Maths-
General
Easy

Question

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

  1. [-1,1]
  2. [negative 1 fourth comma 1 fourth]
  3. [negative 3 over 4 comma 3 over 4]
  4. [negative fraction numerator square root of 3 over denominator 2 end fraction comma fraction numerator square root of 3 over denominator 2 end fraction]

The correct answer is: [-1,1]

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Related Questions to study

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
General
physics-

The equivalent resistance between the terminals A blank a n d blank B in the following circuit is


10capital omega in series with 10capital omega will gives
(10+10)=20capital omega
and 10capital omega in series with 10capital omega will gives
(10+10)=20capital omega

20capital omega in parallel with 20capital omega will gives
open parentheses fraction numerator 20 cross times 20 over denominator 20 plus 20 end fraction close parentheses equals fraction numerator 400 over denominator 40 end fraction equals 10 capital omega

Resistance in series between points A and D
=5+10+5
=20capital omega

The equivalent resistance between the terminals A blank a n d blank B in the following circuit is

physics-General

10capital omega in series with 10capital omega will gives
(10+10)=20capital omega
and 10capital omega in series with 10capital omega will gives
(10+10)=20capital omega

20capital omega in parallel with 20capital omega will gives
open parentheses fraction numerator 20 cross times 20 over denominator 20 plus 20 end fraction close parentheses equals fraction numerator 400 over denominator 40 end fraction equals 10 capital omega

Resistance in series between points A and D
=5+10+5
=20capital omega
General
physics-

The equivalent resistance between points A and B of an infinite network of resistances, each of 1blank capital omega, connected as shown is

Let x be the equivalent resistance of entire network between A and B. Hence, we have

R subscript A B end subscript equals 1 plus resistance of parallel combination of 1capital omega and x capital omega
therefore blank R subscript A B end subscript equals 1 plus fraction numerator x over denominator 1 plus x end fraction
therefore blank x equals 1 plus fraction numerator x over denominator 1 plus x end fraction
⟹ x plus x to the power of 2 end exponent equals 1 plus x plus x
⟹ x to the power of 2 end exponent minus x minus 1 equals 0
⟹ x equals fraction numerator 1 plus square root of 1 plus 4 end root over denominator 2 end fraction
equals fraction numerator 1 plus square root of 5 over denominator 2 end fraction capital omega

The equivalent resistance between points A and B of an infinite network of resistances, each of 1blank capital omega, connected as shown is

physics-General
Let x be the equivalent resistance of entire network between A and B. Hence, we have

R subscript A B end subscript equals 1 plus resistance of parallel combination of 1capital omega and x capital omega
therefore blank R subscript A B end subscript equals 1 plus fraction numerator x over denominator 1 plus x end fraction
therefore blank x equals 1 plus fraction numerator x over denominator 1 plus x end fraction
⟹ x plus x to the power of 2 end exponent equals 1 plus x plus x
⟹ x to the power of 2 end exponent minus x minus 1 equals 0
⟹ x equals fraction numerator 1 plus square root of 1 plus 4 end root over denominator 2 end fraction
equals fraction numerator 1 plus square root of 5 over denominator 2 end fraction capital omega
General
maths-

The period of sin space left parenthesis pi sin space theta right parenthesis is

The period of sin space left parenthesis pi sin space theta right parenthesis is

maths-General
General
maths-

The period of fraction numerator sin space left parenthesis 2 pi x plus a right parenthesis over denominator sin space left parenthesis 2 pi x plus b right parenthesis end fraction is

The period of fraction numerator sin space left parenthesis 2 pi x plus a right parenthesis over denominator sin space left parenthesis 2 pi x plus b right parenthesis end fraction is

maths-General
General
maths-

Period of tan 4x+sec 4x is

Period of tan 4x+sec 4x is

maths-General
General
maths-

The cotangent function whose period 3 pi is

The cotangent function whose period 3 pi is

maths-General
General
physics-

Thirteen resistances each of resistance Rcapital omega are connected in the circuit as shown in the figure. The effective resistance between points A and B is

Resistance R bisecting the circuit can be neglected due to the symmetry of the circuit.
Now, there are four triangles
Effective resistance of each triangle
fraction numerator 1 over denominator R to the power of ´ end exponent end fraction equals fraction numerator 1 over denominator R end fraction plus fraction numerator 1 over denominator 2 R end fraction
equals fraction numerator 2 plus 1 over denominator 2 R end fraction equals fraction numerator 3 over denominator 2 R end fraction
therefore R to the power of ´ end exponent equals fraction numerator 2 over denominator 3 end fraction R
Now the given circuit reduced to

Therefore, effective resistance between A and B,
fraction numerator 1 over denominator R subscript A B end subscript end fraction equals fraction numerator 1 over denominator 2 R to the power of ´ end exponent end fraction plus fraction numerator 1 over denominator 2 R to the power of ´ end exponent end fraction equals fraction numerator 1 over denominator R to the power of ´ end exponent end fraction
⟹ R subscript A B end subscript equals R to the power of ´ end exponent equals fraction numerator 2 R over denominator 3 end fraction capital omega

