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Maths-

General

Easy

Question

$fraction numerator sin space 12 A over denominator sin space 4 A end fraction minus fraction numerator cos begin display style space end style 12 A over denominator cos begin display style space end style 4 A end fraction equals$

6
4
2
1

The correct answer is: 2

sol. $sin space 12 A equals sin space 3 left parenthesis 4 A right parenthesis equals 3 sin space 4 A minus 4 sin cubed space 4 A$
$cos space 12 A equals cos space 3 left parenthesis 4 A right parenthesis equals 4 cos cubed space 4 A minus 3 cos space 4 A$

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If $tan space alpha equals square root of a comma$ where a is rational number which is not a perfect square, then which of the following is a rational number.

If $tan space alpha equals square root of a comma$ where a is rational number which is not a perfect square, then which of the following is a rational number.

$cot space theta equals fraction numerator 2 tan space 71 divided by 2 to the power of ring operator 0 over denominator 1 minus tan squared space 71 divided by 2 end fraction$ then $sin space 3 theta equals$

$cot space theta equals fraction numerator 2 tan space 71 divided by 2 to the power of ring operator 0 over denominator 1 minus tan squared space 71 divided by 2 end fraction$ then $sin space 3 theta equals$

$fraction numerator sin space theta plus sin space 2 theta over denominator 1 plus cos space theta plus cos space 2 theta end fraction equals$

$fraction numerator sin space theta plus sin space 2 theta over denominator 1 plus cos space theta plus cos space 2 theta end fraction equals$

parallel

If $s i n squared space A equals x$ , then $sin space A sin space 2 A sin space 3 A sin space 4 A$ is a polynomial in $x$ , the sum of whose coefficients is

If $s i n squared space A equals x$ , then $sin space A sin space 2 A sin space 3 A sin space 4 A$ is a polynomial in $x$ , the sum of whose coefficients is

The range of all values of $theta to the power of blank$ such that $sin space 3 theta minus cos space 3 theta greater than 0$

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A me tall ic rod e cm long, A squar e cm h cross-section is heated through t" C. If Young's modulus of elasticity of the metal is E and the mean c oeffic ient of linear expansion is a per degree celsius, then the compressional force required to prevent the rod from expanding along it s length is

A me tall ic rod e cm long, A squar e cm h cross-section is heated through t" C. If Young's modulus of elasticity of the metal is E and the mean c oeffic ient of linear expansion is a per degree celsius, then the compressional force required to prevent the rod from expanding along it s length is

Physics-General

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The cylindrical tube of as pray pump has radius, R, o neend of which has n fine holes, each of radius r. If the speed of the liquid in the tube is V, the speed of the ejection of the liquid through the hole sis :

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Physics-General

A vessel with water is place don a weighing pan and it reads 600g.Now a ball ofmass40ganddensity0.80gcm-3issunkintothewater with a p in of negligible volume, as shown in figure keeping it sunk. The weight in g pan will show are a ding

A vessel with water is place don a weighing pan and it reads 600g.Now a ball ofmass40ganddensity0.80gcm-3issunkintothewater with a p in of negligible volume, as shown in figure keeping it sunk. The weight in g pan will show are a ding

Physics-General

$4 s i n space 27 to the power of 0 equals$

$4 s i n space 27 to the power of 0 equals$

parallel

if $A equals 340 to the power of ring operator$ then $square root of 1 minus sin space A end root minus square root of 1 plus sin space A end root equals$

if $A equals 340 to the power of ring operator$ then $square root of 1 minus sin space A end root minus square root of 1 plus sin space A end root equals$

$2 sin space A over 2 equals square root of 1 plus sin space A end root minus square root of 1 minus sin space A end root text then end text$

$2 sin space A over 2 equals square root of 1 plus sin space A end root minus square root of 1 minus sin space A end root text then end text$

$I f space 2 cos space A divided by 2 equals √ left parenthesis 1 plus sin space A right parenthesis plus √ left parenthesis 1 minus sin space A right parenthesis comma space t h e n space A divided by 2 space l i e s space b e t w e e n$

$I f space 2 cos space A divided by 2 equals √ left parenthesis 1 plus sin space A right parenthesis plus √ left parenthesis 1 minus sin space A right parenthesis comma space t h e n space A divided by 2 space l i e s space b e t w e e n$

parallel

$I f space 2 sin space A divided by 2 equals √ left parenthesis 1 plus sin space A right parenthesis plus √ left parenthesis 1 minus sin space A right parenthesis comma space t h e n space A divided by 2 space l i e s space b e t w e e n$

$I f space 2 sin space A divided by 2 equals √ left parenthesis 1 plus sin space A right parenthesis plus √ left parenthesis 1 minus sin space A right parenthesis comma space t h e n space A divided by 2 space l i e s space b e t w e e n$

If $2 cos space A over 2 equals square root of 1 plus sin space A end root minus square root of 1 minus sin space A end root$ , then

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Let $omega$ = – $fraction numerator 1 over denominator 2 end fraction plus i fraction numerator square root of 3 over denominator 2 end fraction$ . Then the value of the determinant $open vertical bar table row 1 1 1 row 1 cell negative 1 minus omega to the power of 2 end exponent end cell cell omega to the power of 2 end exponent end cell row 1 cell omega to the power of 2 end exponent end cell cell omega to the power of 4 end exponent end cell end table close vertical bar$ is

Let $omega$ = – $fraction numerator 1 over denominator 2 end fraction plus i fraction numerator square root of 3 over denominator 2 end fraction$ . Then the value of the determinant $open vertical bar table row 1 1 1 row 1 cell negative 1 minus omega to the power of 2 end exponent end cell cell omega to the power of 2 end exponent end cell row 1 cell omega to the power of 2 end exponent end cell cell omega to the power of 4 end exponent end cell end table close vertical bar$ is

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