Questions JEE Mains

Q1. The circle x 2 + y 2 = 4x + 8y + 5 intersects the line 3x – 4y = m at two distinct points, if

1. –85
2. –35
3. 15
4. 35

Answer: B

Q2. A line AB in three-dimensional space makes angles 45° and 120° with the positive X-axis and the positive Y-axis, respectively. If AB makes an acute angle 𝜃 with the positive Z-axis, then 𝜃 equals

1. 30°
2. 45°
3. 60°
4. 75°

Answer: C

Q3. Let a = j – k and c = i – j – k. Then, the vector b satisfying a × b + c = 0 and a – b = 3, is

1. –i + j – 2k
2. 2i – j + 2k
3. i – j – 2k
4. i + j – 2k

Answer: A

Q4. If the vectors a = i – j + 2k, b = 2i + 4j + k and c = 𝜆i + j + mk are mutually orthogonal, then (l, m) is equal to

1. (–3, 2)
2. (2, –3)
3. (–2, 3)
4. (3, –2)

Answer: A

Q5. If two tangents drawn from a point P to the parabola y 2 = 4x are at right angles, then the locus of P is

1. x = 1
2. 2x + 1 = 0
3. x = –1
4. 2x – 1 = 0

Answer: C

Q6. A person is to count 4500 currency notes. Let a n denotes the number of notes he counts in the n th minute. If a 1 = a 2 = a 10 = 150 and a 10, a 11 ,...are in AP with common difference –2, then the time taken by him to count all notes, is

1. 24 min
2. 34 min
3. 125 min
4. 135 min

Answer: B

Q8. There are two ums. Urn A has 3 distinct red balls and urn B has 9 distinct blue balls. From each urn, two balls are taken out at random and then transferred to the other. The number of ways in which this can be done, is

1. 3
2. 36
3. 66
4. 108

Answer: D

Q9. If 𝛼 and 𝛽 are the roots of the equation x 2 – x + 1 = 0, then 𝛼 2009 + 𝛽 2009 is equal to

1. –2
2. –1
3. 1
4. 2

Answer: C

Q10. The polymer containing strong intermolecular forces e.g., hydrogen bonding, is

1. teflon
2. nylon-66
3. polystyrene
4. natural rubber

Answer: B