Thirteen resistances each of resistance Rcapital omega are connected in the circuit as shown in the figure. The effective resistance between points A and B is

physics-General
Resistance R bisecting the circuit can be neglected due to the symmetry of the circuit.
Now, there are four triangles
Effective resistance of each triangle
fraction numerator 1 over denominator R to the power of ´ end exponent end fraction equals fraction numerator 1 over denominator R end fraction plus fraction numerator 1 over denominator 2 R end fraction
equals fraction numerator 2 plus 1 over denominator 2 R end fraction equals fraction numerator 3 over denominator 2 R end fraction
therefore R to the power of ´ end exponent equals fraction numerator 2 over denominator 3 end fraction R
Now the given circuit reduced to

Therefore, effective resistance between A and B,
fraction numerator 1 over denominator R subscript A B end subscript end fraction equals fraction numerator 1 over denominator 2 R to the power of ´ end exponent end fraction plus fraction numerator 1 over denominator 2 R to the power of ´ end exponent end fraction equals fraction numerator 1 over denominator R to the power of ´ end exponent end fraction
⟹ R subscript A B end subscript equals R to the power of ´ end exponent equals fraction numerator 2 R over denominator 3 end fraction capital omega
General
physics-

Six resistors, each of value 3blank capital omega are connected as shown in the figure. A cell of emf 3V is connected across A B.The effective resistance across A B and the current through the arm A B will be

The equivalent circuit is shown as

We can emit the resistance in the arm DF as balance condition is satisfied.
Therefore, the 3capital omega resistances in arm CD and DE are in series.
therefore R to the power of ´ end exponent equals 3 plus 3 equals 6 capital omega
Similarly, for arms CF and FE, R’’=6capital omega
R to the power of ´ blank end exponent a n d R ´ ´ are in parallel
therefore blank fraction numerator 1 over denominator R to the power of ´ ´ ´ end exponent end fraction equals fraction numerator 1 over denominator 6 end fraction plus fraction numerator 1 over denominator 6 end fraction equals fraction numerator 2 over denominator 6 end fraction equals fraction numerator 1 over denominator 3 end fraction
R’’’=3capital omega
Now, R’’’ and 3capital omega resistances are in parallel
therefore blank fraction numerator 1 over denominator R end fraction equals fraction numerator 1 over denominator 3 end fraction plus fraction numerator 1 over denominator 3 end fraction
⟹ R equals 1.5 capital omega
Moreover, V across AB=3V and resistance in the arm=3capital omega
∴ Current through the arm will be
equals fraction numerator 3 V over denominator 3 capital omega end fraction equals 1 A.

Six resistors, each of value 3blank capital omega are connected as shown in the figure. A cell of emf 3V is connected across A B.The effective resistance across A B and the current through the arm A B will be

physics-General
The equivalent circuit is shown as

We can emit the resistance in the arm DF as balance condition is satisfied.
Therefore, the 3capital omega resistances in arm CD and DE are in series.
therefore R to the power of ´ end exponent equals 3 plus 3 equals 6 capital omega
Similarly, for arms CF and FE, R’’=6capital omega
R to the power of ´ blank end exponent a n d R ´ ´ are in parallel
therefore blank fraction numerator 1 over denominator R to the power of ´ ´ ´ end exponent end fraction equals fraction numerator 1 over denominator 6 end fraction plus fraction numerator 1 over denominator 6 end fraction equals fraction numerator 2 over denominator 6 end fraction equals fraction numerator 1 over denominator 3 end fraction
R’’’=3capital omega
Now, R’’’ and 3capital omega resistances are in parallel
therefore blank fraction numerator 1 over denominator R end fraction equals fraction numerator 1 over denominator 3 end fraction plus fraction numerator 1 over denominator 3 end fraction
⟹ R equals 1.5 capital omega
Moreover, V across AB=3V and resistance in the arm=3capital omega
∴ Current through the arm will be
equals fraction numerator 3 V over denominator 3 capital omega end fraction equals 1 A.
General
physics-

In the circuit shown the value of I in ampere is

We can simplify the network as shown

So, net resistance,
R=2.4+1.6=4.0capital omega
Therefore, current from the battery.
i equals fraction numerator V over denominator R end fraction equals fraction numerator 4 over denominator 4 end fraction equals 1 A
Now, from the circuit (b),
4I’ =6I
⟹ I to the power of ´ end exponent equals fraction numerator 3 over denominator 2 end fraction I
But i=I+I’
equals I plus fraction numerator 3 over denominator 2 end fraction I equals fraction numerator 5 over denominator 2 end fraction I
therefore blank 1 equals fraction numerator 5 over denominator 2 end fraction I
⟹ I equals fraction numerator 2 over denominator 5 end fraction equals 0.4 A

In the circuit shown the value of I in ampere is

physics-General
We can simplify the network as shown

So, net resistance,
R=2.4+1.6=4.0capital omega
Therefore, current from the battery.
i equals fraction numerator V over denominator R end fraction equals fraction numerator 4 over denominator 4 end fraction equals 1 A
Now, from the circuit (b),
4I’ =6I
⟹ I to the power of ´ end exponent equals fraction numerator 3 over denominator 2 end fraction I
But i=I+I’
equals I plus fraction numerator 3 over denominator 2 end fraction I equals fraction numerator 5 over denominator 2 end fraction I
therefore blank 1 equals fraction numerator 5 over denominator 2 end fraction I
⟹ I equals fraction numerator 2 over denominator 5 end fraction equals 0.4 A
General
physics-

The given graph shows the variation of velocity with displacement. Which one of the graph given below correctly represents the variation of acceleration with displacement?

