Question 1 :
The record of a weather station shows that out of the past 250 consecutive days, its weather forecasts were correct 175 times. What is the probability that it was not correct on a given day?

Question 2 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1e8f59b460d7261f4f6.JPG' /> Refer to the above image. A die is thrown 1000 times with the frequencies for the outcomes 1, 2, 3,4, 5 and 6 as given in the above image. Find the probabilty of getting outcome 2

Question 3 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1eff59b460d7261f501.JPG' /> Refer to the above image. A tyre manufacturing company kept a record of the distance covered before a tyre needed to be replaced. The above image shows the results of 1000 cases. If you buy a tyre of this company, what is the probability that it will need to be replaced before it has covered 4000 km?

Question 4 :
In a cricket match, a batswoman hits a boundary 6 times out of 30 balls she plays. Find the probability that she did not hit a boundary.

Question 5 :
Two coins are tossed simultaneously 500 times, and we get Two heads : 105 times, One head : 275 times, No head : 120 times. Find the probability of getting one head.

Question 6 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1f8f59b460d7261f50e.JPG' /> Refer to the above image. An organisation selected 2400 families at random and surveyed them to determine a relationship between income level and the number of vehicles in a family. The information gathered is in the above image. Suppose a family is chosen. Find the probability that the family chosen is earning Rs 13000 – 16000 per month and owning more than 2 vehicles.

Question 7 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1ecf59b460d7261f4fc.JPG' /> Refer to the above image. An insurance company selected 2000 drivers at random (i.e., without any preference of one driver over another) in a particular city to find a relationship between age and accidents. The data obtained are given in the above image. Find the probabillity of the event for a driver chosen at random from the city being 18-29 years of age and having exactly 3 accidents in one year.

Question 8 :
A rectangular plot is given for constructing a house, having a measurement of 40 m long and 15 m in the front. According to the laws, a minimum of 3 m, wide space should be left in the front and back each and 2 m wide space on each of other sides. Find the largest area where house can be constructed.

Question 9 :
A triangular park ABC has sides 120m, 80m and 50m. A gardener Dhania has to put a fence all around it and also plant grass inside. How much area does she need to plant?

Question 10 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d137f59b460d7261f3f9.JPG' /> From the above image, a design is made on a rectangular tile of dimensions 50 cm × 70 cm. The design shows 8 triangles, each of sides 26 cm, 17 cm and 25 cm. Find the remaining area of the tile.

Question 11 :
Write True or False. In a triangle, the sides are given as 11 cm, 12 cm and 13 cm. The length of the altitude is 10.25 cm corresponding to the side having length 12 cm.

Question 12 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1bdf59b460d7261f4b8.JPG' /> Refer to the above image. Kamla has a triangular field with sides 240 m, 200 m, 360 m, where she grew wheat. In another triangular field with sides 240 m, 320 m, 400 m adjacent to the previous field, she wanted to grow potatoes and onions. She divided the field in two parts by joining the mid-point of the longest side to the opposite vertex and grew potatoes in one part and onions in the other part. How much area is been used for onions ? $\begin{pmatrix}1\ hectare = 10000 m^2\end{pmatrix}$

Question 13 :
If the area of an equilateral triangle is $16\sqrt{3}$ $cm^2$, then find the perimeter of the triangle.

Question 14 :
From a point in the interior of an equilateral triangle, perpendiculars are drawn on the three sides. The lengths of the perpendiculars are 14 cm, 10 cm and 6 cm. Find the area of the triangle.

Question 15 :
A circle is drawn with any side of a rhombus as diameter, does it pass through the point of intersection of its diagonals?

Question 16 :
State Yes or No: If bisectors of opposite angles of a cyclic quadrilateral ABCD intersect the circle, circumscribing it at the points P and Q, Then PQ is a diameter of the circle.

Question 17 :
State whether the given statement is true or false:- If A, B, C and D are four points such that $\angle BAC=45^{\circ}$ and $\angle BDC=45^{\circ}$, then A, B, C, D are concyclic.

Question 18 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1a5f59b460d7261f497.png' /> In the above fig, ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If ∠ DBC = 55° and ∠ BAC = 45°, find ∠ BCD.

Question 19 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d120f59b460d7261f3d7.PNG' /> In the above figure, AOC is a diameter of the circle and arc AXB = $\frac{1}{2}$ arc BYC. Find $\angle BOC$.

Question 20 :
Recall that two circles are congruent if they have the same radii. So, we can safely say that equal chords of congruent circles subtend equal angles at their centres. Correct or Incorrect?