If V₁ is the jet velocity and V₀ is the vehicle velocity, then the propulsive efficiency of a rocket is given by

The formula to determine the height of the rocket above the ground at any time during the rocket's flight is given by: h = 119t - 7t2 where t = the time, in seconds, that has elapsed since the rocket was launched, and h = the height, in meters, of the rocket above the ground at time t. The value of h was 0 when the rocket hit the ground. How many seconds after the rocket was launched did it hit the ground?

A

17

B

10

C

7

D

0

If V₁ is the jet velocity and V₀ is the vehicle velocity, then the propulsive efficiency of a rocket is given by

A

$$\frac{{2\left( {\frac{{{{\text{V}}_0}}}{{{{\text{V}}_1}}}} \right)}}{{1 + {{\left( {\frac{{{{\text{V}}_0}}}{{{{\text{V}}_1}}}} \right)}^2}}}$$

B

$$\frac{{\frac{{{{\text{V}}_0}}}{{{{\text{V}}_1}}}}}{{1 + {{\left( {\frac{{{{\text{V}}_0}}}{{{{\text{V}}_1}}}} \right)}^2}}}$$

C

$$\frac{{{{\text{V}}_0}}}{{{{\text{V}}_0} + {{\text{V}}_1}}}$$

D

$$\frac{{{{\text{V}}_1}}}{{{{\text{V}}_0} + {{\text{V}}_1}}}$$

If V₁ is the jet velocity and V₀ is the vehicle velocity, then propulsive efficiency of a turbojet engine is

A

V₁ / (V₀ + V₁)

B

V₀ / (V₀ + V₁)

C

2V₀ / (V₀ + V₁)

D

2V₁ / (V₀ + V₁)

If V₁ is the jet velocity and V₀ is the vehicle velocity, then propulsive efficiency of a turbojet engine is

A

$$\frac{{{{\text{V}}_1}}}{{{{\text{V}}_0} + {{\text{V}}_1}}}$$

B

$$\frac{{{{\text{V}}_0}}}{{{{\text{V}}_0} + {{\text{V}}_1}}}$$

C

$$\frac{{2{{\text{V}}_0}}}{{{{\text{V}}_0} + {{\text{V}}_1}}}$$

D

$$\frac{{2{{\text{V}}_1}}}{{{{\text{V}}_0} + {{\text{V}}_1}}}$$

Consider the following statements with reference to Jet stream. 1. The Jet Stream is a geostrophic wind. 2. There are two permanent jet streams – subtropical jets at mid-latitudes and polar front jets at lower latitudes. 3. Temperature also influences the velocity of the jet stream. The lower the difference in air temperature, the faster the jet stream. Which of the statements given above is/are NOT correct?

A

1 and 2 only

B

2 and 3 only

C

1 and 3 only

D

1, 2, 3

In the question below, are given a statement followed by three courses of actions numbered I, II and III. On the basis of the information given, you have to assume everything in the statement to be true, and then decide which of the suggested courses of action logically follow(s) for pursuing. Statement: Soon you would not need to carry original copies of all vehicle papers like driving licence, vehicle registration certificate, insurance, pollution certificate or the permits issued to commercial vehicles with you. According to a ToI report, the Centre plans to amend Motor Vehicles Rules to make it legal for any citizen to carry digital vehicle documents and simultaneously making it compulsory for traffic police to accept digital version of documents. This means that you would not have to carry physical papers in your vehicle as digital copies of the certificates would be valid. Courses of action: I. The ministry has proposed installation of FASTags on the front windscreens. FASTag is a device that uses radio frequency identification (RFID) technology for making toll payments directly from the user account. II. To avail the facility, one has to store all the vehicle documents on the government's cloud-based service DigiLocker and when asked he/she can simply display the stored certificates on a smartphone or any other digital devices. These digital copies can be shared with other departments as identity and address proof. III. The government has increased the maximum load carrying capacity of heavy vehicles, including trucks, by 20-25 per cent besides scrapping the mandatory annual renewal of fitness certificates for freight carriers. Fitness certificates for trucks would now be renewed in every two years not annually. Which of the following course/courses of action can be said to be said to be a rudimentary course/courses of action?

A

Only III follows

B

Neither I nor III follows

C

None follows

D

All except III and II

E

All I, II and III follow

In the following question, five statements are given followed by four conclusions I, II, III and IV. You have to consider the given statements to be true even, if they seem to be at variance with commonly known facts. Read all the conclusions and decide which of the following logically follows from the given statements disregarding the commonly known facts. Statements: Some Blue are Color. All Color are Sky. No Rocket is Sky. All Rocket are Space. No Space is Color. Conclusions: I. Some Sky being Space is a possibility. II. Some Blue are Sky. III. Some Color being Rocket is a possibility. IV. Some Blue being Rocket, Space, Sky and Color is a possibility.

A

Only I and IV follow

B

Only I and II follow

C

Only IV follows

D

Only I, II and IV follow

E

Only III and IV follow

The propulsive power of the rocket is (where v₁ = Jet velocity, and v₂ = Aircraft velocity)

A

(v₁² -v₂²)/2g

B

(v₁ - v₂)²/2g

C

(v₁² -v₂²)/g

D

(v₁ - v₂)²/g

The propulsive power of the rocket is (where v₁ = Jet velocity and v₂ = Aircraft velocity)

A

$$\frac{{{\text{v}}_1^2 - {\text{v}}_2^2}}{{2{\text{g}}}}$$

B

$$\frac{{{{\left( {{{\text{v}}_1} - {{\text{v}}_2}} \right)}^2}}}{{2{\text{g}}}}$$

C

$$\frac{{{\text{v}}_1^2 - {\text{v}}_2^2}}{{\text{g}}}$$

D

$$\frac{{{{\left( {{{\text{v}}_1} - {{\text{v}}_2}} \right)}^2}}}{{\text{g}}}$$

For a rocket having 95% combustion efficiency, total chemical power of 17MW, a mass flow rate of propellants of 15 kg/s, and effective jet exhaust velocity of 1443 m/s, find the internal efficiency of rocket propulsion.

A

97%

B

95%

C

93%

D

91%

If V₁ is the jet velocity and V₀ is the vehicle velocity, then the propulsive efficiency of a rocket is given by

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