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How many linear equations are satisfied by x = 2 and y =  3?
Infinitely many equations satisfy x = 2 and y = 3 as infinitely many lines pass through a single point.
In the figure, AB ║CD , What is x + y.
In ΔAOB , using angle sum property of triangles, we have
40 + 60 + ∠AOB = 180
⇒ ∠AOB = 180  100 = 80
Also, we have
x + y + ∠AOB = 180 ...(Angles on a line)
⇒ x + y + 80 = 180
⇒ x + y = 100
The area of a triangle with base 8 cm and height 10 cm is
Area = 1/2 x Base x Height
= 1/2 x 8 x 10
= 40 cm^{2 }
Which of the following is a rational number?
0 is an integer and all integers are rational numbers.
The equation 2x + 9 = 0 on number line is represented by:
a point.
As, x = 9/2 is a point.
In the given figure, AB ║ CD, CD ║ EF and y : z = 3 : 7, then x =?
y : z = 3 : 7
Let common ratio be a
y = 3a
z = 7a
x = z (corresponding angle)
x = 7a
x + y =180° (interior angle)
7a + 3a =180°
10 a = 180°
a = 180/10
a = 18
x = 7a
x = 7x 18
x =126°
In the given figure, BO and CO are the bisectors of ∠B and ∠C and respectively. If ∠A = 50° then ∠BOC = ?
In ΔABC we have:
∠A + ∠B + ∠C = 180° [Sum of the angles of a trianlge]
⇒ 50° + ∠B + ∠C = 180°
⇒ ∠B + ∠C = 130°
⇒ 1/2∠B + 1/2∠C = 65°
In ΔOBC we have:
∠OBC + ∠OCB + ∠BOC = 180°
⇒ 1/2∠B + 1/2∠C + ∠BOC = 180° [Using (i)]
⇒ 65° + ∠BOC = 180°
⇒ ∠BOC = 1115°
If 10^{x} = 64, what is the value of ?
10^{x} = 64
⇒
⇒
⇒
Now,
= 8 x 10 = 80
The number of times a particular item occurs in a given data is called its.
The number of times a particular item occurs in a given data is called its Frequency.
In the adjoining figure, y = ?
We have:
3x + 72 = 180° [ AOB is a straight line]
⇒ 3x = 108
⇒ x = 36
Also,
∠AOC + ∠COD + ∠BOD = 180°[ AOB is a straight line]
⇒ 36° + 90° + y = 180°
⇒ y = 54°
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= 1/9
If g = , what is the value of g when t = 64?
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= 16 + 1/2
= 33/2
If in the figure, POQ is a straight line. The three adjacent angles are consecutive numbers, the measure of these angles is
59^{o}, 60^{o}, 61^{o}
Clearly, x + (x + 1) + (x + 2) = 180
⇒ 3x + 3 = 180
⇒ 3(x + 1) = 180
⇒ x + 1 = 60
⇒ x = 59
Hence the angles are 59, 60, 61
If (a, 2) lies on the graph of 3x  y = 10, then the value of a is
(a, 2) lies on the graph of 3x  y = 10
⇒ 3a = 8
⇒ a = 8/3
The midvalue of a class interval is 42. If the class size is 10, then the upper and lower limits of the class are:
Let the lower limit of a class = x
class size = 10
Upper limit = x + 10
Now, mid  value = = x + 5 = 42 (given)
x = 37 = lower limit
x + 10 = 47 = upper limit
pper and lower limits are 47, 37
The sides of a triangle are 35 cm, 54 cm and 61 cm respectively, and its area is 420√5 cm^{2}. The length of its longest altitude is
Since longest altitude is drawn opposite to the shortest side in a triangle.
Area of triangle = 1/2 x Base x Height
⇒ 420√5 = 1/2 x 35 x Height
⇒ Height =
= 24√5 cm
The algebraic sum of the deviations of a set of n values from their mean is:
If be the mean of the n observations q X_{i}, ..., X_{n} then we have
⇒
Let be the mean of n values X_{i}, ..., X_{n}. So, we have
⇒
The sum of the deviations of n values X_{i}, ..., X_{n} from their mean is
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= 0
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= 5/5
= 1
In Fig., the value of x, is
Let,
AB, CD and EF intersect at O
∠COB = ∠AOD (Vertically opposite angle)
∠AOD = 3x + 10 ....(i)
∠AOE + ∠AOD + ∠DOF = 180o (Linear pair)
x + 3x + 10^{o} + 90^{o} = 180^{o}
4x + 100^{o} = 180^{o}
4x = 80^{o}
x = 20^{o}
The equation 2x + 5y = 7 has a unique solution, if x, y are :
There is only one pair i.e., (1, 1) which satisfies the given equation but in positive real numbers, real numbers and rational numbers there are many pairs to satisfy the given linear equation. Hence, unique solution is possible only in case of Natural numbers.
