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All questions of September Week 2 for JEE Exam
If A(–2, – 4), B(2, 3) and C(2, – 2) are three points, then the angle between the lines AB and AC is:- a)3π/4
- b)π/4
- c)
- d)
Correct answer is option 'C'. Can you explain this answer?
If A(–2, – 4), B(2, 3) and C(2, – 2) are three points, then the angle between the lines AB and AC is:
a)
3π/4
b)
π/4
c)
d)
|
Lavanya Menon answered |
Let the slope of the line AB and AC are m1 and m2 respectively.
Then,
Let θ be the angle between AB and BC. Then,
If the slope of the line passing through the points (2, 5) and (x, 1) is 2, then x = …a)-2b)0c)8d)6Correct answer is option 'B''Can you explain this answer?
|
Krishna Iyer answered |
Slope = Change in y coordinates÷change in x coodinates
= (5-1)÷(2-x) =2
5-1 = 4-2x
0 = 2x
x=0
= (5-1)÷(2-x) =2
5-1 = 4-2x
0 = 2x
x=0
If the slope of line m = tan 0°. Therefore, the line is …… to the X-axis.- a)Perpendicular
- b)Parallel
- c)Con current
- d)Co-incident
Correct answer is option 'B'. Can you explain this answer?
If the slope of line m = tan 0°. Therefore, the line is …… to the X-axis.
a)
Perpendicular
b)
Parallel
c)
Con current
d)
Co-incident
|
Knowledge Hub answered |
Slope of x-axis is m = tan 0° = 0.
Since the inclination of every line parallel to x-axis is 0°, so its slope (m) = tan 0° = 0. Therefore, the slope of every horizontal line is 0.
Since the inclination of every line parallel to x-axis is 0°, so its slope (m) = tan 0° = 0. Therefore, the slope of every horizontal line is 0.
Let A(2, 12) and B(6,4) be two points. The slope of a line perpendicular to the line AB is:- a)2
- b)-2
- c)1/2
- d)-1/2
Correct answer is option 'C'. Can you explain this answer?
Let A(2, 12) and B(6,4) be two points. The slope of a line perpendicular to the line AB is:
a)
2
b)
-2
c)
1/2
d)
-1/2
|
Suresh Reddy answered |
Slope of the points A and B is -2 and the lines are perpendicular then
m1×m2 = -1.
∴ the slope is 1/2
The tangent of the angle which the part of the line above the X-axis makes with the positive direction of the X-axis is:- a)Perpendicular line
- b)Slope of a line
- c)Concurrent line
- d)Parallel line
Correct answer is option 'B'. Can you explain this answer?
The tangent of the angle which the part of the line above the X-axis makes with the positive direction of the X-axis is:
a)
Perpendicular line
b)
Slope of a line
c)
Concurrent line
d)
Parallel line
|
Preeti Iyer answered |
The gradient or slope of a line (not parallel to the axis of y) is the trigonometrical tangent of the angle which the line makes with the positive direction of the x-axis. Thus, if a line makes an angle θ with the positive direction of the x-axis, then its slope will be tan θ.
Can you explain the answer of this question below:The points A and B have coordinates (3, 2) and (1, 4) respectively. So, the slope of any line perpendicular to AB is- A:2
- B:1
- C:-1
- D:-2
The answer is b.
The points A and B have coordinates (3, 2) and (1, 4) respectively. So, the slope of any line perpendicular to AB is
A:
2
B:
1
C:
-1
D:
-2
|
Geetika Shah answered |
If the lines are perpendicular to each other then their slopes are in the form m1.m2 = -1.(since product of slopes of two perpendicular lines is -1) Therefore , m = 1.
The value of y, for the line passing through (3, y) and (2, 7) is parallel to the line passing through (-1 , 4) and (0, 6) is:- a)9/7
- b)3/7
- c)9
- d)3
Correct answer is option 'C'. Can you explain this answer?
The value of y, for the line passing through (3, y) and (2, 7) is parallel to the line passing through (-1 , 4) and (0, 6) is:
a)
9/7
b)
3/7
c)
9
d)
3
|
|
Suresh Reddy answered |
As A(3,y) and B(2,7) is parallel to C(-1,4) and D(0,6)
∴ Their slopes are equal
so, (y-7)/(3-1) = (4-6)/(-1-0)
y-7 = 2
y = 9
∴ Their slopes are equal
so, (y-7)/(3-1) = (4-6)/(-1-0)
y-7 = 2
y = 9
Which is untrue about orbital velocity?
- a)increases with the increase in height of satellite
- b)depends on mass and radius of planet around which it revolves
- c)it is independent of mass of satellite
- d)decreases with an increase in radius of orbit
Correct answer is option 'A'. Can you explain this answer?
