Q. If R is a relation on the set {a, b, c} defined by R = {(a, b), (b, c)}, what can be said about R?
A.
Reflexive
B.
Symmetric
C.
Transitive
D.
None of the above
Show solution
Solution
R is neither reflexive, symmetric, nor transitive as it does not satisfy any of the properties.
Correct Answer:
D
— None of the above
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Q. If R is a relation on the set {a, b, c} defined by R = {(a, b), (b, c)}, which property does R NOT have?
A.
Reflexive
B.
Symmetric
C.
Transitive
D.
None of the above
Show solution
Solution
R is not symmetric as (b,c) does not imply (c,b) is in R. It is reflexive and transitive.
Correct Answer:
B
— Symmetric
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Q. If R is a relation on the set {x, y, z} defined by R = {(x, y), (y, z), (z, x)}, what can be said about R?
A.
Reflexive
B.
Symmetric
C.
Transitive
D.
None of the above
Show solution
Solution
R is neither reflexive, symmetric, nor transitive.
Correct Answer:
D
— None of the above
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Q. If sec A = 2, what is the value of cos A?
Show solution
Solution
Since sec A = 1/cos A, we have cos A = 1/2.
Correct Answer:
A
— 1/2
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Q. If sec θ = 2, what is the value of cos θ?
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Solution
Since sec θ = 1/cos θ, if sec θ = 2, then cos θ = 1/2.
Correct Answer:
A
— 1/2
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Q. If sec(x) = 2, what is the value of cos(x)?
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Solution
sec(x) = 1/cos(x), so cos(x) = 1/2.
Correct Answer:
A
— 1/2
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Q. If sin A = 0.6, what is cos A?
A.
0.8
B.
0.6
C.
0.4
D.
0.2
Show solution
Solution
Using the identity sin^2 A + cos^2 A = 1, we have cos A = sqrt(1 - (0.6)^2) = sqrt(1 - 0.36) = sqrt(0.64) = 0.8.
Correct Answer:
A
— 0.8
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Q. If sin A = 0.6, what is the value of cos A?
A.
0.8
B.
0.6
C.
0.4
D.
0.2
Show solution
Solution
Using the identity sin^2 A + cos^2 A = 1, we have cos A = sqrt(1 - (0.6)^2) = sqrt(1 - 0.36) = sqrt(0.64) = 0.8.
Correct Answer:
A
— 0.8
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Q. If sin A = 0.6, what is the value of tan A?
A.
0.8
B.
1.2
C.
0.75
D.
1.5
Show solution
Solution
Using the identity tan A = sin A / cos A, we find cos A = sqrt(1 - (0.6)^2) = 0.8, thus tan A = 0.6 / 0.8 = 0.75.
Correct Answer:
B
— 1.2
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Q. If sin A = 1/2, what are the possible values of A in the range [0°, 360°]?
A.
30°, 150°
B.
45°, 135°
C.
60°, 300°
D.
90°, 270°
Show solution
Solution
sin A = 1/2 at A = 30° and A = 150°.
Correct Answer:
A
— 30°, 150°
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Q. If sin A = 1/2, what is the value of A in degrees?
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Solution
sin A = 1/2 corresponds to A = 30°.
Correct Answer:
A
— 30
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Q. If sin A = 1/√2, what is the value of A?
A.
45°
B.
30°
C.
60°
D.
90°
Show solution
Solution
The angle A for which sin A = 1/√2 is A = 45°.
Correct Answer:
A
— 45°
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Q. If sin A = 3/5, what is the value of cos A?
A.
4/5
B.
3/5
C.
5/4
D.
1/2
Show solution
Solution
Using the identity sin^2 A + cos^2 A = 1, we have cos A = sqrt(1 - (3/5)^2) = sqrt(1 - 9/25) = sqrt(16/25) = 4/5.
Correct Answer:
A
— 4/5
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Q. If sin A = 4/5, what is the value of tan A?
A.
3/4
B.
4/3
C.
5/4
D.
5/3
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Solution
Using the identity tan A = sin A / cos A, we find cos A = 3/5, thus tan A = (4/5) / (3/5) = 4/3.
Correct Answer:
B
— 4/3
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Q. If sin(2x) = 2sin(x)cos(x), what is the double angle formula for sine?
A.
sin(2x) = sin(x) + cos(x)
B.
sin(2x) = 2sin(x)cos(x)
C.
sin(2x) = sin^2(x) - cos^2(x)
D.
sin(2x) = 2sin^2(x)
Show solution
Solution
The double angle formula for sine is sin(2x) = 2sin(x)cos(x).
Correct Answer:
B
— sin(2x) = 2sin(x)cos(x)
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Q. If sin(2θ) = 2sin(θ)cos(θ), what is this identity called?
