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Maths-

General

Easy

Question

The general solution of the equation $sin invisible function application x minus 3 sin invisible function application 2 x plus sin invisible function application 3 x equals cos invisible function application x minus 3 cos invisible function application 2 x plus cos invisible function application 3 x$ is $left parenthesis n element of Z right parenthesis$

$n π + \frac{π}{8}$
$\frac{n π}{2} + \frac{π}{8}$
${(- 1)}^{n} \frac{n π}{2} + \frac{π}{8}$
$2 n π + \cos^{- 1} \frac{2}{3}$

The correct answer is: $fraction numerator n pi over denominator 2 end fraction plus fraction numerator pi over denominator 8 end fraction$

The given equation is
$sin invisible function application x minus 3 sin invisible function application 2 x plus sin invisible function application 3 x equals cos invisible function application x minus 3 cos invisible function application 2 x plus cos invisible function application 3 x$
$rightwards double arrow 2 sin invisible function application 2 x cos invisible function application x minus 3 sin invisible function application 2 x equals 2 cos invisible function application 2 x cos invisible function application x minus 3 cos invisible function application 2 x$
$rightwards double arrow sin invisible function application 2 x blank open parentheses 2 cos invisible function application x minus 3 close parentheses equals cos invisible function application 2 x blank left parenthesis 2 cos invisible function application x minus 3 right parenthesis$
$rightwards double arrow sin invisible function application 2 x equals cos invisible function application 2 x$ (as $cos invisible function application x not equal to 3 divided by 2$ )
$rightwards double arrow tan invisible function application 2 x equals 1 blank rightwards double arrow 2 x equals n pi plus pi divided by 4 rightwards double arrow x equals fraction numerator n pi over denominator 2 end fraction plus fraction numerator pi over denominator 8 end fraction comma blank n element of Z$

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A short solenoid of length 4 cm, radius 2 cm and 100 turns is placed inside and on the axis of a long solenoid of length 80 cm and 1500 turns. A current of 3 A flows through the short solenoid. The mutual inductance of two solenoids is

A short solenoid of length 4 cm, radius 2 cm and 100 turns is placed inside and on the axis of a long solenoid of length 80 cm and 1500 turns. A current of 3 A flows through the short solenoid. The mutual inductance of two solenoids is

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The number of turns in primary coil of a transformer is 20 and the number of turns in the secondary is 10. If the voltage across the primary is 220 V, what is the voltage across the secondary?

The number of turns in primary coil of a transformer is 20 and the number of turns in the secondary is 10. If the voltage across the primary is 220 V, what is the voltage across the secondary?

Physics-General

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$I f tan invisible function application fraction numerator pi over denominator 9 end fraction comma blank x blank a n d tan invisible function application fraction numerator 5 pi over denominator 18 end fraction$ are in A.P. and $tan invisible function application fraction numerator pi over denominator 9 end fraction comma blank y blank a n d tan invisible function application fraction numerator 7 pi over denominator 18 end fraction$ are also in A.P., then

$I f tan invisible function application fraction numerator pi over denominator 9 end fraction comma blank x blank a n d tan invisible function application fraction numerator 5 pi over denominator 18 end fraction$ are in A.P. and $tan invisible function application fraction numerator pi over denominator 9 end fraction comma blank y blank a n d tan invisible function application fraction numerator 7 pi over denominator 18 end fraction$ are also in A.P., then

Sum of all the solutions in $open square brackets 0 comma blank 4 pi close square brackets$ of the equation $tan invisible function application x plus cot invisible function application x plus 1 equals cos invisible function application open parentheses x plus fraction numerator pi over denominator 4 end fraction close parentheses$ is

Sum of all the solutions in $open square brackets 0 comma blank 4 pi close square brackets$ of the equation $tan invisible function application x plus cot invisible function application x plus 1 equals cos invisible function application open parentheses x plus fraction numerator pi over denominator 4 end fraction close parentheses$ is

If $blank open parentheses 1 minus tan invisible function application theta close parentheses open parentheses 1 plus tan invisible function application theta close parentheses sec to the power of 2 end exponent invisible function application theta plus 2 to the power of tan to the power of 2 end exponent invisible function application theta end exponent equals 0 comma$ then the number of values of $theta$ in the interval $left parenthesis negative pi divided by 2 comma blank pi divided by 2 right parenthesis$ are