Which is untrue about orbital velocity?
a)
increases with the increase in height of satellite
b)
depends on mass and radius of planet around which it revolves
c)
it is independent of mass of satellite
d)
decreases with an increase in radius of orbit
|
Om Desai answered |
The untrue statement about orbital velocity is:
1. increases with the increase in height of satellite
Explanation: Orbital velocity is the speed at which an object revolves around a planet or other celestial body in a stable orbit. According to the equation for orbital velocity, v = √(GM/r+h), where G is the gravitational constant, M is the mass of the planet, and r is the radius of the orbit.
As the height of the satellite increases (meaning it gets far to the planet), its h increase , so reasulting in decrease in velocity .
The other statements are true:
2. depends on mass and radius of planet around which it revolves: As mentioned in the equation, orbital velocity depends on both the mass (M) of the planet and the radius (r) of the orbit.
3. it is independent of mass of satellite: The mass of the satellite does not appear in the equation for orbital velocity, so it does not affect the speed at which the satellite orbits the planet.
4. decreases with an increase in radius of orbit: From the equation, we can see that as the radius of the orbit (r) increases, the orbital velocity (v) decreases.
1. increases with the increase in height of satellite
Explanation: Orbital velocity is the speed at which an object revolves around a planet or other celestial body in a stable orbit. According to the equation for orbital velocity, v = √(GM/r+h), where G is the gravitational constant, M is the mass of the planet, and r is the radius of the orbit.
As the height of the satellite increases (meaning it gets far to the planet), its h increase , so reasulting in decrease in velocity .
The other statements are true:
2. depends on mass and radius of planet around which it revolves: As mentioned in the equation, orbital velocity depends on both the mass (M) of the planet and the radius (r) of the orbit.
3. it is independent of mass of satellite: The mass of the satellite does not appear in the equation for orbital velocity, so it does not affect the speed at which the satellite orbits the planet.
4. decreases with an increase in radius of orbit: From the equation, we can see that as the radius of the orbit (r) increases, the orbital velocity (v) decreases.
m1 and m2 are the slope of two perpendicular lines, if- a)m1.m2 = 1
- b)m1= m2
- c)m1 + m2 = 0
- d)1 + m1.m2 = 0
Correct answer is option 'D'. Can you explain this answer?
m1 and m2 are the slope of two perpendicular lines, if
a)
m1.m2 = 1
b)
m1= m2
c)
m1 + m2 = 0
d)
1 + m1.m2 = 0
|
Lakshmi Roy answered |
Explanation:
Two lines are perpendicular if the product of their slopes is -1. So, if m1 and m2 are the slopes of two perpendicular lines, then:
m1.m2 = -1
Rewriting this equation, we get:
1/m1 . 1/m2 = -1
Multiplying both sides by m1.m2, we get:
m2/m1 + m1/m2 = 0
This can be simplified as:
m1.m2 = 0
Therefore, the correct answer is option D.
Two lines are perpendicular if the product of their slopes is -1. So, if m1 and m2 are the slopes of two perpendicular lines, then:
m1.m2 = -1
Rewriting this equation, we get:
1/m1 . 1/m2 = -1
Multiplying both sides by m1.m2, we get:
m2/m1 + m1/m2 = 0
This can be simplified as:
m1.m2 = 0
Therefore, the correct answer is option D.
India’s first artificial satellite was:- a)Sputnik
- b)Rohini
- c)Insat
- d)Aryabhatta
Correct answer is option 'D'. Can you explain this answer?
India’s first artificial satellite was:
a)
Sputnik
b)
Rohini
c)
Insat
d)
Aryabhatta
|
|
Geetika Shah answered |
India's first artificial satellite was Aryabhata. Launched by soviet union on 19 April 1975
A satellite which appears to be at a fixed position at a definite height to an observer is called:- a)Geostationary satellite and geosynchronous satellite
- b)Polar satellite
- c)Geostationary satellite
- d)Geosynchronous satellite
Correct answer is option 'A'. Can you explain this answer?
A satellite which appears to be at a fixed position at a definite height to an observer is called:
a)
Geostationary satellite and geosynchronous satellite
b)
Polar satellite
c)
Geostationary satellite
d)
Geosynchronous satellite
|
Neha Joshi answered |
As the relative velocity of the satellite with respect to the earth is zero, it appears stationary from the Earth surface and therefore it is called is geostationary satellite or geosynchronous satellite.
Two lines are said to be parallel when the difference of their slopes is- a)-1
- b)0
- c)1
- d)2
Correct answer is option 'B'. Can you explain this answer?
Two lines are said to be parallel when the difference of their slopes is
a)
-1
b)
0
c)
1
d)
2
|
Aryan Khanna answered |
Parallel lines and their slopes are easy. Since slope is a measure of the angle of a line from the horizontal, and since parallel lines must have the same angle, then parallel lines have the same slope and lines with the same slope are parallel.