The v minus x equation from the given graph can be written as,
v equals open parentheses negative fraction numerator v subscript 0 end subscript over denominator x subscript 0 end subscript end fraction close parentheses blank x plus v subscript 0 end subscript blank open parentheses i close parentheses
therefore blank a equals fraction numerator d v over denominator d t end fraction equals open parentheses negative fraction numerator v subscript 0 end subscript over denominator x subscript 0 end subscript end fraction close parentheses fraction numerator d x over denominator d t end fraction equals open parentheses negative fraction numerator v subscript 0 end subscript over denominator x subscript 0 end subscript end fraction close parentheses blank v
Substituting v from Eq. (i), we get
a equals open parentheses negative fraction numerator v subscript 0 end subscript over denominator x subscript 0 end subscript end fraction close parentheses open square brackets open parentheses negative fraction numerator v subscript 0 end subscript over denominator x subscript 0 end subscript end fraction close parentheses blank x plus v subscript 0 end subscript close square brackets
blank a equals open parentheses fraction numerator v subscript 0 end subscript over denominator x subscript 0 end subscript end fraction close parentheses to the power of 2 end exponent blank x minus fraction numerator v subscript 0 end subscript superscript 2 end superscript over denominator x subscript 0 end subscript end fraction
Thus, a minus x graph is a straight line with positive slope and negative intercept.

The given graph shows the variation of velocity with displacement. Which one of the graph given below correctly represents the variation of acceleration with displacement?

physics-General
The v minus x equation from the given graph can be written as,
v equals open parentheses negative fraction numerator v subscript 0 end subscript over denominator x subscript 0 end subscript end fraction close parentheses blank x plus v subscript 0 end subscript blank open parentheses i close parentheses
therefore blank a equals fraction numerator d v over denominator d t end fraction equals open parentheses negative fraction numerator v subscript 0 end subscript over denominator x subscript 0 end subscript end fraction close parentheses fraction numerator d x over denominator d t end fraction equals open parentheses negative fraction numerator v subscript 0 end subscript over denominator x subscript 0 end subscript end fraction close parentheses blank v
Substituting v from Eq. (i), we get
a equals open parentheses negative fraction numerator v subscript 0 end subscript over denominator x subscript 0 end subscript end fraction close parentheses open square brackets open parentheses negative fraction numerator v subscript 0 end subscript over denominator x subscript 0 end subscript end fraction close parentheses blank x plus v subscript 0 end subscript close square brackets
blank a equals open parentheses fraction numerator v subscript 0 end subscript over denominator x subscript 0 end subscript end fraction close parentheses to the power of 2 end exponent blank x minus fraction numerator v subscript 0 end subscript superscript 2 end superscript over denominator x subscript 0 end subscript end fraction
Thus, a minus x graph is a straight line with positive slope and negative intercept.
General
physics-

The displacement-time graphs of two moving particles make angles of 30 degree blank a n d blank 45 degree with the x minusaxis. The ratio of their velocities is

Slope of displacement time-graph is velocity
fraction numerator v subscript 1 end subscript over denominator v subscript 2 end subscript end fraction equals fraction numerator tan invisible function application theta subscript 1 end subscript over denominator tan invisible function application theta subscript 2 end subscript end fraction equals fraction numerator tan invisible function application 30 degree over denominator tan invisible function application 45 degree end fraction equals fraction numerator 1 over denominator square root of 3 end fraction
v subscript 1 end subscript blank colon v subscript 2 end subscript equals 1 blank colon blank square root of 3

The displacement-time graphs of two moving particles make angles of 30 degree blank a n d blank 45 degree with the x minusaxis. The ratio of their velocities is

physics-General
Slope of displacement time-graph is velocity
fraction numerator v subscript 1 end subscript over denominator v subscript 2 end subscript end fraction equals fraction numerator tan invisible function application theta subscript 1 end subscript over denominator tan invisible function application theta subscript 2 end subscript end fraction equals fraction numerator tan invisible function application 30 degree over denominator tan invisible function application 45 degree end fraction equals fraction numerator 1 over denominator square root of 3 end fraction
v subscript 1 end subscript blank colon v subscript 2 end subscript equals 1 blank colon blank square root of 3
General
maths-

The minimum and maximum values of 8 cos space 3 x minus 15 sin 3x are

The minimum and maximum values of 8 cos space 3 x minus 15 sin 3x are

maths-General
General
maths-

Extreme Values:The range of f left parenthesis x right parenthesis equals negative 3 cos space square root of 3 plus x plus x squared end root

Extreme Values:The range of f left parenthesis x right parenthesis equals negative 3 cos space square root of 3 plus x plus x squared end root

maths-General