Q. Which of the following functions is not continuous at x = 1?
A.
f(x) = x^2
B.
f(x) = 1/x
C.
f(x) = sin(x)
D.
f(x) = { x, x < 1; 2, x >= 1 }
Show solution
Solution
The function has a jump discontinuity at x = 1, hence it is not continuous.
Correct Answer:
D
— f(x) = { x, x < 1; 2, x >= 1 }
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Q. Which of the following functions is not continuous?
A.
f(x) = x^2
B.
f(x) = 1/x
C.
f(x) = sin(x)
D.
f(x) = e^x
Show solution
Solution
f(x) = 1/x is not continuous at x = 0.
Correct Answer:
B
— f(x) = 1/x
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Q. Which of the following functions is not differentiable at x = 0? f(x) = x^2 sin(1/x) for x ≠ 0 and f(0) = 0.
A.
f(x)
B.
g(x) =
C.
x
D.
.
h(x) = x^3
.
k(x) = x^2
Show solution
Solution
The function f(x) is not differentiable at x = 0 due to the oscillatory nature of sin(1/x) as x approaches 0.
Correct Answer:
A
— f(x)
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Q. Which of the following functions is periodic?
A.
f(x) = x
B.
f(x) = cos(x)
C.
f(x) = e^x
D.
f(x) = ln(x)
Show solution
Solution
The cosine function is periodic with a period of 2π.
Correct Answer:
B
— f(x) = cos(x)
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Q. Which of the following is a family of exponential curves?
A.
y = e^x
B.
y = x^2
C.
y = log(x)
D.
y = sin(x)
Show solution
Solution
The equation y = e^x represents a family of exponential curves for different bases.
Correct Answer:
A
— y = e^x
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Q. Which of the following is a necessary condition for a function to be continuous at a point?
A.
The function must be defined at that point
B.
The function must be differentiable at that point
C.
The function must be bounded
D.
The function must be increasing
Show solution
Solution
A function must be defined at a point to be continuous there.
Correct Answer:
A
— The function must be defined at that point
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Q. Which of the following is a necessary condition for f(x) to be continuous at x = a?
A.
f(a) exists
B.
lim x->a f(x) exists
C.
lim x->a f(x) = f(a)
D.
All of the above
Show solution
Solution
All conditions must be satisfied for f(x) to be continuous at x = a.
Correct Answer:
D
— All of the above
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Q. Which of the following is a one-to-one function?
A.
f(x) = x^2
B.
f(x) = 2x + 3
C.
f(x) = sin(x)
D.
f(x) = e^x
Show solution
Solution
A function is one-to-one if it never takes the same value twice. f(x) = 2x + 3 and f(x) = e^x are one-to-one.
Correct Answer:
B
— f(x) = 2x + 3
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Q. Which of the following is a purely imaginary number?
A.
2 + 3i
B.
0
C.
4
D.
0 + 5i
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Solution
A purely imaginary number has no real part, so 0 + 5i is purely imaginary.
Correct Answer:
D
— 0 + 5i
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Q. Which of the following is a root of the equation z^2 + 1 = 0?
Show solution
Solution
The roots are z = ±i.
Correct Answer:
A
— i
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Q. Which of the following is a subset of {1, 2, 3}?
A.
{1, 2}
B.
{4}
C.
{1, 2, 3, 4}
D.
{2, 3, 4}
Show solution
Solution
A subset is a set that contains elements from another set. {1, 2} is a subset of {1, 2, 3}.
Correct Answer:
A
— {1, 2}
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Q. Which of the following is a subset of {x, y, z}?
A.
{x, y}
B.
{x, y, z, w}
C.
{y, z, w}
D.
{x, y, z, x}
Show solution
Solution
A subset can only contain elements that are in the original set. {x, y} is a valid subset of {x, y, z}.
Correct Answer:
A
— {x, y}
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Q. Which of the following is an even function?
A.
f(x) = x^3
B.
f(x) = x^2
C.
f(x) = sin(x)
D.
f(x) = tan(x)
Show solution
Solution
An even function satisfies f(x) = f(-x). f(x) = x^2 is even.
Correct Answer:
B
— f(x) = x^2
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Q. Which of the following is an identity?
A.
sin^2 x + cos^2 x = 1
B.
tan x = sin x / cos x
C.
sec x = 1/cos x
D.
All of the above
Show solution
Solution
All the given options are trigonometric identities.
Correct Answer:
D
— All of the above
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Q. Which of the following is equivalent to log_a(b^c)?
A.
c * log_a(b)
B.
log_a(b) / c
C.
log_a(c) + log_a(b)
D.
log_a(b) - c
Show solution
Solution
log_a(b^c) = c * log_a(b) by the power rule of logarithms.