Weightlessness is:- a)a situation in which the effective weight of the body becomes zero
- b)a situation in which the effective weight of the body becomes 10N
- c)a situation in which the effective weight of the body becomes 9.8N.
- d)a situation in which the effective mass of the body becomes zero
Correct answer is option 'A'. Can you explain this answer?
Weightlessness is:
a)
a situation in which the effective weight of the body becomes zero
b)
a situation in which the effective weight of the body becomes 10N
c)
a situation in which the effective weight of the body becomes 9.8N.
d)
a situation in which the effective mass of the body becomes zero
|
Akshay Shah answered |
Weight becomes zero in a freefall or when the total force on your body is zero.For example in a freely falling lift the contact force on your body is zero,so the wieghting machine would show zero reading.so you are wieghtless.
Slope of a line is not defined, when q = ……- a)60°
- b)90°
- c)30°
- d)45°
Correct answer is option 'B'. Can you explain this answer?
Slope of a line is not defined, when q = ……
a)
60°
b)
90°
c)
30°
d)
45°
|
|
Neha Sharma answered |
Since tan θ is not defined when θ = 90°, therefore, the slope of a vertical line is not defined. i.e., slope of y-axis is m = tan 90° = ∞ i.e., not defined.
Kepler’s second law states that the straight line joining the planet to the sun sweeps out equal areas in equal time. The statement is equivalent to saying that:- a)longitudnal acceleration is zero
- b)total acceleration is zero
- c)transverse acceleration is zero
- d)radial acceleration is zero
Correct answer is option 'C'. Can you explain this answer?
Kepler’s second law states that the straight line joining the planet to the sun sweeps out equal areas in equal time. The statement is equivalent to saying that:
a)
longitudnal acceleration is zero
b)
total acceleration is zero
c)
transverse acceleration is zero
d)
radial acceleration is zero
|
|
Suresh Reddy answered |
According to the second law the orbital radius and angular velocity of the planet in the elliptical orbit will vary. The planet travels faster when closer to the Sun, then slower when farther from the Sun. Hence we can say that the transverse acceleration is zero while radial and longitudinal accelerations are not zero.
A satellite moves in a circular orbit around earth. The radius of this orbit is one half that of moon’s orbit. The satellite completes one revolution in:
- a)(2) 3/2 lunar month
- b)(2) 3 lunar month
- c)(2) -3/2 lunar month
- d)(2)1/2 lunar month
Correct answer is option 'C'. Can you explain this answer?
A satellite moves in a circular orbit around earth. The radius of this orbit is one half that of moon’s orbit. The satellite completes one revolution in:
a)
(2) 3/2 lunar month
b)
(2) 3 lunar month
c)
(2) -3/2 lunar month
d)
(2)1/2 lunar month
|
|
Suresh Reddy answered |
We know that the time period of revolution for any object in orbit of radius r is 3
T = 2π (r3 / Gm) 1/2
Where m is the mass of earth.
As the ratio of radius of orbit of satellite to that of moon is 1:2
Hence there time period has a ratio of 1: 23/2
T = 2π (r3 / Gm) 1/2
Where m is the mass of earth.
As the ratio of radius of orbit of satellite to that of moon is 1:2
Hence there time period has a ratio of 1: 23/2
The squares of the periods of revolution of the planets are proportional to the ___________of their semimajor axis of its orbit.- a)sqaures
- b)sqaures root
- c)cube
- d)cube roots
Correct answer is option 'C'. Can you explain this answer?
The squares of the periods of revolution of the planets are proportional to the ___________of their semimajor axis of its orbit.
a)
sqaures
b)
sqaures root
c)
cube
d)
cube roots
|
|
Lavanya Menon answered |
The Law of Periods: The square of the period of any planet is proportional to the cube of the semimajor axis of its orbit.
Different planets have different escape velocities because:- a)different planets have different atmosphere
- b)they have different distances from sun
- c)escape velocity depends on the body that has to escape the atmosphere of the planet
- d)they have different masses and sizes
Correct answer is option 'D'. Can you explain this answer?
Different planets have different escape velocities because:
a)
different planets have different atmosphere
b)
they have different distances from sun
c)
escape velocity depends on the body that has to escape the atmosphere of the planet
d)
they have different masses and sizes
|
Nitin Nair answered |
The formula for calculating the escape velocity from the surface of a celestial body (e.g. a planet) is:
where G is the universal gravitation constant, M is the planet’s mass and R is its radius.Different planets have different mass and radius - and therefore different escape velocity.
Slope of a line which cuts intercepts of equal lengths on the axes is: - a)- 1
- b)0
- c)2
- d)√3
Correct answer is option 'A'. Can you explain this answer?
Slope of a line which cuts intercepts of equal lengths on the axes is:
a)
- 1
b)
0
c)
2
d)
√3
|
Varun Kapoor answered |
The equation of line which cuts intercepts of equal lengths on the axes is:
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