Q. In a circle, if a chord is 12 cm long and the distance from the center to the chord is 5 cm, what is the radius of the circle?
A.
10
B.
12
C.
13
D.
15
Solution
Using the formula: radius² = (distance from center to chord)² + (half of chord length)². Here, radius² = 5² + (12/2)² = 25 + 36 = 61, so radius = √61, which is approximately 7.81.
Q. In a circle, if a chord is 12 units long and the distance from the center to the chord is 5 units, what is the radius of the circle?
A.
10
B.
12
C.
13
D.
15
Solution
Using the formula: radius² = (distance from center to chord)² + (half of chord length)². Thus, radius² = 5² + (12/2)² = 25 + 36 = 61, so radius = √61 ≈ 7.81.
Q. In a circle, if a tangent and a chord intersect at a point on the circle, and the angle between them is 30°, what is the angle subtended by the chord at the center?
A.
30°
B.
60°
C.
90°
D.
120°
Solution
The angle subtended by the chord at the center is twice the angle between the tangent and the chord, so it is 2 * 30° = 60°.
Q. In a circle, if the angle subtended by a chord at the center is 80 degrees, what is the angle subtended at any point on the remaining part of the circle?
A.
40
B.
80
C.
100
D.
160
Solution
The angle subtended at the circumference is half of that at the center, so it is 80/2 = 40 degrees.
Q. In a class of 40 students, the average score in Mathematics is 75. If 10 new students join with an average score of 85, what will be the new average?
A.
78
B.
80
C.
82
D.
76
Solution
Total score of 40 students = 40 * 75 = 3000. Total score of 10 new students = 10 * 85 = 850. New average = (3000 + 850) / 50 = 77.
Q. In a class, the ratio of students who prefer Math to those who prefer Science is 3:2. If there are 30 students who prefer Science, how many prefer Math?
A.
45
B.
60
C.
30
D.
40
Solution
Let Math = 3x and Science = 2x. Given 2x = 30, x = 15. Therefore, Math = 3x = 3*15 = 45.
Q. In a group of 4 friends, the average age is 25 years. If one friend leaves and the average age becomes 26 years, what is the age of the friend who left?
A.
24
B.
25
C.
26
D.
27
Solution
Total age of 4 friends = 4 * 25 = 100 years. New total age for 3 friends = 3 * 26 = 78 years. Age of friend who left = 100 - 78 = 22 years.
Q. In a group of 4 friends, the average age is 25 years. If one friend leaves and the average age becomes 27 years, what is the age of the friend who left?
A.
24
B.
26
C.
28
D.
30
Solution
Total age of 4 friends = 4 * 25 = 100. Total age of 3 friends = 3 * 27 = 81. Therefore, the age of the friend who left = 100 - 81 = 19.
Q. In a line graph showing the temperature over a week, if the temperature increased from 20°C to 30°C over three days, what was the average daily increase? (2023)
A.
2°C
B.
3°C
C.
5°C
D.
10°C
Solution
The total increase is 10°C over 3 days, so the average daily increase is 10/3 = 3.33°C, which rounds to 3°C.
Q. In a line graph showing the temperature over a week, if the temperatures recorded are 30°C, 32°C, 31°C, 29°C, 28°C, 33°C, and 34°C, what is the average temperature for the week? (2023)
A.
30°C
B.
31°C
C.
32°C
D.
33°C
Solution
Average temperature = (30 + 32 + 31 + 29 + 28 + 33 + 34) / 7 = 31°C.
Q. In a mixed graph, the average temperature for three cities (A, B, C) over a week is shown. If City A's average temperature is 30°C, City B's is 25°C, and City C's is 20°C, what is the average temperature across all three cities?
A.
25°C
B.
26°C
C.
27°C
D.
28°C
Solution
The average temperature is (30 + 25 + 20) / 3 = 25°C.
Q. In a mixed graph, the total revenue for three different regions (North, South, East) is shown. If the North region contributed $300,000, South $450,000, and East $250,000, which region contributed the least?
A.
North
B.
South
C.
East
D.
All equal
Solution
The East region contributed the least with $250,000.
Quantitative Aptitude is a crucial component of various exams, especially for students preparing for the SSC (Staff Selection Commission) exams. Mastering this subject not only enhances problem-solving skills but also boosts confidence in tackling objective questions. Regular practice with MCQs and practice questions is essential for scoring better and understanding important concepts effectively.
What You Will Practise Here
Number Systems and their properties
Percentage, Ratio, and Proportion calculations
Time, Speed, and Distance problems
Simple and Compound Interest concepts
Algebraic expressions and equations
Data Interpretation and analysis
Mensuration and Geometry basics
Exam Relevance
Quantitative Aptitude is a significant part of the syllabus for CBSE, State Boards, and competitive exams like NEET and JEE. In these exams, students can expect questions that assess their ability to apply mathematical concepts to real-world scenarios. Common question patterns include direct problem-solving, data interpretation, and application of formulas, making it essential for students to be well-prepared.
Common Mistakes Students Make
Misunderstanding the problem statement leading to incorrect assumptions
Neglecting to apply the correct formulas in calculations
Overlooking units of measurement in word problems
Rushing through questions without double-checking calculations
FAQs
Question: What are the best ways to prepare for Quantitative Aptitude in SSC exams? Answer: Regular practice with MCQs, understanding key concepts, and solving previous years' question papers are effective strategies.
Question: How can I improve my speed in solving Quantitative Aptitude questions? Answer: Practicing timed quizzes and focusing on shortcut methods can significantly enhance your speed and accuracy.
Start your journey towards mastering Quantitative Aptitude today! Solve practice MCQs and test your understanding to achieve your exam goals. Remember, consistent practice is the key to success!
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