Q. What is the axis of symmetry for the parabola given by the equation y = 3x^2 + 6x + 2?
A.
x = -1
B.
y = -1
C.
x = 1
D.
y = 1
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Solution
The axis of symmetry for a parabola in the form y = ax^2 + bx + c is given by x = -b/(2a). Here, a = 3 and b = 6, so x = -6/(2*3) = -1.
Correct Answer:
A
— x = -1
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Q. What is the characteristic polynomial of the matrix A = [[1, 2], [3, 4]]?
A.
λ^2 - 5λ - 2
B.
λ^2 - 5λ + 2
C.
λ^2 + 5λ + 2
D.
λ^2 + 5λ - 2
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Solution
The characteristic polynomial is det(A - λI) = det([[1-λ, 2], [3, 4-λ]]) = (1-λ)(4-λ) - 6 = λ^2 - 5λ + 2.
Correct Answer:
B
— λ^2 - 5λ + 2
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Q. What is the characteristic polynomial of the matrix A = [[2, 1], [1, 2]]?
A.
λ^2 - 3λ + 3
B.
λ^2 - 3λ + 1
C.
λ^2 - 5λ + 2
D.
λ^2 - 2λ + 1
Show solution
Solution
The characteristic polynomial is given by det(A - λI) = det([[2-λ, 1], [1, 2-λ]]) = (2-λ)(2-λ) - 1 = λ^2 - 3λ + 3.
Correct Answer:
B
— λ^2 - 3λ + 1
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Q. What is the circumradius of a triangle with sides 5, 12, and 13?
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Solution
For a right triangle, the circumradius R = hypotenuse/2 = 13/2 = 6.5.
Correct Answer:
B
— 7
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Q. What is the circumradius of a triangle with sides 6, 8, and 10?
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Solution
Circumradius R = (abc)/(4K), where K is the area. Area K = 24 (using Heron's formula). R = (6*8*10)/(4*24) = 5.
Correct Answer:
A
— 5
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Q. What is the circumradius of a triangle with sides 7, 24, and 25?
A.
12.5
B.
13
C.
14
D.
15
Show solution
Solution
The circumradius R of a triangle can be calculated using the formula R = (abc)/(4 * Area). Here, Area = 84 cm², so R = (7 * 24 * 25)/(4 * 84) = 13.
Correct Answer:
B
— 13
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Q. What is the circumradius of an equilateral triangle with side length a?
A.
a/√3
B.
a/2
C.
a/√2
D.
a/√3
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Solution
The circumradius R of an equilateral triangle is given by R = a/(√3).
Correct Answer:
D
— a/√3
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Q. What is the circumradius R of a triangle with sides a = 7, b = 24, c = 25?
Show solution
Solution
R = (abc) / (4 * Area). Area = 84, R = (7 * 24 * 25) / (4 * 84) = 12.
Correct Answer:
A
— 12
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Q. What is the circumradius R of a triangle with sides a, b, c?
A.
abc/4A
B.
A/(abc)
C.
2A/(a+b+c)
D.
a+b+c/2
Show solution
Solution
The circumradius R of a triangle is given by the formula R = abc/(4A), where A is the area of the triangle.
Correct Answer:
A
— abc/4A
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Q. What is the coefficient of variation if the mean is 50 and the standard deviation is 5?
A.
5%
B.
10%
C.
15%
D.
20%
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Solution
Coefficient of Variation = (Standard Deviation / Mean) * 100 = (5 / 50) * 100 = 10%.
Correct Answer:
B
— 10%
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Q. What is the coefficient of variation if the mean is 50 and the standard deviation is 10?
A.
20%
B.
10%
C.
15%
D.
25%
Show solution
Solution
Coefficient of variation = (Standard deviation / Mean) * 100 = (10 / 50) * 100 = 20%.
Correct Answer:
A
— 20%
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Q. What is the coefficient of x^0 in the expansion of (3x - 4)^5?
A.
-1024
B.
243
C.
-243
D.
1024
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Solution
The coefficient of x^0 is (-4)^5 = -1024.
Correct Answer:
A
— -1024
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Q. What is the coefficient of x^0 in the expansion of (x + 5)^3?
A.
125
B.
100
C.
75
D.
50
Show solution
Solution
The coefficient of x^0 is C(3,0) * 5^3 = 1 * 125 = 125.
Correct Answer:
A
— 125
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Q. What is the coefficient of x^0 in the expansion of (x + 5)^5?
A.
3125
B.
625
C.
125
D.
25
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Solution
The coefficient of x^0 is C(5,0) * 5^5 = 1 * 3125 = 3125.
Correct Answer:
A
— 3125
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Q. What is the coefficient of x^2 in the expansion of (3x - 4)^4?
A.
144
B.
216
C.
432
D.
