All questions of Where and When? for Grade 9 Exam
Can you explain the answer of this question below:The error in two readings of A are 0.01 and -0.03, then mean absolute error is ?- A:0.002
- B:-0.004
- C:0.02
- D:-0.02
The answer is c.
The error in two readings of A are 0.01 and -0.03, then mean absolute error is ?
A:
0.002
B:
-0.004
C:
0.02
D:
-0.02
|
Bhargavi Bajaj answered |
Mean absolute error = (|0.01|+|-0.03|)/2
= 0.02
= 0.02
For a line whose equation is √3x + y = 8, the length of the perpendicular from the origin is- a)4
- b)8
- c)16
- d)2
Correct answer is option 'A'. Can you explain this answer?
For a line whose equation is √3x + y = 8, the length of the perpendicular from the origin is
a)
4
b)
8
c)
16
d)
2
|
Rajesh Gupta answered |
√3x + y - 8
√3x + y = 8
Dividing by √[(√3)2 + (1)2]
= √[3+1]
= √4
= 2
√3x/2 + y/2 = 8/2
√3x/2 + y/2 = 4
x(√3/2) + y(1/2) = 4.....(1)
Normal form of any line : xcos w + ysin w = p....(2)
Comparing (1) and (2)
p = 4
√3x + y = 8
Dividing by √[(√3)2 + (1)2]
= √[3+1]
= √4
= 2
√3x/2 + y/2 = 8/2
√3x/2 + y/2 = 4
x(√3/2) + y(1/2) = 4.....(1)
Normal form of any line : xcos w + ysin w = p....(2)
Comparing (1) and (2)
p = 4
Which is the most accurate atomic clock?- a)Carbon-12 clock
- b)Carbon atom clock
- c)caesium atom clock
- d)Stop clock
Correct answer is option 'C'. Can you explain this answer?
Which is the most accurate atomic clock?
a)
Carbon-12 clock
b)
Carbon atom clock
c)
caesium atom clock
d)
Stop clock
|
Nandini Patel answered |
According to the most accurate caesium atomic clock in the world, 1 second is the time that elapses during 9,192,631,770 cycles of the radiation produced by the transition between two levels of the caesium 133 atom.
Can you explain the answer of this question below:The method used to measure the distance of a planet from the earth is- A:Parallax method
- B:Archimedes’ method
- C:Newton’s method
- D:Galileo’s method
The answer is a.
The method used to measure the distance of a planet from the earth is
A:
Parallax method
B:
Archimedes’ method
C:
Newton’s method
D:
Galileo’s method
|
Yash Ghoshal answered |
The astronomers mainly use parallax method to find distances to objects like other planets. To calculate the distance to a star or to a planet, astronomers observe it from different places along Earth's orbit around the Sun.
The most suitable instrument for measuring the size of an atom is.- a)Electron microscope
- b)Vernier calliper
- c)Optical Microscope
- d)Screw gauge
Correct answer is 'A'. Can you explain this answer?
The most suitable instrument for measuring the size of an atom is.
a)
Electron microscope
b)
Vernier calliper
c)
Optical Microscope
d)
Screw gauge
|
Mira Sharma answered |
Only electron microscope has resolution of 0.5-0.6 Angstrom which is less than the size of an atom.
Can you explain the answer of this question below: Which of the following is caused by careless handling?
- A:
Systematic error
- B:
Gross error
- C:
Random error
- D:
None of the mentioned
The answer is b.
Which of the following is caused by careless handling?
Systematic error
Gross error
Random error
None of the mentioned
|
|
Nandini Iyer answered |
Gross errors are mostly due to lack of knowledge, judgment and care on the part of experiment. That is Gross error is caused by careless handling.
Which of the following is caused by careless handling?- a)Systematic error
- b)Gross error
- c)Random error
- d)None of the mentioned
Correct answer is option 'B'. Can you explain this answer?
Which of the following is caused by careless handling?
a)
Systematic error
b)
Gross error
c)
Random error
d)
None of the mentioned
|
Trisha Vashisht answered |
Gross errors are mostly due to lack of knowledge, judgment and care on the part of experiment. That is Gross error is caused by careless handling.
