Q. If the cost function is C(x) = 3x^2 + 12x + 5, find the minimum cost. (2020) 2020
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Solution
The minimum cost occurs at x = -b/(2a) = -12/(2*3) = -2. C(-2) = 3(-2)^2 + 12(-2) + 5 = 8.
Correct Answer:
B
— 8
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Q. If the cost function is C(x) = 5x^2 + 20x + 100, find the minimum cost. (2020)
A.
100
B.
120
C.
140
D.
160
Show solution
Solution
The minimum cost occurs at x = -b/(2a) = -20/(2*5) = -2. C(-2) = 5(-2)^2 + 20(-2) + 100 = 120.
Correct Answer:
B
— 120
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Q. If the diameter of a circle is 20 cm, what is its circumference? (2022)
A.
62.83 cm
B.
31.42 cm
C.
20 cm
D.
40 cm
Show solution
Solution
Circumference = πd; C = π * 20 ≈ 62.83 cm.
Correct Answer:
A
— 62.83 cm
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Q. If the first term of a geometric series is 4 and the common ratio is 2, what is the 7th term?
A.
128
B.
256
C.
512
D.
1024
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Solution
The nth term of a geometric series is given by a_n = ar^(n-1). Here, a = 4, r = 2, n = 7. So, a_7 = 4 * 2^(7-1) = 4 * 64 = 256.
Correct Answer:
B
— 256
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Q. If the first term of an arithmetic series is 12 and the last term is 48, what is the common difference if there are 10 terms?
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Solution
In an arithmetic series, the last term can be expressed as a + (n-1)d. Here, 48 = 12 + (10-1)d. Thus, 48 - 12 = 9d, giving d = 4.
Correct Answer:
A
— 4
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Q. If the line 2x + 3y = 6 intersects the x-axis, what is the point of intersection?
A.
(3, 0)
B.
(0, 2)
C.
(0, 3)
D.
(2, 0)
Show solution
Solution
Setting y = 0 gives 2x = 6, thus x = 3. The point of intersection is (3, 0).
Correct Answer:
A
— (3, 0)
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Q. If the line 2x + 3y = 6 intersects the x-axis, what is the x-coordinate of the intersection point?
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Solution
Setting y = 0 gives 2x = 6, thus x = 3. The x-coordinate of the intersection point is 3.
Correct Answer:
B
— 2
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Q. If the line 3x + 4y = 12 intersects the y-axis, what is the point of intersection? (2021)
A.
(0, 3)
B.
(0, 4)
C.
(0, 2)
D.
(0, 1)
Show solution
Solution
Setting x = 0 gives 4y = 12, thus y = 3. The point of intersection is (0, 3).
Correct Answer:
A
— (0, 3)
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Q. If the line 3x - 4y + 12 = 0 intersects the x-axis, what is the x-coordinate of the intersection point? (2021)
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Solution
Setting y = 0 in the equation gives 3x + 12 = 0, thus x = -4.
Correct Answer:
A
— -4
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Q. If the line 3x - 4y + 12 = 0 intersects the y-axis, what is the point of intersection?
A.
(0, 3)
B.
(0, -3)
C.
(0, 4)
D.
(0, -4)
Show solution
Solution
Setting x = 0 gives -4y + 12 = 0, thus y = -3. The point of intersection is (0, -3).
Correct Answer:
D
— (0, -4)
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Q. If the line 3x - 4y + 12 = 0 is parallel to another line, what is the slope of the parallel line?
A.
3/4
B.
-3/4
C.
4/3
D.
-4/3
Show solution
Solution
Rearranging gives y = (3/4)x + 3. The slope of the line is 3/4, so the slope of the parallel line is -3/4.
Correct Answer:
B
— -3/4
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Q. If the line 3x - 4y + 12 = 0 is parallel to which of the following lines?
A.
6x - 8y + 24 = 0
B.
