Maths-
General
Easy
Question
Hint:
In this question, we have to find the range of the given function. For that we will first simplify the equation and later find the range of the simplified equation.
The correct answer is: ![open square brackets negative 1 fourth comma 3 over 4 close square brackets](data:image/png;base64,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)
Related Questions to study
maths-
does not exist Extreme Values; ![cos space invisible function application x plus sin to the power of 4 space x element of](data:image/png;base64,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)
does not exist Extreme Values; ![cos space invisible function application x plus sin to the power of 4 space x element of](data:image/png;base64,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)
maths-General
Maths-
Maths-General
Maths-
The minimum and maximum values of
are
The minimum and maximum values of
are
Maths-General
Maths-
The minimum and maximum values of
are
The minimum and maximum values of
are
Maths-General
Maths-
Maths-General
physics-
A piston fitted in cylindrical pipe is pulled as shown in the figure. A tuning fork is sounded at open end and loudest sound is heard at open length 13cm, 41 cm and 69 cm, the frequency of tuning fork if velocity of sound is
is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAXUAAACzCAMAAABB5XznAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAK4UExURf////7+/vn5+fb29vX19fT09Pf39/39/fDw8Gtrazk5OTo6Ojs7Oz4+Pj09PW1tbdra2ufn5yIiIgAAACYmJjAwMC8vLywsLBsbGxYWFi0tLRoaGhERES4uLisrK1tbW9XV1eXl5SMjIzExMba2ttjY2NPT09fX17i4uEVFRb6+vs7OzoWFhR8fH2ZmZsbGxtHR0SQkJEBAQOLi4uDg4Obm5qampicnJ4CAgNzc3NnZ2UNDQzg4ON7e3vr6+qGhoXx8fOvr67+/v319fZSUlBUVFYKCgp+fnxgYGHd3d6qqqvj4+NLS0kdHR+7u7rW1tfLy8rm5uR0dHV9fX+/v77u7u1paWvz8/J6eniEhIXt7e/Pz88nJyTw8PFZWVuPj44aGhpqamtDQ0EJCQkREROjo6FdXV1NTUwwMDJKSkrq6ul1dXczMzH5+figoKGdnZx4eHqysrN3d3YqKirCwsGxsbCkpKVRUVOrq6m9vb62trWlpaZiYmMTExLGxsU9PT9/f33FxcWNjY5mZma6urlBQUFJSUpCQkMPDwzQ0NMfHx4+PjxkZGdTU1FVVVRISEoeHhxAQEHNzc/Hx8WVlZXV1dUZGRq+vr46OjjIyMre3t4uLi5GRkYODgyUlJfv7+xQUFDY2NqWlpXl5eU1NTcHBwaurq5WVldbW1srKynR0dMLCwqKioqmpqRcXFzc3N6ioqF5eXhwcHLS0tA0NDXp6empqasjIyCAgIEpKSoGBgeTk5L29vUtLS5aWlqOjo25ublxcXMDAwCoqKg8PD42NjVlZWTU1NQ4ODsXFxc3NzWhoaFFRUbKyskFBQT8/P9vb24SEhFhYWAUFBQQEBDMzMwICAry8vJeXlwoKCpOTkxMTE52dnZycnAYGBunp6aSkpImJiYyMjAsLCwEBAQkJCWJiYgAAAOQEdiUAAADodFJOU////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////wCyLaC