The lengths of the sides of ABCare consecutive integers. It ΔABC has perimeter as an equilateral triangle triangle with a side of length 9 cm, what is the length of the shortest side of ΔABC?
Let the sides of ΔABC be n, n + 1, n + 2
⇒ Perimeter = n + n + 1 + n + 2
⇒ (9 + 9 + 9) = 3n + 3
⇒ 27 = 3n + 3
⇒ 3n = 24
⇒ n = 8 cm
Thus, the shortest side is 8 cm
A linear equation in two variables is of the form ax + by + c = 0, where
A linear equation in two variables is of the form ax + by + c = 0 as a and b are cofficient of x and y
so if a = 0 and b = 0 or either of one is zero in that case the equation will be one variable or their will be no equation respectively.
therefore when a ≠ 0 and b ≠ 0 then only the equation will be in two variable
The coordinates of a point above the xaxis lying on yaxis at a distance of 4 units are
It lies on yaxis so it's abscissa = 0 and it lies on yaxis at a distance of 4unit.
Thus point will be (0, 4).
If 10^{2y} = 25, then 10^{y} equals
10^{2y} = 25
10^{2y} = 52
(10^{y})^{2} = (5)^{2}
⇒ 10^{y} = 5
Now 10^{y}
= 1/10^{y}
= 1/5
The area of an equilateral triangle is 81√3cm^{2} . Its height is
Area of equilateral triangle = 81√3cm^{2}
⇒^{ }
⇒ (Side)^{2} = 81 x4
⇒ (Side)^{2} = 324
Side = 18 cm
Now,
Height =
= 9√3cm
In the below figure AB ║ CD ,O is the mid point BC. Which of the following is true?
In ΔAOB andΔDOC
∠OAB = ∠ODC (alternate interior angles)
∠OBAv=v∠OCD
OB = OC (given)
So, from ASA congruence ,we have
ΔAOB ≅ ΔDOC
Now, from CPCT ,we have
AB = CD
OA = OD which means O is the midpoint of AD.
Hence ,all the given statements are true.
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= 1/2
The point C(5, 2) lies in
In 3rd quadrant values of Abscissa and Ordinate both are —ve , i.e, (— , +)
Here,since value of both x and ycoordinate are ve so it will lies in 3rd quadrant
The graph given below shows the frequency distribution of the age of 22 teachers in a school. The number of teachers whose age is less than 40 years is
Add the values corresponding to the height of the bar before 40.
6 + 3 + 4 + 2 = 15
If side of a scalene Δ is doubled then area would be increased by
Area of triangle with sides a, b, c (A) =
New sides are 2a, 2b and 2c
Then
New area =
= =
= 4A
Increased area = 4A  A = 3A
% of increased area = 3A/A x 100 = 300%
⇒
Comparing, we get
Now
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=
=
=
= 5^{2}
= 25
If all the altitudes from the vertices to the opposite sides of a triangle are equal, then the triangle is
In an equilateral triangle all the altitudes, sides, angles, perpendicular bisectors, medians and angular bisectors are equal.
The mean weight of six boys in a group is 48 kg. The individual weights of five of them are 51 kg, 45 kg, 49 kg, 46 kg and 44 kg. The weight of the 6th boy is
Mean weight of six boys = 48 kg
Let the weight of the 6th boy be x kg.
We know:
Mean =
=
=
Given :
Mean = 48 kg
⇒
⇒ 235 + x = 288
⇒ x = 53
⇒ Hence, the weight of the 6th boy is 53 kg
The exterior angle of a triangle is equal to the sum of two
∠1 + ∠2 + ∠3 = 180^{o} (Angle sum property)....(a)
∠3 + ∠4 = 180^{o} (Linear Pair)....(b)
On equating equations a and b, we get
∠1 + ∠2 = ∠4
How many linear equations can be satisfied by x = 2 and y = 3?
There are infinite many eqution which satisfy the given value x = 2, y = 3
for example
x + y = 5
x  y = 1
3x  2y = 0 etc.......
In the adjoining figure, AB = FC, EF = BD and ∠AFE = ∠CBD. Then the rule by which ΔAFE ≌ ΔCBD
In ΔDBC and ΔAEF, we have
AB = FC (given)by adding BF on both sides
AF= CB
∠AFE = ∠CBD (given)
EF = BD (given)
Hence, ΔAFE ≌ ΔCBD by SAS as the corresponding sides and their included angles are equal.
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In ΔABC and ΔPQR. If AB = QP, ∠B = ∠P , BC = PR then which one of the following congruence conditions applies:
Since given two sides and an angle are equal so it obeys SAS.
The mean of six numbers is 23. If one of the numbers is excluded, the mean of the remaining numbers becomes 20. The excluded number is
The mean of the six numbers is 23.
So the sum of six numbers is 23 x 6 = 138
After excluding one number, the mean of the remaining numbers is 20.
