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- 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:
Options- A. 173 m
- B. 200 m
- C. 273 m
- D. 300 m
- Correct Answer
- 273 m
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 = 100√3 m. AC √3 AB = tan 45° = 1 ⟹ AD = AB = 100 m. AD ∴ CD = (AC + AD) = (100√3 + 100) m = 100(√3 + 1) = (100 x 2.73) m = 273 m. - 1. If log 10 (10x) = 2.7532, then log 10 (10000x) is?
Options- A. 4.7532
- B. 5.7532
- C. 3 x 2.7532
- D. None of these Discuss
- 2. We have an angle of 2 1°/ 2 .How big it will look through a glass that magnifies things three times?
Options- A. 2 1° × 4 2
- B. 2 1° × 3 2
- C. 2 1° × 2 2
- D. 2 1° × 5 2 Discuss
- 3. A 200 m long train is running at a speed of 60 km/ hr. Find out the time it takes to pass a man standing at the platform
Options- A. 10 sec
- B. 12 sec
- C. 15 sec
- D. 18 sec Discuss
- 4. The rate of interest for the first 2 years is 5% for the next 3 years is 8% and beyond this. It is 10% per annum. If the simple interest for 8 years is Rs . 1280. What is the principal?
Options- A. Rs. 2500
- B. Rs. 2000
- C. Rs. 3200
- D. Rs. 2440 Discuss
- 5. A pillar 14 cm in diameters is 5 m high. How much material was used to construct it?
Options- A. (77 x 102)cm3
- B. (77 x 104)cm3
- C. (77 x 105)cm3
- D. (77 x 103)cm3 Discuss
- 6. The price of a product is increased by 20%. If the original price is Rs. 300, what is the final price of the product?
Options- A. 350
- B. 360
- C. 365
- D. 370 Discuss
- 7.
The expression ( - 1 ) 132 is equivalent to : 5- 1 + 3- 1
Options- A. 16 9
- B. - 15 8
- C. 15 8
- D. 17 8 Discuss
- 8. What will be the HCF of ( 2 x 3 x 7 x 9 ), ( 2 x 3 x 9 x 11 ) and ( 2 x 3 x 4 x 5 )?
Options- A. 2 x 3 x 7
- B. 2 x 3 x 9
- C. 2 x 3
- D. 2 x 7 x 9 x 11 Discuss
- 9. 75% of a number when added to 75 is equal to the number. The number is?
Options- A. 150
- B. 200
- C. 225
- D. 300 Discuss
- 10. One litre of water is evaporated from 6 litre of a solution containing 5% salt. The percentage of salt?
Options- A. 44/19%
- B. 55/7%
- C. 5%
- D. 6% Discuss
More questions
Correct Answer: 5.7532
Explanation:
log10(103.10x) = log10 103 + log10(10x)
= 3 + 2.7532
= 5.7532
Correct Answer: 2 1° × 5 2
Explanation:
Correct Answer: 12 sec
Explanation:
Speed of the train = (60 x 5/18) m/sec = 50/3 m/sec
Distance covered in passing the standing person = 200m
Required time taken= =200/(50/3) = 200 x (3/50) = 12 sec
Correct Answer: Rs. 2000
Explanation:
r1 = 5%,
r2 = 8%,
r3 = 10%,
t1 = 2 years
t2 = 3 years,
t3 = 8 - (2 + 3) = 3 years
? Principal = (Interest x 100) / [(r1 x t1) + (r2 x t2) + (r3 x t3 )]
= (1280 x 100) / (5 x 2 + 8 x 3 + 10 x 3)
= 128000/(10 + 24 + 30)
= 128000/64
=Rs. 2000
Correct Answer: (77 x 103)cm3
Explanation:
Volume of the cylinder = ?r2h
= (22/7) x 7 x 7 x 500 = 77000
= (77 x 103) cm3
Correct Answer: 360
Explanation:
Final Price = Initial price + Initial price x 20/100
= Initial price x (1+20/100)
= Rs.300x(1.2)
= Rs.360
Correct Answer: 15 8
Explanation:
Correct Answer: 2 x 3
Explanation:
Given factors
2 x 3 x 7 x 9; 2 x 3 x 9 x 11; 2 x 3 x 4 x 5
? Required HCF = Product of common prime factors having least powers = 2 x 3
Correct Answer: 300
Explanation:
75 + 75% of N = N
? N -3N/4 = 75
? N/4 = 75
? N = (75 x 4) = 300
Correct Answer: 6%
Explanation:
Salt in 6 liter = 5% of 6 = 0.30 liter
Salt in new solution = (0.30/5) x 100% = 6%
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