Question 1 :
If a circle touches the side BC of a triangle ABC at P and extended sides AB and AC at Q and R, respectively, Is it TRUE or FALSE that $AQ = \frac { 1 } { 2 } ( BC + CA + AB )$.

Question 2 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b43273b230584979966.PNG' /> In the above figure, AB is a chord of the circle and AOC is its diameter such that $\angle ACB = 50^{\circ}$. If AT is the tangent to the circle at the point A, then $\angle BAT$ is equal to

Question 3 :
Do the centre of a circle touching two intersecting lines lies on the angle bisector of the lines?

Question 4 :
At any point on a circle there can be one and only one tangent . TRUE OR FALSE?

Question 5 :
A chord PQ of a circle is parallel to the tangent drawn at a point R of the circle. Does R bisects the arc PRQ?

Question 6 :
Find the zeroes of the quadratic polynomial using the given sum and product respectively of the zeroes: $\frac{21}{8}$, $\frac{5}{16}$

Question 7 :
Divide the polynomial $p\left(x\right)$ by the polynomial $g\left(x\right)$ and find the quotient and remainder in the following : $p\left(x\right)$ = $x^4–3x^2+4x+5$, $g\left(x\right)$ = $x^2+1-x$

Question 9 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19be4273b230584979a3a.png' /> Look at the graph given above. The graph of $y=p\left(x\right)$, where $p\left(x\right)$ is a polynomial. Here, find the number of zeroes of $p\left(x\right)$.

Question 10 :
Find a quadratic polynomial whose sum and product respectively of the zeroes are as given: $\frac{21}{8}$, $\frac{5}{16}$

Question 11 :
If the sum of the circumferences of two circles with radii $R_1$ and $R_2$ is equal to the circumference of a circle of radius R, then

Question 12 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bb6273b2305849799fd.png' /> Find the area of the shaded region in the above figure , if radii of the two concentric circles with centre O are 7 cm and 14 cm respectively and $\angle AOC$=$40^{\circ}$.

Question 13 :
If the circumferences of two circles are equal, then their areas are also equal. Is it true or false?

Question 14 :
Area of a sector of central angle $200^{\circ}$ of a circle is $770\ cm^2$. Find the length of the corresponding arc of this sector.

Question 15 :
The length of the minute hand of a clock is 5 cm. Find the area swept by the minute hand during the time period $6\ :\ 05\ am$ and $6\ :\ 40\ am$ .

Question 16 :
What are the LCM and HCF (by prime factorisation method) of 96 and 404?

Question 17 :
There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point?

Question 18 :
Using Euclid’s division lemma can we show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m?

Question 19 :
“The product of two consecutive positive integers is divisible by 2'. Is this statement true or false?

Question 20 :
How is 5005 expressed as a product of its prime factors?