Correct Answer:
A
— c * log_a(b)
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Q. Which of the following is NOT a family of curves?
A.
y = kx^2
B.
y = ksin(x)
C.
y = kx
D.
y = k/x
Show solution
Solution
y = kx represents a family of straight lines, but it is not a family of curves.
Correct Answer:
C
— y = kx
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Q. Which of the following is not a subset of {a, b, c}?
A.
{a}
B.
{b, c}
C.
{a, b, c}
D.
{d}
Show solution
Solution
The set {d} does not contain any elements from {a, b, c}, so it is not a subset.
Correct Answer:
D
— {d}
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Q. Which of the following is not continuous at x = 0?
A.
f(x) = x^3
B.
f(x) = e^x
C.
f(x) = 1/x
D.
f(x) = ln(x)
Show solution
Solution
f(x) = 1/x is not continuous at x = 0 as it is undefined there.
Correct Answer:
C
— f(x) = 1/x
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Q. Which of the following is the correct identity for sin(2A)?
A.
2sinAcosA
B.
sin^2A + cos^2A
C.
sinA + cosA
D.
sinAcosA
Show solution
Solution
The double angle formula states that sin(2A) = 2sinAcosA.
Correct Answer:
A
— 2sinAcosA
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Q. Which of the following is the equation of 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 of a hyperbola with transverse axis along the x-axis is x^2/a^2 - y^2/b^2 = 1.
Correct Answer:
A
— x^2/a^2 - y^2/b^2 = 1
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Q. Which of the following is the equation of an ellipse with foci at (0, ±c) and vertices at (0, ±a)?
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 of an ellipse with foci at (0, ±c) and vertices at (0, ±a) is y^2/a^2 + x^2/b^2 = 1.
Correct Answer:
A
— x^2/a^2 + y^2/b^2 = 1
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Q. Which of the following is the range of the function f(x) = x^2 - 4?
A.
(-∞, -4]
B.
[-4, ∞)
C.
(-4, ∞)
D.
[0, ∞)
Show solution
Solution
The minimum value of f(x) is -4 when x=0, so the range is [-4, ∞).
Correct Answer:
B
— [-4, ∞)
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Q. Which of the following is the range of the function f(x) = x^2?
A.
All real numbers
B.
All positive real numbers
C.
All non-negative real numbers
D.
All integers
Show solution
Solution
The function f(x) = x^2 is non-negative for all real x, hence the range is all non-negative real numbers.
Correct Answer:
C
— All non-negative real numbers
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Q. Which of the following is the range of the function f(x) = |x - 1|?
A.
(-∞, 1)
B.
[0, ∞)
C.
(-1, 1)
D.
[1, ∞)
Show solution
Solution
The minimum value of |x - 1| is 0 when x = 1, so the range is [0, ∞).
Correct Answer:
B
— [0, ∞)
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Q. Which of the following is the solution set for the inequality x + 2 > 1?
A.
x > -1
B.
x < -1
C.
x > 1
D.
x < 1
Show solution
Solution
x + 2 > 1 => x > -1.
Correct Answer:
A
— x > -1
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Q. Which of the following is the solution set for the inequality x + 2 > 7?
A.
x > 5
B.
x < 5
C.
x > 9
D.
x < 9
Show solution
Solution
x + 2 > 7 => x > 5.
Correct Answer:
A
— x > 5
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Q. Which of the following is the solution set for the inequality x + 5 > 2?
A.
x > -3
B.
x < -3
C.
x > 3
D.
x < 3
Show solution
Solution
x + 5 > 2 => x > -3.
Correct Answer:
A
— x > -3
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Q. Which of the following is the solution set for the inequality: 3x + 2 > 11?
A.
x > 3
B.
x < 3
C.
x > 2
D.
x < 2
Show solution
Solution
3x + 2 > 11 => 3x > 9 => x > 3.
Correct Answer:
A
— x > 3
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Q. Which of the following is the solution to the inequality 3x + 2 ≥ 11?
A.
x < 3
B.
x > 3
C.
x ≤ 3
D.
x ≥ 3
Show solution
Solution
3x + 2 ≥ 11 => 3x ≥ 9 => x ≥ 3.
Correct Answer:
D
— x ≥ 3
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Q. Which of the following is the solution to the inequality x + 2 > 7?
A.
x < 5
B.
x > 5
C.
x < 9
D.
x > 9
Show solution
Solution
x + 2 > 7 => x > 5.
Correct Answer:
B
— x > 5
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Showing 2791 to 2820 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!
