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Correct Answer is: (d)

Correct Answer is: (c) a virtual image of S in water

As seen from the lens, S is at a distance less than f from the lens.

Correct Answer is: (a) 20 s 

Let the car begin to move and sound its horn at time t₀.

The sound reaches the observer in 1 s.

∴ the observer begins to hear the sound at time t₁ = t₀ + 1 s.

The displacement of the car in 20 s is (1/2) (1.1 m s^-2) (20 s)² = 220 m.

∴ at time t₂ = t₀ + 20 s, the horn is switched off and the car is 110 m away from the observer. The sound emitted by the horn at the instant it is switched off will travel to the observer in a further time (1/3) s.

∴ the observer stops hearing the sound at time t₃ = t₂ + 1/3 s.

∴ the observer hears sound for a duration of

t = t₃ - t₁ = t₂ + 1/3 s - t₁ = (t₀ + 20 s) + 1/3 s - (t₀ + 1 s) = 19 1/3 s.

Given V = 30 kV = 30 × 10³ volt

Energy, E = eV = 1.6 × 10^–19 × 30 × 10³ = 4.8 × 10^–15 joule

(a) Maximum Frequency v_max is given by, E = hv_max

v_max = E/h = (4.8 x 10^-15/6.63 x 10^-34 )

= 7.24 x 10¹⁸ Hz 

 (b) Minimum wavelength,λ_min = c/V_max = 3x 10⁸/7.28 x10¹⁸

= 4.1 × 10^–11 m = 0.041 nm

Given (ϕ₀ = 2.14 eV, v = 6 × 10¹⁴ Hz

(a) Maximum kinetic energy of emitted electron

E_k = hv – (ϕ₀ = 6.63 × 10^–34 × 6 × 10¹⁴ –2.14 × 1.6 × 10^–19

= 0.54 × 10^–19 J =(0.54 x 10^-19/1.6 x 10^-19 eV) = 0.34 eV

(b) Stopping potential v₀ is given by

E_k = eV₀ ⇒V₀ = E_k/e = 0.34eV/e = 0.34V

(c) Maximum speed (v_max ) of emitted electrons is given by

1/2 mv²_max = E_k

or v_max = √2E_k/m = √(2 x 0.54 x 10^-19/9.1 x 10^-31) 

= 3.44 x 10⁵ m/s

Energy of each photon E = hc/λ

= (6.63 x 10^-34 x 3 x 10⁸/550 x 10^-9) = 3.62 x 10^-19 J

Number of photons incident on earth’s surface per second per square metre

= (Total energy per square metre per second/ Energy of one photon)

= (9.388 x 10³/3.62 x 10^-19 )

= 3.8 x 10²¹.

When the beggar was asked to leave, he raised his eyes and looked fearfully at the road, which was gleaming in the afternoon heat. He knew his feet would burn again. However, when the children got him a pair of slippers, the beggar stared at it in amazement. He hurriedly flung his towel over his shoulder. Then, he pushed his feet into them and left, muttering a blessing to the children. In a minute, he had vanished around the corner of the street. He was tired and his feet were worn out. Since he could not have got anything better and Rukku Manni wanted him out of the house, he left in a hurry

A sharp V­shaped line between the eyebrows refers to a frown. This suggests that Rukku Manni was in an angry mood. 

Correct option is C) strings

Correct option is D) I feel sorry for her

Correct option is B) Should

Correct option is A) badly

Correct option is A) so that

Correct option is A) did

Correct option is A) also damaged

Correct option is D) Supposing

F = M\(\frac{d^2x}{dt^2}\)

 Force balance equation of ideal dashpot element.

F = B\(\frac{dx}{dt}\)

The matter can be brought to the notice of PO. If the grievance is against the PO, then the matter can be brought to the notice of DPC or the designated grievance-redressal authority at the block or district level.

No, the cost of the Job Cards, including that of the photographs affixed on it, are covered under the administrative expenses and borne as a part of the programme cost.

It must be ensured that the JC is always in the custody of the household to whom it is issued. If for any reason i.e., updation of record, it is taken by implementing agencies it should be returned on the same day after the updates. JCs found in the possession of any Panchayat or MGNREGA functionary, without a valid reason, will be considered as an offence punishable under Section 25 of the Act.

Yes, a Job Cardholder may apply for a duplicate Job Card, if the original is lost or damaged. The application will be given to the GP and shall be processed in the manner of a new application, with the difference being that the particulars may also be verified using the duplicate copy of the JC maintained by the Panchayat.

Yes, all such complaints shall be disposed off within 15 days.

A signal flow graph is a diagram that represents a set of simultaneous algebraic equations .By taking L.T the time domain differential equations governing a control system can be transferred to a set of algebraic equations in s‐domain.

No, as per Para 4, Schedule II no job card can be cancelled except where it is found to be a duplicate, or if the entire household has permanently migrated to a place outside the Gram Panchayat and no longer lives in the village.

Feedback characteristics of Control Systems:

In control system ,the feedback reduces the error, also reduces the sensitivity of the system to parameter variations .The parameter may vary due to some change in conditions .The variation in parameter affects the performance  of the system. So it is necessary to make the system in sensitive to such parameter variations.

