Chemistry-
General
Easy
Question
Ethylmercaptan is prepared by the reaction of the following, followed by hydrolysis
The correct answer is: ![straight C subscript 2 straight H subscript 5 MgBr plus straight S](data:image/png;base64,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)
Related Questions to study
Maths-
Two adjacent sides of a parallelogram
are given by
and
. The side
is rotated by an acute angle
in the plane of parallelogram so that
becomes AD’. If
makes a right angle with the side AB then the cosine of angle
is given by
Two adjacent sides of a parallelogram
are given by
and
. The side
is rotated by an acute angle
in the plane of parallelogram so that
becomes AD’. If
makes a right angle with the side AB then the cosine of angle
is given by
Maths-General
Maths-
If
then ![stack b with ‾ on top equals](data:image/png;base64,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)
If
then ![stack b with ‾ on top equals](data:image/png;base64,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)
Maths-General
Maths-
If
are non coplanar vectors then the roots of equation ![open square brackets table attributes columnalign left left left columnspacing 1em end attributes row cell left square bracket b with not stretchy bar on top cross times c with not stretchy bar on top c with not stretchy bar on top cross times a with not stretchy bar on top a with not stretchy bar on top cross times b with not stretchy bar on top end cell end table close square brackets x squared](data:image/png;base64,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)
![Error converting from MathML to accessible text.](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALYAAAAjCAYAAAA5W/D0AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAApFJREFUeNrtnDEoRlEUx28GmZRk0LdJBunLIkmymSQpSZKkDJLBbpBdVskki0ySxSRJSjIYpL7BIMlmkL7Uc27vKF7k3XvPd+97z/9f/3p6Oufde37vfufd76GUvaKEIUhaQRgDzJBvyAE2BLABNgSwATYEsCEIYEMQwIYANsCGADbAhgB2DifG1CFiQgAbAtgAGwLYqQIBbAhgQ16fFXzE8P388Xm+gXxOLiXOt5Av+TzAhnK5YneRjxLnD8lDWLGhvLcii+QFPp4h70h9PAFsKHSPvUceJFfIzeixoaKAPUCukufx8Fib68ZN7r9udeRT8hT31wAbYBeibqvkWT6eJm8UEeyoIGBH/3hxMMnZw/31V60z4F4HN0K+4H7ojtwfGOwy+YSv55G8LJBfIqbJOPo53xv53rKotjFMwZao/9d97GNy0w+/o7cA+3zCtEvu5GP98XETGOwz8jD3aa3886RjfomYacfRTX4mj3K+Dp5jE7nEMAVbov6Zf1ekju/ckGAn7/Y+Xrlc8kvETDuOffKS45y5xHCBzLb+uXgJKhLIbfv1bPTLZL8KjydNTNtxvJAbHefQJIb0V/BRUcBe4d7qXdXmvWSJh8dqDfJXazSOKGcLk0T9Mwf2JnlcfX85JWtg15MfhPPbxEw7jmeBFdslhsl8S9U/c2C/eLhIV7AnyNvC+W1iph3HlkCP7RLDZL6l6p85sG/Jc3ysXzVcU/F2WCkg2AcqfkNMq8zX2O6YXyJm2nG0qXh7box7+ZLFTeQSw2S+peqfObB1ka+439R7mb0q/tboSYWRXkH0llOFez59bQMZjPmXunk+db5rFe8Vh4jhq/740zCokALYEMAG2BDA/iER/l8GlEnGPgAnZ2IirgD2KQAAA3R0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW8+KzwvbW8+PG1mZW5jZWQgY2xvc2U9Il0iIG9wZW49IlsiIHNlcGFyYXRvcnM9InwiPjxtdGFibGUgY29sdW1uYWxpZ249ImxlZnQgbGVmdCBsZWZ0IGxlZnQiIGNvbHVtbnNwYWNpbmc9IjFlbSI+PG10cj48bXRkPjxtaSBtYXRodmFyaWFudD0ibm9ybWFsIj5hPC9taT48bW8+JiN4MjAwNTsmI3gyMDA1OyYjeDIwMDU7JiN4MjAwNTs8L21vPjxtbz4rPC9tbz48bW92ZXIgYWNjZW50PSJ0cnVlIj48bWkgbWF0aHZhcmlhbnQ9Im5vcm1hbCI+YjwvbWk+PG1vIGFjY2VudD0iZmFsc2UiPiYjeEFGOzwvbW8+PC9tb3Zlcj48bW8+JiN4MjAwNTsmI3gyMDA1OyYjeDIwMDU7JiN4MjAwNTs8L21vPjxtb3ZlciBhY2NlbnQ9InRydWUiPjxtaSBtYXRodmFyaWFudD0ibm9ybWFsIj5iPC9taT48bW8gYWNjZW50PSJmYWxzZSI+JiN4QUY7PC9tbz48L21vdmVyPjxtbz4rPC9tbz48bW92ZXIgYWNjZW50PSJ0cnVlIj48bWkgbWF0aHZhcmlhbnQ9Im5vcm1hbCI+YzwvbWk+PG1vIGFjY2VudD0iZmFsc2UiPiYjeEFGOzwvbW8+PC9tb3Zlcj48bW8+JiN4MjAwNTsmI3gyMDA1OyYjeDIwMDU7JiN4MjAwNTs8L21vPjxtb3ZlciBhY2NlbnQ9InRydWUiPjxtaSBtYXRodmFyaWFudD0ibm9ybWFsIj5jPC9taT48bW8gYWNjZW50PSJmYWxzZSI+JiN4QUY7PC9tbz48L21vdmVyPjxtbz4rPC9tbz48bW92ZXIgYWNjZW50PSJ0cnVlIj48bWkgbWF0aHZhcmlhbnQ9Im5vcm1hbCI+YTwvbWk+PG1vIGFjY2VudD0iZmFsc2UiPiYjeEFGOzwvbW8+PC9tb3Zlcj48L210ZD48L210cj48L210YWJsZT48L21mZW5jZWQ+PG1pIG1hdGh2YXJpYW50PSJub3JtYWwiPng8L21pPjwvbWF0aD7ZSnisAAAAAElFTkSuQmCC)
![plus left square bracket b with not stretchy bar on top minus c with not stretchy bar on top c with not stretchy bar on top minus a with not stretchy bar on top a with not stretchy bar on top minus b with not stretchy bar on top right square bracket plus 1 equals 0](data:image/png;base64,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)
