Q. Which of the following is true for all angles A?
A.
sin^2 A + cos^2 A = 1
B.
tan A = sin A/cos A
C.
sec A = 1/cos A
D.
All of the above
Show solution
Solution
All the given identities are true for all angles A.
Correct Answer:
D
— All of the above
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Q. Which of the following lines is parallel to the line 4x - 5y + 10 = 0?
A.
y = (4/5)x + 2
B.
y = (5/4)x - 1
C.
y = (4/5)x - 3
D.
y = (-5/4)x + 1
Show solution
Solution
The slope of the given line is 4/5. A line parallel to it must have the same slope, hence y = (4/5)x - 3.
Correct Answer:
C
— y = (4/5)x - 3
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Q. Which of the following measures is NOT a measure of dispersion?
A.
Range
B.
Variance
C.
Mean
D.
Standard Deviation
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Solution
Mean is a measure of central tendency, not dispersion.
Correct Answer:
C
— Mean
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Q. Which of the following measures of dispersion is affected by extreme values?
A.
Range
B.
Interquartile Range
C.
Variance
D.
Standard Deviation
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Solution
Range is affected by extreme values as it is calculated as the difference between the maximum and minimum values.
Correct Answer:
A
— Range
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Q. Which of the following relations is an equivalence relation on the set of integers?
A.
x ~ y if x + y is even
B.
x ~ y if x - y is prime
C.
x ~ y if x > y
D.
x ~ y if x = y
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Solution
The relation x ~ y if x + y is even is reflexive, symmetric, and transitive, thus it is an equivalence relation.
Correct Answer:
A
— x ~ y if x + y is even
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Q. Which of the following relations is not a function?
A.
R = {(1, 2), (2, 3), (3, 4)}
B.
R = {(1, 2), (1, 3)}
C.
R = {(2, 3), (3, 4)}
D.
R = {(4, 5), (5, 6)}
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Solution
R = {(1, 2), (1, 3)} is not a function because the input 1 maps to two different outputs.
Correct Answer:
B
— R = {(1, 2), (1, 3)}
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Q. Which of the following relations on the set of integers is not a function?
A.
R1 = {(1, 2), (1, 3)}
B.
R2 = {(2, 3), (3, 4)}
C.
R3 = {(4, 5)}
D.
R4 = {(5, 6), (6, 7)}
Show solution
Solution
R1 is not a function because the input 1 maps to two different outputs (2 and 3).
Correct Answer:
A
— R1 = {(1, 2), (1, 3)}
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Q. Which of the following represents a family of circles with varying radii?
A.
(x - h)^2 + (y - k)^2 = r^2
B.
(x - h)^2 + (y - k) = r
C.
x^2 + y^2 = r
D.
x^2 + y^2 = kx
Show solution
Solution
The equation (x - h)^2 + (y - k)^2 = r^2 represents a circle centered at (h, k) with radius r.
Correct Answer:
A
— (x - h)^2 + (y - k)^2 = r^2
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Q. Which of the following represents a family of curves for the equation y = a sin(bx)?
A.
Linear functions
B.
Exponential functions
C.
Sine waves with varying amplitudes and frequencies
D.
Quadratic functions
Show solution
Solution
The equation y = a sin(bx) represents sine waves where 'a' is the amplitude and 'b' is the frequency.
Correct Answer:
C
— Sine waves with varying amplitudes and frequencies
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Q. Which of the following represents a family of curves for the equation y = ax^2 + bx + c?
A.
Linear functions
B.
Quadratic functions
C.
Cubic functions
D.
Exponential functions
Show solution
Solution
The equation y = ax^2 + bx + c represents a family of quadratic functions where 'a', 'b', and 'c' are constants.
Correct Answer:
B
— Quadratic functions
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Q. Which of the following represents a family of exponential curves?
A.
y = ae^(bx)
B.
y = ax^2 + bx + c
C.
y = a sin(bx)
D.
y = a log(bx)
Show solution
Solution
The equation y = ae^(bx) represents a family of exponential curves where a and b are constants.
Correct Answer:
A
— y = ae^(bx)
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Q. Which of the following represents a family of straight lines?
A.
y = mx + c
B.
y = ax^2 + bx + c
C.
y = e^x
D.
y = sin(x)
Show solution
Solution
The equation y = mx + c represents a family of straight lines for different values of m and c.
Correct Answer:
A
— y = mx + c
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Q. Which of the following represents a hyperbola with transverse axis along the x-axis?
A.
x^2/a^2 - y^2/b^2 = 1
B.
y^2/a^2 - x^2/b^2 = 1
C.
x^2/b^2 - y^2/a^2 = 1
D.
y^2/b^2 - x^2/a^2 = 1
Show solution
Solution
The equation x^2/a^2 - y^2/b^2 = 1 represents a hyperbola with transverse axis along the x-axis.
Correct Answer:
A
— x^2/a^2 - y^2/b^2 = 1
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Q. Which of the following represents the solution to the inequality 4 - x < 1?
A.
x > 3
B.
x < 3
C.
x > 4
D.
x < 4
Show solution
Solution
4 - x < 1 => -x < -3 => x > 3
Correct Answer:
A
— x > 3
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Q. Which of the following represents the solution to the inequality 4 - x < 2?
A.
x < 2
B.
x > 2
C.
x < 4
D.
x > 4
Show solution
Solution
4 - x < 2 => -x < -2 => x > 2.
Correct Answer:
B
— x > 2
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Q. Which of the following represents the solution to the inequality 6x - 4 ≤ 2x + 8?
A.
x ≤ 3
B.
x ≥ 3
C.
x < 3
D.
x > 3
Show solution
Solution
6x - 4 ≤ 2x + 8 => 4x ≤ 12 => x ≤ 3.