3x + 4y - 12 = 0
C.
x + 2y - 5 = 0
D.
2x - 3y + 6 = 0
Show solution
Solution
Parallel lines have the same slope. The slope of the given line is 3/4, which is the same as the slope of 6x - 8y + 24 = 0.
Correct Answer:
A
— 6x - 8y + 24 = 0
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Q. If the line 7x + 2y = 14 is transformed to slope-intercept form, what is the slope?
A.
-7/2
B.
7/2
C.
2/7
D.
-2/7
Show solution
Solution
Rearranging to y = -7/2x + 7 shows that the slope is -7/2.
Correct Answer:
A
— -7/2
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Q. If the quadratic equation x² + 5x + k = 0 has roots -2 and -3, find k. (2020)
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Solution
The product of the roots gives k = (-2)(-3) = 6.
Correct Answer:
A
— 6
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Q. If the radius of a circle is 4 cm, what is the length of a chord that is 3 cm from the center? (2014)
A.
5 cm
B.
6 cm
C.
7 cm
D.
8 cm
Show solution
Solution
Using Pythagoras theorem: chord length = 2√(r² - d²) = 2√(4² - 3²) = 2√(16 - 9) = 2√7 ≈ 5.29 cm.
Correct Answer:
A
— 5 cm
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Q. If the radius of a circle is decreased by 2 cm, how does the area change? (Original radius is 10 cm) (2021)
A.
Decreases by 12.56 cm²
B.
Decreases by 25.12 cm²
C.
Decreases by 31.4 cm²
D.
Decreases by 50.24 cm²
Show solution
Solution
Original area = π(10)² = 314 cm²; New area = π(8)² = 201.06 cm². Change = 314 - 201.06 = 112.94 cm².
Correct Answer:
B
— Decreases by 25.12 cm²
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Q. If the radius of a circle is decreased by 2 cm, how does the area change? (Use π = 3.14) (2020)
A.
Decreases by 12.56 cm²
B.
Decreases by 25.12 cm²
C.
Increases by 12.56 cm²
D.
Remains the same
Show solution
Solution
Area change = π[(r-2)² - r²] = π[-4r + 4] = 3.14 * (-4r + 4).
Correct Answer:
B
— Decreases by 25.12 cm²
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Q. If the radius of a circle is doubled, how does the area change? (2021)
A.
It doubles
B.
It triples
C.
It quadruples
D.
It remains the same
Show solution
Solution
Area = πr²; if r is doubled, area = π(2r)² = 4πr², so it quadruples.
Correct Answer:
C
— It quadruples
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Q. If the radius of a circle is halved, by what factor does the circumference decrease? (2020)
A.
1/2
B.
1/4
C.
1/3
D.
1/6
Show solution
Solution
Circumference = 2πr; If r is halved, new circumference = πr; Factor = 1/2.
Correct Answer:
A
— 1/2
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Q. If the radius of a circle is halved, how does the circumference change? (2021)
A.
Halved
B.
Remains the same
C.
Doubled
D.
Tripled
Show solution
Solution
Circumference = 2πr. If radius is halved, new circumference = 2π(r/2) = πr, which is halved.
Correct Answer:
A
— Halved
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Q. If the radius of a circle is halved, how does the circumference change? (2022) 2022
A.
Halved
B.
Remains the same
C.
Doubled
D.
Quadrupled
Show solution
Solution
Circumference = 2πr. If radius is halved, new circumference = 2π(r/2) = πr, which is halved.
Correct Answer:
A
— Halved
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Q. If the radius of a circle is tripled, by what factor does the area increase? (2021)
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Solution
Area increases by a factor of (3r)²/r² = 9.
Correct Answer:
C
— 9
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Q. If the radius of a circle is tripled, how does the area change? (2019)
A.
Increases by 3 times
B.
Increases by 6 times
C.
Increases by 9 times
D.
Remains the same
Show solution
Solution
Area = πr². If radius is tripled, new area = π(3r)² = 9πr², which is 9 times the original area.
