Maths-

General

Easy

Question

$cos squared space open parentheses 60 to the power of ring operator plus x close parentheses minus cos squared space open parentheses 60 to the power of ring operator minus x close parentheses element of open square brackets negative m over 2 comma m over 2 close square brackets not stretchy rightwards double arrow straight m equals$

1
3
$- \sqrt{3}$
$\sqrt{3}$

Hint:

In this question, we have to find the value of m in $cos squared space open parentheses 60 to the power of ring operator plus x close parentheses minus cos squared space open parentheses 60 to the power of ring operator minus x close parentheses element of open square brackets negative m over 2 comma m over 2 close square brackets$ . For this first we will simplify the given trigonometric function then assume the range of the function to find the range of the given function. Then we will compare the range derived o the range given to find the required value of m.

The correct answer is: $square root of 3$

$space space space space cos squared open parentheses 60 plus x close parentheses minus cos squared open parentheses 60 minus x close parentheses equals open square brackets cos open parentheses 60 plus x close parentheses plus cos space open parentheses 60 minus x close parentheses close square brackets open square brackets cos space open parentheses 60 plus x close parentheses minus cos open parentheses 60 minus x close parentheses close square brackets equals open parentheses 2. cos space 60. cos space x close parentheses open parentheses negative 2. sin 60. sin space x close parentheses equals open parentheses 2.1 half. cos space x close parentheses open parentheses negative 2. fraction numerator square root of 3 over denominator 2 end fraction. sin space x close parentheses equals negative square root of 3. cos space x. sin space x equals negative fraction numerator square root of 3 over denominator 2 end fraction. sin space 2 x space F o r space m a x i m u m space v a l u e space o f space f left parenthesis x right parenthesis comma space sin space 2 x equals 1 f left parenthesis x right parenthesis equals fraction numerator negative square root of 3 over denominator 2 end fraction cross times 1 equals fraction numerator negative square root of 3 over denominator 2 end fraction F o r space m i n i m u m space v a l u e space o f space f space left parenthesis x right parenthesis comma space sin space 2 x space equals negative 1 f left parenthesis x right parenthesis equals fraction numerator negative square root of 3 over denominator 2 end fraction cross times negative 1 equals fraction numerator square root of 3 over denominator 2 end fraction A s space space cos squared open parentheses 60 plus x close parentheses minus cos squared open parentheses 60 minus x close parentheses element of open square brackets fraction numerator negative square root of 3 over denominator 2 end fraction comma fraction numerator square root of 3 over denominator 2 end fraction close square brackets S o comma space m equals square root of 3$

$cos squared space open parentheses 60 to the power of ring operator minus x close parentheses plus cos squared space open parentheses 60 to the power of ring operator plus x close parentheses element of$

space space space space cos squared space open parentheses 60 to the power of ring operator minus x close parentheses plus cos squared space open parentheses 60 to the power of ring operator plus x close parentheses equals open parentheses cos space open parentheses 60 plus x close parentheses plus cos open parentheses 60 minus x close parentheses close parentheses squared minus 2 cos space open parentheses 60 minus x close parentheses. cos space open parentheses 60 plus x close parentheses equals open parentheses 2. cos space 60. cos space x close parentheses squared minus open parentheses cos space 2 x space plus cos space 120 space close parentheses equals 4 cross times 1 fourth cross times cos squared x minus cos space 2 x space minus open parentheses fraction numerator negative 1 over denominator 2 end fraction close parentheses equals cos squared x minus cos space 2 x plus 1 half equals cos squared x minus 2 cos squared x plus 1 plus 1 half equals 3 over 2 minus cos squared x

For maximum value of f (x),

cos squared x equals 0

f (x)=

3 over 2 minus 0 equals 3 over 2

For minimum value of f (x),

cos squared x equals 1

f (x)=

3 over 2 minus 1 equals 1 half

So,

cos squared space open parentheses 60 to the power of ring operator minus x close parentheses plus cos squared space open parentheses 60 to the power of ring operator plus x close parentheses element of open square brackets 1 half comma 3 over 2 close square brackets

$cos squared space open parentheses 60 to the power of ring operator minus x close parentheses plus cos squared space open parentheses 60 to the power of ring operator plus x close parentheses element of$

Maths-General

space space space space cos squared space open parentheses 60 to the power of ring operator minus x close parentheses plus cos squared space open parentheses 60 to the power of ring operator plus x close parentheses equals open parentheses cos space open parentheses 60 plus x close parentheses plus cos open parentheses 60 minus x close parentheses close parentheses squared minus 2 cos space open parentheses 60 minus x close parentheses. cos space open parentheses 60 plus x close parentheses equals open parentheses 2. cos space 60. cos space x close parentheses squared minus open parentheses cos space 2 x space plus cos space 120 space close parentheses equals 4 cross times 1 fourth cross times cos squared x minus cos space 2 x space minus open parentheses fraction numerator negative 1 over denominator 2 end fraction close parentheses equals cos squared x minus cos space 2 x plus 1 half equals cos squared x minus 2 cos squared x plus 1 plus 1 half equals 3 over 2 minus cos squared x