576
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Solution
The coefficient of x^2 is C(4,2) * (3)^2 * (-4)^2 = 6 * 9 * 16 = 864.
Correct Answer:
C
— 432
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Q. What is the coefficient of x^2 in the expansion of (x - 4)^6?
A.
240
B.
360
C.
480
D.
720
Show solution
Solution
Using the binomial theorem, the coefficient of x^2 in (a + b)^n is given by nCk * a^(n-k) * b^k. Here, n=6, a=x, b=-4, and k=2. Thus, the coefficient is 6C2 * (1)^4 * (-4)^2 = 15 * 16 = 240.
Correct Answer:
B
— 360
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Q. What is the coefficient of x^3 in the expansion of (2x + 3)^5?
A.
90
B.
100
C.
120
D.
150
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Solution
Using the binomial theorem, the coefficient of x^3 is given by C(5,3) * (2)^3 * (3)^(5-3) = 10 * 8 * 9 = 720.
Correct Answer:
A
— 90
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Q. What is the coefficient of x^4 in the expansion of (2x + 3)^6?
A.
540
B.
720
C.
810
D.
960
Show solution
Solution
The coefficient of x^4 is C(6,4) * (2)^4 * (3)^(6-4) = 15 * 16 * 9 = 2160.
Correct Answer:
C
— 810
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Q. What is the coefficient of x^4 in the expansion of (2x - 3)^5?
A.
240
B.
300
C.
360
D.
420
Show solution
Solution
The coefficient of x^4 is C(5, 4) * (2)^4 * (-3)^1 = 5 * 16 * (-3) = -240.
Correct Answer:
C
— 360
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Q. What is the coefficient of x^4 in the expansion of (x + 1)^6?
Show solution
Solution
The coefficient of x^4 is C(6,4) = 15.
Correct Answer:
D
— 35
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Q. What is the coefficient of x^5 in the expansion of (x + 1/2)^10?
A.
252
B.
210
C.
120
D.
300
Show solution
Solution
The coefficient of x^5 is C(10,5) * (1/2)^5 = 252 * 1/32 = 7.875.
Correct Answer:
A
— 252
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Q. What is the coefficient of x^5 in the expansion of (x + 2)^7?
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Solution
The coefficient of x^5 is C(7,5)(2)^2 = 21 * 4 = 84.
Correct Answer:
C
— 35
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Q. What is the coefficient of x^5 in the expansion of (x + 2)^8?
A.
672
B.
1280
C.
960
D.
720
Show solution
Solution
The coefficient of x^5 is C(8,5) * (2)^3 = 56 * 8 = 448.
Correct Answer:
A
— 672
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Q. What is the coefficient of x^5 in the expansion of (x + 3)^8?
A.
1680
B.
1440
C.
1260
D.
1080
Show solution
Solution
Using the binomial theorem, the coefficient of x^5 in (x + 3)^8 is given by 8C5 * (3)^3 = 56 * 27 = 1512.
Correct Answer:
A
— 1680
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Q. What is the coefficient of x^6 in the expansion of (x + 5)^8?
A.
6720
B.
5600
C.
4480
D.
3360
Show solution
Solution
The coefficient of x^6 is C(8,6) * (5)^2 = 28 * 25 = 700.
Correct Answer:
A
— 6720
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Q. What is the common ratio of the geometric series 4, 12, 36, ...?
Show solution
Solution
The common ratio r = 12/4 = 3.
Correct Answer:
A
— 3
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Q. What is the composition of functions f(g(x)) if f(x) = x + 1 and g(x) = 2x?
A.
2x + 1
B.
2x - 1
C.
x + 2
D.
x + 1
Show solution
Solution
f(g(x)) = f(2x) = 2x + 1.
Correct Answer:
A
— 2x + 1
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Q. What is the condition for the lines 2x + 3y = 6 and 4x + 6y = 12 to be parallel?
A.
They have the same slope
B.
They intersect
C.
They are identical
D.
None of the above
Show solution
Solution
Both lines can be rewritten in slope-intercept form. The first line has slope -2/3 and the second line has the same slope, hence they are parallel.
Correct Answer:
A
— They have the same slope
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Q. What is the condition for the lines represented by ax^2 + 2hxy + by^2 = 0 to be parallel?
A.
h^2 = ab
B.
h^2 > ab
C.
h^2 < ab
D.
h^2 = 0
Show solution
Solution
The condition for the lines to be parallel is given by h^2 = ab.
Correct Answer:
A
— h^2 = ab
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Q. What is the condition for the lines represented by the equation 2x^2 + 3xy + y^2 = 0 to be coincident?
A.
D = 0
B.
D > 0
C.
D < 0
D.
D = 1
Show solution
Solution
The lines are coincident if the discriminant D of the quadratic equation is zero.
Correct Answer:
A
— D = 0
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Showing 2221 to 2250 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!
