Major Competitive Exams

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Q. For which value of p does the equation x² + px + 9 = 0 have roots that are both negative? (2021)

A. -6
B. -4
C. -3
D. -2

Solution

For both roots to be negative, p must be positive and p² > 4*9. Thus, p > 6, so p = -4 is valid.

Correct Answer: B — -4

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Q. For which value of p does the equation x² - px + 9 = 0 have roots 3 and 3? (2021)

A. 6
B. 3
C. 9
D. 0

Solution

The sum of the roots is 3 + 3 = 6, hence p = 6.

Correct Answer: A — 6

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Q. For which value of p is the function f(x) = { x^2 + p, x < 0; 3x - 1, x >= 0 } continuous at x = 0?

A. -1
B. 0
C. 1
D. 2

Solution

Setting the two pieces equal at x = 0 gives us p = -1.

Correct Answer: B — 0

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Q. From a deck of 52 cards, how many ways can you choose 5 cards?

A. 2598960
B. 1001
C. 3125
D. 1024

Solution

The number of ways to choose 5 cards from 52 is 52C5 = 2598960.

Correct Answer: A — 2598960

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Q. From a group of 10 people, how many ways can a committee of 4 be formed?

A. 210
B. 120
C. 150
D. 180

Solution

The number of ways to choose 4 people from 10 is given by 10C4 = 210.

Correct Answer: A — 210

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Q. From a group of 8 people, how many ways can a team of 3 be selected? (2022)

A. 56
B. 24
C. 36
D. 48

Solution

The number of ways to choose 3 people from 8 is given by 8C3 = 56.

Correct Answer: A — 56

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Q. From a group of 8 people, how many ways can a team of 4 be selected?

A. 70
B. 56
C. 80
D. 90

Solution

The number of ways to choose 4 people from 8 is given by 8C4 = 70.

Correct Answer: B — 56

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Q. From a point A, the angle of elevation of the top of a building is 45 degrees. If the height of the building is 20 meters, how far is point A from the base of the building?

A. 10 m
B. 20 m
C. 30 m
D. 40 m

Solution

Using tan(45°) = height/distance, we have 1 = 20/distance. Therefore, distance = 20 m.

Correct Answer: B — 20 m

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Q. From a point on the ground, the angle of elevation of the top of a hill is 30 degrees. If the distance from the point to the base of the hill is 100 meters, what is the height of the hill?

A. 50 m
B. 60 m
C. 70 m
D. 80 m

Solution

Using tan(30°) = height/100, we have 1/√3 = height/100. Therefore, height = 100/√3 ≈ 57.74 m.

Correct Answer: A — 50 m

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Q. From a point on the ground, the angle of elevation of the top of a hill is 30 degrees. If the height of the hill is 50 meters, how far is the point from the base of the hill?

A. 50 m
B. 75 m
C. 100 m
D. 125 m

Solution

Using tan(30°) = height/distance, we have 1/√3 = 50/distance. Therefore, distance = 50√3 ≈ 86.6 m.

Correct Answer: C — 100 m

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Q. From a point on the ground, the angle of elevation to the top of a 40 m high building is 45 degrees. How far is the point from the base of the building?

A. 40 m
B. 20 m
C. 30 m
D. 50 m

Solution

Using tan(45°) = height/distance, we have distance = height/tan(45°) = 40/1 = 40 m.

Correct Answer: A — 40 m

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Q. From a point on the ground, the angle of elevation to the top of a 75 m high building is 45 degrees. How far is the point from the building?

A. 75 m
B. 50 m
C. 100 m
D. 25 m

Solution

Using tan(45°) = height/distance, we have distance = height/tan(45°) = 75/1 = 75 m.

Correct Answer: A — 75 m

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Q. From a point on the ground, the angle of elevation to the top of a building is 45 degrees. If the building is 50 meters tall, how far is the point from the base of the building?

A. 50 m
B. 25 m
C. 100 m
D. 75 m

Solution

Distance = height / tan(angle) = 50 / 1 = 50 m.

Correct Answer: A — 50 m

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Q. From a point on the ground, the angle of elevation to the top of a hill is 30 degrees. If the distance from the point to the base of the hill is 100 meters, what is the height of the hill?

A. 100√3 m
B. 50 m
C. 100 m
D. 50√3 m

Solution

Using tan(30°) = height/distance, we have height = distance * tan(30°) = 100 * (1/√3) = 100/√3 = 50 m.

Correct Answer: B — 50 m

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Q. From a point on the ground, the angle of elevation to the top of a hill is 30 degrees. If the height of the hill is 100 m, how far is the point from the base of the hill? (2022)

A. 173.21 m
B. 100 m
C. 200 m
D. 150 m

Solution

Distance = height / tan(30) = 100 / (1/√3) = 100√3 ≈ 173.21 m.

