CASE STUDY BASED QUESTIONS

1) A game at a stall in New Year carnival involves spinning a wheel first as a first step to complete the game with

certain rules. If the wheel stops at a particular number, then the player is allowed to roll a 6 faced

unbiased dice.Rules of Game:

(a) If the wheel stops at a particular number, then the player is allowed to roll a unbiased dice.

(b) If the wheel stops at any other number, player get to try again and only one extra try allowed.

(c) If player reach the next stage and roll a dice, he may get a prize depending on the number on dice.

(i) What is the probability of getting an even number on the wheel?

(ii) If getting an odd number on the wheel allows a player to roll the die, then what is the probability of his rolling the die?

(iii) If the player is allowed to roll the dice and getting a number greater than 4 entitles him to get prize, what is the probability

of his winning the prize?

OR
If getting a square number on the wheel allows a player to roll the dice, then what is the probability of his rolling the dice?

2) A child is working on a pencil. The pencil has three shapes. Cone shape on the upper part, cylindrical at the centre and
hemisphere is at lower part. The child starts sharpening the pencil.

(i) What is the volume of the cone shape part which contains 0.6 cm diameter and 2 cm height?

(ii) What is the volume of cylindrical part when its length is 10cm?

(iii) Find the mass of the pencil, given that 1cm3 of wood has approximately 2.5g mass.

OR From a solid cylinder whose height is 2.4 cm and diameter is 1.4cm a conical cavity of same height and same

diameter is hollowed out.Find the volume of the remaining solid to the nearest cm 3(  22/7 ).

3) A carpenter used to make and sell different kinds of wooden pen stands like rectangular, cuboidal, cylindrical, and
conical. Aarav went to his shop and asked him to make a pen stand as explained below.
Pen stand must be of the cuboidal shape with three conical depressions, which can hold 3 pens. The dimensions of the
cuboidal part must be 20 cm×15 cm× 5 cm and the radius and depth of each conical depression must be 0.6 cm and 2.1 cm
respectively. Based on the above information, answer the following questions.

Based on the above information, answer the following questions:

(i) Find the total volume of the conical depression.
(ii) Find the volume of cuboid.
(iii) If the cost of wood used is Rs.5 per cm3, then find the total cost of making the pen stand. OR

If the total surface area of a solid hemisphere is 462cm2, find its volume.
 4) The man made different shapes on a wood turning machine as shown in the figure.

(i) The sphere has a radius of 1.5cm. What is its volume?

(ii) The cone contains the radius of 1cm and height 2cm. What is its volume?
(iii) Find the capacity of the hemi-spherical bowl in cm 3, given the circumference of the edge of the hemi-spherical bowl is

132cm. (Use ). OR
If the surface areas of two spheres are in the ratio of 16 : 9, then find the ratio of their volumes.

5) A cottage industry produces a certain number of pottery articles each day. It was observed on Monday that the cost of
production of each article (in rupees) was 3 more than twice the number of articles produced on that day. However on
Tuesday, it was observed that the cost of production was 3 less than thrice the number of articles produced on that day.
The cost of production was Rs. 90 and Rs. 60 on Monday and Tuesday, respectively. Based on this information answer the
following questions:
(i) Write the quadratic equation representing these situations.
(ii) Find the number of articles produced and cost of each article produced on Monday?

6) In a class test, the sum of Ranjitha’s marks in mathematics and English is 40. Had she got 3 marks more in mathematics
 and 4 marks less in English, the product of the marks would have been 360. On the other hand, Ranjitha’s friend, Malati
scored 3 marks less in mathematics and 2 marks more in English than what Ranjitha scored. Based on this information,
answer the following questions.
(i) Write the quadratic equation representing the above situation.
(ii) How many marks did Ranjitha scored in mathematics? OR
How many marks did Ranjitha scored in English?
(iii) Find the sum of the Malathi’s marks in both the subjects. OR
Find the number of articles produced and cost of each article produced on Tuesday?

(iv) Write the discriminant of .

