Q. Find the angle between the vectors (1, 0, 0) and (0, 1, 0).
A.
0 degrees
B.
90 degrees
C.
45 degrees
D.
180 degrees
Show solution
Solution
The angle θ = cos⁻¹((u · v) / (|u| |v|)) = cos⁻¹(0) = 90 degrees.
Correct Answer:
B
— 90 degrees
Learn More →
Q. Find the angle between the vectors A = (1, 2, 2) and B = (2, 0, 2).
A.
0°
B.
45°
C.
60°
D.
90°
Show solution
Solution
cos(θ) = (A · B) / (|A| |B|). A · B = 1*2 + 2*0 + 2*2 = 6. |A| = √(1^2 + 2^2 + 2^2) = 3, |B| = √(2^2 + 0^2 + 2^2) = 2√2. cos(θ) = 6 / (3 * 2√2) = 1/√2, θ = 45°.
Correct Answer:
C
— 60°
Learn More →
Q. Find the angle between the vectors A = (1, 2, 2) and B = (2, 1, 1).
A.
60°
B.
45°
C.
30°
D.
90°
Show solution
Solution
cos(θ) = (A · B) / (|A| |B|). A · B = 1*2 + 2*1 + 2*1 = 6; |A| = √(1^2 + 2^2 + 2^2) = 3; |B| = √(2^2 + 1^2 + 1^2) = √6. Thus, cos(θ) = 6 / (3√6) = 1/√6, θ = 45°.
Correct Answer:
B
— 45°
Learn More →
Q. Find the angle between the vectors A = (3, -2, 1) and B = (1, 1, 1) if A · B = |A||B|cos(θ).
A.
60°
B.
45°
C.
90°
D.
30°
Show solution
Solution
A · B = 3*1 + (-2)*1 + 1*1 = 3 - 2 + 1 = 2. |A| = √(3^2 + (-2)^2 + 1^2) = √14, |B| = √3. cos(θ) = 2/(√14 * √3). θ = 60°.
Correct Answer:
A
— 60°
Learn More →
Q. Find the angle between the vectors A = (3, -2, 1) and B = (1, 1, 1).
A.
60°
B.
45°
C.
90°
D.
30°
Show solution
Solution
cos(θ) = (A · B) / (|A| |B|). A · B = 3*1 + (-2)*1 + 1*1 = 2. |A| = √(3^2 + (-2)^2 + 1^2) = √14, |B| = √3. θ = cos^(-1)(2/(√14 * √3)).
Correct Answer:
A
— 60°
Learn More →
Q. Find the area between the curves y = x^2 and y = 4 from x = -2 to x = 2.
Show solution
Solution
The area between the curves is given by ∫(from -2 to 2) (4 - x^2) dx = [4x - x^3/3] from -2 to 2 = 16/3.
Correct Answer:
B
— 16/3
Learn More →
Q. Find the area between the curves y = x^2 and y = 4 from x = 0 to x = 2.
Show solution
Solution
The area between the curves y = x^2 and y = 4 is given by ∫(from 0 to 2) (4 - x^2) dx = [4x - x^3/3] from 0 to 2 = (8 - 8/3) = 4/3.
Correct Answer:
A
— 4
Learn More →
Q. Find the area between the curves y = x^3 and y = x from x = 0 to x = 1.
A.
1/4
B.
1/3
C.
1/2
D.
1/6
Show solution
Solution
The area between the curves is given by ∫(from 0 to 1) (x - x^3) dx = [x^2/2 - x^4/4] from 0 to 1 = (1/2 - 1/4) = 1/4.
Correct Answer:
B
— 1/3
Learn More →
Q. Find the area of the triangle formed by the points (0, 0), (4, 0), and (0, 3).
Show solution
Solution
Area = 1/2 * base * height = 1/2 * 4 * 3 = 6.
Correct Answer:
A
— 6
Learn More →
Q. Find the area of the triangle formed by the points A(1, 2, 3), B(4, 5, 6), and C(7, 8, 9) using the vector product.
Show solution
Solution
Area = 0.5 * |AB × AC| = 0, as points are collinear.
Correct Answer:
A
— 0
Learn More →
Q. Find the area of the triangle with vertices (0,0), (4,0), and (4,3).
Show solution
Solution
Area = 1/2 * base * height = 1/2 * 4 * 3 = 6.
Correct Answer:
B
— 12
Learn More →
Q. Find the area under the curve y = e^x from x = 0 to x = 1.
Show solution
Solution
The area is given by the integral from 0 to 1 of e^x dx. This evaluates to [e^x] from 0 to 1 = e - 1.
Correct Answer:
A
— e - 1
Learn More →
Q. Find the area under the curve y = x^2 + 2x from x = 0 to x = 3.
Show solution
Solution
The area under the curve is given by ∫(from 0 to 3) (x^2 + 2x) dx = [x^3/3 + x^2] from 0 to 3 = (27/3 + 9) = 18.