Correct Answer: A — 173.21 m

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Q. From a point on the ground, the angle of elevation to the top of a hill is 45 degrees. If the height of the hill is 50 m, how far is the point from the base of the hill?

A. 25 m
B. 50 m
C. 70 m
D. 100 m

Solution

Using tan(45°) = height/distance, we have 1 = 50/distance. Therefore, distance = 50 m.

Correct Answer: B — 50 m

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Q. From a point on the ground, the angle of elevation to the top of a hill is 45 degrees. If the height of the hill is 20 m, how far is the point from the base of the hill?

A. 20 m
B. 10 m
C. 30 m
D. 40 m

Solution

Using tan(45°) = height/distance, we have 1 = 20/distance. Therefore, distance = 20 m.

Correct Answer: A — 20 m

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Q. From a point on the ground, the angle of elevation to the top of a hill is 45 degrees. If the height of the hill is 40 m, how far is the point from the base of the hill?

A. 20 m
B. 40 m
C. 60 m
D. 80 m

Solution

Using tan(45°) = height/distance, we have 1 = 40/distance. Therefore, distance = 40 m.

Correct Answer: B — 40 m

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Q. From a point on the ground, the angle of elevation to the top of a hill is 45 degrees. If the height of the hill is 100 m, how far is the point from the base of the hill?

A. 100 m
B. 50 m
C. 200 m
D. 150 m

Solution

Using tan(45°) = height/distance, we have distance = height/tan(45°) = 100/1 = 100 m.

Correct Answer: A — 100 m

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Q. From a point on the ground, the angle of elevation to the top of a hill is 45 degrees. If the point is 100 meters away from the base of the hill, what is the height of the hill?

A. 100 meters
B. 50 meters
C. 200 meters
D. 150 meters

Solution

Height = distance * tan(angle) = 100 * tan(45°) = 100 meters.

Correct Answer: A — 100 meters

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Q. From a point on the ground, the angle of elevation to the top of a hill is 45 degrees. If the point is 10 meters away from the base of the hill, what is the height of the hill?

A. 10 meters
B. 5 meters
C. 15 meters
D. 20 meters

Solution

Let h be the height of the hill. tan(45°) = h/10. Therefore, h = 10 * tan(45°) = 10 * 1 = 10 meters.

Correct Answer: A — 10 meters

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Q. From a point on the ground, the angle of elevation to the top of a tower is 60 degrees. If the tower is 30 m high, how far is the point from the base of the tower?

A. 15 m
B. 30 m
C. 20 m
D. 10 m

Solution

Using tan(60°) = height/distance, we have √3 = 30/distance. Therefore, distance = 30/√3 m.

Correct Answer: A — 15 m

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Q. From a set of 8 different books, how many ways can you choose 3 books?

A. 56
B. 84
C. 28
D. 70

Solution

The number of ways to choose 3 books from 8 is given by 8C3 = 56.

Correct Answer: B — 84

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Q. From the bar graph depicting the number of students enrolled in various courses, which course had the highest enrollment?

A. Mathematics
B. Science
C. Literature
D. Art

Solution

The bar graph indicates that Science had the highest enrollment among the courses.

Correct Answer: B — Science

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Q. From the bar graph depicting the number of visitors to a park over five days, which day had the least visitors?

A. Monday
B. Tuesday
C. Wednesday
D. Thursday

Solution

Monday had the least visitors with only 50 people recorded.

Correct Answer: A — Monday

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Q. From the bar graph representing the expenditure of households, which category had the highest expenditure?

A. Food
B. Housing
C. Transportation
D. Entertainment

Solution

The bar graph indicates that housing had the highest expenditure among the categories.

Correct Answer: B — Housing

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Q. From the bar graph representing the expenditure on different departments, which department had the highest budget allocation?

A. Education
B. Health
C. Infrastructure
D. Defense

Solution

The bar graph clearly shows that the infrastructure department received the highest budget allocation.

Correct Answer: C — Infrastructure

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Q. From the bar graph representing the population of different cities, which city has a population closest to 1 million?

A. City A
B. City B
C. City C
D. City D

Solution

The bar graph shows that City B has a population closest to 1 million.

Correct Answer: B — City B

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Q. From the bar graph showing the expenditure on different categories, which category saw the highest expenditure?

A. Education
B. Healthcare
C. Transportation
D. Entertainment

Solution

The bar graph indicates that Healthcare had the highest expenditure among the categories.

Correct Answer: B — Healthcare

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Q. From the bar graph showing the production of different crops, which crop showed the most significant growth?

A. Wheat
B. Rice
C. Corn
D. Barley

Solution

The bar graph illustrates that wheat showed the most significant growth in production.

Correct Answer: A — Wheat

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Major Competitive Exams

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