7) As shown in the above figure, there is a rectangular field with shorter side being . It is given that the diagonal is 60 more
than the shorter side and the longer side is more than the shorter side by 30. According to this, answer the following
questions.

(i) Form an equation for this case in terms of .

(ii) Compare the above obtained equation with general form of quadratic equation and write the values of a, b and c?

(iii) Find the lengths of shorter side, longer side and also area of the rectangle. OR

If one of the root of the equation is , then find the value of

8) Class teacher draw the shape of quadrilateral on board. Ankit observed the shape and explored on his notebook in
different ways as shown below.
 (i) In fig.1, if ABCD is a trapezium with AB parallel to CD. E and F are the points on the non-parallel sides AD and BC

respectively such that EF is parallel to AB then ____________.

(ii) In fig.2, in ; if PQ//BC and AP = 2.4 cm, AQ = 2cm, QC = 3cm, BC = 6cm then find AB.
(iii) In fig.1 if AB//CD and , , and then find the value of . OR
In fig.2, ifRS//EF, , , and then find value of
9) Seema placed a light bulb at point O on the ceiling and directly below it placed a table. Now, she put a cardboard of shape
ABCD between table and lighted bulb. Then a shadow of ABCD is casted on the table as A'B'C'D' (see figure). Quadrilateral
A'B'C'D' in an enlargement of ABCD with scale factor 1 : 2, Also, AB = 1.5 cm, BC = 25cm, CD = 2.4 cm and AD = 2.1 cm;
, , and .

(i) What is the measurement of .

(ii) What is the sum of the angles .
(iii) What is the ratio of the sides and OR
State whether the following quadrilaterals are similar or not.
10) In a town of the country side, there was a game going on of hockey. To win, the player needs to make the puck enter the

goal arena, which is represented by the area of region ADE in the above shown image. The player was positioned at point B

and the puck was at point C, as shown in the figure such that DE is parallel to BC. So, solve the questions asked below using

the information used above.

(i) Does the line DE divides the two sides of the ground AB and AC in the same ratio.
(ii) In the given figure, if , then find the value of .

OR
If D, E are points on the sides AB and AC of such that AD = 6cm, BD = 9cm, AE = 8cm, EC =12cm. Prove that DE||BC.

(iii) In the given figure, DE//BC then find the value of EC.

11) Rohan is very intelligent in maths. He always try to relate the concept of maths in daily life. One day he is walking away
from the base of a lamp post at a speed of 1 m/s. Lamp is 4.5 m above the ground.

(i) If after 2 second, length of shadow is 1 meter, what is the height of Rohan?
 (ii) What is the minimum time after which his shadow will become larger than his original height? OR
What is the distance of Rohan from pole at this point?
(iii) What will be the length of his shadow after 4 seconds?
12) Tania is very intelligent in maths. She always try to relate the concept of maths in daily life. One day she
plans to cross a river and want to know how far it is to the other side. She takes measurements on her side
of the river and make the drawing as shown below.

(i) Which similarity criterion is used in solving the above problem?

(ii) Write the respective angles and corresponding ratio of the sides that are equal as per the above criteria.
(iii) What is the distance across the river? OR
What is the approximate length of AD as shown in the figure?
13) Aruna visited to her uncle’s house. From a point A, where Aruna was standing, a bus and building come in a straight line as
shown in the figure.
Based on the above information, answer the following questions:

(i) Which similarity criteria can be seen in this case, if bus and building are considered in a straight line? (ii) If the distance
 between Aruna and the bus is twice as much as height of the bus,then find the height of the bus. (iii) If the distance of
Aruna from the building is twelve times the height of the bus, then find the ratio of the heights of the bus and the building.
OR
What is the ratio of distance between Aruna and top of the bus to the distance between tops of the
bus and the building?
14) The Circus Arts Program is one of the most popular activities at Camp Lohikan. It brings a level of excitement and

enthusiasm to the camp experience that can't be found at home or in school. A circus artist is climbing a 20 m long rope,

which is tightly stretched and tied from the top of a vertical pole to the ground such that the angle made by the rope with

the ground level is 300.

