Q. If A = (2, 3, 4) and B = (x, y, z) such that A · B = 20, find the value of x + y + z.
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Solution
A · B = 2x + 3y + 4z = 20. If we assume x = 2, y = 2, z = 2, then 2*2 + 3*2 + 4*2 = 20, thus x + y + z = 6.
Correct Answer:
C
— 7
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Q. If A = (3, -1, 2) and B = (k, 4, -1) are orthogonal, find k.
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Solution
A · B = 3k - 4 - 2 = 0. Thus, 3k - 6 = 0, k = 2.
Correct Answer:
A
— -2
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Q. If A = (3, -2, 1) and B = (4, 0, -1), what is the value of A · B?
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Solution
A · B = 3*4 + (-2)*0 + 1*(-1) = 12 + 0 - 1 = 11.
Correct Answer:
A
— -1
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Q. If A = (a, b, c) and B = (1, 2, 3) such that A · B = 0, what is the relation between a, b, and c?
A.
a + 2b + 3c = 0
B.
a - 2b + 3c = 0
C.
a + b + c = 0
D.
a - b - c = 0
Show solution
Solution
A · B = a*1 + b*2 + c*3 = 0. Thus, a + 2b + 3c = 0.
Correct Answer:
A
— a + 2b + 3c = 0
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Q. If A = (a, b, c) and B = (1, 2, 3), and A · B = 14, find a + b + c.
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Solution
a*1 + b*2 + c*3 = 14. One possible solution is a = 2, b = 4, c = 0, so a + b + c = 6.
Correct Answer:
C
— 7
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Q. If A = (a, b, c) and B = (1, 2, 3), and A · B = 14, what is the equation?
A.
a + 2b + 3c = 14
B.
a - 2b + 3c = 14
C.
a + 2b - 3c = 14
D.
a - 2b - 3c = 14
Show solution
Solution
A · B = a*1 + b*2 + c*3 = 14.
Correct Answer:
A
— a + 2b + 3c = 14
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Q. If A = (a, b, c) and B = (1, 2, 3), find the value of a if A · B = 10.
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Solution
A · B = a*1 + b*2 + c*3 = 10. If b = 2 and c = 1, then a + 4 + 3 = 10, so a = 3.
Correct Answer:
C
— 3
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Q. If A = (a, b, c) and B = (1, 2, 3), what is the scalar product A · B?
A.
a + 2b + 3c
B.
a - 2b - 3c
C.
a * b * c
D.
a^2 + b^2 + c^2
Show solution
Solution
A · B = a*1 + b*2 + c*3 = a + 2b + 3c.
Correct Answer:
A
— a + 2b + 3c
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Q. If A = (x, y) and B = (y, x), what is the scalar product A · B?
A.
x^2 + y^2
B.
xy
C.
x^2 - y^2
D.
0
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Solution
A · B = x*y + y*x = 2xy.
Correct Answer:
A
— x^2 + y^2
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Q. If A = (x, y, z) and B = (1, 1, 1) such that A · B = 6, find x + y + z.
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Solution
A · B = x + y + z = 6. Thus, x + y + z = 6.
Correct Answer:
B
— 6
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Q. If A = (x, y, z) and B = (1, 1, 1), find the scalar product A · B.
A.
x + y + z
B.
x - y + z
C.
x + y - z
D.
x - y - z
Show solution
Solution
A · B = x*1 + y*1 + z*1 = x + y + z.
Correct Answer:
A
— x + y + z
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Q. If A = (x, y, z) and B = (1, 2, 3), and A · B = 14, find the value of x + y + z.
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Solution
A · B = x*1 + y*2 + z*3 = 14; Let x + y + z = k; We can find values satisfying this equation.
Correct Answer:
C
— 7
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Q. If A = (x, y, z) and B = (2, 2, 2), and A · B = 12, what is the value of x + y + z?
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Solution
A · B = 2x + 2y + 2z = 12, thus x + y + z = 6.
Correct Answer:
A
— 6
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Q. If A = (x, y, z) and B = (2, 3, 4), and A · B = 10, find the value of x + y + z.
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Solution
x*2 + y*3 + z*4 = 10. One possible solution is x = 1, y = 1, z = 1, so x + y + z = 3.
Correct Answer:
C
— 3
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Q. If A = (x, y, z) and B = (2, 3, 4), find the value of x if A · B = 10.
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Solution
A · B = x*2 + y*3 + z*4 = 10. If y = 0 and z = 0, then x = 5.
Correct Answer:
B
— 2
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Q. If A = 1i + 1j + 1k and B = 2i + 2j + 2k, what is A · B?
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Solution
A · B = (1)(2) + (1)(2) + (1)(2) = 2 + 2 + 2 = 6.
