Question
51
गणित
Mr Murmu walked 6 km to reach the station from his house, then he boarded a train whose average speed was 60 km/hr and thus reached his destination. In this way he took total 3 hours. If the average speed of the entire journey was 32 km/hr then the average speed of walking is:
(A)
3 km/hr
(B)
4.5 km/hr
(C)
4 km/hr
(D)
None of the above
Correct Answer:
4 km/hr
Explanation:
Total distance = 32 × 3 = 96 km. Distance travelled by train = 96 - 6 = 90 km. Time taken by train = 90/60 = 1.5 hours. Walking time = 3 - 1.5 = 1.5 hours. Therefore, walking speed = 6/1.5 = 4 km/h.
Total distance = 32 × 3 = 96 km. Distance travelled by train = 96 - 6 = 90 km. Time taken by train = 90/60 = 1.5 hours. Walking time = 3 - 1.5 = 1.5 hours. Therefore, walking speed = 6/1.5 = 4 km/h.
Question
52
गणित
The sum of the curved surface area and total surface area of a solid cylinder is 2068 cm². If radius of its base is 7 cm, then what is the volume of this cylinder? (Use π = 22/7)
(A)
3080 cm³
(B)
2080 cm³
(C)
2075 cm³
(D)
None of the above
Correct Answer:
3080 cm³
Explanation:
Curved surface area + total surface area = 2πrh + 2πr(h+r) = 4πrh + 2πr². Putting r = 7 and π = 22/7 gives 88h + 308 = 2068, so h = 20 cm. Volume = πr²h = (22/7) × 49 × 20 = 3080 cm³. Therefore, the correct answer is 3080 cm³.
Curved surface area + total surface area = 2πrh + 2πr(h+r) = 4πrh + 2πr². Putting r = 7 and π = 22/7 gives 88h + 308 = 2068, so h = 20 cm. Volume = πr²h = (22/7) × 49 × 20 = 3080 cm³. Therefore, the correct answer is 3080 cm³.
Question
53
गणित
If x = sec θ + tan θ and y = sec θ - tan θ, then the relation between x and y is:
(A)
x² + y² = 0
(B)
x² = y²
(C)
x² = y
(D)
xy = 1
Correct Answer:
xy = 1
Explanation:
xy = (sec θ + tan θ)(sec θ - tan θ) = sec²θ - tan²θ = 1. Therefore, the relation between x and y is xy = 1.
xy = (sec θ + tan θ)(sec θ - tan θ) = sec²θ - tan²θ = 1. Therefore, the relation between x and y is xy = 1.
Question
54
गणित
Two circles each of radius 36 cm are intersecting each other such that each circle is passing through the center of the other circle. What is the length of common chord to the two circles?
(A)
35√3 cm
(B)
34√3 cm
(C)
36√3 cm
(D)
None of the above
Correct Answer:
36√3 cm
Explanation:
Both circles have radius 36 cm and each circle passes through the center of the other, so the distance between their centers is 36 cm. The common chord bisects the line joining the centers. Half of the chord = √(36² - 18²) = 18√3 cm. Therefore, the full chord is 36√3 cm.
Both circles have radius 36 cm and each circle passes through the center of the other, so the distance between their centers is 36 cm. The common chord bisects the line joining the centers. Half of the chord = √(36² - 18²) = 18√3 cm. Therefore, the full chord is 36√3 cm.
Question
55
गणित
A, B, and C started a business with initial investments of ₹20,000, ₹25,000, and ₹10,000, respectively. Five months after the start, A invested an additional ₹4,000. Six months after the start, C invested an additional ₹8,000. Four months after the start, B withdrew ₹8,000. At the end of the year, they would earn a profit of ₹x. In what ratio will they share the profit at the end of the year?
(A)
42:67:59
(B)
67:59:42
(C)
67:42:59
(D)
None of the above
Correct Answer:
67:59:42
Explanation:
A's capital-month = 20000×5 + 24000×7 = 268000. B's = 25000×4 + 17000×8 = 236000. C's = 10000×6 + 18000×6 = 168000. Therefore, the profit-sharing ratio is 67:59:42.
