admin

If ax = by, then:

by
Question:
If ax = by, then:

[A].

log a = x
b y

[B].

log a = x
log b y

[C].

log a = y
log b x

[D].

None of these

Answer: Option C

Explanation:

ax = by

log ax = log by

x log a = y log b

log a = y .
log b x

Which of the following statements is not correct?

by
Question: Which of the following statements is not correct?
[A].

log10 10 = 1

[B].

log (2 + 3) = log (2 x 3)

[C].

log10 1 = 0

[D].

log (1 + 2 + 3) = log 1 + log 2 + log 3

Answer: Option B

Explanation:

(a) Since logaa = 1, so log10 10 = 1.

(b) log (2 + 3) = log 5 and log (2 x 3) = log 6 = log 2 + log 3

      log (2 + 3) log (2 x 3)

(c) Since loga 1 = 0, so log10 1 = 0.

(d) log (1 + 2 + 3) = log 6 = log (1 x 2 x 3) = log 1 + log 2 + log 3.

So, (b) is incorrect.

A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30° with the man’s eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes 60°. What is the distance between the base of the tower and the point P?

by
Question: A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30° with the man’s eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes 60°. What is the distance between the base of the tower and the point P?
[A].

43 units

[B].

8 units

[C].

12 units

[D].

Data inadequate

Answer: Option D

Explanation:

One of AB, AD and CD must have given.

So, the data is inadequate.

Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30° and 45° respectively. If the lighthouse is 100 m high, the distance between the two ships is:

by
Question: Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30° and 45° respectively. If the lighthouse is 100 m high, the distance between the two ships is:
[A].

173 m

[B].

200 m

[C].

273 m

[D].

300 m

Answer: Option C

Explanation:

Let AB be the lighthouse and C and D be the positions of the ships.

Then, AB = 100 m, ACB = 30° and ADB = 45°.

AB = tan 30° = 1         AC = AB x 3 = 1003 m.
AC 3
AB = tan 45° = 1         AD = AB = 100 m.
AD
CD = (AC + AD) = (1003 + 100) m
= 100(3 + 1)
= (100 x 2.73) m
= 273 m.