A.
Pythagorean Identity
B.
Double Angle Identity
C.
Sum Formula
D.
Product Formula
Show solution
Solution
This is known as the Double Angle Identity for sine.
Correct Answer:
B
— Double Angle Identity
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Q. If sin(x) = 0, what are the possible values of x?
A.
nπ
B.
nπ/2
C.
nπ + π/2
D.
nπ + π
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Solution
sin(x) = 0 at x = nπ, where n is any integer.
Correct Answer:
A
— nπ
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Q. If sin(x) = 0, what is the value of cos(x)?
A.
1
B.
0
C.
-1
D.
undefined
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Solution
If sin(x) = 0, then cos(x) can be either 1 or -1 depending on the angle x.
Correct Answer:
A
— 1
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Q. If sin(x) = 0, what is the value of tan(x)?
A.
0
B.
1
C.
undefined
D.
∞
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Solution
tan(x) = sin(x)/cos(x). If sin(x) = 0, then tan(x) is undefined when cos(x) = 0.
Correct Answer:
C
— undefined
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Q. If sin(x) = 0, what is the value of x?
A.
0
B.
π
C.
2π
D.
All of the above
Show solution
Solution
sin(x) = 0 at x = nπ, where n is any integer, hence all of the above.
Correct Answer:
D
— All of the above
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Q. If sin(x) = 1/2, what are the possible values of x in [0, 2π]?
A.
π/6, 5π/6
B.
π/4, 3π/4
C.
0, π
D.
π/3, 2π/3
Show solution
Solution
sin(x) = 1/2 at x = π/6 and x = 5π/6 in the interval [0, 2π].
Correct Answer:
A
— π/6, 5π/6
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Q. If sin(x) = 1/2, what is the value of x in degrees?
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Solution
sin(30°) = 1/2, so x = 30°.
Correct Answer:
A
— 30
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Q. If sin(x) = 1/2, what is the value of x in the interval [0, 2π]?
A.
π/6
B.
5π/6
C.
7π/6
D.
11π/6
Show solution
Solution
The angles where sin(x) = 1/2 in the interval [0, 2π] are x = π/6 and x = 5π/6.
Correct Answer:
A
— π/6
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Q. If sin(x) = 1/2, what is the value of x in the range [0, 2π]?
A.
π/6
B.
π/3
C.
5π/6
D.
7π/6
Show solution
Solution
x = π/6 and 5π/6.
Correct Answer:
A
— π/6
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Q. If sin(x) = 1/√2, what is cos(x)?
A.
1/√2
B.
0
C.
√2/2
D.
1
Show solution
Solution
Using the identity sin^2(x) + cos^2(x) = 1, we have cos^2(x) = 1 - (1/√2)^2 = 1 - 1/2 = 1/2. Thus, cos(x) = ±1/√2.
Correct Answer:
A
— 1/√2
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Q. If sin(x) = 1/√2, what is tan(x)?
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Solution
tan(x) = sin(x)/cos(x) = (1/√2)/(1/√2) = 1.
Correct Answer:
B
— √2
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Q. If sin(x) = 1/√2, what is the value of cos(x)?
A.
1/√2
B.
0
C.
√2/2
D.
1
Show solution
Solution
Using the identity sin^2(x) + cos^2(x) = 1, we have cos^2(x) = 1 - (1/√2)^2 = 1 - 1/2 = 1/2. Therefore, cos(x) = 1/√2.
Correct Answer:
A
— 1/√2
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Q. If sin(x) = 3/5, what is cos(x)?
A.
4/5
B.
3/5
C.
5/4
D.
1/5
Show solution
Solution
Using the identity sin^2(x) + cos^2(x) = 1, we have cos^2(x) = 1 - (3/5)^2 = 1 - 9/25 = 16/25. Therefore, cos(x) = ±4/5. The positive value is taken as x is in the first quadrant.
Correct Answer:
A
— 4/5
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Q. If sin(x) = 3/5, what is the value of cos(x)?
A.
4/5
B.
3/5
C.
5/4
D.
1/5
Show solution
Solution
Using the identity sin^2(x) + cos^2(x) = 1, we have cos^2(x) = 1 - (3/5)^2 = 1 - 9/25 = 16/25. Therefore, cos(x) = ±4/5.
Correct Answer:
A
— 4/5
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Q. If sin(α) = 0.6, what is the value of cos(α) using the identity?
A.
0.8
B.
0.6
C.
0.4
D.
0.2
Show solution
Solution
Using sin^2(α) + cos^2(α) = 1, we find cos(α) = √(1 - 0.6^2) = √(1 - 0.36) = √0.64 = 0.8.
Correct Answer:
A
— 0.8
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Showing 1351 to 1380 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!