Correct Answer:
C
— 15
Learn More →
Q. Find the area under the curve y = x^2 from x = 0 to x = 2.
Show solution
Solution
The area under the curve y = x^2 from 0 to 2 is given by the integral ∫(from 0 to 2) x^2 dx = [x^3/3] from 0 to 2 = (2^3/3) - (0^3/3) = 8/3.
Correct Answer:
C
— 8/3
Learn More →
Q. Find the area under the curve y = x^2 from x = 0 to x = 3.
Show solution
Solution
Area = ∫ from 0 to 3 of x^2 dx = [1/3 * x^3] from 0 to 3 = 9.
Correct Answer:
A
— 9
Learn More →
Q. Find the area under the curve y = x^2 from x = 1 to x = 3.
A.
8/3
B.
10/3
C.
9/3
D.
7/3
Show solution
Solution
The area is given by the integral ∫ (x^2) dx from 1 to 3. This evaluates to [x^3/3] from 1 to 3 = (27/3 - 1/3) = 26/3.
Correct Answer:
B
— 10/3
Learn More →
Q. Find the area under the curve y = x^4 from x = 0 to x = 1.
A.
1/5
B.
1/4
C.
1/3
D.
1/2
Show solution
Solution
The area under the curve y = x^4 from 0 to 1 is given by ∫(from 0 to 1) x^4 dx = [x^5/5] from 0 to 1 = 1/5.
Correct Answer:
A
— 1/5
Learn More →
Q. Find the area under the curve y = x^4 from x = 0 to x = 2.
Show solution
Solution
The area is given by the integral from 0 to 2 of x^4 dx. This evaluates to [x^5/5] from 0 to 2 = (32/5) = 16.
Correct Answer:
C
— 16
Learn More →
Q. Find the argument of the complex number z = -1 - i.
A.
-3π/4
B.
3π/4
C.
π/4
D.
-π/4
Show solution
Solution
The argument of z = -1 - i is θ = tan^(-1)(-1/-1) = 3π/4.
Correct Answer:
A
— -3π/4
Learn More →
Q. Find the arithmetic mean of the first five prime numbers.
Show solution
Solution
First five primes: 2, 3, 5, 7, 11. Mean = (2 + 3 + 5 + 7 + 11) / 5 = 28 / 5 = 5.6.
Correct Answer:
C
— 7
Learn More →
Q. Find the arithmetic mean of the numbers 12, 15, 18, 21, and 24.
Show solution
Solution
Mean = (12 + 15 + 18 + 21 + 24) / 5 = 90 / 5 = 18.
Correct Answer:
A
— 18
Learn More →
Q. Find the coefficient of x^0 in the expansion of (2x + 3)^4.
Show solution
Solution
The coefficient of x^0 is C(4, 0) * (2x)^0 * 3^4 = 1 * 81 = 81.
Correct Answer:
A
— 81
Learn More →
Q. Find the coefficient of x^1 in the expansion of (x + 2)^5.
Show solution
Solution
The coefficient of x^1 is C(5,1) * 2^4 = 5 * 16 = 80.
Correct Answer:
B
— 20
Learn More →
Q. Find the coefficient of x^2 in the expansion of (3x - 4)^6.
A.
540
B.
720
C.
480
D.
360
Show solution
Solution
The coefficient of x^2 is C(6,2) * (3)^2 * (-4)^4 = 15 * 9 * 256 = 34560.
Correct Answer:
B
— 720
Learn More →
Q. Find the coefficient of x^3 in the expansion of (2x - 3)^6.
A.
-540
B.
-720
C.
540
D.
720
Show solution
Solution
The coefficient of x^3 is C(6,3)(2)^3(-3)^3 = 20 * 8 * (-27) = -4320.
Correct Answer:
A
— -540
Learn More →
Q. Find the coefficient of x^3 in the expansion of (x + 1/2)^6.
Show solution
Solution
The coefficient of x^3 is C(6,3) * (1/2)^3 = 20 * 1/8 = 2.5.
Correct Answer:
B
— 15
Learn More →
Q. Find the coefficient of x^3 in the expansion of (x + 2)^6.
A.
80
B.
120
C.
160
D.
240
Show solution
Solution
The coefficient of x^3 is C(6,3) * (2)^3 = 20 * 8 = 160.
Correct Answer:
B
— 120
Learn More →
Q. Find the coefficient of x^3 in the expansion of (x - 1)^5.
Show solution
Solution
The coefficient of x^3 is C(5,3) * (-1)^2 = 10.
Correct Answer:
A
— -10
Learn More →
Q. Find the coefficient of x^3 in the expansion of (x - 1)^6.
A.
-20
B.
-15
C.
-10
D.
-6
Show solution
Solution
The coefficient of x^3 is C(6,3) * (-1)^3 = 20 * (-1) = -20.
Correct Answer:
A
— -20
Learn More →
Q. Find the coefficient of x^3 in the expansion of (x - 3)^5.
A.
-135
B.
-90
C.
-60
D.
-45
Show solution
Solution
The coefficient of x^3 is C(5,3) * (-3)^2 = 10 * 9 = -90.
Correct Answer:
A
— -135
Learn More →
Showing 451 to 480 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!
