Q. If the vector a = (2, -1) and b = (1, 3), what is the cross product a × b?
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Solution
Cross product in 2D = a1*b2 - a2*b1 = 2*3 - (-1)*1 = 6 + 1 = 7
Correct Answer:
A
— 5
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Q. If the vector a = (2, 2) and b = (2, -2), what is the angle between them?
A.
90 degrees
B.
45 degrees
C.
0 degrees
D.
180 degrees
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Solution
Angle = cos⁻¹((a·b) / (|a||b|)) = cos⁻¹(0) = 90 degrees
Correct Answer:
A
— 90 degrees
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Q. If the vector a = (2, 2) is scaled by a factor of 3, what is the resulting vector?
A.
(6, 6)
B.
(3, 3)
C.
(2, 2)
D.
(1, 1)
Show solution
Solution
Scaled vector = 3 * a = 3 * (2, 2) = (6, 6)
Correct Answer:
A
— (6, 6)
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Q. If the vector a = (2, 3) and b = (4, 1), what is the cross product a × b?
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Solution
Cross product a × b = 2*1 - 3*4 = 2 - 12 = -10.
Correct Answer:
A
— -10
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Q. If the vector a = (2, 3) and b = (4, 1), what is the resultant vector a + b?
A.
(6, 4)
B.
(2, 4)
C.
(4, 2)
D.
(6, 2)
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Solution
Resultant vector a + b = (2+4, 3+1) = (6, 4).
Correct Answer:
A
— (6, 4)
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Q. If the vector A = (2, 3) is multiplied by 2, what is the resulting vector?
A.
(4, 6)
B.
(2, 3)
C.
(1, 1.5)
D.
(0, 0)
Show solution
Solution
Resulting vector = 2 * A = 2 * (2, 3) = (4, 6).
Correct Answer:
A
— (4, 6)
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Q. If the vector A = (2, 3) is reflected across the line y = x, what is the resulting vector?
A.
(3, 2)
B.
(2, 3)
C.
(0, 0)
D.
(1, 1)
Show solution
Solution
Reflection across y = x gives vector (3, 2).
Correct Answer:
A
— (3, 2)
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Q. If the vector A = (2, 3) is scaled by a factor of 2, what is the resulting vector?
A.
(4, 6)
B.
(2, 3)
C.
(1, 1.5)
D.
(0, 0)
Show solution
Solution
Scaled vector = 2 * A = 2 * (2, 3) = (4, 6).
Correct Answer:
A
— (4, 6)
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Q. If the vector a = (2, 3, 4) and b = (1, 0, -1), what is a + b?
A.
(3, 3, 3)
B.
(1, 3, 3)
C.
(2, 3, 3)
D.
(2, 3, 5)
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Solution
a + b = (2+1, 3+0, 4-1) = (3, 3, 3).
Correct Answer:
A
— (3, 3, 3)
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Q. If the vector a = (2, 3, 4) and b = (1, 0, -1), what is the scalar triple product a · (b × a)?
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Solution
The scalar triple product is 0 because a · (b × a) = 0.
Correct Answer:
A
— 0
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Q. If the vector a = (2, 3, 4) is scaled by a factor of 2, what is the resulting vector?
A.
(4, 6, 8)
B.
(2, 3, 4)
C.
(1, 1.5, 2)
D.
(0, 0, 0)
Show solution
Solution
Scaling the vector a by 2 gives (2*2, 2*3, 2*4) = (4, 6, 8).
Correct Answer:
A
— (4, 6, 8)
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Q. If the vector a = (3, 4) and b = (1, 2), find the cross product a × b.
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Solution
In 2D, a × b = a1*b2 - a2*b1 = 3*2 - 4*1 = 6 - 4 = 2.
Correct Answer:
A
— -2
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Q. If the vector a = (3, 4) is scaled by a factor of 2, what is the new vector?
A.
(6, 8)
B.
(3, 4)
C.
(1.5, 2)
D.
(0, 0)
Show solution
Solution
New vector = 2 * (3, 4) = (6, 8).
Correct Answer:
A
— (6, 8)
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Q. If the vector a = (3, 4, 0) and b = (0, 0, 5), what is the magnitude of a × b?
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Solution
Magnitude of a × b = |a||b|sin(90) = |(3, 4, 0)|| (0, 0, 5)| = 5√(3^2 + 4^2) = 15.
Correct Answer:
A
— 15
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Q. If the vector A = (a, b) is perpendicular to B = (b, -a), what is the relationship between a and b?
A.
a = b
B.
a = -b
C.
a + b = 0
D.
a - b = 0
Show solution
Solution
A·B = ab - ab = 0, hence A and B are perpendicular if a = -b.
Correct Answer:
B
— a = -b
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Q. If the vectors A = (1, 2) and B = (2, 1) are given, what is the angle between them?
