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RS Aggarwal Solutions Class 10 Chapter 8 Trigonometric Identities Ex 8a

These Solutions are part of RS Aggarwal Solutions Class 10. Here we have given RS Aggarwal Solutions Class 10 Chapter 8 Trigonometric Identities Ex 8a.

Other Exercises

• RS Aggarwal Solutions Class 10 Chapter 8 Trigonometric Identities Ex 8a
• RS Aggarwal Solutions Class 10 Chapter 8 Trigonometric Identities Ex 8b
• RS Aggarwal Solutions Class 10 Chapter 8 Trigonometric Identities Ex 8c
• RS Aggarwal Solutions Class 10 Chapter 8 Trigonometric Identities MCQ
• RS Aggarwal Solutions Class 10 Chapter 8 Trigonometric Identities Test Yourself

Question 1.
Solution:

Question 2.
Solution:

Question 3.
Solution:

Question 4.
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Question 5.
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Question 6.
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Question 7.
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Question 8.
Solution:

Question 9.
Solution:

Question 10.
Solution:

Question 11.
Solution:

Question 12.
Solution:

Question 13.
Solution:

Question 14.
Solution:

Question 15.
Solution:

Question 16.
Solution:

Question 17.
Solution:

Question 18.
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Question 19.
Solution:

Question 20.
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Question 21.
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Question 22.
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Question 23.
Solution:

Question 24.
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Question 25.
Solution:

Question 26.
Solution:

Question 27.
Solution:
(i)

(ii)

Question 28.
Solution:

Question 29.
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Question 30.
Solution:

Question 31.
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Question 32.
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Question 33.
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Question 34.
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Question 35.
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Question 36.
Solution:
(i)

(ii)

(iii)

Question 37.
Solution:

We hope the RS Aggarwal Solutions Class 10 Chapter 8 Trigonometric Identities Ex 8a help you. If you have any query regarding RS Aggarwal Solutions Class 10 Chapter 8 Trigonometric Identities Ex 8a, drop a comment below and we will get back to you at the earliest.

RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data,Cumulative Frequency Graph and O give MCQ

These Solutions are part of RS Aggarwal Solutions Class 10. Here we have given RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data,Cumulative Frequency Graph and O give MCQ.

Other Exercises

• RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Ex 9a
• RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Ex 9b
• RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Ex 9c
• RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Ex 9d
• RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Ex 9e
• RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Ex 9f
• RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data MCQ
• RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Test Yourself

Question 1.
Solution:
Correct option: (d)
Range is not a measure of central tendency.

Question 2.
Solution:
Correct option: (a)
Mean cannot be determined graphically.

Question 3.
Solution:
Correct option: (a)
Since mean is the average of all observations, it is influenced by extreme values.

Question 4.
Solution:
Correct option: (c)
Mode can be obtained graphically from a histogram.

Question 5.
Solution:
Correct option: (d)
Ogives are used to determine the median of a frequency distribution.

Question 6.
Solution:
Correct option: (b)
The cumulative frequency table is useful in determining the median.

Question 7.
Solution:
Correct option: (b)
Median is given by the abscissa of the point of intersection of the Less than Type and More than Type cumulative frequency curves.

Question 8.
Solution:
Correct option: (b)
For a grouped data,
\(\sum { f }_{ i }\left( { x }_{ i }-\bar { x } \right) =0\)

Question 9.
Solution:
Correct option: (b)
By formula method,
\(\bar { x } =\quad A+h\left[ \frac { \sum { { f }_{ i }{ u }_{ i } } }{ \sum { { f }_{ i } } } \right] \)
where \({ u }_{ i }=\quad \frac { \left( { x }_{ i }-A \right) }{ h } \)

Question 10.
Solution:
Correct option: (c)
d_i‘s are the deviations from A of midpoints of the classes.

Question 11.
Solution:
Correct option: (b)
While computing the mean of the grouped data, we assume that the frequencies are centred at the class marks of the classes.

Question 12.
Solution:
Correct option: (b)
Mode = (3 x median) – (2 x mean)

Question 13.
Solution:
Correct option: (c)
Since the abscissa of the point of intersection of both the ogives gives the median, we have median = 20.5

Question 14.
Solution:

Question 15.
Solution:
Correct option: (c)
Class having maximum frequency is the modal class.
Here, maximum frequency = 30
Hence, the modal class is 30 – 40.

Question 16.
Solution:
Correct option: (b)
Mode = \({ x }_{ k }+h.\left\{ \frac { { f }_{ k }-{ f }_{ k-1 } }{ \left( { 2f }_{ k }-{ f }_{ k-1 }-{ f }_{ k+1 } \right) } \right\} \)

Question 17.
Solution:
Correct option: (a)
Median = \(l+\left\{ h\times \frac { \left( \frac { N }{ 2 } -cf \right) }{ f } \right\} \)

Question 18.
Solution:
Correct option: (c)
Mean = 8.9
Median = 9
Mode = 3Median – 2Mean
= 3 x 9 – 2 x 8.9
= 27 – 17.8
= 9.2.