For maximum value of f (x),

cos squared x equals 0

f (x)=

3 over 2 minus 0 equals 3 over 2

For minimum value of f (x),

cos squared x equals 1

f (x)=

3 over 2 minus 1 equals 1 half

So,

cos squared space open parentheses 60 to the power of ring operator minus x close parentheses plus cos squared space open parentheses 60 to the power of ring operator plus x close parentheses element of open square brackets 1 half comma 3 over 2 close square brackets

General

physics-

The effective capacitance between points $X$ and $Y$ shown in figure. Assuming $C subscript 2 end subscript equals 10 blank mu$ F and that outer capacitors are all $4 blank mu$ F is

The arrangement shows a Wheatstone bridge.
As

fraction numerator C subscript 1 end subscript over denominator C subscript 3 end subscript end fraction equals fraction numerator C subscript 4 end subscript over denominator C subscript 5 end subscript end fraction equals 1 comma blank

therefore the bridge is balanced.

fraction numerator 1 over denominator C subscript s subscript 1 end subscript end subscript end fraction equals fraction numerator 1 over denominator 4 end fraction plus fraction numerator 1 over denominator 4 end fraction equals fraction numerator 2 over denominator 4 end fraction equals fraction numerator 1 over denominator 2 end fraction comma C subscript s subscript 1 end subscript end subscript equals 2 mu blank F

Similarly,

C subscript s end subscript subscript 2 end subscript equals 2 mu blank F

therefore

effective capacitance

equals C subscript p end subscript equals C subscript s end subscript subscript 1 end subscript plus C subscript s end subscript subscript 2 end subscript equals 2 plus 2 plus equals 4 mu blank F

The effective capacitance between points $X$ and $Y$ shown in figure. Assuming $C subscript 2 end subscript equals 10 blank mu$ F and that outer capacitors are all $4 blank mu$ F is

physics-General

The arrangement shows a Wheatstone bridge.
As

fraction numerator C subscript 1 end subscript over denominator C subscript 3 end subscript end fraction equals fraction numerator C subscript 4 end subscript over denominator C subscript 5 end subscript end fraction equals 1 comma blank

therefore the bridge is balanced.

fraction numerator 1 over denominator C subscript s subscript 1 end subscript end subscript end fraction equals fraction numerator 1 over denominator 4 end fraction plus fraction numerator 1 over denominator 4 end fraction equals fraction numerator 2 over denominator 4 end fraction equals fraction numerator 1 over denominator 2 end fraction comma C subscript s subscript 1 end subscript end subscript equals 2 mu blank F

Similarly,

C subscript s end subscript subscript 2 end subscript equals 2 mu blank F

therefore

effective capacitance

equals C subscript p end subscript equals C subscript s end subscript subscript 1 end subscript plus C subscript s end subscript subscript 2 end subscript equals 2 plus 2 plus equals 4 mu blank F

General

physics-

The four capacitors, each of 25 $mu$ F are connected as shown in figure. The DC voltmeter reads 200 V. the change on each plate of capacitor is

Charge on each plate of each capacitor

Q equals plus-or-minus C V equals plus-or-minus 25 cross times 10 to the power of negative 6 end exponent cross times 200

equals plus-or-minus 5 cross times 10 to the power of negative 3 end exponent C

The four capacitors, each of 25 $mu$ F are connected as shown in figure. The DC voltmeter reads 200 V. the change on each plate of capacitor is

physics-General

Charge on each plate of each capacitor

Q equals plus-or-minus C V equals plus-or-minus 25 cross times 10 to the power of negative 6 end exponent cross times 200

equals plus-or-minus 5 cross times 10 to the power of negative 3 end exponent C

General

physics-

For the circuit shown in figure the charge on 4 $mu$ F capacitor is

Combined capacity of

1 blank mu F

and

5 mu F blank

= 1 + 5=

6 blank mu F

Now,

4 mu F blank

and

6 mu F

are in series.

therefore blank fraction numerator 1 over denominator C subscript s end subscript end fraction equals fraction numerator 1 over denominator 4 end fraction plus fraction numerator 1 over denominator 6 end fraction plus fraction numerator 3 plus 2 over denominator 12 end fraction equals fraction numerator 5 over denominator 12 end fraction

C subscript s end subscript equals fraction numerator 12 over denominator 5 end fraction mu F

Charge in the arm containing

4 mu F blank

capacitor is

q equals C subscript s end subscript cross times V equals fraction numerator 12 over denominator 5 end fraction cross times 10 equals 24 blank mu C