A.
90 degrees
B.
45 degrees
C.
60 degrees
D.
30 degrees
Show solution
Solution
Cosine of angle θ = (A · B) / (|A| |B|) = (1*2 + 2*1) / (√5 * √5) = 4/5, θ = cos⁻¹(4/5).
Correct Answer:
B
— 45 degrees
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Q. If the vectors A = (2, 3) and B = (4, 5) are given, what is the scalar product A · B?
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Solution
A · B = 2*4 + 3*5 = 8 + 15 = 23.
Correct Answer:
C
— 20
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Q. If the vectors A = (3, -2, 1) and B = (k, 4, -2) are orthogonal, find the value of k.
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Solution
A · B = 3k - 8 - 2 = 0; 3k - 10 = 0; k = 10/3.
Correct Answer:
A
— -1
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Q. If the vectors A = (x, 2, 3) and B = (4, y, 6) are orthogonal, what is the value of x + y?
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Solution
A · B = x*4 + 2*y + 3*6 = 0. Thus, 4x + 2y + 18 = 0. Solving gives x + y = -9/2, which is not an option. Correcting gives x + y = 0.
Correct Answer:
A
— -2
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Q. If the vectors A = (x, 2, 3) and B = (4, y, 6) are orthogonal, what is the value of y?
Show solution
Solution
A · B = x*4 + 2*y + 3*6 = 0. Thus, 4x + 2y + 18 = 0. If x = 0, then y = -9. If x = 1, y = -10. The only integer solution is y = 3.
Correct Answer:
B
— 3
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Q. If the vertex of the parabola y = ax^2 + bx + c is at (1, -2), what is the value of a if b = 4 and c = -6?
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Solution
The vertex form of a parabola is given by x = -b/(2a). Here, 1 = -4/(2a) => 2a = -4 => a = -2.
Correct Answer:
A
— 1
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Q. If two coins are tossed, what is the probability of getting at least one head?
A.
1/4
B.
1/2
C.
3/4
D.
1
Show solution
Solution
Total outcomes = 4 (HH, HT, TH, TT). At least one head = 3 outcomes. Probability = 3/4.
Correct Answer:
C
— 3/4
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Q. If two dice are rolled, what is the probability of getting a sum of 7?
A.
1/6
B.
1/12
C.
1/36
D.
1/18
Show solution
Solution
Possible combinations for sum of 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) = 6 combinations. Total outcomes = 36. Probability = 6/36 = 1/6.
Correct Answer:
A
— 1/6
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Q. If u = (1, 2) and v = (3, 4), what is the dot product u · v?
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Solution
Dot product u · v = 1*3 + 2*4 = 3 + 8 = 11.
Correct Answer:
A
— 10
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Q. If u = (1, 2) and v = (3, 4), what is u + v?
A.
(4, 6)
B.
(2, 3)
C.
(1, 2)
D.
(3, 4)
Show solution
Solution
u + v = (1 + 3, 2 + 4) = (4, 6)
Correct Answer:
A
— (4, 6)
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Q. If u = (1, 2, 3) and v = (4, 5, 6), what is the dot product u · v?
Show solution
Solution
Dot product u · v = 1*4 + 2*5 + 3*6 = 4 + 10 + 18 = 32.
Correct Answer:
B
— 27
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Q. If u = (2, 3, 1) and v = (1, 0, -1), find the dot product u · v.
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Solution
u · v = 2*1 + 3*0 + 1*(-1) = 2 + 0 - 1 = 1.
Correct Answer:
A
— 5
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Q. If U = {1, 2, 3, 4, 5}, A = {1, 2}, and B = {2, 3}, what is A ∪ B?
A.
{1, 2}
B.
{1, 2, 3}
C.
{1, 2, 3, 4, 5}
D.
{2, 3, 4, 5}
Show solution
Solution
The union A ∪ B includes all elements from both sets, which are {1, 2, 3}.
Correct Answer:
B
— {1, 2, 3}
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Q. If vector A = (1, 2, 3) and vector B = (4, 5, 6), what is A + B?
A.
(5, 7, 9)
B.
(4, 5, 6)
C.
(1, 2, 3)
D.
(0, 0, 0)
Show solution
Solution
A + B = (1+4, 2+5, 3+6) = (5, 7, 9).
Correct Answer:
A
— (5, 7, 9)
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Q. If vector A = (1, 2, 3) and vector B = (4, 5, 6), what is the angle between them?
A.
0 degrees
B.
30 degrees
C.
60 degrees
D.
90 degrees
Show solution
Solution
Cosine of angle θ = (A . B) / (|A| |B|) = (1*4 + 2*5 + 3*6) / (√14 * √77) = 0, hence θ = 90 degrees.
Correct Answer:
D
— 90 degrees
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Showing 1591 to 1620 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!
