Questions JEE Mains
1. The circle x2 + y2 = 4x + 8y + 5 intersects the line 3x – 4y = m at two distinct points, if
(a) –85 < m < –35
(b) –35 < m < 15
(c) 15 < m < 65
(d) 35 < m < 85
Ans. b
2. 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
2. 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
(a) 30°
(b) 45°
(b) 45°
(c) 60°
(d) 75°
(d) 75°
Ans. c
3. Let a = j – k and c = i – j – k. Then, the vector b satisfying a × b + c = 0 and a – b = 3, is
6. A person is to count 4500 currency notes. Let an denotes the number of notes he counts in the nth minute. If a1 = a2 = a10 = 150 and a10, a11,...are in AP with common difference –2, then the time taken by him to count all notes, is
3. Let a = j – k and c = i – j – k. Then, the vector b satisfying a × b + c = 0 and a – b = 3, is
(a) –i + j – 2k
(b) 2i – j + 2k
(c) i – j – 2k
(d) i + j – 2k
Ans. a
4. 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
(a) (–3, 2)
(b) (2, –3)
(c) (–2, 3)
(d) (3, –2)
Ans. a
5. If two tangents drawn from a point P to the parabola y2 = 4x are at right angles, then the locus of P is
(a) x = 1
(b) 2x + 1 = 0
(c) x = –1
(d) 2x – 1 = 0
Ans. c
6. A person is to count 4500 currency notes. Let an denotes the number of notes he counts in the nth minute. If a1 = a2 = a10 = 150 and a10, a11,...are in AP with common difference –2, then the time taken by him to count all notes, is
(a) 24 min
(b) 34 min
(b) 34 min
(c) 125 min
(d) 135 min
(d) 135 min
Ans. b
7. Consider the system of linear equations
8. 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
9. If 𝛼 and 𝛽 are the roots of the equation x2 – x + 1 = 0, then 𝛼2009 + 𝛽2009 is equal to
7. Consider the system of linear equations
x1 + 2x2 + x3 = 3
2x1 + 3x2 + x3 = 3
3x1 + 5x2 + 2x3 = 1
The system has
(a) infinite number of solutions
(b) exactly 3 solutions
(c) a unique solution
(d) no solution
Ans. d
8. 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
(a) 3
(b) 36
(b) 36
(c) 66
(d) 108
(d) 108
Ans. d
9. If 𝛼 and 𝛽 are the roots of the equation x2 – x + 1 = 0, then 𝛼2009 + 𝛽2009 is equal to
(a) –2
(b) –1
(b) –1
(c) 1
(d) 2
(d) 2
Ans. c
10. The polymer containing strong intermolecular forces e.g., hydrogen bonding, is
10. The polymer containing strong intermolecular forces e.g., hydrogen bonding, is
(a) teflon
(b) nylon-66
(c) polystyrene
(d) natural rubber