Question 19.
Solution:

Question 20.
Solution:

Question 21.
Solution:

Question 22.
Solution:

Question 23.
Solution:
Correct option: (c)
For a symmetrical distribution,
we have  Mean = mode = median

Question 24.
Solution:
Correct option: (c)
Number of families having income more than Rs. 20000 = 50
Number of families having income more than Rs. 25000 = 37
Hence, number of families having income range 20000 to 25000 = 50 – 37 = 13

Question 25.
Solution:

Question 26.
Solution:
Correct option: (d)
Mean of 20 numbers = 0
Hence, sum of 20 numbers = 0 x 20 = 0
Now, the mean can be zero if
sum of 10 numbers is (S) and the sum of remaining 10 numbers is (-S),
sum of 11 numbers is (S) and the sum of remaining 9 numbers is (-S), …….
sum of 19 numbers is (S) and the 20^th number is (-S), then their sum is zero.
So, at the most, 19 numbers can be greater than zero.

Question 27.
Solution:

Question 28.
Solution:

Question 29.
Solution:
(a) – (s)
The most frequent value in a data is known as mode.
(b) – (r)
Mean cannot be determined graphically.
(c) – (q)
An ogive is used to determine median.
(d) – (p)
Standard deviation is not a measure of central tendency.

Question 30.
Solution:

Question 31.
Solution:

We hope the RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data MCQ help you. If you have any query regarding RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data MCQ, drop a comment below and we will get back to you at the earliest.

RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data,Cumulative Frequency Graph and O give Ex 9f

These Solutions are part of RS Aggarwal Solutions Class 10. Here we have given RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data,Cumulative Frequency Graph and O give Ex 9f.

Other Exercises

• RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Ex 9a
• RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Ex 9b
• RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Ex 9c
• RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Ex 9d
• RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Ex 9e
• RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Ex 9f
• RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data MCQ
• RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Test Yourself

Question 1.
Solution:

Question 2.
Solution:
Class having maximum frequency is the modal class.
Here, maximum frequency = 27
Hence, the modal class is 40 – 50.
Thus, the lower limit of the modal class is 40.

Question 3.
Solution:

Question 4.
Solution:

Question 5.
Solution:

Question 6.
Solution:

Question 7.
Solution:

Question 8.
Solution:

Question 9.
Solution:

Question 10.
Solution:

Question 11.
Solution:

Question 12.
Solution:

Question 13.
Solution:

Question 14.
Solution:

Question 15.
Solution:

Question 16.
Solution:

Question 17.
Solution:

Question 18.
Solution:

Question 19.
Solution:

Question 20.
Solution:

Question 21.
Solution:

Question 22.
Solution:

We hope the RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Ex 9f help you. If you have any query regarding RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Ex 9f, drop a comment below and we will get back to you at the earliest.

RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data,Cumulative Frequency Graph and O give Ex 9e

These Solutions are part of RS Aggarwal Solutions Class 10. Here we have given RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data,Cumulative Frequency Graph and O give Ex 9e.

Other Exercises

• RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Ex 9a
• RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Ex 9b
• RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Ex 9c
• RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Ex 9d
• RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Ex 9e
• RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Ex 9f
• RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data MCQ
• RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Test Yourself

Question 1.
Solution:

We plot the points (10, 5), (20, 8), (30, 12), (40, 15), (50, 18), (60, 22), (70, 29), (80, 38), (90, 45) and (100, 53) to get the ‘less than type’ ogive as follows:

Here, N = 53 ⇒ N/2 = 26.5.
At y = 26.5, affix A.
Through A, draw a horizontal line meeting the curve at P.
Through P, a vertical line is drawn which meets OX at M.
OM = 68 units
Hence, median marks = 68

Question 2.
Solution:
We plot the points (15, 2), (30, 5), (45, 9), (60, 17), (75, 39), (90, 54), (105, 70) and (120, 80) to get the ‘less than type’ ogive as follows:

Here, N = 80 ⇒ N/2 = 40.
At y = 40, affix A.
Through A, draw a horizontal line meeting the curve at P.
Through P, a vertical line is drawn which meets OX at M.
OM = 78 units
Hence, median number of wickets = 78

Question 3.
Solution:

We plot the points (0, 100), (10, 96), (20, 90), (30, 80), (40, 70), (50, 45), (60, 23) and (70, 5) to get the ‘more than type’ ogive as follows:

Here, N = 100 ⇒ N/2 = 50.
At y = 50, affix A.
Through A, draw a horizontal line meeting the curve at P.
Through P, a vertical line is drawn which meets OX at M.
OM = 47 units
Hence, median marks = 47.

Question 4.
Solution:

We plot the points (135, 50), (140, 45), (145, 37), (150, 28), (155, 16) and (160, 2) to get the ‘more than type’ ogive as follows:

Here, N = 50 ⇒ N/2 = 25.
At y = 25, affix A.
Through A, draw a horizontal line meeting the curve at P.
Through P, a vertical line is drawn which meets OX at M.
OM = 151 units
Hence, median height = 151 cm.

