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Maths-

General

Easy

Question

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

$\tan \frac{θ}{2}$
$\cot \frac{θ}{2}$
$\tan θ$
$\cot θ$

The correct answer is: $tan space theta$

sol. $text Use, end text sin text end text 2 theta equals 2 sin space theta cos space theta text and end text$
$cos space 2 theta equals 2 cos squared space theta minus 1$

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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 $sin space 3 theta minus cos space 3 theta greater than 0$

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

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 :

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 :

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

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

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

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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

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

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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If $omega$ ( $not equal to$ 1) is a cube root of unity, then $open vertical bar table row 1 cell 1 plus i plus omega to the power of 2 end exponent end cell cell omega to the power of 2 end exponent end cell row cell 1 minus i end cell cell negative 1 end cell cell omega to the power of 2 end exponent minus 1 end cell row cell negative i end cell cell negative i plus omega minus 1 end cell cell negative 1 end cell end table close vertical bar$ equals

If $omega$ ( $not equal to$ 1) is a cube root of unity, then $open vertical bar table row 1 cell 1 plus i plus omega to the power of 2 end exponent end cell cell omega to the power of 2 end exponent end cell row cell 1 minus i end cell cell negative 1 end cell cell omega to the power of 2 end exponent minus 1 end cell row cell negative i end cell cell negative i plus omega minus 1 end cell cell negative 1 end cell end table close vertical bar$ equals

Find the value of ‘a’ if the three equations, (a + 1)³x + (a + 2)³y = (a + 3)³, (a + 1) x + (a + 2)y = (a + 3) & x + y = 1 are consistent.

Find the value of ‘a’ if the three equations, (a + 1)³x + (a + 2)³y = (a + 3)³, (a + 1) x + (a + 2)y = (a + 3) & x + y = 1 are consistent.

The condition for the expression ax² + 2hxy + by² + 2gx + 2fy + c to be resolved into rational linear factors in the determinant form is -

The condition for the expression ax² + 2hxy + by² + 2gx + 2fy + c to be resolved into rational linear factors in the determinant form is -

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