(i) Find the height of the pole in the above situation.

(ii) If , find the value of . OR

If then find the value of .

(iii) Find the value of .
15) Authority wants to construct a slide in a city park for children. The slide was to be constructed for children below the age of
12 years. Authority prefers the top of the slide at a height of 4 m above the ground and inclined at an angle of 30° to the
ground. Based on the following figure related to slide answer the questions:
 (i) What is the value of distance AB?
(ii) From the given figure, find the value of .

(iii) If , then find the value of . OR

From the given figure, write the values of any four trigonometric ratios with respect to .
Hide and Seek: Three friends-Anshu, Vijay and Vishal are playing hide and seek in a park. Anshu and Vijay hide in the
shrubs and Vishal have to find both of them. If the positions of three friends are at A, B and C respectively as shown in the

figure and forms a right angled triangle such that , and , then answer the following
questions:

(i) What is the measure of ?

(ii) What is the measure of

(iii) Find the value of OR

If , then find the value of .

16)Birds are the messengers that tell us about the health of the planet. Bird, any of the more than 10400 living species unique
in having feathers, the major characteristic that distinguishes them from other animals. Birds are important for
 environment as well as for human beings, they play a vital role in many of the ecosystems. Returning back to his home from
school, Suresh noticed a beautiful bird on an electric pole. He stood at a 15 m distance from the pole, to see the bird
carefully. His feet were making an angle of 45° with the top of the pole. Neglecting the bird’s height, answer the following
questions:

(i) From the above given figure, find the height of the pole.

(ii) If , prove that OR

If and then find the value of .

(iii) From the above given figure, find AC.
17)Anita a student of class 10th, has to make a project on “Introduction to Trigonometry”. She decides to make a bird house which
is triangular in shape. She uses cardboard to make the bird house as shown in the figure. Considering the front side of bird
house as right angled triangle PQR, right angled at R, answer the following questions based on the given below figure:

(i) From the above figure, If then find the value of .

(ii) From the above figure, If then find the value of .
(iii) If be an acute angle and , then find, value of . OR
 If and , then find the value of .
18)Golf is a game played in an open field where the golfer plays his golf ball into a hole by using different types of clubs (golf
instruments). In golf, a golfer plays a number of holes in a given order. 18 holes played in an order controlled by the golf
course design, normally make up a game.

On your approach shot to the ninth green, the Global Positioning System (GPS) your cart is equipped with tells you the pin
is 120 meter away. The distance plate states the straight line distance to the hole is 60 meter.

(i) Express in terms of

(ii) Write the value of .

(iii) If and then find the value of . OR

If , then find the value of k.

19)A test consists of ‘True’ or ‘False’ questions. One mark is awarded for every correct answer while mark is deducted for
every wrong answer. A student knew answers to some of the questions. Rest of the questions he attempted by guessing.
He answered 120 questions and got 90 marks.
 (i) Represent the above situations in the form of pair of linear equations in two variables.
(ii) How many questions did he answer correctly? OR
How many questions did he guess?
(iii) If answer to all questions he attempted by guessing were wrong and answered 80 correctly, then how many marks he
got?
20)Find whether the lines representing the following pair of linear equations intersect at a point or parallel or coincident:

OR

On comparing the ratios find out whether the following pair of equations are consistent or inconsistent:

21) Is it true to say that the pair of equations and has a unique solution? Justify your answer.
22) Check graphically whether the pair of equations x + 3y = 6 and 2x – 3y = 12 is consistent. If so, solve them graphically.
OR
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. Represent the situation algebraically and solve them by substitution method.
23) Draw the graphs of the pair of linear equations and . Also find the points where the lines meet the
X-axis. OR
Determine graphically whether the following pair of linear equations and has:
 (i) a unique solution (ii) infinitely many solutions (iii) no solution
24) Amit is planning to buy a house and the layout is given below. The design and the measurement has been made such that
areas of two bedrooms and kitchen together is 95 sq.m.
Based on the given information, answer the following questions.

