Question 1 :
Scale factor means the ratio of the sides of the triangle to be constructed with the corresponding sides of the given triangle . State whether the above statement is TRUE or FALSE ?

Question 2 :
To construct a triangle similar to a given ∆ABC with its sides $\frac{8}{5}$ of the corresponding sides of ∆ABC draw a ray BX such that ∠CBX is an acute angle and X is on the opposite side of A with respect to BC. The minimum number of points to be located at equal distances on ray BX is

Question 3 :
Draw a right triangle ABC in which BC = 12 cm, AB = 5 cm and ∠B = 90$^{\circ}$. Construct a triangle similar to it and of scale factor $\frac{2}{3}$. Is the new triangle also a right triangle?

Question 6 :
If $\tan 2A = \cot \begin{pmatrix}A – 18^{\circ}\end{pmatrix}$, where 2A is an acute angle, find the value of A.

Question 7 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bcc273b230584979a1a.JPG' /> The above image represents two tangents TP and TQ drawn to a circle with centre O from an external point T . Then

Question 8 :
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 9 :
Is it TRUE or FALSE, that if angle between two tangents drawn from a point P to a circle of radius a and centre O is $90^{\circ}$, then OP = $a \sqrt{2}$ ?

Question 10 :
A bag contains lemon flavoured candies only. Malini takes out one candy without looking into the bag. What is the probability that she takes out an orange flavoured candy?

Question 11 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19be9273b230584979a40.PNG' /> Gopi buys a fish from a shop for his aquarium. The shopkeeper takes out one fish at random from a tank containing 5 male fish and 8 female fish. What is the probability that the fish taken out is a male fish?

Question 12 :
A bag contains a red ball, a blue ball and a yellow ball, all the balls being of the same size. Kritika takes out a ball from the bag without looking into it. What is the probability that she takes out the blue ball?

Question 13 :
The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find the two numbers.

Question 16 :
The Angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. Find the height of the tower.

Question 17 :
From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foof is 45°. Determine the height of the tower.

Question 18 :
A contractor plans to install two slides for the children to play in a park. For the children below the age of 5 yr, she prefers to have a slide whose top is at a height of 1.5 m and is inclined at an angle of 30° to the ground, whereas for elder children, she wants to have a steep slide at a height of 3 m and inclined at an angle of 60° to the ground. What should be the length of the slides in each case?

Question 19 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bfb273b230584979a53.PNG' /> Find the mean of the above given data.

Question 20 :
If number of observations(n) is odd, then median equals _______ observation?

Question 21 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c06273b230584979a5f.PNG' /> In a retail market, fruit vendors were selling mangoes kept in packing boxes. These boxes contained varying number of mangoes. The data was the distribution of mangoes according to the number of boxes. Find the mean number of mangoes kept in a packing box.

Question 23 :
Water flows at the rate of 10m/minute through a cylindrical pipe 5 mm in diameter. How long would it take to fill a conical vessel whose diameter at the base is 40 cm and depth 24 cm?

Question 24 :
A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment.

Question 25 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bc8273b230584979a15.JPG' /> In the above fig. In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato, and the other potatoes are placed 3 m apart in a straight line. There are ten potatoes in the line. A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in, and she continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run?

Question 26 :
For what value of n, are the nth terms of two APs: 63, 65, 67, . . . and 3, 10, 17, . . . equal?

Question 27 :
Find the sum of the following AP: 2, 7, 12, . . ., to 10 terms.

Question 28 :
While computing mean of grouped data, we assume that the frequencies are

Question 29 :
Consider the following frequency distribution of the heights of 60 students of a class : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b8e273b2305849799c9.PNG' /> The sum of the lower limit of the modal class and upper limit of the median class is?

Question 30 :
A bag contains 3 red balls, 5 white balls and 7 black balls. What is the probability that a ball drawn from the bag at random will be neither red nor black?