If
are non coplanar vectors then the roots of equation ![open square brackets table attributes columnalign left left left columnspacing 1em end attributes row cell left square bracket b with not stretchy bar on top cross times c with not stretchy bar on top c with not stretchy bar on top cross times a with not stretchy bar on top a with not stretchy bar on top cross times b with not stretchy bar on top end cell end table close square brackets x squared](data:image/png;base64,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)
![Error converting from MathML to accessible text.](data:image/png;base64,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)
![plus left square bracket b with not stretchy bar on top minus c with not stretchy bar on top c with not stretchy bar on top minus a with not stretchy bar on top a with not stretchy bar on top minus b with not stretchy bar on top right square bracket plus 1 equals 0](data:image/png;base64,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)
Maths-General
Maths-
If the squares of the lengths of the tangents from a point P to the circles
,
and
are in A.P then
are in
If the squares of the lengths of the tangents from a point P to the circles
,
and
are in A.P then
are in
Maths-General
Chemistry-
In the following redox reaction,
Number of moles of
reduced by 1 mole of
is
In the following redox reaction,
Number of moles of
reduced by 1 mole of
is
Chemistry-General
Maths-
The vector
equals
The vector
equals
Maths-General
Maths-
Let
be three non zero vectors,
such that
angle between
and
is
,
is perpendicular to both
and
. (where
Greatest integer function and
Fractional part of
. If
, then which of the following is correct for ![f left parenthesis x right parenthesis](data:image/png;base64,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)
Let
be three non zero vectors,
such that
angle between
and
is
,
is perpendicular to both
and
. (where
Greatest integer function and
Fractional part of
. If
, then which of the following is correct for ![f left parenthesis x right parenthesis](data:image/png;base64,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)
Maths-General
Maths-
If
and
are two values of a for which the unit vector
is linearly dependent with
and
then
is equal to
If
and
are two values of a for which the unit vector
is linearly dependent with
and
then
is equal to
Maths-General
Maths-
are three vectors such that
and
for
. Then the value of
is equal to
are three vectors such that
and
for
. Then the value of
is equal to
Maths-General
Maths-
The point which is at a distance of 12 units from the point whose position vector is
on the line which is parallel to
is
then ![alpha plus beta plus gamma equals](data:image/png;base64,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)
The point which is at a distance of 12 units from the point whose position vector is
on the line which is parallel to
is
then ![alpha plus beta plus gamma equals](data:image/png;base64,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)
Maths-General
Maths-
A unit vector
in the plane of
is such that
where
is
A unit vector
in the plane of
is such that
where
is
Maths-General
Maths-
If
. Then altitude of the parallel piped formed by the vectors
having base formed by
is
and
,
are reciprocal system of vectors)
If
. Then altitude of the parallel piped formed by the vectors
having base formed by
is
and
,
are reciprocal system of vectors)
Maths-General
Maths-
If the four faces of a tetrahedron are represented by the equations
and
then volume of the tetrahedron (in cubic units) is
If the four faces of a tetrahedron are represented by the equations
and
then volume of the tetrahedron (in cubic units) is
Maths-General
Maths-
If
where
, then the value of
is
If
where
, then the value of
is
Maths-General
Maths-
The vector
turn by a right angle about origin
so that it passes through
. then the vector in new position is
The vector
turn by a right angle about origin
so that it passes through
. then the vector in new position is
Maths-General