Question 1 :
If a transversal intersects two parallel lines, then each pair of alternate interior angles is equal. Is it true?

Question 2 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1cff59b460d7261f4d2.png' /> In the above fig, there are two pairs of vertically opposite angles. One pair is $\angle AOD$ and $\angle BOC$. Can you find the other pair?

Question 3 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61cc1ad778c526e972caf086.JPG' /> In the above figure, lines PQ and RS intersect each other at point O. If $ \angle POR $ : $ \angle ROQ$ = 5 : 7, find $ \angle POS$ (in degrees).

Question 4 :
If a transversal intersects two lines such that a pair of alternate interior angles is equal, then are the two lines parallel?

Question 5 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61cc1ad978c526e972caf08d.PNG' /> In the above fig, if $PQ \parallel ST$, $\angle PQR = 110^{\circ}$ and $\angle RST = 130^{\circ}$, find $\angle QRS$.

Question 6 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1d3f59b460d7261f4d7.png' /> In the above fig, $AB \parallel CD$ and $CD \parallel EF$. Also $EA \perp AB$. If $\angle BEF = 55^{\circ}$, find the value of $x$.

Question 7 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1d6f59b460d7261f4dc.png' /> In the above figure, lines AB and CD intersect at O. If $ \angle AOC + \angle BOE = 70^{\circ} $ and $ \angle BOD = 40^{\circ}$, find $ \angle BOE$ and reflex $\angle COE$.

Question 8 :
If the sum of two adjacent angles is 180°, then the non-common arms of the angles form a line. Is it true?

Question 9 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1e2f59b460d7261f4ed.png' /> In the above fig, if lines PQ and RS intersect at point T, such that $\angle PRT = 40^{\circ}$, $\angle RPT = 95^{\circ}$ and $\angle TSQ = 75^{\circ}$, find $\angle SQT$.

Question 10 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1dcf59b460d7261f4e4.png' /> In the above fig, if $AB \parallel CD$, $EF \perp CD$ and $\angle GED = 126^{\circ}$, find $\angle GEF$.

Question 11 :
Find the amount of water displaced by a solid spherical ball of diameter 28 cm.

Question 12 :
The diameter of the moon is approximately one fourth of the diameter of the earth. Find the ratio of their surface areas.

Question 13 :
In a cylinder, radius is doubled and height is halved, curved surface area will be _________?

Question 14 :
State true or false: If the edge of the cube is a, then Total surface area of cube = $6a^{2}$

Question 15 :
A shot-putt is a metallic sphere of radius 4.9 cm. If the density of the metal is 7.8 g per $cm^3$ , find the mass of the shot-putt.

Question 16 :
The length, breadth and height of a room are 5 m, 4 m and 3 m respectively. Find the cost of white washing the walls of the room and the ceiling at the rate of Rs 7.50 per $m^2$ .

Question 17 :
State true or false: If a sphere is inscribed in a cube, then the ratio of the volume of the cube to the volume of the sphere will be 6 : π.

Question 18 :
The diameter of a roller is 84 cm and its length is 120 cm. It takes 500 complete revolutions to move once over to level a playground. Find the area of the playground in $m^2$ .Assume $\pi$ =$\frac{22}{7}$.

Question 19 :
The surface area of a sphere of radius 5 cm is five times the area of the curved surface of a cone of radius 4 cm. Find the height of the cone (taking $\pi=\frac{22}{7}$).

Question 20 :
How many litres of milk can a hemispherical bowl of diameter 10.5 cm hold?

Question 21 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d154f59b460d7261f421.jpg' /> In the above figure, ABCD and AEFG are two parallelograms. If $\angle C = 55^{\circ}$, determine $\angle F$.

Question 22 :
ABCD is a rectangle and P, Q, R and S are mid-points of the sides AB, BC, CD and DA respectively. The quadrilateral PQRS is a __________.

Question 23 :
If the diagonals of a parallelogram are equal, then it is a ____________.

Question 24 :
One angle of a quadrilateral is of $108^{\circ}$ and the remaining three angles are equal. Find each of the three equal angles.

Question 25 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d204f59b460d7261f520.PNG' /> Using the above fig, we can say that if each pair of opposite sides of a quadrilateral is equal, then it is a _______________.

Question 26 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1e8f59b460d7261f4f7.JPG' /> From above the image Consider the frequency distribution table which gives the weights of 38 students of a class. Find the probability that the weight of a student in the class lies in the interval 46-50 kg.

Question 27 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1f5f59b460d7261f509.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 Rs16000 or more per month and owning exactly 1 vehicle.

Question 28 :
True or false. The uncertainty of ‘probably’ can be measured numerically by means of ‘probability’.

Question 29 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1edf59b460d7261f4fe.JPG' /> From the above image, the percentage of marks obtained by a student in the monthly unit tests are mentioned in the image. Based on this data, find the probability that the student gets more than 70% marks in a unit test.

Question 30 :
A coin is tossed 1000 times with the following frequencies: Head : 455, Tail : 545. Compute the probability of the event of getting a Head.

Question 31 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1ecf59b460d7261f4fd.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 probabilities of the event for a driver chosen at random from the city being 30-50 years of age and having one or more accidents in a year.

Question 32 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1f4f59b460d7261f508.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 less than Rs 7000 per month and does not own any vehicle.

Question 33 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1e6f59b460d7261f4f4.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 3

Question 34 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1f3f59b460d7261f507.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 10000 – 13000 per month and owning exactly 2 vehicles.