What is the distance of the point (3,3) from the line 2(x-3) = 3(y+5)?- a)5/3
- b)6
- c)
- d)
Correct answer is option 'C'. Can you explain this answer?
What is the distance of the point (3,3) from the line 2(x-3) = 3(y+5)?
a)
5/3
b)
6
c)
d)
|
|
Naina Sharma answered |
2(x-3) = 3(y+5)
2x - 6 = 3y + 15
2x - 3y = 21
2x - 3y - 21 = 0
Using distance formula = |ax1 + by1 + c|/(a2 + b2)1/2
= (6-9-21)/((2)2 + (3)2)1/2
= 24/(13)1/2
2x - 6 = 3y + 15
2x - 3y = 21
2x - 3y - 21 = 0
Using distance formula = |ax1 + by1 + c|/(a2 + b2)1/2
= (6-9-21)/((2)2 + (3)2)1/2
= 24/(13)1/2
The error in two readings of A are 0.01 and -0.03, then mean absolute error is ?- a)0.002
- b)-0.004
- c)0.02
- d)-0.02
Correct answer is 'C'. Can you explain this answer?
The error in two readings of A are 0.01 and -0.03, then mean absolute error is ?
a)
0.002
b)
-0.004
c)
0.02
d)
-0.02
|
Anagha Sharma answered |
Mean absolute error = (|0.01|+|-0.03|)/2
= 0.02
= 0.02
Error in the measurement of radius of a sphere is 1%. The error in the calculated value of its volume is- a)1%
- b)3%
- c)5%
- d)7%
Correct answer is option 'B'. Can you explain this answer?
Error in the measurement of radius of a sphere is 1%. The error in the calculated value of its volume is
a)
1%
b)
3%
c)
5%
d)
7%
|
|
Raghav Bansal answered |
∵ V = (4/3)πr3
% error is volume = 3 × error in radius = 3 × 1 = 3%
% error is volume = 3 × error in radius = 3 × 1 = 3%
The distance between the parallel lines 4x-3y+5 = 0 and 4x-3y+15 = 0 is :- a)4 units
- b)2 units
- c)3.5 units
- d)5 units
Correct answer is option 'B'. Can you explain this answer?
The distance between the parallel lines 4x-3y+5 = 0 and 4x-3y+15 = 0 is :
a)
4 units
b)
2 units
c)
3.5 units
d)
5 units
|
|
Raghav Bansal answered |
4x - 3y + 5 = 0, 4x - 3y + 15 = 0
A = 4, B = -3 c1 = 5, c2 = 15
|c1 - c2|/[A2 + B2]1/2
= |5 - 15|/[(4)2 + (-3)2]½
= 10/5
= 2
A = 4, B = -3 c1 = 5, c2 = 15
|c1 - c2|/[A2 + B2]1/2
= |5 - 15|/[(4)2 + (-3)2]½
= 10/5
= 2
A point P is in the interior of angle BAC, such that P lies on the bisector of angle BAC. What can be said about the distance of PM if PN = 2cm where PM and PN are perpendiculars from P on the lines BA and AC?- a)PM = 2 PN
- b)PM = 3 PN
- c)PM =2 cm
- d)PM =3.5 cm
Correct answer is option 'C'. Can you explain this answer?
A point P is in the interior of angle BAC, such that P lies on the bisector of angle BAC. What can be said about the distance of PM if PN = 2cm where PM and PN are perpendiculars from P on the lines BA and AC?
a)
PM = 2 PN
b)
PM = 3 PN
c)
PM =2 cm
d)
PM =3.5 cm
|
Krishna Iyer answered |
In Δ PAM & Δ PAN, angle (PAM) = angle (PAN) (Since AP bisects the angle (BAC)) angle (AMP) = angle (ANP) = 900
PA = PA (common)
By AAS congruence, Δ PAM and Δ PAN are congruent.
MP = NP = 2 cm
PA = PA (common)
By AAS congruence, Δ PAM and Δ PAN are congruent.
MP = NP = 2 cm
Angstrom is the unit of- a)time
- b)mass
- c)light
- d)length
Correct answer is option 'D'. Can you explain this answer?
Angstrom is the unit of
a)
time
b)
mass
c)
light
d)
length
|
Vishal Giri answered |
Ya ri8 angstrom this unit used to measure length. 1 A = 10^ - 10 m
1 fermi is equal to:- a)10-10 m
- b)1010 m
- c)1015 m
- d)10-15 m
Correct answer is option 'D'. Can you explain this answer?
