Question 1 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b44273b230584979968.PNG' /> In the above figure, if O is the centre of a circle, PQ is a chord and the tangent PR at P makes an angle of $50^{\circ}$ with PQ, then $\angle POQ$ is equal to

Question 2 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b42273b230584979965.PNG' /> In the above figure, if $\angle AOB = 125^{\circ}$, then $\angle COD$ is equal to

Question 3 :
In a circle of radius 21 cm, an arc subtends an angle of $60^{\circ}$ at the centre. Find area of the segment formed by the corresponding chord.

Question 4 :
In a circle of radius 21 cm , an arc subtends an angle of $60^{\circ}$ at the centre. Find area of the sector formed by the arc.

Question 5 :
Find the coordinates of the point which divides the join of $\left(–1, 7\right)$ and $\left(4, –3\right)$ in the ratio 2 : 3.

Question 6 :
The point A (2, 7) lies on the perpendicular bisector of line segment joining the points P (6, 5) and Q (0, – 4). State true or false.

Question 7 :
Name the type of triangle formed by the points $\left(5, – 2\right)$, $\left(6, 4\right)$ and $\left(7, – 2\right)$.

Question 8 :
Name the type of the triangle formed by the points $\left(3,2\right)$ , $\left(2,3\right)$ , $\left(-2,-3\right)$.

Question 9 :
In the following pair of equations: 2x + y = 6 and 2x – y + 2 = 1, find the ratio of the areas of the two triangles formed by the lines representing these equations with the x-axis and the lines with the y-axis.

Question 10 :
The cost of 2 kg of apples and 1kg of grapes on a day was found to be Rs. 160. After a month, the cost of 4 kg of apples and 2 kg of grapes is Rs. 300. Which of these represent the situation algebraically?

Question 11 :
(sec A + tan A) (1 – sin A) = ______

Question 12 :
Is this equality correct ?$(cosec A – sin A) (sec A – cos A)= \frac{1}{tan A +cot A}$

Question 14 :
If one of the zeroes of the cubic polynomial $x^3+ax^2+bx+c$ is -1, then the product of other two zeroes is:

Question 15 :
Check whether the following is quadratic equation : $x^2 + 3x + 1 = (x-2)^2$

Question 16 :
State True or False whether the following quadratic equation has two distinct real roots: $3x^2-4x+1=0$

Question 17 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bec273b230584979a43.PNG' /> A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8, and these are equally likely outcomes. What is the probability that it will point at a number greater than 2?

Question 18 :
Two dice, one blue and one grey, are thrown at the same time. Write down all the possible outcomes. What is the probability that the sum of the two numbers appearing on the top of the dice is 13?

Question 19 :
16 glass spheres each of radius 2 cm are packed into a cuboidal box of internal dimensions 16 cm × 8 cm × 8 cm and then the box is filled with water. Find the volume of water filled in the box.

Question 20 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c04273b230584979a5d.PNG' /> Consider the above distribution of daily wages of 50 workers of a factory. Find the mean daily wages of the workers of the factory by using an appropriate method.

Question 21 :
<img style='object-fit:contain' src='61b19a74273b230584979936' /> The table above shows the daily expenditure on food of 25 households in a locality. Find the mean daily expenditure on food by a suitable method.

Question 22 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c4f273b230584979ab3.PNG' /> In the above fig, ∠ ACB = 90° and CD ⊥ AB. Is $\frac{BC^2}{AC^2} = \frac{BD}{AD}$ ?

Question 23 :
For going to a city B from city A, there is a route via city C such that AC is perpendicular to CB, AC = 2 x km and CB = 2 (x + 7) km. It is proposed to construct a 26 km highway which directly connects the two cities A and B. Find how much distance will be saved in reaching city B from city A after the construction of the highway.

Question 24 :
The houses of a row are numbered consecutively from 1 to 49. Show that there is a value of x such that the sum of the numbers of the houses preceding the house numbered x is equal to the sum of the numbers of the houses following it. Find this value of x.

Question 25 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bc9273b230584979a17.JPG' /> A small terrace at a football ground comprises of 15 steps each of which is 50 m long and built of solid concrete. Each step has a rise of 0.25 m and a tread of 0.5 m. Calculate the total volume of concrete required to build the terrace.