If the angle of projection is double the angle of inclination (α) of the plane on which particle is projected, the ratio of times of flight up the inclined plane and down the inclined plane, will be

If the angle of projection is double the angle of inclination ($$\alpha $$) of the plane on which particle is projected, the ratio of times of flight up the inclined plane and down the inclined plane, will be

A

$$\frac{1}{2}\,\cos \alpha $$

B

$$\frac{1}{2}\,\sin \alpha $$

C

$$\frac{1}{2}\,\tan \alpha $$

D

$$2\cos \alpha $$

Flight to five different cities Mumbai, Delhi, Goa, Hyderabad, Bengaluru on five different days of week in a random order. Flight to Hyderabad is either on Friday or Saturday. There are no flights on Monday and Wednesday. Weekend flight are to Goa and Delhi. A day before a flight to Hyderabad, there is flight to Mumbai. Two days after the flight to Goa, there is flight to Bengaluru. There is a flight to Delhi on ....?

A

Sunday

B

Monday

C

Tuesday

D

Saturday

Simplify the value of $$\frac{{{\text{0}}{\text{.9}} \times {\text{0}}{\text{.9}} \times {\text{0}}{\text{.9 + 0}}{\text{.2}} \times {\text{0}}{\text{.2}} \times {\text{0}}{\text{.2 + 0}}{\text{.3}} \times {\text{0}}{\text{.3}} \times {\text{0}}{\text{.3}} - {\text{3}} \times 0.9 \times {\text{0}}{\text{.2}} \times {\text{0}}{\text{.3}}}}{{{\text{0}}{\text{.9}} \times {\text{0}}{\text{.9 + 0}}{\text{.2}} \times {\text{0}}{\text{.2 + 0}}{\text{.3}} \times {\text{0}}{\text{.3}} - 0.9 \times {\text{0}}{\text{.2}} - {\text{0}}{\text{.2}} \times {\text{0}}{\text{.3}} - 0.3 \times 0.9}} = ?$$

A

1.4

B

0.054

C

0.8

D

1.0

$$\frac{{38 \times 38 \times 38 + 34 \times 34 \times 34 + 28 \times 28 \times 28 - 38 \times 34 \times 84}}{{38 \times 38 + 34 \times 34 + 28 \times 28 - 38 \times 34 - 34 \times 28 - 38 \times 28}}$$ is equal to = ?

A

24

B

32

C

44

D

100

The time of flight (t) of a projectile on an upward inclined plane is (where u = Velocity of projection, $$\alpha $$ = Angle of projection and $$\beta $$ = Inclination of the plane with the horizontal.)

A

$${\text{t}} = \frac{{{\text{g}}\cos \beta }}{{2{\text{u}}\sin \left( {\alpha - \beta } \right)}}$$

B

$${\text{t}} = \frac{{2{\text{u}}\sin \left( {\alpha - \beta } \right)}}{{{\text{g}}\cos \beta }}$$

C

$${\text{t}} = \frac{{{\text{g}}\cos \beta }}{{2{\text{u}}\sin \left( {\alpha + \beta } \right)}}$$

D

$${\text{t}} = \frac{{2{\text{u}}\sin \left( {\alpha + \beta } \right)}}{{{\text{g}}\cos \beta }}$$

The time of flight (t) of a projectile on an upward inclined plane is
(where u = Velocity of projection, $$\alpha $$ = Angle of projection and $$\beta $$ = Inclination of the plane with the horizontal.)

A

$${\text{t}} = \frac{{{\text{g}}\cos \beta }}{{2{\text{u}}\sin \left( {\alpha - \beta } \right)}}$$

B

$${\text{t}} = \frac{{2{\text{u}}\sin \left( {\alpha - \beta } \right)}}{{{\text{g}}\cos \beta }}$$

C

$${\text{t}} = \frac{{{\text{g}}\cos \beta }}{{2{\text{u}}\sin \left( {\alpha + \beta } \right)}}$$

D

$${\text{t}} = \frac{{2{\text{u}}\sin \left( {\alpha + \beta } \right)}}{{{\text{g}}\cos \beta }}$$

In the following question, a given question is followed by information in two statements. You have to decide the data in which statement (s) is sufficient to answer the question and mark your answer accordingly. Amita, Priya, Sebastian, Trisha, Mauli, Jovita and Angelin have their flights to be departed from different airports such as Mumbai airport, Delhi airport, Chandigarh airport, Bangalore airport, Assam airport, Chennai airport and Amritsar airport. From which airport does Jovita’s flight depart? I. Trisha’s flight is from Assam airport. Mauli and Priya do not have their flights from Amritsar. Angelin’s flight is not from Chennai airport. II. Amita’s flight is from Bangalore airport. Jovita’s flight is not from Mumbai airport. Sebastian’s flight is departing from Delhi airport.

A

Statement I alone is sufficient while statement II alone is not sufficient.

B

Statement II alone is sufficient while statement I alone is not sufficient.

C

Either statement I alone or statement II alone is sufficient to answer the question.

D

Neither statement I nor statement II is sufficient to answer the question.

E

Both statement I and statement II together are necessary to answer the question.

For the given values of initial velocity of projection and angle of inclination of the plane, the maximum range for a projectile projected upwards will be obtained, if the angle of projection is

A

$$\alpha = \frac{\pi }{4} - \frac{\beta }{2}$$

B

$$\alpha = \frac{\pi }{2} + \frac{\beta }{2}$$

C

$$\alpha = \frac{\beta }{2} - \frac{\pi }{2}$$

D

$$\alpha = \frac{\pi }{4} - \frac{\beta }{4}$$

E

$$\alpha = \frac{\pi }{2} - \frac{\beta }{2}$$

When a body resting on an inclined surface just begins to slide down the inclined plane under the action of its own weight, then the angle of inclination of the inclined plane is

A

Greater than the angle of repose

B

Less than the angle of repose

C

Equal to the angle of repose

D

Vertical

E

Horizontal

Flight A usually takes 1 hour more than Flight B to travel a distance of 7200 km. Due to engine trouble, the speed of flight B becomes 5/6 times of its actual speed, so it takes 36 minutes more than Flight A to complete the same journey. What is the speed of Flight A (in km/hr)?

A

800

B

900

C

750

D

720

If the angle of projection is double the angle of inclination (α) of the plane on which particle is projected, the ratio of times of flight up the inclined plane and down the inclined plane, will be

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