Q. The slopes of the lines represented by the equation 2x^2 + 3xy + y^2 = 0 are:
A.
-1, -2
B.
1, 2
C.
-1, 1
D.
2, -2
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Solution
The slopes can be found by solving the quadratic equation derived from the given equation.
Correct Answer:
A
— -1, -2
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Q. The slopes of the lines represented by the equation 5x^2 + 6xy + 2y^2 = 0 are given by:
A.
-3/5 and -2/5
B.
2/5 and -5/2
C.
1/2 and -2
D.
None of the above
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Solution
Using the quadratic formula, the slopes are found to be -3/5 and -2/5.
Correct Answer:
A
— -3/5 and -2/5
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Q. The slopes of the lines represented by the equation 5x^2 + 6xy + 2y^2 = 0 are:
A.
-3/5, -2/5
B.
2/5, 3/5
C.
1, -1
D.
0, ∞
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Solution
The slopes can be calculated using the quadratic formula, yielding -3/5 and -2/5.
Correct Answer:
A
— -3/5, -2/5
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Q. The sum of the roots of the equation 2x^2 - 3x + 1 = 0 is equal to what?
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Solution
Using Vieta's formulas, the sum of the roots is -(-3)/2 = 3/2.
Correct Answer:
B
— 3/2
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Q. The sum of the roots of the equation 2x^2 - 4x + k = 0 is 3. What is the value of k?
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Solution
The sum of the roots is given by -b/a = 4/2 = 2. Setting this equal to 3 gives k = 1.
Correct Answer:
A
— 1
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Q. The sum of the roots of the equation 3x^2 - 12x + 9 = 0 is:
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Solution
The sum of the roots is given by -b/a = 12/3 = 4.
Correct Answer:
C
— 4
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Q. The sum of the roots of the equation x^2 - 7x + 10 = 0 is?
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Solution
The sum of the roots is given by -b/a = 7/1 = 7.
Correct Answer:
C
— 7
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Q. The sum of the roots of the quadratic equation 2x^2 - 4x + k = 0 is 3. What is the value of k?
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Solution
Using the sum of roots formula -b/a, we have 4/2 = 2, thus 2 + 1 = 3, so k = 1.
Correct Answer:
B
— 2
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Q. The sum of the roots of the quadratic equation 3x^2 - 12x + 9 = 0 is equal to what?
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Solution
Using Vieta's formulas, the sum of the roots is -(-12)/3 = 4.
Correct Answer:
B
— 4
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Q. The sum of the roots of the quadratic equation 3x^2 - 12x + 9 = 0 is:
Show solution
Solution
Using Vieta's formulas, the sum of the roots is -(-12)/3 = 4.
Correct Answer:
B
— 4
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Q. The sum of the roots of the quadratic equation 3x^2 - 12x + k = 0 is 4. What is the value of k?
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Solution
Using Vieta's formulas, sum of roots = -b/a = 12/3 = 4, hence k = 8.
Correct Answer:
C
— 8
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Q. The sum of the roots of the quadratic equation x^2 - 7x + 10 = 0 is:
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Solution
The sum of the roots is given by -b/a = 7/1 = 7.
Correct Answer:
B
— 7
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Q. The value of (1 + i)^2 is?
A.
2i
B.
2
C.
0
D.
1 + 2i
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Solution
(1 + i)^2 = 1^2 + 2(1)(i) + i^2 = 1 + 2i - 1 = 2.
Correct Answer:
B
— 2
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Q. The value of cos(tan^(-1)(x)) is:
A.
1/√(1+x^2)
B.
x/√(1+x^2)
C.
√(1+x^2)/x
D.
0
Show solution
Solution
Using the right triangle definition, cos(tan^(-1)(x)) = adjacent/hypotenuse = 1/√(1+x^2).
Correct Answer:
A
— 1/√(1+x^2)
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Q. The value of sin(tan^(-1)(x)) is:
A.
x/√(1+x^2)
B.
√(1-x^2)
C.
1/√(1+x^2)
D.
x
Show solution
Solution
Using the right triangle definition, sin(tan^(-1)(x)) = opposite/hypotenuse = x/√(1+x^2).
Correct Answer:
A
— x/√(1+x^2)
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Q. The value of sin^(-1)(-1) is:
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Solution
sin^(-1)(-1) corresponds to the angle whose sine is -1, which is -π/2.