So the sum of five numbers is 20 x 5 = 100
The difference between them is
138  100 = 38
Read the text carefully and answer the questions:
Ashok is studying in 9th class in Govt School, Chhatarpur. Once he was at his home and was doing his geometry homework.
He was trying to measure three angles of a triangle using the Dee, but his dee was old and his Dee's numbers were erased and the lines on the dee were visible.
Let us help Ashok to find the angles of the triangle.
He found that the second angle of the triangle was three times as large as the first. The measure of the third angle is double of the first angle.
What was the value of the second angle?
90°
Read the text carefully and answer the questions:
Ashok is studying in 9th class in Govt School, Chhatarpur. Once he was at his home and was doing his geometry homework.
He was trying to measure three angles of a triangle using the Dee, but his dee was old and his Dee's numbers were erased and the lines on the dee were visible.
Let us help Ashok to find the angles of the triangle.
He found that the second angle of the triangle was three times as large as the first. The measure of the third angle is double of the first angle.
What was the value of ∠4 as shown the figure?
120°
Read the text carefully and answer the questions:
Ashok is studying in 9th class in Govt School, Chhatarpur. Once he was at his home and was doing his geometry homework.
He was trying to measure three angles of a triangle using the Dee, but his dee was old and his Dee's numbers were erased and the lines on the dee were visible.
Let us help Ashok to find the angles of the triangle.
He found that the second angle of the triangle was three times as large as the first. The measure of the third angle is double of the first angle.
What was the sum of all three angles measured by Ashok using Dee?
180°
Read the text carefully and answer the questions:
Ashok is studying in 9th class in Govt School, Chhatarpur. Once he was at his home and was doing his geometry homework.
He was trying to measure three angles of a triangle using the Dee, but his dee was old and his Dee's numbers were erased and the lines on the dee were visible.
Let us help Ashok to find the angles of the triangle.
He found that the second angle of the triangle was three times as large as the first. The measure of the third angle is double of the first angle.
What was the value of the first angle?
30°
Read the text carefully and answer the questions:
Ashok is studying in 9th class in Govt School, Chhatarpur. Once he was at his home and was doing his geometry homework.
He was trying to measure three angles of a triangle using the Dee, but his dee was old and his Dee's numbers were erased and the lines on the dee were visible.
Let us help Ashok to find the angles of the triangle.
He found that the second angle of the triangle was three times as large as the first. The measure of the third angle is double of the first angle.
What was the value of the third angle?
60°
Read the text carefully and answer the questions:
Roshan decorated one of his bathroom wall with tiles as shown in the picture. He was having tiles of four colours orange, yellow, green and blue. He fitted the tiles in 8 columns and 12 rows. The size of one tile was 1 foot x 1 foot and the area of each tile is 1 foot².
He arranged the tile in such a way that colour of tiles in each row and column were in the pattern:
Orange> Yellow> green>Blue>Orange>..... and so on.
Which colour tile was fitted at the point with coordinates (5, 3)?
Green
Read the text carefully and answer the questions:
Roshan decorated one of his bathroom wall with tiles as shown in the picture. He was having tiles of four colours orange, yellow, green and blue. He fitted the tiles in 8 columns and 12 rows. The size of one tile was 1 foot x 1 foot and the area of each tile is 1 foot².
He arranged the tile in such a way that colour of tiles in each row and column were in the pattern:
Orange> Yellow> green>Blue>Orange>..... and so on.
Which colour tile was fitted at the point with coordinates (7, 7)?
Orange
Read the text carefully and answer the questions:
Roshan decorated one of his bathroom wall with tiles as shown in the picture. He was having tiles of four colours orange, yellow, green and blue. He fitted the tiles in 8 columns and 12 rows. The size of one tile was 1 foot x 1 foot and the area of each tile is 1 foot².
He arranged the tile in such a way that colour of tiles in each row and column were in the pattern:
Orange> Yellow> green>Blue>Orange>..... and so on.
Which colour tile was fitted at the point with coordinate (2, 5)?
Yellow
Read the text carefully and answer the questions:
Roshan decorated one of his bathroom wall with tiles as shown in the picture. He was having tiles of four colours orange, yellow, green and blue. He fitted the tiles in 8 columns and 12 rows. The size of one tile was 1 foot x 1 foot and the area of each tile is 1 foot².
He arranged the tile in such a way that colour of tiles in each row and column were in the pattern:
Orange> Yellow> green>Blue>Orange>..... and so on.?
What is the area of the tiles fitted in the rectangular part OABX?
48 foot²
Read the text carefully and answer the questions:
Roshan decorated one of his bathroom wall with tiles as shown in the picture. He was having tiles of four colours orange, yellow, green and blue. He fitted the tiles in 8 columns and 12 rows. The size of one tile was 1 foot x 1 foot and the area of each tile is 1 foot².
He arranged the tile in such a way that colour of tiles in each row and column were in the pattern:
Orange> Yellow> green>Blue>Orange>..... and so on.
What is the ordinate of top row tiles?
12
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