1 fermi is equal to:
a)
10-10 m
b)
1010 m
c)
1015 m
d)
10-15 m
|
|
Rohit Shah answered |
One fermi or femtometre is equal 10^-15 m. This unit is used to measure nuclear dimensions.
Can you explain the answer of this question below: Approximate ratio of 1 fermi to 1 angstrom is …………..
- A:
10-5m
- B:
10-15m
- C:
10-9m
- D:
10-6m
The answer is a.
Approximate ratio of 1 fermi to 1 angstrom is …………..
10-5m
10-15m
10-9m
10-6m
|
|
Shreya Gupta answered |
As, 1 fermi = 10-15 m and 1 angstrom = 10^-10 m;
So, approximate ratio = 10^-5 m
Considering a fixed distance from the origin, how many points can be plotted on the y axis?- a)2
- b)3
- c)4
- d)no points
Correct answer is option 'A'. Can you explain this answer?
Considering a fixed distance from the origin, how many points can be plotted on the y axis?
a)
2
b)
3
c)
4
d)
no points
|
|
Neha Joshi answered |
Let the fixed distance be d. Since the point has to lie on Y axis, therefore abscissa of such points is 0. Hence the points can be (0, d) and (0, -d). So, Option A is the correct answer.PS: This is the link to my YouTube channel Mechnovashia:https://www.youtube.com/channel/UCI89XUuzHmY8xLV4ovBWWUwSubscribe to this channel for more such simplified explanations and concepts. ☺️
The accuracy in the measurement of time for 20 oscillations of pendulum for the following measurements, t1 = 39.6 s, t2 = 39.9 s and t3 = 39.5 s is:
- a)± 0.005 s
- b)± 0.3 s
- c)± 0.5 s
- d)± 0.4 s
Correct answer is option 'A'. Can you explain this answer?
The accuracy in the measurement of time for 20 oscillations of pendulum for the following measurements, t1 = 39.6 s, t2 = 39.9 s and t3 = 39.5 s is:
a)
± 0.005 s
b)
± 0.3 s
c)
± 0.5 s
d)
± 0.4 s
|
Niharika Nair answered |
Given,
t1 = 39.6 s
t2 = 39.9s
t3 = 39.5 s
Least count of measuring instrument = 0.1 s
[As measurements have only one decimal place] Percision in the measurement = Least count of the measuring instrument =0.1 s
Mean value of time for 20 oscillations
t1 = 39.6 s
t2 = 39.9s
t3 = 39.5 s
Least count of measuring instrument = 0.1 s
[As measurements have only one decimal place] Percision in the measurement = Least count of the measuring instrument =0.1 s
Mean value of time for 20 oscillations
Absolute errors in the measurements
Δt1 = t - t1 = 39.7 - 39.6 = 0.1s
Δt2 = t - t2 = 39.7 - 39.9 = -0.2 s
Δt3 = t - t3 = 39.7 - 39.5 = 0.2 s
Δt1 = t - t1 = 39.7 - 39.6 = 0.1s
Δt2 = t - t2 = 39.7 - 39.9 = -0.2 s
Δt3 = t - t3 = 39.7 - 39.5 = 0.2 s
Mean absolute error
(rounding-off upto decimal place)∴ Accuracy of measurement = ±0.2 s
The most suitable instrument for measuring the size of an atom is.- a)Electron microscope
- b)Vernier calliper
- c)Optical Microscope
- d)Screw gauge
Correct answer is option 'A'. Can you explain this answer?
The most suitable instrument for measuring the size of an atom is.
a)
Electron microscope
b)
Vernier calliper
c)
Optical Microscope
d)
Screw gauge
|
|
Rashi Sharma answered |
Only electron microscope has resolution of 0.5-0.6 Angstrom which is less than the size of an atom.
Which of the following is caused by careless handling?- a)Systematic error
- b)Gross error
- c)Random error
- d)None of the mentioned
Correct answer is 'B'. Can you explain this answer?