6AAAACXBIWXMAABcRAAAXEQHKJvM/AAAFlUlEQVR4Xu2dQZKzIBSEcwbccgbuoQt23sClK67gnvJy3OeHDJlAzJ+AZnhg+ktq5k2latSXrrYBEy8AAAAA+AASz+uzIFIYcIUJ5Xvy90jeMb9ZChjjvrIw1gV/lYaJ2ffk75HMjGome4xTsHm1cnGrKR6+JQWQbCq4tQ1qmgJHHdjqq5NjtU7b9XDzC+vLntWokJxW6+Y7u16T1ofv6Tqxr5t7n+XCVmi9AN+q9cp83VcnB1qngNrXTezryDAlgK9T8OjryDAlgK9TsPF1X54caJ2CmnwdY9NCwNcpsF0P+gxfLwN8nYI57DrGpoWAr1OADEMBfJ0CZcLNI8OUAb5OQSvzMFJ+VA7QehJjP/rqI9S2blpp11f+0avSoPUkBi58tRs5369eJff1YPMV53WrB1/tZp7E78FB60mMTB/ds5Hf/0Vl8+u1ZpjRHO56eHDQehKz0UfbtLLlrvWKfL3iDDNPR9ukBLuHT2g9CanZ4MudSB16Kbmv3/tc85xj3y2+2slsjK8s0HoaNrAf27UoBdU0v17znKM19kMf0ZN9aFHQeiKCHzL2+EBrml93eb3arh+ciYmnFKD1RKwvH2hUbDBV+XrNGeYiBT+QYkYWfq4WWk/GNm53p2TPoyPDumkqUu8X+/DQZWg9mf1iV5rFbxjWTZPZ7exyfRxiQevpjMbsWj2dmXkYYdU2v15z121m35Me52kT9aH1DKzH5M/GKLF9ryqbX6/8Okc1ZVu76rtth6H1LEbGhqxdtGfSR1O3YN00C7lwk6N21/QnZ2BoPQ/b9gwbVCt/ugZVk69Xn2Ecdid5attn8VTp0PoOBsPTvvpxnLh+HvBrWjetP8P8MBqu359T1cpY/5/eQus7mHvGxethqlw0Dy6AeaCy+fXaM4xHDpqb/v8Lqcq+/up9gdb3oRZj+z48a7xUg+BcLy/6inXTvcz9xNnUDyraZTUuYnrTc2j9CFbTrvFa9MswjuOwLKvQjPNJvO6563o9vt5KhgmYV21sn7n7Lm3ObcVsy99fOAOtH0WNw2o1rm1mEcuSNktTm6/7sjmkVBmX/X5U6/lCPYHWb8joUF7zMV+X9uy9vh45PCEam7aVYR6Jlwpe8xGt244Pq2Zdl73SciKt20N5fxr1HPd12/Fem87xcP1BAq1nmIByvi5nOyj46bgj/zOZ36r1/b5ujbw33DfcwfrZDhbSmH/ae5oM83Aobzig9cUaeQzv3IAhCa+Lb80w+319saMy3+4fuJlSuU3YbeYcG3aYQhlGuuASdD7/ZApf34V0nf/VfP6/igXSdoYpm9dtWr91PvtkeC5fL5jXr0g1rJPJv7XXZmzqywYprPVflI+DGZxJ6yb9s5G1rZvC1wvwrRmmovl1ZJhCnErr7fq6LxsEWqegVV9HhikEfJ2CaGyKDFMI+DoFyDAUwNcp2Mw5wtcLAF+nIPJ1ZJhCwNcpiASCDFMI+DoFm7wOXy8AfJ2CWCDIMGWAr1OwGZv6skGgdQpaXjeFrxcAvk5B5OvIMIWAr1Ow8XVfNgi0TkFTvh5sHhmmEPB1CiJfR4YpBHydgo2v+7JBoHUK2vL1e5+RYQoBX6cAGYaCE2ld6pyu1+XrvmyRIf1bz6D1j5Gx6zX5etsZJgdonQJyXw8333SGyQFap6A2X/flyYHWKajJ15FhCgFfpyAamyLDFAK+TgEyDAXwdQo2c47w9QLA1ymIfB0ZphDwdQo2Y1NfnhxonYLa8jp8vQDf6+uUB2q7HmzeZhhfnRzJuFiv9CRPxu1PV7pfmk/ul3+J4Nm/uzHph5DM3W/netOdjpd/urtxuK278vrnrSB58M5k38lvF3JcLIP7QUIvfFEHA+VJrhzyOw4TAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAuVwu/wAjaT7dOpd9YgAAAABJRU5ErkJggg==)
A piston fitted in cylindrical pipe is pulled as shown in the figure. A tuning fork is sounded at open end and loudest sound is heard at open length 13cm, 41 cm and 69 cm, the frequency of tuning fork if velocity of sound is