Question 5.
Solution:

We plot the points (140, 156), (160, 153), (180, 145), (200, 130), (220, 90), (240, 40) and (260, 10) to get the ‘more than type’ ogive as follows:

Here, N = 156 ⇒ N/2 = 78.
At y = 78, affix A.
Through A, draw a horizontal line meeting the curve at P.
Through P, a vertical line is drawn which meets OX at M.
OM = 226 units
Hence, median consumption of electricity = 226 units

Question 6.
Solution:

We plot the points (50, 100), (55, 98), (60, 90), (65, 78), (70, 54)and (75, 16) to get the ‘more than type’ ogive as follows:

Here, N = 100 ⇒ N/2 = 50.
At y = 50, affix A.
Through A, draw a horizontal line meeting the curve at P.
Through P, a vertical line is drawn which meets OX at M.
OM = 70.5 units
Hence, median production yield = 70.5 kg/ha

Question 7.
Solution:
Less Than Series:

We plot the points (200, 5), (300, 11), (400, 22), (500, 35), (600, 40), (700, 44), (800, 47) and (900, 49) to get ‘less than type’ ogive.

More Than Series:

We plot the points (100, 49), (200, 44), (300, 38), (400, 27), (500, 14), (600,9), (700, 5) and (800, 2) to get more than ogive.

Question 8.
Solution:
More than series

We plot the points (400, 230), (450, 210), (500, 175), (550, 135), (600, 103), (650, 79), (700, 52), (750, 34)

Hence,N = 230 ⇒ N/2 = 115.
Take a point A(0, 115) on the y-axis and draw AP||x-axis meeting the curve at P, Draw PM ⊥ x-axis intersecting x-axis at M
Then,OM = 590
Hence median = 590.

Question 9.
Solution:
(i) Less than series:

Plot the points (5, 2), (10, 7), (15, 13), (20, 21), (25, 31), (30, 56), (35, 76), (40, 94), (45, 98) and (50, 100)

Join these points free hand to get the curve representing “less than” cumulative curve.

(ii)From the given table we may prepare the ‘more than’ series as shown below:

Now, on the same graph paper as above, we plot the point (0, 100), (5, 98), (10, 93), (15, 87), (20, 79), (25, 69), (30, 44), (35, 24) and (40, 6) and (45, 2)
Join these points free hand to get required curve
Here N = 100 ⇒ N/2 = 50
Two curves intersect at point P(28, 50)
Hence, the median = 28.

Question 10.
Solution:
We may prepare less than series and more than series

(i)Less than series :

Now on graph paper plot the points (140, 0), (144, 3), (148, 12), (152, 36), (156, 67), (160, 109), (164, 173), (168, 248), (172, 330), (176, 416), (180, 450)

(ii)More than series :

Now on the same graph plot the points (140, 450), (144, 447), (148, 438), (152, 414), (156, 383), (160, 341), (164, 277), (168, 202), (172, 120), (176, 34), (180, 0)

The curves intersect at (167, 225).
Hence, 167 is the median.

We hope the RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Ex 9e help you. If you have any query regarding RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Ex 9e, drop a comment below and we will get back to you at the earliest.

RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and O give Ex 9a

These Solutions are part of RS Aggarwal Solutions Class 10. Here we have given RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data,Cumulative Frequency Graph and O give Ex 9a.

Other Exercises

• RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Ex 9a
• RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Ex 9b
• RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Ex 9c
• RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Ex 9d
• RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Ex 9e
• RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Ex 9f
• RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data MCQ
• RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Test Yourself

Question 1.
Solution:

Question 2.
Solution:

​
Question 3.
Solution:

Question 4.
Solution:
We have

Question 5.
Solution:
We have

Question 6.
Solution:
We have

Question 7.
Solution:

Question 8.
Solution:

Question 9.
Solution:

Question 10.
Solution:

Question 11.
Solution:

Question 12.
Solution:

Question 13.
Solution:
We have
7+f₁+12+f₂+8+5=50 ⇒ f₂= 18-f₁

Question 14.
Solution:

Question 15.
Solution:
We have, Let A = 25 be the assumed mean

Hence mean = 28.

Question 16.
Solution:
Let the assumed mean be 150, h = 20

Hence, Mean = 146.25.

Question 17.
Solution:
Let A = 50 be the assumed mean, we have

Question 18.
Solution:

Question 19.
Solution:

Question 20.
Solution:

Question 21.
Solution:

​
Question 22.
Solution:

Question 23.
Solution:

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Question 24.
Solution:

Question 25.
Solution:
Let h = 20 and assume mean = 550, we prepare the table given below:

Hence the mean of the frequency distribution is 544.

Question 26.
Solution:
The given series is an inclusive series, making it an exclusive series, we have

Question 27.
Solution:
The given series is an inclusive series making it an exclusive series,we get

Hence, Mean = 34.87 years.

Question 28.
Solution:

Question 29.
Solution:

We hope the RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Ex 9a help you. If you have any query regarding RS Aggarwal Solutions Class 10 Chapter 9 Mean, Median, Mode of Grouped Data Ex 9a, drop a comment below and we will get back to you at the earliest