Which of the following is caused by careless handling?
a)
Systematic error
b)
Gross error
c)
Random error
d)
None of the mentioned
|
.mie. answered |
Ys the answr is B ... as systematic errors arises due to faulty instruments.... random errors are those errors, which occur irregularly and hence are random. These can arise due to random and unpredictable fluctuations in experimental conditions For example, when the same person repeats the same observation, it is very likely that he may get different readings every time... Gross Errors: This category basically takes into account human oversight and other mistakes while reading, recording and the readings ...(^_^)
What is the percentage error in the physical quantity A if it is related to four other physical quantities a, b, c and d as 
The percentage error in measurement of a, b, c and d are 1%, 3%, 2% and 2% respectively.
Correct answer is '14'. Can you explain this answer?
What is the percentage error in the physical quantity A if it is related to four other physical quantities a, b, c and d as The percentage error in measurement of a, b, c and d are 1%, 3%, 2% and 2% respectively.
The percentage error in measurement of a, b, c and d are 1%, 3%, 2% and 2% respectively.
|
Soumya Mukherjee answered |
Percentage error in A
A student measures the distance covered and time taken by a body under free fall which was intially at rest. He uses this data for estimating g, the acceleration due to gravity. If the maximum percentage error in measurement of the distance and the time are e1 and e2 respectively, then the maximum possible percentage error in the estimation of g is- a)e2 - e1
- b)e1 + 2e2
- c)e1 + e2
- d)e1 - 2e2
Correct answer is option 'B'. Can you explain this answer?
A student measures the distance covered and time taken by a body under free fall which was intially at rest. He uses this data for estimating g, the acceleration due to gravity. If the maximum percentage error in measurement of the distance and the time are e1 and e2 respectively, then the maximum possible percentage error in the estimation of g is
a)
e2 - e1
b)
e1 + 2e2
c)
e1 + e2
d)
e1 - 2e2
|
|
Priya Deshpande answered |
From the releation
h= 1/2gt2 ⇒ g = 2h/t2
h= 1/2gt2 ⇒ g = 2h/t2
Taking natural logarithms on both sides, we get
ln (g) = ln (h) - 2ln (t) + ln (2)
Differentiating
for maximum permissible errors , we add both the errors . so
At a certain place, the acceleration due to gravity is determined using a simple pendulum. The length of the pendulum is 25.0 cm and a stopwatch with least count is 1 s measures the time taken by the pendulum for 40 oscilations to be 50 s. the accuracy in the measurement of g is- a)4.40 %
- b)3.40 %
- c)2.40 %
- d)5.40 %
Correct answer is option 'A'. Can you explain this answer?
At a certain place, the acceleration due to gravity is determined using a simple pendulum. The length of the pendulum is 25.0 cm and a stopwatch with least count is 1 s measures the time taken by the pendulum for 40 oscilations to be 50 s. the accuracy in the measurement of g is
a)
4.40 %
b)
3.40 %
c)
2.40 %
d)
5.40 %
|
|
Tanishq Unni answered |
Can you explain the answer of this question below: Approximate ratio of 1 fermi to 1 angstrom is …
- A:
10-5m
- B:
10-15m
- C:
10-9m
- D:
10-6m
The answer is a.
Approximate ratio of 1 fermi to 1 angstrom is …
10-5m
10-15m
10-9m
10-6m
|
|
Bhargavi Bajaj answered |
To find the approximate ratio of 1 fermi to 1 angstrom, we need to convert both units to a common unit of length.
1 fermi (fm) is a unit of length in the metric system, and it is equal to 10^-15 meters (m).
1 angstrom (Å) is also a unit of length in the metric system, and it is equal to 10^-10 meters (m).
To find the ratio, we can divide 1 fermi by 1 angstrom:
Ratio = 1 fm / 1 Å
Since both units are in meters, we can convert the units before dividing:
Ratio = (1 fm / 10^-15 m) / (1 Å / 10^-10 m)
Simplifying the expression:
Ratio = (1 fm * 10^-10 m) / (1 Å * 10^-15 m)
Ratio = 10^-10 / 10^-15
Using the rules of exponents, we can subtract the exponents:
Ratio = 10^5
Therefore, the approximate ratio of 1 fermi to 1 angstrom is 10^5.
1 fermi (fm) is a unit of length in the metric system, and it is equal to 10^-15 meters (m).