is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAXUAAACzCAMAAABB5XznAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAK4UExURf////7+/vn5+fb29vX19fT09Pf39/39/fDw8Gtrazk5OTo6Ojs7Oz4+Pj09PW1tbdra2ufn5yIiIgAAACYmJjAwMC8vLywsLBsbGxYWFi0tLRoaGhERES4uLisrK1tbW9XV1eXl5SMjIzExMba2ttjY2NPT09fX17i4uEVFRb6+vs7OzoWFhR8fH2ZmZsbGxtHR0SQkJEBAQOLi4uDg4Obm5qampicnJ4CAgNzc3NnZ2UNDQzg4ON7e3vr6+qGhoXx8fOvr67+/v319fZSUlBUVFYKCgp+fnxgYGHd3d6qqqvj4+NLS0kdHR+7u7rW1tfLy8rm5uR0dHV9fX+/v77u7u1paWvz8/J6eniEhIXt7e/Pz88nJyTw8PFZWVuPj44aGhpqamtDQ0EJCQkREROjo6FdXV1NTUwwMDJKSkrq6ul1dXczMzH5+figoKGdnZx4eHqysrN3d3YqKirCwsGxsbCkpKVRUVOrq6m9vb62trWlpaZiYmMTExLGxsU9PT9/f33FxcWNjY5mZma6urlBQUFJSUpCQkMPDwzQ0NMfHx4+PjxkZGdTU1FVVVRISEoeHhxAQEHNzc/Hx8WVlZXV1dUZGRq+vr46OjjIyMre3t4uLi5GRkYODgyUlJfv7+xQUFDY2NqWlpXl5eU1NTcHBwaurq5WVldbW1srKynR0dMLCwqKioqmpqRcXFzc3N6ioqF5eXhwcHLS0tA0NDXp6empqasjIyCAgIEpKSoGBgeTk5L29vUtLS5aWlqOjo25ublxcXMDAwCoqKg8PD42NjVlZWTU1NQ4ODsXFxc3NzWhoaFFRUbKyskFBQT8/P9vb24SEhFhYWAUFBQQEBDMzMwICAry8vJeXlwoKCpOTkxMTE52dnZycnAYGBunp6aSkpImJiYyMjAsLCwEBAQkJCWJiYgAAAOQEdiUAAADodFJOU////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////wCyLaC6AAAACXBIWXMAABcRAAAXEQHKJvM/AAAFlUlEQVR4Xu2dQZKzIBSEcwbccgbuoQt23sClK67gnvJy3OeHDJlAzJ+AZnhg+ktq5k2latSXrrYBEy8AAAAA+AASz+uzIFIYcIUJ5Xvy90jeMb9ZChjjvrIw1gV/lYaJ2ffk75HMjGome4xTsHm1cnGrKR6+JQWQbCq4tQ1qmgJHHdjqq5NjtU7b9XDzC+vLntWokJxW6+Y7u16T1ofv6Tqxr5t7n+XCVmi9AN+q9cp83VcnB1qngNrXTezryDAlgK9T8OjryDAlgK9TsPF1X54caJ2CmnwdY9NCwNcpsF0P+gxfLwN8nYI57DrGpoWAr1OADEMBfJ0CZcLNI8OUAb5OQSvzMFJ+VA7QehJjP/rqI9S2blpp11f+0avSoPUkBi58tRs5369eJff1YPMV53WrB1/tZp7E78FB60mMTB/ds5Hf/0Vl8+u1ZpjRHO56eHDQehKz0UfbtLLlrvWKfL3iDDNPR9ukBLuHT2g9CanZ4MudSB16Kbmv3/tc85xj3y2+2slsjK8s0HoaNrAf27UoBdU0v17znKM19kMf0ZN9aFHQeiKCHzL2+EBrml93eb3arh+ciYmnFKD1RKwvH2hUbDBV+XrNGeYiBT+QYkYWfq4WWk/GNm53p2TPoyPDumkqUu8X+/DQZWg9mf1iV5rFbxjWTZPZ7exyfRxiQevpjMbsWj2dmXkYYdU2v15z121m35Me52kT9aH1DKzH5M/GKLF9ryqbX6/8Okc1ZVu76rtth6H1LEbGhqxdtGfSR1O3YN00C7lwk6N21/QnZ2BoPQ/b9gwbVCt/ugZVk69Xn2Ecdid5attn8VTp0PoOBsPTvvpxnLh+HvBrWjetP8P8MBqu359T1cpY/5/eQus7mHvGxethqlw0Dy6AeaCy+fXaM4xHDpqb/v8Lqcq+/up9gdb3oRZj+z48a7xUg+BcLy/6inXTvcz9xNnUDyraZTUuYnrTc2j9CFbTrvFa9MswjuOwLKvQjPNJvO6563o9vt5KhgmYV21sn7n7Lm3ObcVsy99fOAOtH0WNw2o1rm1mEcuSNktTm6/7sjmkVBmX/X5U6/lCPYHWb8joUF7zMV+X9uy9vh45PCEam7aVYR6Jlwpe8xGt244Pq2Zdl73SciKt20N5fxr1HPd12/Fem87xcP1BAq1nmIByvi5nOyj46bgj/zOZ36r1/b5ujbw33DfcwfrZDhbSmH/ae5oM83Aobzig9cUaeQzv3IAhCa+Lb80w+319saMy3+4fuJlSuU3YbeYcG3aYQhlGuuASdD7/ZApf34V0nf/VfP6/igXSdoYpm9dtWr91PvtkeC5fL5jXr0g1rJPJv7XXZmzqywYprPVflI+DGZxJ6yb9s5G1rZvC1wvwrRmmovl1ZJhCnErr7fq6LxsEWqegVV9HhikEfJ2CaGyKDFMI+DoFyDAUwNcp2Mw5wtcLAF+nIPJ1ZJhCwNcpiASCDFMI+DoFm7wOXy8AfJ2CWCDIMGWAr1OwGZv6skGgdQpaXjeFrxcAvk5B5OvIMIWAr1Ow8XVfNgi0TkFTvh5sHhmmEPB1CiJfR4YpBHydgo2v+7JBoHUK2vL1e5+RYQoBX6cAGYaCE2ld6pyu1+XrvmyRIf1bz6D1j5Gx6zX5etsZJgdonQJyXw8333SGyQFap6A2X/flyYHWKajJ15FhCgFfpyAamyLDFAK+TgEyDAXwdQo2c47w9QLA1ymIfB0ZphDwdQo2Y1NfnhxonYLa8jp8vQDf6+uUB2q7HmzeZhhfnRzJuFiv9CRPxu1PV7pfmk/ul3+J4Nm/uzHph5DM3W/netOdjpd/urtxuK278vrnrSB58M5k38lvF3JcLIP7QUIvfFEHA+VJrhzyOw4TAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAuVwu/wAjaT7dOpd9YgAAAABJRU5ErkJggg==)
physics-General
physics-
In a sine wave, position of different particles at time
is shown in figure. The equation for this wave travelling along positive
can be
![](data:image/png;base64,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)
In a sine wave, position of different particles at time
is shown in figure. The equation for this wave travelling along positive
can be
![](data:image/png;base64,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)
physics-General
Maths-
The function ![sin space open parentheses x squared close parentheses](data:image/png;base64,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)
is
The function ![sin space open parentheses x squared close parentheses](data:image/png;base64,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)
is
Maths-General
Maths-
The period of the function
where [.] de-notes the greatest integer function, is
The period of the function
where [.] de-notes the greatest integer function, is
Maths-General
Maths-
The period of the function
is
The period of the function
is
Maths-General
Maths-
In any
=
In any
=
Maths-General
Maths-
In
=
In
=
Maths-General
Maths-
In ![straight triangle A B C comma sum a left parenthesis sin space B minus sin space C right parenthesis equals](data:image/png;base64,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)
In ![straight triangle A B C comma sum a left parenthesis sin space B minus sin space C right parenthesis equals](data:image/png;base64,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)
Maths-General
Maths-
If the period of
is
then n=
If the period of
is
then n=
Maths-General
Maths-
Let
where
where [ ] is the integral part of x. If the period of f(x) is
, then ![a element of](data:image/png;base64,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)
Let
where
where [ ] is the integral part of x. If the period of f(x) is
, then ![a element of](data:image/png;base64,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)
Maths-General