Q. If the odds in favor of an event are 3:2, what is the probability of the event occurring?
A.
0.6
B.
0.4
C.
0.5
D.
0.3
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Solution
Probability = Odds in favor / (Total odds) = 3 / (3 + 2) = 3/5 = 0.6.
Correct Answer:
A
— 0.6
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Q. If the pair of lines represented by ax^2 + 2hxy + by^2 = 0 are perpendicular, then:
A.
a + b = 0
B.
a - b = 0
C.
h = 0
D.
a = b
Show solution
Solution
For the lines to be perpendicular, the condition a + b = 0 must hold.
Correct Answer:
A
— a + b = 0
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Q. If the pair of lines represented by the equation ax^2 + 2hxy + by^2 = 0 are perpendicular, then:
A.
a + b = 0
B.
a - b = 0
C.
h = 0
D.
a = b
Show solution
Solution
For the lines to be perpendicular, the condition a*b + h^2 = 0 must hold.
Correct Answer:
A
— a + b = 0
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Q. If the parabola y = ax^2 + bx + c has its vertex at (1, -2), what is the value of a if it passes through the point (0, 0)?
Show solution
Solution
Using the vertex form y = a(x - 1)^2 - 2 and substituting (0, 0), we get 0 = a(0 - 1)^2 - 2 => 2 = a => a = 2.
Correct Answer:
B
— 2
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Q. If the parabola y^2 = 16x opens to the right, what is the value of p?
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Solution
In the equation y^2 = 4px, we have 4p = 16, thus p = 4.
Correct Answer:
B
— 4
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Q. If the parabola y^2 = 20x opens to the right, what is the value of p?
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Solution
In the equation y^2 = 4px, we have 4p = 20, thus p = 20/4 = 5.
Correct Answer:
A
— 5
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Q. If the points (1, 2), (3, 4), and (5, 6) are collinear, what is the slope of the line?
A.
1
B.
2
C.
0
D.
undefined
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Solution
Slope = (4-2)/(3-1) = 1, and it remains the same for other points.
Correct Answer:
A
— 1
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Q. If the points A(1, 2), B(3, 4), and C(5, 6) are collinear, what is the area of triangle ABC?
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Solution
Area = 1/2 | x1(y2-y3) + x2(y3-y1) + x3(y1-y2) | = 0.
Correct Answer:
A
— 0
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Q. If the polynomial P(x) = x^3 - 6x^2 + 11x - 6 has a root at x = 1, what is P(2)?
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Solution
P(2) = 2^3 - 6(2^2) + 11(2) - 6 = 8 - 24 + 22 - 6 = 0.
Correct Answer:
D
— 3
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Q. If the position vector of a point is (5, 12), what is its distance from the origin?
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Solution
Distance = √(5^2 + 12^2) = √(25 + 144) = √169 = 13
Correct Answer:
A
— 13
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Q. If the position vector of a point is given by r = (2t, 3t, 4t), what is the velocity vector?
A.
(2, 3, 4)
B.
(4, 6, 8)
C.
(2t, 3t, 4t)
D.
(0, 0, 0)
Show solution
Solution
Velocity vector = dr/dt = (2, 3, 4)
Correct Answer:
A
— (2, 3, 4)
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Q. If the position vector of a point P is (2, 3, 4), what is the distance from the origin to point P?
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Solution
Distance = √(2^2 + 3^2 + 4^2) = √(4 + 9 + 16) = √29 ≈ 5.385.
Correct Answer:
B
— 6
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Q. If the position vector of a point P is (x, y, z) and the vector a = (1, 2, 3), what is the projection of P onto a?
A.
(1, 2, 3)
B.
(2, 4, 6)
C.
(0, 0, 0)
D.
(x, y, z)
Show solution
Solution
Projection of P onto a = ((P · a) / |a|^2) * a.
Correct Answer:
D
— (x, y, z)
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Q. If the position vector of a point P is given by r = (2t, 3t, 4t), find the coordinates of P when t = 1.
A.
(2, 3, 4)
B.
(1, 1, 1)
C.
(0, 0, 0)
D.
(2, 4, 6)
Show solution
Solution
Substituting t = 1, r = (2*1, 3*1, 4*1) = (2, 3, 4).
Correct Answer:
A
— (2, 3, 4)
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Q. If the position vector of point P is (3, -2) and Q is (1, 4), what is the vector PQ?
A.
(-2, 6)
B.
(2, -6)
C.
(4, -6)
D.
(6, 2)
Show solution
Solution
Vector PQ = Q - P = (1 - 3, 4 - (-2)) = (-2, 6).
Correct Answer:
A
— (-2, 6)
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Q. If the position vector of point P is (3, 4) and Q is (1, 2), what is the vector PQ?
