoSampr4uiYWcTjJMMZExd0lxpioOMkwxkTFSYYxJipOMowxUXGSYYyJipMMY0xUnGQYY6LiJMMYExUnGcaYqDjJMMZExUmGMSYqTjKMMVFxkmGMiYqTDGNMVJxkGGOi4iTDGBPV/wPaelGNKAAkrwAAAABJRU5ErkJggg==)
In the adjoining diagram, a wavefront AB, moving in air is incident on a plane glass surface XY. Its position CD after refraction through a glass slab is shown also along with the normals drawn at A and D. The refractive index of glass with respect to air (
) will be equal to
![](data:image/png;base64,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)
physics-General
chemistry-
Which statement is not correct for n=5,m=2:
Which statement is not correct for n=5,m=2:
chemistry-General
chemistry-
In P-atom find out the no. of paired electrons for l=1 and m =0-
In P-atom find out the no. of paired electrons for l=1 and m =0-
chemistry-General
chemistry-
For H- atom, the energy required for the removal electron from various sub-shells is given at under:
The order of the energies would be:
For H- atom, the energy required for the removal electron from various sub-shells is given at under:
The order of the energies would be:
chemistry-General
physics-
Immiscible transparent liquids A, B, C, D and E are placed in a rectangular container of glass with the liquids making layers according to their densities. The refractive index of the liquids are shown in the adjoining diagram. The container is illuminated from the side and a small piece of glass having refractive index 1.61 is gently dropped into the liquid layer. The glass piece as it descends downwards will not be visible in
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)
Immiscible transparent liquids A, B, C, D and E are placed in a rectangular container of glass with the liquids making layers according to their densities. The refractive index of the liquids are shown in the adjoining diagram. The container is illuminated from the side and a small piece of glass having refractive index 1.61 is gently dropped into the liquid layer. The glass piece as it descends downwards will not be visible in
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)
physics-General