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\(f(x) = \begin{cases}|2x^2 - 3x - 7|&; x\le - 1\\2&;-1 < x \le\frac{-\sqrt3}2\\1&; \frac{-\sqrt3}2 < x \le \frac{-1}{\sqrt2}\\1 &; \frac{-1}{\sqrt2} < x \le \frac{-1}2\\ - 1&;\frac{-1}2 < x < \frac12\\0&;\frac12 \le x < \frac1{\sqrt2}\\1&;\frac1{\sqrt2} \le x<\frac{\sqrt3}2 \\2&; \frac{\sqrt3}2 \le x< 1\\3&; 1 \le x < 2\\2x -1&;x\ge 2 \end{cases}\)

Hence, f(x) is discontinuous at 

\(x = \frac{-\sqrt3}2 , \frac{-1}{\sqrt2}, \frac{-1}2, \frac12, \frac1{\sqrt2}, \frac{\sqrt3}2, 1.\)

Total number of points of discontinuity is 7.

 Food security means capacity to ensure balanced diet to the poorest citizen of a country. Lower amounts of  cultivation of any crops by growers (say farmers) directly relates to the loss of this valuable genetic resource over time.

As we see in case of 

1.Rice :  Recent survey by FAO i.e. Food & Agricultural Organisation Rice is a global need thus is basis for food security of whole world.Over three billion people across the world eat rice every day.

2.Wheat : WHEAT is one of the main staple crops in the world and provides 20% of daily protein and calories. Its need is second after rice.

3.Tea :  Tea leaves  cultivation and its need to people around the world accounts much more. For a country with better tea production has more export to other country thus increase its levi and decrease with high demands.

4.Pulse : Pulses are an important source of protein and of micronutrients such as amino acids, iron and zinc also have a low glycaemic index and have low fat content. It is also sufficient for balanced diet to defeat hunger.

5. Rubber : Mainly its plantation causes food insecurity as its plants takes all the effective nutrients of soil thus affect all other crops to grow thus has a major implication on livlihood.

6.  Jute, Sugarcane, Cotton :  All the three crops come under commercial  expansion of crops under food security.For enhancing its cultivation deverent country has taken several steps as in INDIA Government has initiated NATIONAL FOOD SECURITY MISSION-COMMERCIAL CROPS (COTTON, JUTE & SUGARCANE).

Bus bar differential protection. 

To provide synchronising signal 

To provide voltage indication 

To facilitate the carrier communication 

Construction: The moving part is a coil wound on a light aluminium frame, mounted on a shaft made of stainless steel which is pivoted at either ends on jewel bearing made of sapphire. The coil is placed between poles of a permanent magnet. Moving system is made light as far as possible to have high torque and weight ratio. There are two phosphor bronze springs of very less resistance. This is used as terminals for the current to pass through the coil and out of coil. It is also serves the purpose of control force. 

Aluminium coil former acts as a damping device by eddy current damping. There is a knife edge pointer and a counter weight to avoid its sagging.

Working: When ever a current carrying conductor is placed in a magnetic field a force is experiences by the conductor. Moving coil meters work on this principle.

Force = BINL 

As the BNL is constant, force (F) is directly proportional to current (I). 

That is FαI. Where B is magnetic flux, N is number of turns and L is length of coil. 

(b) Jim Corbertt

Sulphation: During normal discharge of battery Pb so₄ is formed. This Pb so₄ is chemically reversible by passing current. These split up to their original constituents. But under certain condition crystalline lead sulphate is formed (Example: under charging after some time without trickle charging). This Pb so₄ is chemically irreversible. So if the sulphation occurs the battery life decreases. Efficiency decreases and the active material starts falling of the grid. 

Equation for Nickel cadmium battery. 

Ni (OH₄) + Cd +2 kOH →Ni (OH₂) + Cd OH₂ + kOH (during charging) 

(Nickel hydrate + cadmium + potassium hydroxide → Nickel hydroxide + cadmium hydroxide + potassium hydroxide.) 

Ni (OH₂) + Cd OH₂ + kOH → Ni (OH₄) + Cd +2 kOH (during discharge) 

We see that there is no change in electrolyte. It just acts as a catalyst. So there is no need to change the electrolyte. 

A simple lead acid battery consists of positive and negative electrodes Immersed in an electrolyte. The positive electrodes are Pbo₂ (lead oxide) and the negative electrodes are Pb (spongy lead). The electrolyte is dilute sulphuric acid.

On discharging the battery

Pbo₂ + Pb +2 H₂ so₄ →Pbso₄ + Pbso₄ + 2 H₂o

Lead acid is converted into lead sulphate. Spongy lead is also converted into lead sulphate and H₂ so₄ used up in the process. Only water is remain. So the specific gravity of the cell comes down. 

On charging the battery

Pbso₄ + Pbso₄ + 2 H₂o → Pbo₂ + Pb +2 H₂ so₄

Here the products are converted to their original constituents and the acid is released. So the specific gravity rises as the cell is charged. How much ever larger be the cell the voltage of each cell will be approx. 2.15 V when fully charged. 

The positive plate is made of a paste lead oxide, lead sulphate that is fitted in a mesh like material and is connected to grid. All positive plates are made common and connected to a grid. 

The negative plate is made of spongy lead also it is in mesh and connected to grid. These are also grouped together. 