Effect of feedback on sensitivity :

The parameters of any control system changes with the change environment conditions. Also these parameters cannot be constant throughout the life. These parameter variations affect the performance of the system. For example, the resistance of winding of a motor changes due to change in temperature during its operation.

• Sensitivity to model uncertainties 

S^T_G  = Ratio of % change in sys T.F./Ratio of % change in process T.F.

\(\frac{ΔT}{\frac{T}{\frac{ΔG}{G}}}\) = \(\frac{θ\,in\,T}{θ\,in\,G}=\frac{θ\,T\,G}{θ\,G\,T}\) 

Open loop:

Δγ(s) = ΔG(s)R(s)  ΔT(s) = \(\frac{Δγ(s)}{R(s)}\) = ΔG(s)

Closed‐loop:

T(s) = \(\frac{G}{1+GH}\) ,\(\frac{θT}{θG}=\frac{(1+GH)-GH}{(1+GH)^2}\) = \(\frac{1}{(1+GH)^2}\) 

S^T_G = \(\frac{θTG}{θGT}\) = \(\frac{1}{(1+GH)^2}\) \(\frac{G}{\frac{G}{1+GH}}\) =   \(\frac{1}{(1+GH)}\) 

→ Reduced SK below that of the open‐loop sys by increasing G*H (>>1.0).

S_H^T =  \(\frac{θTH}{θHT}\)  = \(\frac{-GH}{1+GH}\)

* if GH >>1.0 →SK =  -1 

Feedback components should not be varied with environmental changes →change in H(s) directly affects output response

Commonly used frequency response analysis Methods are:

• Bode plot

• Nyquist plot 

• Nichols chart

The transmittance is the gain acquired by the signal when it travels from one node to another node in signal flow graph.

Yes, as per Para 11, Schedule II normally, applications for work must be for at least fourteen days of continuous work, other than the works relating to access to sanitation facilities, for which application for work shall be for atleast six days of continuous work. As per Para 10, Schedule II there shall be no limit on the number of days of employment for which a person may apply, or on the number of days of employment actually provided subject to the aggregate entitlement of the household.

Within a fortnight after due verification is completed on finding out eligibility of a household, the job cards should be issued to all such eligible households.

Advantages of Bode Plot: 

• Multiplication of Magnitudes can be converted into addition 

• A simple method of sketching Bode Plot is based on asymptotic approximations. Such information on straight line asymptotes is sufficient if only rough information on frequency‐  response characteristics is needed. 

• Should the exact curve be desired, corrections can be made easily to these basic asymptotic plots. 

•    Low frequency response contains sufficient information about the physical characteristics of most of the practical systems. 

• Experimental determination of a transfer function is possible through Bode plot analysis.

A signal flow graph is a diagram that represents a set of simultaneous linear algebraic equations. By taking Laplace transfer, the time domain differential equations governing a control system can be transferred to a set of algebraic equation in s‐domain. A signal‐flow graph consists of a network in which nodes are connected by directed branches. It depicts the flow of signals from one point of a system to another and gives the relationships among the signals.

Source is the input node in the signal flow graph and it has only outgoing branches. Sink is an output node in the signal flow graph and it has only incoming branches.

Basic Elements of a Signal flow graph

•Node ‐ a point representing a signal or variable. 

• Branch – unidirectional line segment joining two nodes. 

• Path – a branch or a continuous sequence of branches that can be traversed from one node to another node. 

• Loop – a closed path that originates and terminates on the same node and along the path no node is met twice. 

• Nonteaching loops – two loops are said to be non touching if they do not have a common node.

The loops are said to be non touching if they do not have common nodes.

The work done by the field is negative. This is because the charge is moved against the force exerted by the field.

Mason’s gain formula :

The relationship between an input variable and an output variable of signal flow graph is given by the net gain between the input and the output nodes is known as overall gain of the system. Mason‘s gain rule for the determination of the overall system gain is given below.

M = \(\frac{1}{Δ}\displaystyle\sum_{K=1}^{N} \)P_kΔ_k = \(\frac{X_{out}}{X_{in}}\) 

Where M = gain between X_in and X_out

X_out = output node variable

X_in = input node variable

N = total number of forward paths

P_K = = path gain of the k_th forward path 

Δ = 1‐(sum of loop gains of all individual loop) + (sum of gain product of all possible combinations of two non touching loops) – (sum of gain products of all possible combination of three non touching loops) 

Masons Gain formula states that the overall gain of the system is

M = \(\frac{1}{Δ}\) \(\displaystyle\sum_{n=1}^{N}\)P_hΔ_h = \(\frac{X_{out}}{x_{in}}\) 

Where M =   gain between X_in and X_out

X_out = output node variable

X_in = input node variable

N = total number of forward paths

P_k = path gain of the k the forward path

Δ    = 1‐(sum of loop gains of all individual loop) + (sum of gain product of all possible combinations of two non touching loops) – (sum of gain products of all possible combination of three non touching loops)