Q. If vector A = (1, 2, 3) and vector B = (4, 5, 6), what is the vector A - B?
A.
(-3, -3, -3)
B.
(3, 3, 3)
C.
(5, 7, 9)
D.
(0, 0, 0)
Show solution
Solution
A - B = (1-4, 2-5, 3-6) = (-3, -3, -3).
Correct Answer:
A
— (-3, -3, -3)
Learn More →
Q. If vector A = (2, 2, 2) and vector B = (1, 1, 1), what is the scalar triple product A . (B × A)?
Show solution
Solution
A . (B × A) = 0, since B × A = 0.
Correct Answer:
A
— 0
Learn More →
Q. If vector A = (3, -2, 1) and vector B = (1, 4, -3), what is the cross product A × B?
A.
(-5, -10, 14)
B.
(5, 10, -14)
C.
(10, 14, 5)
D.
(14, -5, 10)
Show solution
Solution
A × B = |i j k|\n|3 -2 1|\n|1 4 -3| = (-5, -10, 14).
Correct Answer:
A
— (-5, -10, 14)
Learn More →
Q. If vectors A = (x, 2, 3) and B = (1, y, 4) are perpendicular, what is the value of x + y?
Show solution
Solution
A · B = x*1 + 2*y + 3*4 = 0. Thus, x + 2y + 12 = 0. Solving gives x + y = -6.
Correct Answer:
B
— 2
Learn More →
Q. If vectors A = 3i + 4j and B = 2i - j, what is the scalar product A · B?
Show solution
Solution
A · B = (3)(2) + (4)(-1) = 6 - 4 = 2.
Correct Answer:
C
— 10
Learn More →
Q. If x + 2y = 10 and 2x - y = 3, what is the value of x?
Show solution
Solution
From the first equation, x = 10 - 2y. Substituting into the second gives 2(10 - 2y) - y = 3, solving gives y = 4, x = 2.
Correct Answer:
C
— 3
Learn More →
Q. If x = cos^(-1)(-1/2), what is the value of x?
A.
π/3
B.
2π/3
C.
π/4
D.
π/6
Show solution
Solution
x = cos^(-1)(-1/2) = 2π/3
Correct Answer:
B
— 2π/3
Learn More →
Q. If x = cos^(-1)(1/2), then the value of sin(x) is:
Show solution
Solution
If x = cos^(-1)(1/2), then x = π/3. Therefore, sin(x) = sin(π/3) = √3/2.
Correct Answer:
B
— √3/2
Learn More →
Q. If x = cos^(-1)(1/2), then what is the value of sin(x)?
Show solution
Solution
If x = cos^(-1)(1/2), then cos(x) = 1/2, which corresponds to x = π/3. Therefore, sin(x) = sin(π/3) = √3/2.
Correct Answer:
B
— √3/2
Learn More →
Q. If x = cos^(-1)(1/2), then what is the value of sin^(-1)(x)?
A.
π/3
B.
π/6
C.
π/4
D.
0
Show solution
Solution
Since x = cos^(-1)(1/2) = π/3, then sin^(-1)(1/2) = π/6.
Correct Answer:
B
— π/6
Learn More →
Q. If x = cos^(-1)(1/2), then what is the value of sin^(-1)(√(1 - (1/2)^2))?
A.
π/3
B.
π/4
C.
π/2
D.
0
Show solution
Solution
Since cos^(-1)(1/2) = π/3, we have sin^(-1)(√(1 - (1/2)^2)) = sin^(-1)(√(3/4)) = π/3.
Correct Answer:
A
— π/3
Learn More →
Q. If x = cos^(-1)(1/2), then what is the value of x?
A.
π/3
B.
π/4
C.
π/2
D.
0
Show solution
Solution
cos^(-1)(1/2) = π/3.
Correct Answer:
A
— π/3
Learn More →
Q. If x = cos^(-1)(1/2), what is sin(x)?
Show solution
Solution
If x = cos^(-1)(1/2), then x = π/3, thus sin(x) = sin(π/3) = √3/2.
Correct Answer:
A
— √3/2
Learn More →
Q. If x = cos^(-1)(1/2), what is the value of sin(x)?
Show solution
Solution
Using the identity sin(x) = sqrt(1 - cos^2(x)), we have sin(x) = sqrt(1 - (1/2)^2) = √3/2.
Correct Answer:
A
— √3/2
Learn More →
Q. If x = sin^(-1)(-1), then the value of x is:
Show solution
Solution
sin^(-1)(-1) corresponds to the angle -π/2.
Correct Answer:
A
— -π/2
Learn More →
Q. If x = sin^(-1)(-1), what is the value of x?
Show solution
Solution
sin^(-1)(-1) corresponds to the angle -π/2.