1 angstrom (Å) is also a unit of length in the metric system, and it is equal to 10^-10 meters (m).
To find the ratio, we can divide 1 fermi by 1 angstrom:
Ratio = 1 fm / 1 Å
Since both units are in meters, we can convert the units before dividing:
Ratio = (1 fm / 10^-15 m) / (1 Å / 10^-10 m)
Simplifying the expression:
Ratio = (1 fm * 10^-10 m) / (1 Å * 10^-15 m)
Ratio = 10^-10 / 10^-15
Using the rules of exponents, we can subtract the exponents:
Ratio = 10^5
Therefore, the approximate ratio of 1 fermi to 1 angstrom is 10^5.
What is the number of significant figures in 0.310×103 ?- a)6
- b)2
- c)4
- d)3
Correct answer is option 'D'. Can you explain this answer?
What is the number of significant figures in 0.310×103 ?
a)
6
b)
2
c)
4
d)
3
|
|
Suresh Kumar answered |
10^ powers are not considered as significant figures....
& in the case of decimal points....the zero present at the beginning & in between the numbers is considered as significant digit....
Hence;in this case the significant figures are 3...
& in the case of decimal points....the zero present at the beginning & in between the numbers is considered as significant digit....
Hence;in this case the significant figures are 3...
Which of the following statements is incorrect?- a)Displacement is independent of the choice of origin of the axis.
- b)Displacement may or may not be equal to the distance travelled.
- c)When a particle returns to its starting point, its displacement is not zero.
- d)Displacement does not tell the nature of the actual motion of a particle between the points.
Correct answer is option 'C'. Can you explain this answer?
Which of the following statements is incorrect?
a)
Displacement is independent of the choice of origin of the axis.
b)
Displacement may or may not be equal to the distance travelled.
c)
When a particle returns to its starting point, its displacement is not zero.
d)
Displacement does not tell the nature of the actual motion of a particle between the points.
|
Dev Patel answered |
When a particle returns to it's initial position, Initial and final positions will be same therefore net displacement of the particle is zero. Hence the given statement is false.
The point on y-axis equidistant from the points (3,2) and (-1,3) is- a)(0,-3)
- b)(0,-3/2)
- c)(0,3/2)
- d)(0,3)
Correct answer is option 'B'. Can you explain this answer?
The point on y-axis equidistant from the points (3,2) and (-1,3) is
a)
(0,-3)
b)
(0,-3/2)
c)
(0,3/2)
d)
(0,3)
|
|
Gitanjali Tiwari answered |
Given:
Points A (3,2) and B (-1,3)
Point P on y-axis equidistant from A and B
To find:
Coordinates of point P
Approach:
1. Find the distance between points A and B.
2. Find the midpoint of line AB.
3. Find the equation of the line passing through the midpoint and perpendicular to AB.
4. Find the intersection point of the line with the y-axis.
Calculation:
Step 1: Find the distance between points A and B using the distance formula.
Distance between two points (x1, y1) and (x2, y2) is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Using the formula, we have:
dAB = sqrt((-1 - 3)^2 + (3 - 2)^2)
= sqrt((-4)^2 + (1)^2)
= sqrt(16 + 1)
= sqrt(17)
Step 2: Find the midpoint of line AB.
Midpoint formula:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
Using the formula, we have:
Midpoint = ((-1 + 3)/2, (3 + 2)/2)
= (2/2, 5/2)
= (1, 5/2)
Step 3: Find the equation of the line passing through the midpoint and perpendicular to AB.
The slope of line AB is given by:
mAB = (y2 - y1)/(x2 - x1)
Using the formula, we have:
mAB = (3 - 2)/(-1 - 3)
= 1/(-4)
= -1/4
The slope of the line perpendicular to AB is the negative reciprocal of mAB.
m_perpendicular = -1/mAB
= -1/(-1/4)
= 4
Using the point-slope form of a line, the equation of the line passing through the midpoint is:
y - y1 = m(x - x1)
Substituting the values, we have:
y - (5/2) = 4(x - 1)
Simplifying the equation, we get:
y - 5/2 = 4x - 4
Step 4: Find the intersection point of the line with the y-axis.
