Question
Draw the graphs of the equations x = 2 and y = -3.
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Two circles with centres O and O' intersect at two points A and B. A line PQ is drawn parallel to OO' through A or B, intersecting the circles at P and Q. Prove that PQ = 2OO'.
In the adjoining figure, ABCD is a parallelogram. If P and Q are points on AD and BCrespectively such that $\text{AP}=\frac{1}{2}\text{AD}$ and $\text{CQ}=\frac{1}{2}\text{BC},$ prove that AQCP is a parallelogram.
→In $\triangle\text{ABC,}$ side AB is produced to D such that BD = BC. If $\angle\text{B}=60^{\circ},$ and $\angle\text{B}=60^{\circ},$ prove that:
→- AD > CD and
- AD > AC.
If the length of a rectangle is reduced by 5 units and its breadth is increased by 3 units, then the area of the rectangle is reduced by 9 square units. If length is reduced by 3 units and breadth is increased by 2 units, then the area of rectangle will increase by 67 square units. Then find the length and breadth of the rectangle.
The sum of the deviations of a set of n values $x_1, x_2, x_3,..., x_n$ measured from $15$ and $-3$ are $-90$ and $54$ respectively. Find the value of n and mean.
→Compute the area of trapezium PQRS in figure.
Use the given letters to write the answer.
i. There are ‘a’ trees in the village Lat. If the number of trees increases every year by ’b‘. then how many trees will there be after ‘x’ years?
ii. For the parade there are y students in each row and x such row are formed. Then, how many students are there for the parade in all ?
iii. The tens and units place of a two digit number is m and n respectively. Write the polynomial which represents the two digit number.
i. There are ‘a’ trees in the village Lat. If the number of trees increases every year by ’b‘. then how many trees will there be after ‘x’ years?
ii. For the parade there are y students in each row and x such row are formed. Then, how many students are there for the parade in all ?
iii. The tens and units place of a two digit number is m and n respectively. Write the polynomial which represents the two digit number.
Plot the points R(-3,-4), S(3,-l) on the same co-ordinate system.
Steps for plotting the points:
i. Draw X-axis and Y-axis on the plane. Show the origin.
ii. Draw a line parallel to Y-axis at a distance of 3 units in the -ve direction of X-axis.
iii. Draw another line parallel to X-axis at a distance of 4 units in the -ve direction of Y-axis.
iv. Intersection of these lines is the point R (-3, -4).
v. The point S can be plotted in the same manner.
Steps for plotting the points:
i. Draw X-axis and Y-axis on the plane. Show the origin.
ii. Draw a line parallel to Y-axis at a distance of 3 units in the -ve direction of X-axis.
iii. Draw another line parallel to X-axis at a distance of 4 units in the -ve direction of Y-axis.
iv. Intersection of these lines is the point R (-3, -4).
v. The point S can be plotted in the same manner.
Write the answers to the following questions with reference to the figure given below:
i. Write the name of the opposite ray of ray RP
ii. Write the intersection set of ray PQ and ray RP.
iii. Write the union set of ray PQ and ray QR.
iv. State the rays of which seg QR is a subset.
v. Write the pair of opposite rays with common end point R.
vi. Write any two rays with common end point S.
vii. Write the intersection set of ray SP and ray ST.
In the given figure, AB and CD are straight lines through the centre O of a circle. If $\angle\text{AOC}=80^\circ$ and $\angle\text{CDE}=40^\circ,$ find
→- $\angle\text{DCE}$
- $\angle\text{ABC}$