Maths-
General
Easy
Question
If graph of the function y= f(x) is continuous and passes through point (3, 1) then ![stack l i m with x rightwards arrow 3 below blank fraction numerator l n left parenthesis 3 f left parenthesis x right parenthesis minus 2 right parenthesis over denominator 2 left parenthesis 1 minus f left parenthesis x right parenthesis right parenthesis end fraction text is equal end text](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMkAAAAoCAYAAABU3t4iAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAZpE86XgAABp5JREFUeNrtXWGEXUcUHk88az0lVq1Ya1mxqmqFilixqkRERMRSsaoilqiIyI8S/VFVq0R+rKr+qVWrokpERESVFatWrGXFqoi1RFVV9c/7sWI96/E6xzvPjumZuWfuvTPz3s18HHbmzZxz331z7pxz5tyzQryZuC7pTp/wvYPzYiG2/IQ+xLSkjYI8apJGS+T7DOfHQmz5CZ6wj4s1z4I4obQ/lPQL8mtJ2pX0jaQRw/xzkppILyQdMfB1wfuS1j3co9OSHkjak3QgaVvSxwHlJ0TEcUm/55h3AhezijVJc5Lq2rhfifmgEH8ryvCuha8r1nGxlonfJM1LaijX+wz7QshPiIhLkn7OMe+upBvMsXtE35xBrgtfE2568pN0TBgeMKHkJwTCl5Jua+3P0E9YQdOpiT+8CtgdZhn8JyXtMORm8V0wLLxF/EzFjKSnge5fi+gLKT8hAO7jbqK2b6KCfIC+yhguhmFtd6hb+IKSXUW/5Lz22UNJHYXmmXyfa04+8P+OGFc37F5lY8ZgGoaSnxAIu6gEavsaMa6pOeBtA7+ORrcM42B3GSf625ZrBUd/Cf8+k/G0PvB834YkbaJDH0N+QiDU0JxS268NTva+w2IGHMUdahN3JJtcF76ryG9bmKNmtkXaYZBgfLdHks5GVNKEQDgluhEpU1s1K9YIZ7zOkNFARREMORy+t3AB2s4ifJo7k6ggxyPJTwiMefQ9TG1b/6rF1Mhybk1ysvj2ziqWBB169e04vyNpWfPNQspPiIBvNf8D2guGcXo/N1Q7jX6OTS6HLzzBH+MChd1py2Ju3UA+ZWIUgxpHGGN9yE+IBIgynbe0bf3UoR8cuH2ECwn8DjiB/0PSFQY/G9+3RfckX1WKC5LuGXj4OMx7gjsJB+kwMSeo1I+86SBloYlRGlM7q39D8w1mcTG1kNZwMXP5UXzrqFRjxDg4jDyn9flKC+E6+nnldyq89lnfjUr9yJsO0k/Ik4gIu8I/Hvj2MKgJjm+8kuRN/RgEfCr4KRiQ7LjDHO/CV/VnrkW8F7HlD7SSUCkYVDrIbXQQwbH9F5+4PdsdYvNLaKpAePHzAbxZYIrMpTXDWkiTaK7uC/75DUT8/kJTd8Vg0vbOmCCM/kp0sxY6zEVN9V8U3RD/AQZoTudVEj31g+q7j4qyhV8WnN8JdHyPoVN8GfvH8UaMprVVWSXZwgXIxSlxmMVQwx1tSRsDgYeXkt7DNmQyPyioJD+JwwxuULgXeZVkl3A8qXSQp7hjqIB08mVD/7G0tiqrJPvEb27DQ/H/syPd9/tB0OdLRZRERU3QmQaZSkKlYFDpINAeNowbZvAsGqFJ5JdcleSSML+vQuE1YVnsEUoz5FFJTGMy51EpGNx0ENf+hGo5tw20IsBEmsr5AFTRZsp2UZIv0ApqWx4ImUpCpWAUSQex9SdUMwIEQZrnGfObIjtdpiXoc7m8SvK96B4eDxXdSagUDD3Nw5Sm4dqfUE0lMdn6KlYEnVKkYo2IPo0YdpwaseY6GeZcbiWhUjCKpIPY+mPCV2mhWNdGlQfyWTLItpAWGOY1HE5DSLeXvg+R0R8JM30VA0agBBfQ79FlQyT1isIXIq+XiXE7imICz0X0e8ZclYRKwSiaDpKV1hEaZZQWKgMhyhP5OtHvGHwMeKpD3honknkSrw/mQCiWCiGDb/MITa9eVRpd9jgqCuxeEHGdMVzjNJqBMG4TlfAr0T3jc3X4BxLcEjpCmEsATaFjtx3gekOVJ6piyaAqp8R4BbeEjq0E0D30nXz/CKHLE1UtyzcpSYmgSuhw3ivx/SOELk9UtZJBrbS0/d5QTmkh30oSujxRevMwwQiqhA7nXXefShKjPFF6hz2BhKmETpsx1/dOEqM8UaqG0udOVkccRpzOBpBpK6FTlpLkzX+KVZ4oKcmAAFKf//QsI6uETmxzK0Z5omRulYB15cbX0IGcYM6F9IIGcyzwbnpWwqwSOpzSQj6VJEZ5ouS4lwA47u+FJOFHcHkbDxblLj4hbRhBR/Oqp+/ALaETOwQcozxRKhlUErZxO182fH49w/4Ge3oqw37/xOP1c0vocA7sfEe3QpcnSiWDSnzC7QheKVB9J4FEtZMZ496S9LXwlw3s4kBvGOz6PC8fuSJ0eaL0n6xKwhm86S/xyeUCF58E0A+npbESHGOUJ0r/E7EE9DIoG2hSLXqUNYv2dD8gTwmgIohRniiVDCoBddyKp5T2K8edgWsGwQ7iEjWrGlJ5ogHEf6+IkawsNy5vAAAB4HRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtdW5kZXI+PG1yb3c+PG1pPmw8L21pPjxtaT5pPC9taT48bWk+bTwvbWk+PC9tcm93Pjxtcm93PjxtaT54PC9taT48bW8+JiN4MjE5Mjs8L21vPjxtbj4zPC9tbj48L21yb3c+PC9tdW5kZXI+PG1vPiYjeDIwMEE7PC9tbz48bWk+JiN4QTA7PC9taT48bWZyYWM+PG1yb3c+PG1pPmw8L21pPjxtaT5uPC9taT48bW8+KDwvbW8+PG1uPjM8L21uPjxtaT5mPC9taT48bW8+KDwvbW8+PG1pPng8L21pPjxtbz4pPC9tbz48bW8+LTwvbW8+PG1uPjI8L21uPjxtbz4pPC9tbz48L21yb3c+PG1yb3c+PG1uPjI8L21uPjxtbz4oPC9tbz48bW4+MTwvbW4+PG1vPi08L21vPjxtaT5mPC9taT48bW8+KDwvbW8+PG1pPng8L21pPjxtbz4pPC9tbz48bW8+KTwvbW8+PC9tcm93PjwvbWZyYWM+PG10ZXh0PiYjeEEwO2lzJiN4QTA7ZXF1YWw8L210ZXh0PjwvbWF0aD4L7DviAAAAAElFTkSuQmCC)
The correct answer is: ![negative fraction numerator 3 over denominator 2 end fraction](data:image/png;base64,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)
Related Questions to study
maths-
A function f from integers to integers is defined as
then the sum of digits k is
A function f from integers to integers is defined as
then the sum of digits k is
maths-General
maths-
Let f(x)
a prime number. The number of points at which f(x) is non-differentiable is ( [.] G.I.F )
Let f(x)
a prime number. The number of points at which f(x) is non-differentiable is ( [.] G.I.F )
maths-General
maths-
If graph of the function y= f(x) is continuous and passes through point (3, 1) then
is equal
If graph of the function y= f(x) is continuous and passes through point (3, 1) then
is equal
maths-General
maths-
Let f be twice differentiable real valued function satisfying