For the circuit shown in figure the charge on 4 $mu$ F capacitor is

physics-General

Combined capacity of

1 blank mu F

and

5 mu F blank

= 1 + 5=

6 blank mu F

Now,

4 mu F blank

and

6 mu F

are in series.

therefore blank fraction numerator 1 over denominator C subscript s end subscript end fraction equals fraction numerator 1 over denominator 4 end fraction plus fraction numerator 1 over denominator 6 end fraction plus fraction numerator 3 plus 2 over denominator 12 end fraction equals fraction numerator 5 over denominator 12 end fraction

C subscript s end subscript equals fraction numerator 12 over denominator 5 end fraction mu F

Charge in the arm containing

4 mu F blank

capacitor is

q equals C subscript s end subscript cross times V equals fraction numerator 12 over denominator 5 end fraction cross times 10 equals 24 blank mu C

General

Maths-

The minimum and maximum values of $sin to the power of 4 x plus cos to the power of 4 space x$ are

space space space space space sin to the power of 4 x plus cos to the power of 4 space x equals open parentheses sin squared x close parentheses squared plus open parentheses cos squared x close parentheses squared equals open parentheses sin squared x plus cos squared x close parentheses squared minus 2 sin squared x. cos squared x equals 1 minus fraction numerator sin squared space 2 x over denominator 2 end fraction F o r space m a x i m u m space v a l u e space o f space f left parenthesis x right parenthesis comma sin space 2 x equals 0 S o comma space f left parenthesis x right parenthesis equals 1 minus 0 over 2 equals 1 F o e space m i n i m u m space v a l u e space o f space f left parenthesis x right parenthesis comma space sin space 2 x space equals 1 S o comma space f left parenthesis x right parenthesis equals 1 minus 1 squared over 2 equals 1 half

The minimum and maximum values of $sin to the power of 4 x plus cos to the power of 4 space x$ are

Maths-General

space space space space space sin to the power of 4 x plus cos to the power of 4 space x equals open parentheses sin squared x close parentheses squared plus open parentheses cos squared x close parentheses squared equals open parentheses sin squared x plus cos squared x close parentheses squared minus 2 sin squared x. cos squared x equals 1 minus fraction numerator sin squared space 2 x over denominator 2 end fraction F o r space m a x i m u m space v a l u e space o f space f left parenthesis x right parenthesis comma sin space 2 x equals 0 S o comma space f left parenthesis x right parenthesis equals 1 minus 0 over 2 equals 1 F o e space m i n i m u m space v a l u e space o f space f left parenthesis x right parenthesis comma space sin space 2 x space equals 1 S o comma space f left parenthesis x right parenthesis equals 1 minus 1 squared over 2 equals 1 half

General

physics-

Figure shows a network of eight resistors, each equal to 2 $blank capital omega$ , connected to a 3V battery of negligible internal resistance. The current $I$ in the circuit is

physics-General

General

physics-

The equivalent resistance between $A blank a n d blank B$ in the given circuit is

physics-General

General

chemistry-

Which of the following is/are the rate determining step(s) of the given reaction?

chemistry-General

General

Maths-

Maximum value of $fraction numerator 1 over denominator square root of 7 sin space x plus square root of 29 cos space x plus 7 end fraction$

Maths-General

General

Maths-

The minimum and maximum values of $2 square root of 2 cos space x plus sin space x$ are

f(x) =

2 square root of 2 cos space x plus sin space x

As minimum and maximum value of a sin x + b cos x is

negative square root of a squared plus b squared end root a n d space space square root of a squared plus b squared end root

So, minimum value

equals negative square root of 1 squared plus open parentheses 2 square root of 2 close parentheses squared end root equals negative square root of 9 equals negative 3

Maximum value =

equals square root of 1 squared plus open parentheses 2 square root of 2 close parentheses squared end root equals square root of 9 equals 3

The minimum and maximum values of $2 square root of 2 cos space x plus sin space x$ are

Maths-General

f(x) =

2 square root of 2 cos space x plus sin space x

As minimum and maximum value of a sin x + b cos x is

negative square root of a squared plus b squared end root a n d space space square root of a squared plus b squared end root

So, minimum value

equals negative square root of 1 squared plus open parentheses 2 square root of 2 close parentheses squared end root equals negative square root of 9 equals negative 3

Maximum value =

equals square root of 1 squared plus open parentheses 2 square root of 2 close parentheses squared end root equals square root of 9 equals 3

General

chemistry-

(A) and(C) are different compound s and rotate the plane-polarised light in the same direction, andboth are dextrorotatory. Both (A) and(C) do not show diastereomers, whichof the following statements are correct?

chemistry-General

General

chemistry-

Which of the following dienes and dienophiles could be used to synthesise the following compound (A) ?

chemistry-General

General

Maths-

16 sin $x cos space x cos space 2 x cos space 4 x cos space 8 x element of$

Maths-General

General

physics-

Five conductors are meeting at a point x as shown in the figure. What is the value of current in fifth conductor?