To find the intersection point, substitute x = 0 in the equation of the line:
y - 5/2 = 4(0) - 4
y - 5/2 = -4
Simplifying the equation, we have:
y = -4 + 5/2
y = -8/2 + 5/2
y = -3/2
Therefore, the coordinates of point P are (0, -3/2).
Hence, the correct answer is option B) (0, -3/2).
Points A (3,2) and B (-1,3)
Point P on y-axis equidistant from A and B
To find:
Coordinates of point P
Approach:
1. Find the distance between points A and B.
2. Find the midpoint of line AB.
3. Find the equation of the line passing through the midpoint and perpendicular to AB.
4. Find the intersection point of the line with the y-axis.
Calculation:
Step 1: Find the distance between points A and B using the distance formula.
Distance between two points (x1, y1) and (x2, y2) is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Using the formula, we have:
dAB = sqrt((-1 - 3)^2 + (3 - 2)^2)
= sqrt((-4)^2 + (1)^2)
= sqrt(16 + 1)
= sqrt(17)
Step 2: Find the midpoint of line AB.
Midpoint formula:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
Using the formula, we have:
Midpoint = ((-1 + 3)/2, (3 + 2)/2)
= (2/2, 5/2)
= (1, 5/2)
Step 3: Find the equation of the line passing through the midpoint and perpendicular to AB.
The slope of line AB is given by:
mAB = (y2 - y1)/(x2 - x1)
Using the formula, we have:
mAB = (3 - 2)/(-1 - 3)
= 1/(-4)
= -1/4
The slope of the line perpendicular to AB is the negative reciprocal of mAB.
m_perpendicular = -1/mAB
= -1/(-1/4)
= 4
Using the point-slope form of a line, the equation of the line passing through the midpoint is:
y - y1 = m(x - x1)
Substituting the values, we have:
y - (5/2) = 4(x - 1)
Simplifying the equation, we get:
y - 5/2 = 4x - 4
Step 4: Find the intersection point of the line with the y-axis.
To find the intersection point, substitute x = 0 in the equation of the line:
y - 5/2 = 4(0) - 4
y - 5/2 = -4
Simplifying the equation, we have:
y = -4 + 5/2
y = -8/2 + 5/2
y = -3/2
Therefore, the coordinates of point P are (0, -3/2).
Hence, the correct answer is option B) (0, -3/2).
Which of the following statements is incorrect?- a)Path length is a scalar quantity whereas displacement is a vector quantity.
- b)The magnitude of displacement is always equal to the path length traversed by an object over a given time interval.
- c)The displacement depends only on the end points whereas path length depends on the actual path followed.
- d)The path length is always positive whereas displacement can be positive, negative and zero.
Correct answer is option 'B'. Can you explain this answer?
Which of the following statements is incorrect?
a)
Path length is a scalar quantity whereas displacement is a vector quantity.
b)
The magnitude of displacement is always equal to the path length traversed by an object over a given time interval.
c)
The displacement depends only on the end points whereas path length depends on the actual path followed.
d)
The path length is always positive whereas displacement can be positive, negative and zero.
|
|
Jyoti Sengupta answered |
In one dimensional motion, the path length and magnitude of displacement are equal only if the object does not change its direction during the course of motion. In all other cases, the path length is greater than the magnitude of displacement.
What is the angle made by the perpendicular from the origin to the line x+ √3y = 2 with the positive direction of x axis?- a)60°
- b)135°
- c)30°
- d)45°
Correct answer is option 'A'. Can you explain this answer?
What is the angle made by the perpendicular from the origin to the line x+ √3y = 2 with the positive direction of x axis?
a)
60°
b)
135°
c)
30°
d)
45°
|
Learners Habitat answered |
- The given equation is
- x +√3y = 2
- On dividing both sides by
- [(−1)2 + (√3)2]1/2 = √4 = 2
- = x/2 + √3y/2 = 2/2
- Therefore , the equation becomes
- = (1/2)x + (√3/2)y = 1
- = x cos 60° + y sin 60° = 1
- Normal form of any line is : x cosw + y sinw = p
- w = 60°
What will be the co-ordinates of foot of perpendicular line drawn from the point (-1,3) to the line 3x-4y-16=0?- a) (1/5,2/5)
- b)(2/25,5/25)
- c)(68/25,-49/25)
- d)(-49/25,68/25)
Correct answer is option 'C'. Can you explain this answer?
