Maths-
General
Easy
Question
If
and
are two matrices such that the product AB is null matrix, then
is
- 0
- Multiple of
![pi](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAAKCAYAAABv7tTEAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAAHZJREFUeNpjYEAFWUD8DYj/48HlaHoYFgKxLBCvAeIAJHEQ34eBALgL1QwD94FYHJ8GFqgTkflfCNliCcT70fh7CWmKBOL5SPxwqF/xgmlAnIjEbwbiKcQEggESvxWIdwOxChBzYdMACuZzaGKmQPwJiBczUAIA0CEatBcOsq8AAABPdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPiYjeDNDMDs8L21pPjwvbWF0aD4fatH3AAAAAElFTkSuQmCC)
- An odd multiple of
/2 - None of the above
The correct answer is: An odd multiple of
/2
Given, AB = 0
![table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell therefore open square brackets table attributes columnalign center columnspacing 1em end attributes row cell cos squared invisible function application alpha cos invisible function application alpha sin invisible function application alpha end cell row cell cos invisible function application alpha sin invisible function application alpha sin squared invisible function application alpha end cell end table close square brackets cross times open square brackets table attributes columnalign center columnspacing 1em end attributes row cell cos squared invisible function application beta cos invisible function application beta sin invisible function application beta end cell row cell cos invisible function application beta sin invisible function application beta sin invisible function application beta end cell end table close square brackets end cell row cell equals open square brackets table attributes columnalign left left columnspacing 1em end attributes row 0 0 row 0 0 end table close square brackets end cell row cell not stretchy rightwards double arrow open square brackets table attributes columnspacing 1em end attributes row cell cos invisible function application alpha cos invisible function application beta cos invisible function application left parenthesis alpha minus beta right parenthesis cos invisible function application alpha sin invisible function application beta cos invisible function application left parenthesis alpha minus beta right parenthesis end cell row cell cos invisible function application beta sin invisible function application alpha cos invisible function application left parenthesis alpha minus beta right parenthesis sin invisible function application alpha sin invisible function application beta cos invisible function application left parenthesis alpha minus beta right parenthesis end cell end table close square brackets end cell row cell equals open square brackets table attributes columnalign left left columnspacing 1em end attributes row 0 0 row 0 0 end table close square brackets end cell row cell not stretchy rightwards double arrow cos invisible function application left parenthesis alpha minus beta right parenthesis equals 0 end cell row cell not stretchy rightwards double arrow alpha minus beta text is an odd multiple of end text pi over 2 end cell end 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)
Related Questions to study
maths-
If
and
Then,
if
If
and
Then,
if
maths-General
maths-
The function
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is
The function
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is
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is a function from R to R, then
is
is a function from R to R, then
is
maths-General
maths-
Which of the following functions is one-to -one?
Which of the following functions is one-to -one?
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For
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, where N is the set of natural numbers is defined as
For
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Let
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.Then,
Let
be defined by
.Then,
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The mapping
given
where N is the set of natural number, is
The mapping
given
where N is the set of natural number, is
maths-General
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defined by
is
The function
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Let A be a set containing 10 distinct elements, then the total number of distinct function from A to A is
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maths-General
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are two sets, and function
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, then the function
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are two sets, and function
is defined by
, then the function
is
maths-General
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Let
and The number of one to one functions from A to B is
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and The number of one to one functions from A to B is
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is
If denotes the set of all real numbers, then the function
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If
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for
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If
is defined by
for
, then
is (where C denotes the set of all complex numbers)
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maths-
Let
be defined as
is
Let
be defined as
is
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Let
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Let
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maths-General