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Maths-

General

Easy

Question

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

$2 n π + \frac{π}{6} < θ < 2 n π + \frac{5 π}{6}$
$\frac{2 n π}{3} + \frac{π}{12} < θ < \frac{2 n π}{3} + \frac{5 π}{12}$
$2 n π - \frac{π}{6} < θ < 2 n π + \frac{π}{6}$
$\frac{n π}{3} - \frac{π^{6}}{6} < θ < \frac{n π}{3} + \frac{π}{6}$

The correct answer is: $fraction numerator 2 n pi over denominator 3 end fraction plus pi over 12 less than theta less than fraction numerator 2 n pi over denominator 3 end fraction plus fraction numerator 5 pi over denominator 12 end fraction$

sol. $2 n pi plus pi over 4 less or equal than 3 theta less or equal than 2 n pi plus fraction numerator 5 pi over denominator 4 end fraction$

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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

Physics-General

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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

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Physics-General

parallel

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

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

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

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

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

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

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

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

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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If the following equations x + y – 3 = 0(1 + $lambda$ ) x + (2 + $lambda$ ) y – 8 = 0x – (1 + $lambda$ ) y + (2 + $lambda$ ) = 0 are consistent then the value of $lambda$ is

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