Correct Answer:
B
— x ≥ 3
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Q. Which of the following represents the solution to the inequality 7x - 4 < 10?
A.
x < 2
B.
x > 2
C.
x < 3
D.
x > 3
Show solution
Solution
7x - 4 < 10 => 7x < 14 => x < 2.
Correct Answer:
C
— x < 3
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Q. Which of the following represents the solution to the inequality x/3 + 2 < 5?
A.
x < 9
B.
x > 9
C.
x < 6
D.
x > 6
Show solution
Solution
x/3 + 2 < 5 => x/3 < 3 => x < 9.
Correct Answer:
A
— x < 9
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Q. Which of the following represents the solution to the inequality x/3 - 2 < 1?
A.
x < 9
B.
x > 9
C.
x ≤ 9
D.
x ≥ 9
Show solution
Solution
x/3 - 2 < 1 => x/3 < 3 => x < 9.
Correct Answer:
A
— x < 9
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Q. Which of the following sets is a power set of F = {1, 2}?
A.
{{1}, {2}}
B.
{{}, {1}, {2}, {1, 2}}
C.
{{1, 2}}
D.
{{1, 2}, {1}}
Show solution
Solution
The power set of F = {1, 2} is {{}, {1}, {2}, {1, 2}}.
Correct Answer:
B
— {{}, {1}, {2}, {1, 2}}
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Q. Which of the following sets is a power set of F = {a, b}?
A.
{∅, {a}, {b}}
B.
{∅, {a}, {b}, {a, b}}
C.
{a, b}
D.
{a, b, ∅}
Show solution
Solution
The power set of F = {a, b} is {∅, {a}, {b}, {a, b}}.
Correct Answer:
B
— {∅, {a}, {b}, {a, b}}
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Q. Which of the following sets is a universal set for the sets A = {1, 2} and B = {2, 3}?
A.
{1, 2, 3}
B.
{2, 3, 4}
C.
{1, 2, 4}
D.
{1, 3}
Show solution
Solution
A universal set contains all elements under consideration. Here, {1, 2, 3} contains all elements from both A and B.
Correct Answer:
A
— {1, 2, 3}
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Q. Which of the following sets is equal to the power set of G = {x, y}?
A.
{∅, {x}, {y}, {x, y}}
B.
{x, y}
C.
{∅, {x, y}}
D.
{x, y, ∅}
Show solution
Solution
The power set of a set with n elements has 2^n subsets. For G, n=2, so the power set is {∅, {x}, {y}, {x, y}}.
Correct Answer:
A
— {∅, {x}, {y}, {x, y}}
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Q. Which of the following sets is equal to the set of all subsets of {1, 2}?
A.
{{1}, {2}}
B.
{{}, {1}, {2}, {1, 2}}
C.
{{1, 2}}
D.
{{1, 2}, {1}, {2}}
Show solution
Solution
The power set of {1, 2} is {{}, {1}, {2}, {1, 2}}.
Correct Answer:
B
— {{}, {1}, {2}, {1, 2}}
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Q. Which of the following sets is not a subset of {1, 2, 3, 4}?
A.
{1, 2}
B.
{2, 3, 4}
C.
{5}
D.
{1, 2, 3}
Show solution
Solution
A subset can only contain elements from the original set. {5} is not a subset of {1, 2, 3, 4}.
Correct Answer:
C
— {5}
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Q. Which of the following sets is not a subset of {x | x is a natural number}?
A.
{1, 2}
B.
{0}
C.
{3, 4}
D.
{5, 6}
Show solution
Solution
The set {0} is not a subset of the natural numbers, as natural numbers start from 1.
Correct Answer:
B
— {0}
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Q. Which of the following statements is true about continuous functions?
A.
They can be differentiated everywhere
B.
They are always bounded
C.
They can be integrated
D.
They can have jump discontinuities
Show solution
Solution
Continuous functions can be integrated over an interval, but they are not necessarily differentiable or bounded.
Correct Answer:
C
— They can be integrated
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Showing 2821 to 2847 of 2847 (95 Pages)
Mathematics Syllabus (JEE Main) MCQ & Objective Questions
The Mathematics Syllabus for JEE Main is crucial for students aiming to excel in competitive exams. Understanding this syllabus not only helps in grasping key concepts but also enhances your ability to tackle objective questions effectively. Practicing MCQs and important questions from this syllabus is essential for solid exam preparation, ensuring you are well-equipped to score better in your exams.
What You Will Practise Here
Sets, Relations, and Functions
Complex Numbers and Quadratic Equations
Permutations and Combinations
Binomial Theorem
Sequences and Series
Limits and Derivatives
Statistics and Probability
Exam Relevance
The Mathematics Syllabus (JEE Main) is not only relevant for JEE but also appears in CBSE and State Board examinations. Students can expect a variety of question patterns, including direct MCQs, numerical problems, and conceptual questions. Mastery of this syllabus will prepare you for similar topics in NEET and other competitive exams, making it vital for your overall academic success.
Common Mistakes Students Make
Misinterpreting the questions, especially in word problems.
Overlooking the importance of units and dimensions in problems.
Confusing formulas related to sequences and series.
Neglecting to practice derivations, leading to errors in calculus.
Failing to apply the correct methods for solving probability questions.
FAQs
Question: What are the key topics in the Mathematics Syllabus for JEE Main? Answer: Key topics include Sets, Complex Numbers, Permutations, Binomial Theorem, and Calculus.
Question: How can I improve my performance in Mathematics MCQs? Answer: Regular practice of MCQs and understanding the underlying concepts are essential for improvement.
Now is the time to take charge of your exam preparation! Dive into solving practice MCQs and test your understanding of the Mathematics Syllabus (JEE Main). Your success is just a question away!