Correct Answer:
A
— 6
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Q. If A = 2i - j and B = -i + 3j, what is the value of A · B?
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Solution
A · B = (2)(-1) + (-1)(3) = -2 - 3 = -5.
Correct Answer:
A
— -1
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Q. If A = 6i + 8j and B = 3i + 4j, what is the scalar product A · B?
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Solution
A · B = (6)(3) + (8)(4) = 18 + 32 = 50.
Correct Answer:
B
— 54
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Q. If A = 7i + 24j and B = 24i - 7j, calculate A · B.
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Solution
A · B = (7)(24) + (24)(-7) = 168 - 168 = 0.
Correct Answer:
A
— 0
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Q. If A = i + 2j + 3k and B = 4i + 5j + 6k, find A · B.
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Solution
A · B = (1)(4) + (2)(5) + (3)(6) = 4 + 10 + 18 = 32.
Correct Answer:
B
— 30
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Q. If A = [[1, 0], [0, 1]] and B = [[2, 3], [4, 5]], what is AB?
A.
[2, 3], [4, 5]
B.
[1, 0], [0, 1]
C.
[0, 0], [0, 0]
D.
[6, 8], [12, 15]
Show solution
Solution
AB = [[1*2 + 0*4, 1*3 + 0*5], [0*2 + 1*4, 0*3 + 1*5]] = [[2, 3], [4, 5]].
Correct Answer:
A
— [2, 3], [4, 5]
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Q. If A = [[1, 0], [0, 1]] is the identity matrix, what is A^n for any integer n?
A.
A
B.
0
C.
I
D.
None of the above
Show solution
Solution
A^n = I for any integer n, where I is the identity matrix.
Correct Answer:
C
— I
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Q. If A = [[1, 2], [3, 4]] and B = [[5, 6], [7, 8]], what is A + B?
A.
[6, 8], [10, 12]
B.
[1, 2], [3, 4]
C.
[5, 6], [7, 8]
D.
[8, 10], [10, 12]
Show solution
Solution
A + B = [[1+5, 2+6], [3+7, 4+8]] = [[6, 8], [10, 12]].
Correct Answer:
A
— [6, 8], [10, 12]
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Q. If A = [[1, 2], [3, 4]], find A^2.
A.
[7, 10], [15, 22]
B.
[1, 2], [3, 4]
C.
[10, 13], [22, 29]
D.
[-1, -2], [-3, -4]
Show solution
Solution
A^2 = A * A = [[1*1 + 2*3, 1*2 + 2*4], [3*1 + 4*3, 3*2 + 4*4]] = [[7, 10], [15, 22]].
Correct Answer:
A
— [7, 10], [15, 22]
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Q. If A = [[1, 2], [3, 4]], find the determinant of A.
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Solution
The determinant of A is (1*4) - (2*3) = 4 - 6 = -2.
Correct Answer:
B
— 2
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Q. If A = [[1, 2], [3, 4]], what is A^2?
A.
[7, 10; 15, 22]
B.
[1, 2; 3, 4]
C.
[10, 14; 22, 30]
D.
[-1, -2; -3, -4]
Show solution
Solution
A^2 = A * A = [[1*1 + 2*3, 1*2 + 2*4], [3*1 + 4*3, 3*2 + 4*4]] = [[7, 10], [15, 22]].
Correct Answer:
A
— [7, 10; 15, 22]
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Q. If A = [[1, 2], [3, 4]], what is the adjoint of A?
A.
[[4, -2], [-3, 1]]
B.
[[1, 3], [2, 4]]
C.
[[2, 1], [4, 3]]
D.
[[0, 0], [0, 0]]
Show solution
Solution
The adjoint of A is [[4, -2], [-3, 1]].
Correct Answer:
A
— [[4, -2], [-3, 1]]
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Q. If A = [[1, 2], [3, 4]], what is the determinant of A?
Show solution
Solution
The determinant of A is (1*4) - (2*3) = 4 - 6 = -2.
Correct Answer:
A
— -2
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Q. If A = [[1, 2], [3, 4]], what is the eigenvalue of A?
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Solution
The eigenvalues are found from the characteristic polynomial λ^2 - 5λ + 2 = 0, which gives λ = 5.
Correct Answer:
A
— 5
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Q. If A = [[1, 2], [3, 4]], what is the inverse of A?
A.
[[4, -2], [-3, 1]]
B.
[[-2, 1], [1.5, -0.5]]
C.
[[-2, 1], [1.5, -0.5]]
D.
[[4, -2], [-3, 1]]
Show solution
Solution
The inverse of A is (1/det(A)) * adj(A) = (1/(-2)) * [[4, -2], [-3, 1]] = [[-2, 1], [1.5, -0.5]].
Correct Answer:
A
— [[4, -2], [-3, 1]]
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Showing 1051 to 1080 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!