Correct Answer:
A
— -π/2
Learn More →
Q. If x = sin^(-1)(-1/2), then what is the value of x?
A.
-π/6
B.
π/6
C.
-π/3
D.
π/3
Show solution
Solution
sin^(-1)(-1/2) = -π/6, since sin(-π/6) = -1/2.
Correct Answer:
A
— -π/6
Learn More →
Q. If x = sin^(-1)(-1/2), what is the value of x?
A.
-π/6
B.
π/6
C.
π/4
D.
0
Show solution
Solution
sin^(-1)(-1/2) = -π/6, since sin(-π/6) = -1/2.
Correct Answer:
A
— -π/6
Learn More →
Q. If x = sin^(-1)(1/2), then the value of cos(x) is:
Show solution
Solution
If x = sin^(-1)(1/2), then x = π/6. Therefore, cos(x) = cos(π/6) = √3/2.
Correct Answer:
B
— √3/2
Learn More →
Q. If x = sin^(-1)(1/2), what is the value of cos(x)?
Show solution
Solution
If x = sin^(-1)(1/2), then x = π/6. Therefore, cos(x) = cos(π/6) = √3/2.
Correct Answer:
B
— √3/2
Learn More →
Q. If x = sin^(-1)(1/3), then what is the value of cos(x)?
A.
√(8)/3
B.
√(2)/3
C.
1/3
D.
2/3
Show solution
Solution
Using the identity cos(x) = √(1 - sin^2(x)), we find cos(sin^(-1)(1/3)) = √(1 - (1/3)^2) = √(8)/3.
Correct Answer:
A
— √(8)/3
Learn More →
Q. If x = sin^(-1)(1/3), then what is the value of cos^(-1)(√(1 - (1/3)^2))?
A.
π/3
B.
π/2
C.
2π/3
D.
π/4
Show solution
Solution
Using the identity cos^(-1)(√(1 - sin^2(x))) = π/2 - x, we find that cos^(-1)(√(1 - (1/3)^2)) = π/2 - sin^(-1)(1/3).
Correct Answer:
B
— π/2
Learn More →
Q. If x = sin^(-1)(1/√2), then what is the value of cos(x)?
A.
1/2
B.
√2/2
C.
√3/2
D.
1
Show solution
Solution
If x = sin^(-1)(1/√2), then sin(x) = 1/√2. Therefore, cos(x) = √(1 - sin^2(x)) = √(1 - (1/√2)^2) = √(1/2) = √2/2.
Correct Answer:
B
— √2/2
Learn More →
Q. If x = sin^(-1)(1/√2), then what is the value of cos^(-1)(x)?
A.
π/4
B.
π/3
C.
π/2
D.
π/6
Show solution
Solution
Since x = sin^(-1)(1/√2) = π/4, then cos^(-1)(x) = π/2 - π/4 = π/4.
Correct Answer:
A
— π/4
Learn More →
Q. If x = sin^(-1)(3/5), what is cos(x)?
A.
4/5
B.
3/5
C.
5/4
D.
1/5
Show solution
Solution
Using the identity cos^2(x) + sin^2(x) = 1, we find cos(x) = √(1 - (3/5)^2) = 4/5.
Correct Answer:
A
— 4/5
Learn More →
Q. If x = sin^(-1)(3/5), what is the value of cos(x)?
A.
4/5
B.
3/5
C.
2/5
D.
1/5
Show solution
Solution
Using the identity cos(x) = sqrt(1 - sin^2(x)), we have cos(x) = sqrt(1 - (3/5)^2) = sqrt(16/25) = 4/5.
Correct Answer:
A
— 4/5
Learn More →
Q. If x = tan^(-1)(1), then the value of x is:
Show solution
Solution
tan^(-1)(1) = π/4.
Correct Answer:
A
— π/4
Learn More →
Q. If x = tan^(-1)(1), what is the value of x?
A.
π/4
B.
π/3
C.
π/6
D.
0
Show solution
Solution
tan^(-1)(1) = π/4, since tan(π/4) = 1.
Correct Answer:
A
— π/4
Learn More →
Q. If x = tan^(-1)(1/√3), what is the value of x?
A.
π/6
B.
π/4
C.
π/3
D.
0
Show solution
Solution
tan^(-1)(1/√3) = π/6, since tan(π/6) = 1/√3.
Correct Answer:
A
— π/6
Learn More →
Q. If x = tan^(-1)(√3), then what is the value of sin^(-1)(x)?
A.
π/3
B.
π/4
C.
π/2
D.
π/6
Show solution
Solution
x = tan^(-1)(√3) = π/3, thus sin^(-1)(x) = sin^(-1)(√3/2) = π/3.
Correct Answer:
A
— π/3
Learn More →
Showing 1621 to 1650 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!