A.
(2, 2)
B.
(4, 6)
C.
(2, 4)
D.
(1, 1)
Show solution
Solution
Vector PQ = Q - P = (1 - 3, 2 - 4) = (-2, -2).
Correct Answer:
A
— (2, 2)
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Q. If the probability of an event A is 0.3, what is the probability of the event not occurring?
A.
0.7
B.
0.3
C.
0.5
D.
0.2
Show solution
Solution
Probability of not A = 1 - P(A) = 1 - 0.3 = 0.7.
Correct Answer:
A
— 0.7
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Q. If the probability of an event A is 0.7, what is the probability of the event not occurring?
A.
0.3
B.
0.7
C.
0.5
D.
0.1
Show solution
Solution
Probability of not A = 1 - P(A) = 1 - 0.7 = 0.3.
Correct Answer:
A
— 0.3
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Q. If the probability of an event is 0.7, what is the probability of its complement?
A.
0.3
B.
0.7
C.
1
D.
0.5
Show solution
Solution
Probability of complement = 1 - P(event) = 1 - 0.7 = 0.3.
Correct Answer:
A
— 0.3
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Q. If the probability of an event is 0.7, what is the probability of the event not occurring?
A.
0.3
B.
0.7
C.
0.5
D.
0.1
Show solution
Solution
Probability of not occurring = 1 - P(event) = 1 - 0.7 = 0.3.
Correct Answer:
A
— 0.3
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Q. If the probability of event A is 0.4 and event B is 0.5, what is the probability of both events occurring if they are independent?
A.
0.2
B.
0.4
C.
0.5
D.
0.6
Show solution
Solution
P(A and B) = P(A) * P(B) = 0.4 * 0.5 = 0.2.
Correct Answer:
A
— 0.2
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Q. If the quadratic equation ax^2 + bx + c = 0 has roots 3 and -2, what is the value of a?
Show solution
Solution
Using the fact that the product of the roots is c/a and the sum is -b/a, we can set a = 1, b = -1, c = -6.
Correct Answer:
A
— 1
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Q. If the quadratic equation x^2 + 2px + p^2 - 4 = 0 has real roots, what is the condition on p?
A.
p > 2
B.
p < 2
C.
p = 2
D.
p >= 2
Show solution
Solution
The discriminant must be non-negative: (2p)^2 - 4(1)(p^2 - 4) >= 0 => 4p^2 - 4p^2 + 16 >= 0, which is always true. Thus, p can be any real number.
Correct Answer:
D
— p >= 2
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Q. If the quadratic equation x^2 + 2px + p^2 - 4 = 0 has roots that are equal, what is the value of p?
Show solution
Solution
Setting the discriminant to zero: (2p)^2 - 4(1)(p^2 - 4) = 0 leads to p = ±2.
Correct Answer:
C
— -2
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Q. If the quadratic equation x^2 + 2x + k = 0 has equal roots, what is the value of k?
Show solution
Solution
For equal roots, the discriminant must be zero: 2^2 - 4*1*k = 0, leading to k = 1.
Correct Answer:
C
— -1
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Q. If the quadratic equation x^2 + 2x + k = 0 has no real roots, what is the condition on k?
A.
k < 0
B.
k > 0
C.
k >= 0
D.
k <= 0
Show solution
Solution
For no real roots, the discriminant must be less than zero: 2^2 - 4*1*k < 0, hence k > 1.
Correct Answer:
A
— k < 0
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Q. If the quadratic equation x^2 + 2x + k = 0 has no real roots, what is the condition for k?
A.
k < 0
B.
k > 0
C.
k >= 0
D.
k <= 0
Show solution
Solution
For no real roots, the discriminant must be less than zero: 2^2 - 4*1*k < 0 => 4 - 4k < 0 => k > 1.
Correct Answer:
A
— k < 0
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Q. If the quadratic equation x^2 + 2x + k = 0 has roots that are equal, what is the value of k?
Show solution
Solution
For equal roots, the discriminant must be zero: 2^2 - 4*1*k = 0 leads to k = -1.
Correct Answer:
D
— -2
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Q. If the quadratic equation x^2 + 4x + c = 0 has one root equal to -2, what is the value of c?
Show solution
Solution
If one root is -2, then substituting x = -2 gives: (-2)^2 + 4(-2) + c = 0 => 4 - 8 + c = 0 => c = 4.
Correct Answer:
A
— 0
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Q. If the quadratic equation x^2 + 4x + k = 0 has roots -2 and -2, what is the value of k?
Show solution
Solution
Using the formula for roots, k = (-2)^2 - 4*(-2) = 4 + 8 = 12.
Correct Answer:
B
— 4
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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!
