Q. If the lengths of the legs of a right triangle are 8 and 15, what is the length of the hypotenuse?
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Solution
Using the Pythagorean theorem, c = √(8² + 15²) = √(64 + 225) = √289 = 17.
Correct Answer:
A
— 17
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Q. If the lengths of the legs of a right triangle are 9 and 12, what is the perimeter of the triangle?
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Solution
Hypotenuse = √(9² + 12²) = √(81 + 144) = √225 = 15. Perimeter = 9 + 12 + 15 = 36.
Correct Answer:
B
— 32
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Q. If the lengths of the legs of a right triangle are equal, what type of triangle is it?
A.
Isosceles
B.
Equilateral
C.
Scalene
D.
Right
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Solution
A right triangle with equal legs is an isosceles triangle.
Correct Answer:
A
— Isosceles
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Q. If the lengths of the sides of a triangle are 5, 12, and 13, what type of triangle is it?
A.
Acute
B.
Obtuse
C.
Right
D.
Equilateral
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Solution
Since 5² + 12² = 13², it is a right triangle.
Correct Answer:
C
— Right
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Q. If the lengths of the sides of a triangle are 9, 12, and 15, is it a right triangle?
A.
Yes
B.
No
C.
It depends
D.
Cannot be determined
Show solution
Solution
Check using the Pythagorean theorem: 15² = 9² + 12², 225 = 81 + 144, 225 = 225. It is a right triangle.
Correct Answer:
A
— Yes
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Q. If the lengths of the two legs of a right triangle are equal, what is the measure of the angles opposite those legs?
A.
45 degrees
B.
60 degrees
C.
30 degrees
D.
90 degrees
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Solution
In an isosceles right triangle, the angles opposite the equal legs are both 45 degrees.
Correct Answer:
A
— 45 degrees
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Q. If the lengths of two tangents drawn from an external point to a circle are equal, what can be said about the point?
A.
It is inside the circle
B.
It is on the circle
C.
It is outside the circle
D.
It is the center of the circle
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Solution
If the lengths of two tangents from an external point are equal, the point must be outside the circle.
Correct Answer:
C
— It is outside the circle
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Q. If the price of a shirt is increased by 25% and then decreased by 20%, what is the final price if the original price was $40?
A.
$36
B.
$38
C.
$40
D.
$42
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Solution
New price after increase = 40 + 25% of 40 = 50; New price after decrease = 50 - 20% of 50 = 40.
Correct Answer:
B
— $38
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Q. If the quadratic equation x^2 + 2x + k = 0 has no real roots, what must be true about k?
A.
k > 0
B.
k < 0
C.
k = 0
D.
k >= 0
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Solution
For no real roots, the discriminant must be less than zero: 2^2 - 4*1*k < 0, thus k > 1.
Correct Answer:
B
— k < 0
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Q. If the radius of a circle is 7 cm, what is the length of a tangent drawn from a point 10 cm away from the center?
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Solution
Using the tangent length formula: length = √(distance from center² - radius²) = √(10² - 7²) = √(100 - 49) = √51, which is approximately 7.14.
Correct Answer:
A
— 5
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Q. If the radius of a circle is 7 units, what is the length of a tangent drawn from a point 10 units away from the center?
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Solution
Using the tangent length formula: length = √(distance from center² - radius²) = √(10² - 7²) = √(100 - 49) = √51 ≈ 7.14.
Correct Answer:
A
— 5
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Q. If the ratio of boys to girls in a class is 3:2 and there are 15 boys, how many girls are there?
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Solution
Let the number of girls be 2x. Then, 3x = 15; x = 5. Number of girls = 2x = 10.
Correct Answer:
B
— 10
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Q. If the ratio of the ages of A and B is 3:4 and the sum of their ages is 56, what is A's age?
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Solution
Let A's age be 3x and B's age be 4x. Then, 3x + 4x = 56, 7x = 56, x = 8. A's age = 3x = 24.
Correct Answer:
B
— 28
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Q. If the ratio of the lengths of two rectangles is 5:7 and the length of the first rectangle is 25 cm, what is the length of the second rectangle?
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Solution
Let the length of the first rectangle = 5x and the second = 7x. Given 5x = 25, x = 5. Therefore, length of the second rectangle = 7x = 7*5 = 35.
Correct Answer:
A
— 30
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Q. If the ratio of the lengths of two rectangles is 7:4 and the length of the first rectangle is 28 cm, what is the length of the second rectangle?