Correct Answer:
A
— -π/2
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Q. The value of sin^(-1)(sin(π/4)) is:
A.
π/4
B.
3π/4
C.
0
D.
π/2
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Solution
Since π/4 is in the range of sin^(-1), sin^(-1)(sin(π/4)) = π/4.
Correct Answer:
A
— π/4
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Q. The value of sin^(-1)(√3/2) is:
A.
π/3
B.
π/6
C.
π/4
D.
π/2
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Solution
sin^(-1)(√3/2) corresponds to the angle whose sine is √3/2, which is π/3.
Correct Answer:
A
— π/3
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Q. The value of tan^(-1)(√3) is:
A.
π/3
B.
π/4
C.
π/6
D.
π/2
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Solution
tan^(-1)(√3) corresponds to the angle whose tangent is √3, which is π/3.
Correct Answer:
A
— π/3
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Q. The vertices of the ellipse 9x^2 + 16y^2 = 144 are located at?
A.
(±4, 0)
B.
(0, ±3)
C.
(±3, 0)
D.
(0, ±4)
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Solution
The vertices of the ellipse 9x^2 + 16y^2 = 144 are located at (±3, 0).
Correct Answer:
C
— (±3, 0)
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Q. What are the solutions of the equation cos(x) + sin(x) = 1?
A.
x = 0
B.
x = π/4
C.
x = π/2
D.
x = π
Show solution
Solution
The only solution is x = 0.
Correct Answer:
A
— x = 0
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Q. What are the solutions of the equation cos(x) = -1/2 in the interval [0, 2π]?
A.
2π/3, 4π/3
B.
π/3, 5π/3
C.
π/2, 3π/2
D.
0, π
Show solution
Solution
The solutions are x = 2π/3 and 4π/3.
Correct Answer:
A
— 2π/3, 4π/3
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Q. What are the solutions of the equation cos(x) = -1/2?
A.
2π/3
B.
4π/3
C.
π/3
D.
5π/3
Show solution
Solution
The solutions are x = 2π/3 and x = 4π/3.
Correct Answer:
A
— 2π/3
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Q. What are the solutions of the equation cos^2(x) - 1/2 = 0?
A.
x = π/4
B.
x = 3π/4
C.
x = 5π/4
D.
x = 7π/4
Show solution
Solution
The solutions are x = π/4, 3π/4, 5π/4, and 7π/4.
Correct Answer:
A
— x = π/4
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Q. What are the solutions of the equation sin(2x) = 0 in the interval [0, 2π]?
A.
0, π, 2π
B.
0, π/2, π
C.
0, π/4, π/2
D.
0, 3π/2
Show solution
Solution
The solutions are x = 0, π, and 2π.
Correct Answer:
A
— 0, π, 2π
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Q. What are the solutions of the equation sin(2x) = 0?
A.
x = nπ/2
B.
x = nπ
C.
x = nπ + π/2
D.
x = nπ + π
Show solution
Solution
sin(2x) = 0 implies 2x = nπ, thus x = nπ/2 for n ∈ Z.
Correct Answer:
A
— x = nπ/2
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Q. What are the solutions of the equation sin(x) = sin(π/3)?
A.
x = π/3
B.
x = 2π/3
C.
x = 4π/3
D.
x = 5π/3
Show solution
Solution
The solutions are x = π/3 + 2nπ and x = 2π/3 + 2nπ.
Correct Answer:
A
— x = π/3
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Q. What are the solutions of the equation sin^2(x) - sin(x) = 0?
A.
x = nπ
B.
x = nπ + π/2
C.
x = nπ + 2π
D.
x = nπ + π
Show solution
Solution
Factoring gives sin(x)(sin(x) - 1) = 0, so sin(x) = 0 or sin(x) = 1. Thus, x = nπ or x = π/2 + 2nπ.
Correct Answer:
A
— x = nπ
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Q. What is the 75th percentile of the data set {10, 20, 30, 40, 50}?
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Solution
The 75th percentile (Q3) is the value below which 75% of the data falls, which is 40.
Correct Answer:
A
— 40
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Q. What is the 7th term of the sequence defined by a_n = 2^n + 3^n?
A.
2187
B.
243
C.
256
D.
729
Show solution
Solution
a_7 = 2^7 + 3^7 = 128 + 2187 = 2315.
Correct Answer:
A
— 2187
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Showing 2161 to 2190 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!