If $blank open parentheses 1 minus tan invisible function application theta close parentheses open parentheses 1 plus tan invisible function application theta close parentheses sec to the power of 2 end exponent invisible function application theta plus 2 to the power of tan to the power of 2 end exponent invisible function application theta end exponent equals 0 comma$ then the number of values of $theta$ in the interval $left parenthesis negative pi divided by 2 comma blank pi divided by 2 right parenthesis$ are

parallel

If $open vertical bar 2 sin invisible function application theta minus c o s e c blank theta close vertical bar greater or equal than 1$ and $theta not equal to fraction numerator n pi over denominator 2 end fraction comma blank n element of I$ , then

If $open vertical bar 2 sin invisible function application theta minus c o s e c blank theta close vertical bar greater or equal than 1$ and $theta not equal to fraction numerator n pi over denominator 2 end fraction comma blank n element of I$ , then

If $S equals open curly brackets x element of N blank colon 2 plus log subscript 2 end subscript invisible function application square root of x plus 1 end root greater than 1 minus log subscript 1 divided by 2 end subscript invisible function application square root of 4 minus x to the power of 2 end exponent end root close curly brackets comma$ then

If $S equals open curly brackets x element of N blank colon 2 plus log subscript 2 end subscript invisible function application square root of x plus 1 end root greater than 1 minus log subscript 1 divided by 2 end subscript invisible function application square root of 4 minus x to the power of 2 end exponent end root close curly brackets comma$ then

$log subscript 4 end subscript invisible function application 18$ is

$log subscript 4 end subscript invisible function application 18$ is

parallel

If $sin invisible function application 6 theta plus sin invisible function application 4 theta plus sin invisible function application 2 theta equals 0 comma$ then $theta blank$ is equal to $blank open parentheses n element of Z close parentheses$

If $sin invisible function application 6 theta plus sin invisible function application 4 theta plus sin invisible function application 2 theta equals 0 comma$ then $theta blank$ is equal to $blank open parentheses n element of Z close parentheses$

The area of the circle and the area of a regular polygon of $n$ sides and of perimeter equal to that of the circle are in the ratio of

The area of the circle and the area of a regular polygon of $n$ sides and of perimeter equal to that of the circle are in the ratio of

$I f blank x element of open parentheses pi comma fraction numerator 3 pi over denominator 2 end fraction close parentheses comma blank t h e n blank 4 cos to the power of 2 end exponent invisible function application open parentheses fraction numerator pi over denominator 4 end fraction minus fraction numerator x over denominator 2 end fraction close parentheses plus square root of 4 sin to the power of 4 end exponent invisible function application x plus sin to the power of 2 end exponent invisible function application 2 x end root$ is always equal to

$I f blank x element of open parentheses pi comma fraction numerator 3 pi over denominator 2 end fraction close parentheses comma blank t h e n blank 4 cos to the power of 2 end exponent invisible function application open parentheses fraction numerator pi over denominator 4 end fraction minus fraction numerator x over denominator 2 end fraction close parentheses plus square root of 4 sin to the power of 4 end exponent invisible function application x plus sin to the power of 2 end exponent invisible function application 2 x end root$ is always equal to

parallel

If $tan invisible function application theta plus sin invisible function application theta equals m blank a n d tan invisible function application theta minus sin invisible function application theta equals n comma$ then

If $tan invisible function application theta plus sin invisible function application theta equals m blank a n d tan invisible function application theta minus sin invisible function application theta equals n comma$ then

$I f blank x subscript 1 end subscript blank a n d blank x subscript 2 end subscript$ are two distinct roots of the equation $a cos invisible function application x plus b sin invisible function application x equals c comma blank t h e n tan invisible function application fraction numerator x subscript 1 end subscript plus x subscript 2 end subscript over denominator 2 end fraction$ is equal to

$I f blank x subscript 1 end subscript blank a n d blank x subscript 2 end subscript$ are two distinct roots of the equation $a cos invisible function application x plus b sin invisible function application x equals c comma blank t h e n tan invisible function application fraction numerator x subscript 1 end subscript plus x subscript 2 end subscript over denominator 2 end fraction$ is equal to

$I f fraction numerator sin invisible function application open parentheses x plus y close parentheses over denominator sin invisible function application open parentheses x minus y close parentheses end fraction equals fraction numerator a plus b over denominator a minus b end fraction comma blank t h e n fraction numerator tan invisible function application x over denominator tan invisible function application y end fraction blank i s blank e q u a l blank t o$

$I f fraction numerator sin invisible function application open parentheses x plus y close parentheses over denominator sin invisible function application open parentheses x minus y close parentheses end fraction equals fraction numerator a plus b over denominator a minus b end fraction comma blank t h e n fraction numerator tan invisible function application x over denominator tan invisible function application y end fraction blank i s blank e q u a l blank t o$

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