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Solution
Let the lengths be 7x and 4x. Given 7x = 28, x = 4. Therefore, the length of the second rectangle = 4x = 4*4 = 16.
Correct Answer:
A
— 16
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Q. If the ratio of the lengths of two ropes is 5:7 and the total length of the ropes is 72 meters, what is the length of the shorter rope?
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Solution
Let the lengths be 5x and 7x. Given 5x + 7x = 72, 12x = 72, x = 6. Therefore, shorter rope = 5x = 5*6 = 30.
Correct Answer:
B
— 25
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Q. If the ratio of the lengths of two sides of a triangle is 3:5 and the perimeter is 64 cm, what is the length of the longer side?
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Solution
Let the sides be 3x and 5x. Then, 3x + 5x = 64, 8x = 64, x = 8. Therefore, the longer side = 5x = 5*8 = 40.
Correct Answer:
B
— 25
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Q. If the ratio of the lengths of two sides of a triangle is 7:9 and the longer side is 36 cm, what is the length of the shorter side?
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Solution
Let the shorter side be 7x and the longer side be 9x. Given 9x = 36, x = 4. Therefore, shorter side = 7x = 7*4 = 28.
Correct Answer:
A
— 28
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Q. If the ratio of the number of apples to oranges is 7:3 and there are 42 apples, how many oranges are there?
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Solution
Let apples = 7x and oranges = 3x. Given 7x = 42, x = 6. Therefore, oranges = 3x = 3*6 = 18.
Correct Answer:
A
— 18
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Q. If the ratio of the speeds of two cars is 5:7 and the faster car travels 140 km in an hour, how far does the slower car travel in the same time?
A.
100
B.
120
C.
140
D.
160
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Solution
Let speeds be 5x and 7x. Given 7x = 140, x = 20. Slower car's speed = 5x = 5*20 = 100 km.
Correct Answer:
A
— 100
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Q. If the ratio of two numbers is 7:9 and their sum is 128, what are the two numbers?
A.
56, 72
B.
49, 81
C.
63, 72
D.
70, 58
Show solution
Solution
Let the numbers be 7x and 9x. Then, 7x + 9x = 128, 16x = 128, x = 8. Therefore, the numbers are 7*8 = 56 and 9*8 = 72.
Correct Answer:
A
— 56, 72
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Q. If the ratio of two numbers is 7:9 and their sum is 128, what is the larger number?
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Solution
Let the numbers be 7x and 9x. Then, 7x + 9x = 128, 16x = 128, x = 8. Larger number = 9x = 9*8 = 72.
Correct Answer:
A
— 72
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Q. If the roots of the equation x^2 + 3x + 2 = 0 are a and b, what is the value of a + b? (2022)
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Solution
The sum of the roots is -b/a = -3/1 = -3.
Correct Answer:
A
— -3
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Q. If the roots of the equation x^2 + 3x + k = 0 are equal, what is the value of k?
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Solution
For equal roots, the discriminant must be zero: 3^2 - 4*1*k = 0, hence k = 9.
Correct Answer:
A
— -9
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Q. If the roots of the equation x^2 + 5x + k = 0 are 1 and 4, what is the value of k?
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Solution
Using the product of roots, k = 1*4 = 4.
Correct Answer:
C
— 6
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Q. If the roots of the equation x^2 + 6x + 9 = 0 are equal, what is the value of the root? (2023)
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Solution
The equation can be factored as (x+3)(x+3)=0, hence the root is -3.
Correct Answer:
A
— -3
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Q. If the roots of the equation x^2 + px + q = 0 are 4 and -1, what is the value of p?
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Solution
Using the sum of roots formula, p = -(4 + (-1)) = -3.
Correct Answer:
B
— 5
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Q. If the roots of the equation x^2 + px + q = 0 are 4 and -2, what is the value of p?
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Solution
Using the sum of roots formula, p = -(4 + (-2)) = -2.
Correct Answer:
A
— 2
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Q. If the roots of the equation x^2 - 10x + k = 0 are 5 and 5, what is the value of k?
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Solution
The product of the roots is 5*5 = 25, hence k = 25.
Correct Answer:
A
— 25
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Q. If the sales of Product C increased by 50 units, what would be the new total sales?
A.
2050
B.
2100
C.
2150
D.
2200
Show solution
Solution
The new total sales would be 2000 + 50 = 2050.
Correct Answer:
B
— 2100
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Showing 901 to 930 of 1468 (49 Pages)
Quantitative Aptitude (SSC) MCQ & Objective Questions
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!
