Question
61
गणित
ABC is a right-angle triangle and angle ABC = 90 degrees. BD is a perpendicular on the side AC. What is the value of BD?
(A)
AD × DC
(B)
BC × AB
(C)
BC × CD
(D)
AD × AC
Correct Answer:
AD × DC
Explanation:
In a right-angled triangle, when a perpendicular is drawn from the right angle to the hypotenuse, BD² = AD × DC. Thus, among the given options, AD × DC represents BD². The question appears to have a printing error where BD² is intended.
In a right-angled triangle, when a perpendicular is drawn from the right angle to the hypotenuse, BD² = AD × DC. Thus, among the given options, AD × DC represents BD². The question appears to have a printing error where BD² is intended.
Question
62
गणित
An article is sold at 25 percent loss. If its cost price is doubled and selling price is increased by Rs. 660, then there is a profit of 20 percent. What is the original cost price of the article?
(A)
Rs. 480
(B)
Rs. 500
(C)
Rs. 400
(D)
Rs. 360
Correct Answer:
Rs. 400
Explanation:
Let the original cost price be C. Original selling price = 75%C. New cost price = 2C and new selling price = 75%C + 660. For a 20% profit, new selling price = 2.4C. Thus, 0.75C + 660 = 2.4C, giving C = Rs. 400.
Let the original cost price be C. Original selling price = 75%C. New cost price = 2C and new selling price = 75%C + 660. For a 20% profit, new selling price = 2.4C. Thus, 0.75C + 660 = 2.4C, giving C = Rs. 400.
Question
63
गणित
Average age of 7 students of a class is 28 years. Average age of first three students is 30 years. Age of fourth student is 4 years less than the age of fifth student. Ages of last two students is same and is 5 more than the average age of first three students. What is the average age of fourth and fifth student?
(A)
20 years
(B)
36 years
(C)
16 years
(D)
18 years
Correct Answer:
18 years
Explanation:
Total age of 7 students = 7×28 = 196 years. Total age of first three = 3×30 = 90 years. Each of the last two students is 35 years old, so their total age is 70 years. Therefore, the total age of the fourth and fifth students = 196−90−70 = 36 years. Their average age = 36/2 = 18 years.
Total age of 7 students = 7×28 = 196 years. Total age of first three = 3×30 = 90 years. Each of the last two students is 35 years old, so their total age is 70 years. Therefore, the total age of the fourth and fifth students = 196−90−70 = 36 years. Their average age = 36/2 = 18 years.
Question
64
गणित
The compound interest (compounding annually) on a certain sum at the rate of 8 percent per annum for two years is Rs. 6656. What would be the simple interest on the same sum at the same rate of interest for two years?
(A)
Rs. 6200
(B)
Rs. 5200
(C)
Rs. 6400
(D)
Rs. 5400
Correct Answer:
Rs. 6400
Explanation:
Compound interest for two years = P[(1.08)²−1] = 0.1664P = 6656. Therefore, P = Rs. 40000. Simple interest = P×8×2/100 = Rs. 6400.
Compound interest for two years = P[(1.08)²−1] = 0.1664P = 6656. Therefore, P = Rs. 40000. Simple interest = P×8×2/100 = Rs. 6400.
Question
65
गणित
Salaries of B, C, D and E are in the ratio of 2:3:4:5 respectively. Their salaries are increased by 20 percent, 30 percent, 40 percent and 50 percent respectively. If the increased salary of D is Rs. 560, then what is the sum of the original salaries of B, C, D and E?
(A)
Rs. 1400
(B)
Rs. 1500
(C)
Rs. 1600
(D)
Rs. 1700
Correct Answer:
Rs. 1400
Explanation:
D's original salary = 560/1.40 = Rs. 400. Since D represents 4 parts, one part = Rs. 100. Therefore, the original salaries of B, C, D and E are Rs. 200, 300, 400 and 500 respectively. Their sum is Rs. 1400.
D's original salary = 560/1.40 = Rs. 400. Since D represents 4 parts, one part = Rs. 100. Therefore, the original salaries of B, C, D and E are Rs. 200, 300, 400 and 500 respectively. Their sum is Rs. 1400.
Question
66
गणित
The slant height of a cone is 20 cm. If the area of its base is 616 cm², then what is the curved surface area of this cone? (Use π = 22/7)
(A)
870 cm²
(B)
880 cm²
(C)
900 cm²
(D)
920 cm²
Correct Answer:
880 cm²
Explanation:
Base area πr² = 616. Thus, (22/7)r² = 616, giving r = 14 cm. Curved surface area = πrl = (22/7)×14×20 = 880 cm².
Base area πr² = 616. Thus, (22/7)r² = 616, giving r = 14 cm. Curved surface area = πrl = (22/7)×14×20 = 880 cm².
Question
67
गणित
Which of the following is equal to sec A -cos A?
(A)
sin A × cot A
(B)
cot A × cos A
(C)
tan A × sin A
(D)
cos A × sin A
Correct Answer:
tan A × sin A
Question
68
गणित
If a + b = 6 and ab = 5 then what is the value of a³+b³?
(A)
116
(B)
106
(C)
136
(D)
126
Correct Answer:
126
Explanation:
Using the identity a³+b³ = (a+b)³ − 3ab(a+b), we get a³+b³ = 6³ − 3×5×6 = 216−90 = 126.
Using the identity a³+b³ = (a+b)³ − 3ab(a+b), we get a³+b³ = 6³ − 3×5×6 = 216−90 = 126.
Question
69
गणित
What is the sum of all the common terms between the given series S1 and S2? S1 = 2, 9, 16, ......, 632 and S2 = 7, 11, 15, ......, 743
(A)
7140
(B)
6750
(C)
6860
(D)
6974
Correct Answer:
6974
Explanation:
In S1, the terms are 2, 9, 16, ... with common difference 7. In S2, the terms are 7, 11, 15, ... with common difference 4. The common terms are 23, 51, 79, ..., 611. The sum of all these common terms is 6974.
In S1, the terms are 2, 9, 16, ... with common difference 7. In S2, the terms are 7, 11, 15, ... with common difference 4. The common terms are 23, 51, 79, ..., 611. The sum of all these common terms is 6974.
Question
70
गणित
A alone can do 2/5 of a work in 12 days. B is 25 percent more efficient than A. C alone can do the same work in 12 days less than B. D is 25 percent less efficient than C. If they all work together, then the work will be completed in how many days?
(A)
300/47
(B)
180/43
(C)
200/51
(D)
240/53
Correct Answer:
240/53
Explanation:
A completes 2/5 of the work in 12 days, so A’s one-day efficiency is 1/30. B is 25% more efficient, so B’s efficiency is 1/24 and B completes the work in 24 days. C takes 12 days less than B, so C completes the work in 12 days and has efficiency 1/12. D is 25% less efficient than C, so D’s efficiency is 1/16. Their combined efficiency is 53/240. Therefore, the required time is 240/53 days.
A completes 2/5 of the work in 12 days, so A’s one-day efficiency is 1/30. B is 25% more efficient, so B’s efficiency is 1/24 and B completes the work in 24 days. C takes 12 days less than B, so C completes the work in 12 days and has efficiency 1/12. D is 25% less efficient than C, so D’s efficiency is 1/16. Their combined efficiency is 53/240. Therefore, the required time is 240/53 days.
Total Questions:
150
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