These plates are separated by a micro porous separator for the diffusion of electrolyte. 

The electrolyte is prepared by adding sulphuric acid to distilled water drops by drop and stirring it until the reasoned specific gravity is attained. 

Every thing is placed in a container of hard rubber. The cells of a battery are connected by a cell connector. The container is leak proof.

Main transformer: This steps down the 3Φ 415V supply to the require value of voltage.

Synchronizing transformer for phase sequence: This gives the synchronizing signal to the firing card. That is, the pulses from this card if fed to the firing card. The firing card gives pulses to the SCR of R or Y or B depending upon which phase is positive maximum.

Half control module: This has a diode and a SCR for each phase. The firing card controls the firing angle of SCR. 

Firing card: This gives the firing pulses to SCR depending on phase sequence and the feed back from output. 

Controller card: This card monitors the output and gives signal to firing card to conduct at certain angle to maintain constant output voltage. 

Power supply card: This gives power supply for the controller card, firing card and protection.

The megohmmeter, commonly called a megger for short, is used to measure very high resistance values. It is primarily used to test the insulation of conductors. To measure high resistance values, a high voltage is applied, either by the use of a handcranked generator or electronic power supply. 

SCR is meant for silicon controlled rectifier. 

Clamp-on ammeter is used to check the current in a circuit, without being physically connected in a circuit. They are convenient to use in the field since the circuit does not have to be opened to take a current reading. 

Specific gravity of a substance is the comparison of density of the substance with the density of pure water. 

Specific gravity = Density of the substance / density of pure water. 

= kg / cm² kg / cm² 

= (No unit)

Specific gravity is only number. 

It has no unit. Specific gravity of pure water is one.

Specific gravity of fully charged lead acid battery is 1.215. Specific gravity should always be corrected to 27°C. 

Corrected specific gravity is equal to indicated specific gravity ± (t - 27°C)*0.0007. 

Indicated specific gravity = 1.205 and ‘t’ means electrolyte temperature. 

We can measure reactive power of 3 phase circuit by dingle phase wattmeter by connecting the current coil in series with a line or load and connecting the pressure coil across the other two lines. 

Reactive power = 3√ V * I * sinϕ Watts. 

It is an instrument to measure voltage. It is always connected in parallel to the power supply. 

The function of heat exchanger is to transfer heat efficiently and economically between two fluids. Heat is transferred from the fluid, which has higher temperature to the fluid, which has lower temperature. The modes of heat transfer are, 

a. Conduction – Heat transfer in solids by momentum of molecules. 

b. Convection – Heat transfer in liquids by movement of molecules. 

c. Radiation – Heat transfer by energy waves.

There are three types of flow in heat exchangers 

a. Parallel flow. 

b. Counter flow. 

c. Transverse flow. 

Correct option is A) silent

• The number of road accident deaths of females are less compared to males.  
• The reasons are: they follow road rules, they are cautious and responsible.

• Women has been allowed to inherit property, legislation related to marriage divorce have been passed.
• It has allowed for equal status and wages at the work place.
• Girls education has been encouraged. More and more schools have been set up.

The angle of incidence corresponding to which angle of refraction becomes 90º is called the critical angle.

Conditions:

i Light should travel from denser medium to rarer medium

ii For total internal reflection angle of incidence must be greater than critical angle.

We know z axis makes an angle 90° with the x axis and y axis and makes an angle 0° with z axis itself.

So the dcs of z axis are (cos90°, cos90°, cos0°) = (0,0,1).

When we charge a metal sphere negatively by bringing a positively charged rod near its left surface, the electrons get attracted towards the left side and positive charges on right side. Now, when the sphere is earthed the electrons from earth flow to the sphere to neutralise the positive charge collected on the right side. Now, when the positively charged rod is removed the negative charges get distributed over the metal surface and the sphere gets negatively charged.

Resistance, R = P l/A

diameter d = 1 mm

r = d/2 = 0.5 mm

or r = 5 x 10^-4 m

R = 1.963 x 10^-8 x \(\frac2{\pi(5\times10^{-4})^2}\)

= 1.963 x 2/25π

= 0.05 π

Current, i = E/r+R

= 3/1+0.05 A

= 2.86 A

When the natural frequency of the air column is tuned to the frequency of the vibrating tuning fork, resonance occurs and a loud sound results. The vibrating tuning fork forces air particles within the air column into vibrational motion. In this resonance situation, the tuning fork and the air column share the same vibrational frequency. 

Hence, resonance occurs when two interconnected objects share the same vibrational frequency. When one of the objects is vibrating, it forces the second object into vibrational motion. The result is a large vibration. And if a sound wave within the audible range of human hearing is produced, a loud sound is heard.

a =10 ms^-2

t = 2s; 

w = 0;

v = ? 

v = u + at 

v = 0 + 10 × 2 

= 20 ms^-1

If a system of three concurrent and coplanar forces is in equilibrium, then Lami’s theorem states that the magnitude of each force of the system is proportional to sine of the angle between the other two forces. The constant of proportionality is same for all three forces

(d) decreases with distance from centre

(c) C remains same, Q doubled

The photodiode is reverse biased for operating in the photoconductive mode. As the photodiode is in reverse bias the width of the depletion layer increases. This reduces the junction capacitance and thereby the response time. In effect, the reverse bias causes faster response times for the photodiode. The photocurrent is linearly proportional to the illuminance.