Correct Answer:
C
— Increases by 9 times
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Q. If the revenue function is R(x) = 100x - 2x^2, find the number of units that maximizes revenue. (2021)
Show solution
Solution
Max revenue occurs at x = -b/(2a) = 100/(2*2) = 25.
Correct Answer:
B
— 50
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Q. If the revenue function is R(x) = 20x - 0.5x^2, find the quantity that maximizes revenue. (2021)
Show solution
Solution
R'(x) = 20 - x = 0 gives x = 20. This maximizes revenue.
Correct Answer:
B
— 20
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Q. If the revenue function is R(x) = 50x - 0.5x^2, find the number of units that maximizes revenue. (2023)
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Solution
Max revenue occurs at x = -b/(2a) = -50/(2*-0.5) = 50.
Correct Answer:
A
— 25
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Q. If the roots of the equation x² + 2x + k = 0 are 1 and -3, what is the value of k? (2020)
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Solution
Using the sum and product of roots: 1 + (-3) = -2 and 1 * (-3) = -3, thus k = 3.
Correct Answer:
C
— 3
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Q. If the roots of the equation x² + 2x + k = 0 are real and distinct, what is the condition for k? (2020)
A.
k > 1
B.
k < 1
C.
k > 4
D.
k < 4
Show solution
Solution
The discriminant must be greater than zero: 2² - 4*1*k > 0, which simplifies to k < 1.
Correct Answer:
C
— k > 4
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Q. If the roots of the equation x² + 5x + 6 = 0 are a and b, what is the value of a + b? (2019)
Show solution
Solution
The sum of the roots is given by -b/a = -5/1 = -5.
Correct Answer:
A
— 5
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Q. If the roots of the equation x² + 5x + k = 0 are -2 and -3, find k. (2020)
Show solution
Solution
Using the product of roots: k = (-2)(-3) = 6.
Correct Answer:
A
— 6
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Showing 481 to 510 of 973 (33 Pages)
Mathematics (MHT-CET) MCQ & Objective Questions
Mathematics plays a crucial role in the MHT-CET exams, serving as a foundation for various scientific and engineering disciplines. Practicing MCQs and objective questions not only enhances your problem-solving skills but also boosts your confidence in tackling important questions during exams. Engaging with practice questions is essential for effective exam preparation, helping you identify your strengths and areas that need improvement.
What You Will Practise Here
Algebra: Understanding equations, inequalities, and functions.
Geometry: Key concepts of shapes, theorems, and properties.
Trigonometry: Ratios, identities, and applications in problems.
Calculus: Basics of differentiation and integration.
Statistics: Data interpretation, mean, median, and mode.
Probability: Fundamental principles and problem-solving techniques.
Coordinate Geometry: Graphing lines, circles, and conic sections.
Exam Relevance
Mathematics is a significant component of various examinations including CBSE, State Boards, NEET, and JEE. In these exams, you can expect a mix of direct application questions and conceptual problems. Common question patterns include multiple-choice questions that test your understanding of formulas, definitions, and theorems, making it imperative to be well-versed in the subject matter.
Common Mistakes Students Make
Misinterpreting the question, leading to incorrect answers.
Overlooking the importance of units in calculations.
Rushing through problems without checking for calculation errors.
Neglecting to review fundamental concepts before advanced topics.
FAQs
Question: What types of questions can I expect in Mathematics (MHT-CET)?Answer: You can expect a variety of MCQs that cover theoretical concepts, problem-solving, and application-based questions.
Question: How can I improve my performance in Mathematics (MHT-CET)?Answer: Regular practice of Mathematics (MHT-CET) MCQ questions and understanding the underlying concepts will significantly enhance your performance.
Start solving practice MCQs today to test your understanding and sharpen your skills. Remember, consistent practice is the key to success in Mathematics (MHT-CET) and achieving your academic goals!