A's capital-month = 20000×5 + 24000×7 = 268000. B's = 25000×4 + 17000×8 = 236000. C's = 10000×6 + 18000×6 = 168000. Therefore, the profit-sharing ratio is 67:59:42.
Question
56
गणित
What is the value of 5 sin²60° + 7 sin²45° + 8 cos²45°?
(A)
45/4
(B)
4/45
(C)
49/4
(D)
4/49
Correct Answer:
45/4
Explanation:
5 sin²60° + 7 sin²45° + 8 cos²45° = 5×3/4 + 7×1/2 + 8×1/2 = 15/4 + 14/4 + 16/4 = 45/4.
5 sin²60° + 7 sin²45° + 8 cos²45° = 5×3/4 + 7×1/2 + 8×1/2 = 15/4 + 14/4 + 16/4 = 45/4.
Question
57
गणित
Two trains start simultaneously from Ranchi and Giridih stations, moving towards each other on the same track at speeds of 30 km/h and 40 km/h, respectively. The distance between the two stations is 560 km. A sparrow, perched on top of one train, flies towards the other train; upon reaching it, the sparrow reverses its direction and continues this pattern. If the sparrow's speed is 80 km/h, what total distance does it cover before being crushed between the trains?
(A)
70 km
(B)
560 km
(C)
640 km
(D)
650 km
Correct Answer:
640 km
Explanation:
The relative speed of the two trains is 30 + 40 = 70 km/h. Time taken to meet = 560/70 = 8 hours. The sparrow flies at 80 km/h, so the distance covered = 80×8 = 640 km.
The relative speed of the two trains is 30 + 40 = 70 km/h. Time taken to meet = 560/70 = 8 hours. The sparrow flies at 80 km/h, so the distance covered = 80×8 = 640 km.
Question
58
गणित
3 men and 5 women together can finish a job in 3 days. Working on the same job 3 women take 5 days more than the time required by 2 men. What is the ratio of efficiency of man to a woman?
(A)
2:1
(B)
3:2
(C)
5:2
(D)
4:1
Correct Answer:
5:2
Explanation:
Let the efficiency of a man be m and that of a woman be w. From the given condition, 1/(3w) = 1/(2m) + 5. Also, 3m + 5w = 1/3. Solving these equations gives m:w = 5:2.
Let the efficiency of a man be m and that of a woman be w. From the given condition, 1/(3w) = 1/(2m) + 5. Also, 3m + 5w = 1/3. Solving these equations gives m:w = 5:2.
Question
59
गणित
The ratio of milk to water in a 100 litres mixture is 2:3. If 10 litres of this mixture are withdrawn and replaced with milk, and this process is repeated 2 more times, what is the percentage of milk in the final mixture?
(A)
56.26
(B)
56.86
(C)
57.27
(D)
57.86
Correct Answer:
56.26
Explanation:
Initially, milk = 40 litres and water = 60 litres. Each time 10% of the mixture is removed and replaced with milk, the amount of water becomes 0.9 times its previous amount. After three operations, water = 60×(0.9)³ = 43.74 litres. Milk = 56.26 litres. Therefore, the percentage of milk is 56.26%.
Initially, milk = 40 litres and water = 60 litres. Each time 10% of the mixture is removed and replaced with milk, the amount of water becomes 0.9 times its previous amount. After three operations, water = 60×(0.9)³ = 43.74 litres. Milk = 56.26 litres. Therefore, the percentage of milk is 56.26%.
Question
60
गणित
ABC is an equilateral triangle. If the area of the triangle is 36√3, then what is the radius of the circle circumscribing the triangle ABC?
(A)
2√3
(B)
3√3
(C)
4√3
(D)
6√3
Correct Answer:
4√3
Explanation:
The area of an equilateral triangle is (√3/4)a². Thus, (√3/4)a² = 36√3, giving a² = 144 and a = 12 cm. The circumradius of an equilateral triangle is R = a/√3 = 12/√3 = 4√3 cm.
The area of an equilateral triangle is (√3/4)a². Thus, (√3/4)a² = 36√3, giving a² = 144 and a = 12 cm. The circumradius of an equilateral triangle is R = a/√3 = 12/√3 = 4√3 cm.
Total Questions:
150
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