The angles of elevation of top and bottom of a flag kept on a flag post from 30 metres distance, are 45and 30 degrespectively. Height of the flag is [taking√3 = 1.732]

A flag of height 4 metres is standing on the top of a building. The angle of elevation of the top of the flag from a point X is 45° and the angle of elevation of the top of building from X is 30°. Point X is on the ground level. What is the height (in metres) of the building?

A

√3 + 2

B

2(√3 + 1)

C

4(√3 + 1)

D

(√3 + 1)

A map shows the elevations of Darjeeling, Gangtok, Kalimpong, Pelling, and Siliguri. Kalimpong is at a lower elevation than Gangtok, Pelling is at a lower elevation than Gangtok. Pelling is at a higher elevation than Siliguri. Darjeeling is at a higher elevation than Gangtok. Which of the following statements can be inferred from the paragraph above? i. Pelling is at a higher elevation than Kalimpong ii. Kalimpong is at a lower elevation than Darjeeling iii. Kalimpong is at a higher elevation than Siliguri iv. Siliguri is at a lower elevation than Gangtok

A

Only ii

B

Only ii and iii

C

Only ii and iv

D

Only iii and iv

A tower stands on the top of a building which is 40 metres high. The angle of depression of a point situated on the ground from the top and bottom of thetower are found to be 60and 45 degrespectively. What is the height (in metres) of tower?

A

20\u221a3

B

30(\u221a3 + 1)

C

40(\u221a3 \u2013 1)

D

50(\u221a3 \u2013 1)

The notification for six different posts - Clerk, PRO, Lecturer, Accountant, Watchman and Principal- are to be released on consecutive Fridays. The schedule of the releasing is to be in accordance with the following conditions: (i) Clerk post must be released a week before the Watchman post. (ii) Lecturer post must not be released immediately after the first release. (iii) PRO post must be released on the Friday following the Friday on which the Principal post is released. (iv) Accountant post must be released on the fifth Friday and should not be immediately preceded by the PRO post. (v) The Watchman post must not be released last. Which of the following notifications will be released immediately after the PRO post?

A

Watchman

B

Principal

C

Clerk

D

Lecturer

Which of the following statements is/are incorrect? Carnatic was a subah under Mughal Empire which came under Governor of Deccan. The Nawab of Carnatic Sadat-Ullah-Khan(1710-1732) founded independent state of Carnatic by making his office hereditary. He appointed his nephew Dost Ali Khan(1732-1740) as his successor without the permission of Nizam of Hyderabad.

A

1 and 3

B

1 and 2

C

Only 2

D

None of the above

March List I with List II : List I List II (A) Supplementary angles (I) Angles less than 90° (B) Complementary angles (II) Two angles whose sum is 180° (C) Acute angles (III) Angles greater than 90° but less than 180° (D) Obtuse angles (IV) Two angles whose sum is 90° Choose the correct answer from the options given below :

A

(A) - (III), (B) - (II), (C) - (I), (D) - (IV)

B

(A) - (IV), (B) - (II), (C) - (III), (D) - (I)

C

(A) - (II), (B) - (IV), (C) - (I), (D) - (III)

D

(A) - (II), (B) - (IV), (C) - (III), (D) - (I)

A pole is standing on the top of a house. The height of the house is 25 metres. The angle of elevation of the top of the house from point P is 45° and the angle of elevation of the top of the pole from P is 60°. Point P is on the ground level. What is the height (in metres) of the pole?

A

10(√3 + 1)

B

15(√3 + 1)

C

25(√3 - 1)

D

20(√3 - 1)

From a height of h units, a man observes the angle of elevation as α and angle of depression as β of the top and bottom respectively of a tower of height H (> 4h). To what further height should be climb so that the values of angle of elevation and angle of depression get interchanged for the top and bottom of the tower?

A

H - h units

B

H - 2h units

C

H - 3h units

D

H - 4h units

How far is point 'R' from Point 'T'? Statement (I): Point 'R' is 5 metres to the north of point 'M'. Point 'U' is 4 metres to the east of point 'R'. Point 'T' is to the west of point 'R' such that points 'U' 'R' and 'T' form a straight line of metres. Statement (II): Point 'Z' is metres to the south of point 'T'. Point 'U' is metres to the east of point 'T'. Point 'M' is metres to the east of point 'Z'. Point 'R' is metres to the north of point 'M'. Point 'R' lies on the line formed by joining points 'T' and 'U'.

A

Statement (I) and (III) are independently sufficient to answer the question.

B

Statement (I) and (II) are together required to answer the question.

C

Statement (I) alone is sufficient to answer the question while statement (II) is not sufficient to answer the question.

D

Statement (II) alone is sufficient to answer (I) is not sufficient to answer the question.

On the top of a hemispherical dome of radius r, there stands a flag of height h. From a point on the ground, the elevation of the top of the flag is 30°. After moving a distance d towards the dome, when the flag is just visible, the elevation is 45°. The ratio of h to r is equal to

A

√2 – 1

B

\(\frac{{\sqrt 3 + 1}}{{2\sqrt 2 }}\)

C

\(\frac{{\sqrt 3 + 1}}{{2\sqrt 2 }}d\)

D

\(\frac{{\left( {\sqrt 3 + 1} \right)\left( {\sqrt 2 - 1} \right)}}{{2\sqrt 2 }}d\)

The angles of elevation of top and bottom of a flag kept on a flag post from 30 metres distance, are 45and 30 degrespectively. Height of the flag is [taking√3 = 1.732]

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