According to Kirchhoff’s first law
(5A)+(4A)+(-3A)+(-5A)+I=0
Or I=-1A

Five conductors are meeting at a point x as shown in the figure. What is the value of current in fifth conductor?

physics-General

According to Kirchhoff’s first law
(5A)+(4A)+(-3A)+(-5A)+I=0
Or I=-1A

General

physics-

The figure shows a network of currents. The magnitude of current is shown here. The current I will be

Regarding Kirchhoff’s junction rule, the circuit can be redrawn as

Current in arm,

A B equals 10 minus 6 equals 4 A

Current in arm,

D C equals 6 plus 2 equals 8 A

Current in arm,

B C equals 4 plus 1 equals 5 A

Hence,

I equals 5 plus 8 equals 13 A

The figure shows a network of currents. The magnitude of current is shown here. The current I will be

physics-General

Regarding Kirchhoff’s junction rule, the circuit can be redrawn as

Current in arm,

A B equals 10 minus 6 equals 4 A

Current in arm,

D C equals 6 plus 2 equals 8 A

Current in arm,

B C equals 4 plus 1 equals 5 A

Hence,

I equals 5 plus 8 equals 13 A

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13

In this question, we have to find the value of m in . For this first we will simplify the given trigonometric function then assume the range of the function to find the range of the given function. Then we will compare the range derived o the range given to find the required value of m.

The correct answer is:

Related Questions to study

The effective capacitance between points and shown in figure. Assuming F and that outer capacitors are all F is

The effective capacitance between points and shown in figure. Assuming F and that outer capacitors are all F is

The four capacitors, each of 25 F are connected as shown in figure. The DC voltmeter reads 200 V. the change on each plate of capacitor is

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Figure shows a network of eight resistors, each equal to 2, connected to a 3V battery of negligible internal resistance. The current in the circuit is

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The equivalent resistance between in the given circuit is

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Which of the following is/are the rate determining step(s) of the given reaction?

Which of the following is/are the rate determining step(s) of the given reaction?

Maximum value of

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The minimum and maximum values of are

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(A) and(C) are different compound s and rotate the plane-polarised light in the same direction, andboth are dextrorotatory. Both (A) and(C) do not show diastereomers, whichof the following statements are correct?

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Which of the following dienes and dienophiles could be used to synthesise the following compound (A) ?

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16 sin

16 sin

Five conductors are meeting at a point x as shown in the figure. What is the value of current in fifth conductor?

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1
3
$- \sqrt{3}$
$\sqrt{3}$

The correct answer is: $square root of 3$

The effective capacitance between points $X$ and $Y$ shown in figure. Assuming $C subscript 2 end subscript equals 10 blank mu$ F and that outer capacitors are all $4 blank mu$ F is

The effective capacitance between points $X$ and $Y$ shown in figure. Assuming $C subscript 2 end subscript equals 10 blank mu$ F and that outer capacitors are all $4 blank mu$ F is

The four capacitors, each of 25 $mu$ F are connected as shown in figure. The DC voltmeter reads 200 V. the change on each plate of capacitor is

The four capacitors, each of 25 $mu$ F are connected as shown in figure. The DC voltmeter reads 200 V. the change on each plate of capacitor is

For the circuit shown in figure the charge on 4 $mu$ F capacitor is

For the circuit shown in figure the charge on 4 $mu$ F capacitor is

The minimum and maximum values of $sin to the power of 4 x plus cos to the power of 4 space x$ are

The minimum and maximum values of $sin to the power of 4 x plus cos to the power of 4 space x$ are

Figure shows a network of eight resistors, each equal to 2 $blank capital omega$ , connected to a 3V battery of negligible internal resistance. The current $I$ in the circuit is

Figure shows a network of eight resistors, each equal to 2 $blank capital omega$ , connected to a 3V battery of negligible internal resistance. The current $I$ in the circuit is

The equivalent resistance between $A blank a n d blank B$ in the given circuit is

The equivalent resistance between $A blank a n d blank B$ in the given circuit is

Maximum value of $fraction numerator 1 over denominator square root of 7 sin space x plus square root of 29 cos space x plus 7 end fraction$

Maximum value of $fraction numerator 1 over denominator square root of 7 sin space x plus square root of 29 cos space x plus 7 end fraction$

The minimum and maximum values of $2 square root of 2 cos space x plus sin space x$ are

The minimum and maximum values of $2 square root of 2 cos space x plus sin space x$ are

16 sin $x cos space x cos space 2 x cos space 4 x cos space 8 x element of$

16 sin $x cos space x cos space 2 x cos space 4 x cos space 8 x element of$