where
and
then
Statement -1:![vertical line f left parenthesis x right parenthesis vertical line less or equal than 5 for all x greater than 0](data:image/png;base64,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)
Statement -2:
is decreasing ![for all x greater than 0.](data:image/png;base64,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)
Let f be twice differentiable real valued function satisfying
where
and
then
Statement -1:![vertical line f left parenthesis x right parenthesis vertical line less or equal than 5 for all x greater than 0](data:image/png;base64,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)
Statement -2:
is decreasing ![for all x greater than 0.](data:image/png;base64,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)
maths-General
maths-
Let
Then which one of the following is true ?
Let
Then which one of the following is true ?
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andE..
then-
andE..
then-
maths-General
maths-
If for a non-zero x, af
where
then
f(x)dx=
If for a non-zero x, af
where
then
f(x)dx=
maths-General
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Which of the following is correct?
Which of the following is correct?
chemistry-General
chemistry-
In the thermal power stations, electricity is produced by producing heat energy from the burning of coal. This is an example of ..
In the thermal power stations, electricity is produced by producing heat energy from the burning of coal. This is an example of ..
chemistry-General
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Burning of a candle is an example of ..
Burning of a candle is an example of ..
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physics-
A bob attached to a string is held horizontal and released. The tension and vertical distance from point of suspension can be represented by.
![](data:image/png;base64,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)
A bob attached to a string is held horizontal and released. The tension and vertical distance from point of suspension can be represented by.
![](data:image/png;base64,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)
physics-General
physics-
A ball whose size is slightly smaller than width of the tube of radius 2.5 m is projected from bottommost point of a smooth tube fixed in a vertical plane with velocity of 10 m/s. If N1 and N2 are the normal reactions exerted by inner side and outer side of the tube on the ball
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)
A ball whose size is slightly smaller than width of the tube of radius 2.5 m is projected from bottommost point of a smooth tube fixed in a vertical plane with velocity of 10 m/s. If N1 and N2 are the normal reactions exerted by inner side and outer side of the tube on the ball
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)
physics-General
physics-
A conical pendulum is moving in a circle with angular velocity was shown. If tension in the string is T, which of following equations are correct ?
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)
A conical pendulum is moving in a circle with angular velocity was shown. If tension in the string is T, which of following equations are correct ?
![](data:image/png;base64,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)
physics-General
physics-
A pendulum bob is swinging in a vertical plane such that its angular amplitude is less than 900 . At its highest point, the string is cut. Which trajectory is possible for the bob afterwards.
A pendulum bob is swinging in a vertical plane such that its angular amplitude is less than 900 . At its highest point, the string is cut. Which trajectory is possible for the bob afterwards.
physics-General
physics-
Block of 1 kg is initially in equilibrium and is hanging by two identical springs A and B as shown in figures. If spring A is cut from lower point at t=0 then, find acceleration of block in ms–2 at t = 0.
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)
Block of 1 kg is initially in equilibrium and is hanging by two identical springs A and B as shown in figures. If spring A is cut from lower point at t=0 then, find acceleration of block in ms–2 at t = 0.
![](data:image/png;base64,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)
physics-General