What will be the co-ordinates of foot of perpendicular line drawn from the point (-1,3) to the line 3x-4y-16=0?
a)
(1/5,2/5)
b)
(2/25,5/25)
c)
(68/25,-49/25)
d)
(-49/25,68/25)
|
Meera Nambiar answered |
Given: point (-1,3) and line 3x-4y-16=0
To find: co-ordinates of foot of perpendicular line drawn from the point (-1,3) to the line 3x-4y-16=0
Concept used: Equation of line, Distance between point and line, Foot of perpendicular
Solution:
Step 1: Convert the given equation of line in slope-intercept form
3x - 4y - 16 = 0
=> 4y = 3x - 16
=> y = (3/4)x - 4
Step 2: Find the slope of the given line
The slope of the given line is (3/4)
Step 3: Find the slope of the line perpendicular to the given line
The slope of the line perpendicular to the given line is -4/3 (negative reciprocal of the slope of the given line)
Step 4: Write the equation of the line perpendicular to the given line passing through the point (-1,3)
Using point-slope form, the equation of the line perpendicular to the given line passing through the point (-1,3) is:
y - 3 = (-4/3)(x + 1)
=> y = (-4/3)x + (5/3)
Step 5: Find the intersection point of the given line and the perpendicular line
Solving the equations of the two lines, we get:
(3/4)x - 4 = (-4/3)x + (5/3)
=> (25/12)x = (17/3)
=> x = (68/25)
Substituting x in the equation of the perpendicular line, we get:
y = (-4/3)(68/25) + (5/3)
=> y = -49/25
Therefore, the co-ordinates of the foot of perpendicular line drawn from the point (-1,3) to the line 3x-4y-16=0 is (68/25,-49/25).
Hence, option (C) is the correct answer.
To find: co-ordinates of foot of perpendicular line drawn from the point (-1,3) to the line 3x-4y-16=0
Concept used: Equation of line, Distance between point and line, Foot of perpendicular
Solution:
Step 1: Convert the given equation of line in slope-intercept form
3x - 4y - 16 = 0
=> 4y = 3x - 16
=> y = (3/4)x - 4
Step 2: Find the slope of the given line
The slope of the given line is (3/4)
Step 3: Find the slope of the line perpendicular to the given line
The slope of the line perpendicular to the given line is -4/3 (negative reciprocal of the slope of the given line)
Step 4: Write the equation of the line perpendicular to the given line passing through the point (-1,3)
Using point-slope form, the equation of the line perpendicular to the given line passing through the point (-1,3) is:
y - 3 = (-4/3)(x + 1)
=> y = (-4/3)x + (5/3)
Step 5: Find the intersection point of the given line and the perpendicular line
Solving the equations of the two lines, we get:
(3/4)x - 4 = (-4/3)x + (5/3)
=> (25/12)x = (17/3)
=> x = (68/25)
Substituting x in the equation of the perpendicular line, we get:
y = (-4/3)(68/25) + (5/3)
=> y = -49/25
Therefore, the co-ordinates of the foot of perpendicular line drawn from the point (-1,3) to the line 3x-4y-16=0 is (68/25,-49/25).
Hence, option (C) is the correct answer.
A drunkard is walking along a straight road. He takes 5 steps forward and 3 steps backward and so on. Each step is 1m long and takes 1s. There is a pit on the road 11 m away from the starting point. The drunkard will fall into the pit after:- a)21 s
- b)29 s
- c)31 s
- d)37 s
Correct answer is option 'B'. Can you explain this answer?
A drunkard is walking along a straight road. He takes 5 steps forward and 3 steps backward and so on. Each step is 1m long and takes 1s. There is a pit on the road 11 m away from the starting point. The drunkard will fall into the pit after:
a)
21 s
b)
29 s
c)
31 s
d)
37 s
|
Geetika Shah answered |
Displacement in first eight steps = (5 - 3) m = 2 m
Time taken for first eight steps = 8 s
Time taken by the drunkard to cover first 6 m of journey = 8/2 * 6 = 24 s
If the drunkard takes 5 steps more, he will fall into the pit. So the time taken by the drunkard to cover last five steps = 5 s
Total time taken = 24 s + 5 s = 29 s
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