(i) Form the pair of linear equations in two variables from this situation.
(ii) Find the length of the outer boundary of the layout.
(iii) Solve the above formed equations to find the values of x and y OR
Find the number of solutions for the pair of equations formed in the above situation.
25) Raman usually go to a dry fruit shop with his mother. He observes the following two situations.
On 1st day: The cost of 2 kg of almonds and 1 kg of cashew was Rs 1600.
On 2nd day: The cost of 4 kg of almonds and 2 kg of cashew was Rs 3000.
Denoting the cost of 1 kg almonds by Rs x and cost of 1 kg cashew by Rs y, answer the following questions.

(i) Represent algebraically the situation of day-1.

(ii) Represent algebraically the situation of day-2.
(iii) Solve the following equations formed in the above situations by any algebraic method and find the values of x and y.
OR
 Check whether the following equations formed in the above situations have unique solution or no solutions or infinitely
many solutions.
26) Wilton Norman “Wilt” Chamberlain was an American basketball player, and played in the NBA during the 1960s. At 7 feet 1
inch, he was the tallest and heaviest player in the league for most of his career, and he was one of the most famous people
in the game for many years. He is the first and only basketball player to score 100 points in an NBA game.

In the 1961–1962 NBA basketball season, Wilt Chamberlain of the Philadelphia Warriors made 30 baskets. Some of the
baskets were free throws (worth 1 point each) and some were field goals (worth 2 points each). The number of field goals
was 10 more than the number of free throws.)
(i) Represent the two cases algebraically (pair of linear equations).
(ii) How many field goals and free throws did he make? OR
Check whether the above formed system of equations are consistent or inconsistent.
(iii) On solving the above equations, find the total number of points scored.
27)From Bengaluru bus stand, if Riddhima buys 4 tickets to Madurai and 6 tickets to Rameswaram, the total cost is
Rs. 92; but if she buys 6 tickets to Madurai and 10 tickets to Rameswaram, the total cost is Rs. 148.

Considering the fares from Bengaluru to Madurai and that to Rameswaram as and respectively, then answer the
following questions:
(i) Represent the situation-I algebraically.
 (ii) Represent the situation – II algebraically.
(iii) What is the fare from Bengaluru to Madurai and Bengaluru to Rameswaram? OR
Write about the number of solutions for the system of linear equations formed in the above situations.
28) Mr. Sanjay arranged a lunch party for some of his friends. The expense of the lunch are partly fixed and partly
proportional to number of guests. The expenses amount to Rs. 650 for 7 guests and Rs. 970 for 11 guests.

Denote the fixed expense by Rs. and proportional expense per person by Rs. and answer the following questions:
(i) Represent the following situations algebraically.
(ii) Write about the number of solutions for the pair of linear equations obtained in the above situation.
(iii) Find the fixed expense and proportional expense per person. OR
If there would be (i) 15 guests (ii) 35 guests at the lunch party, then what is the total amount he has to pay
29) Sulphur dioxide (SO2) is a colourless gas at ambient temperature and pressure. It is soluble in water and forms sulfurous
acid which is slowly oxidized to sulphuric acid by dissolved oxygen. Sulphur dioxide is a major air pollutant and has
significant impacts upon human health. In addition, the concentration of sulfur dioxide in the atmosphere can influence the
habitat suitability for plant communities, as well as animal life. Sulphur dioxide emissions are a precursor to acid rain and
atmospheric particulates.

To find out the concentration of SO2 in the air (in parts per million, i.e. ppm), the data was collected for 30 localities in a
Delhi and is presented below:
 Concentration of Frequency
SO2 (in ppm)
0.00-0.04 4
0.04-0.08 9
0.08-0.12 9
0.12-0.16 2
0.16-0.20 4
0.20-0.24 2
Based on the above information, answer the following questions.
(i) What is the lower limit of median value of concentration of SO 2 in the air?
(ii) How many localities are having SO2 in the range of 0.04-0.16 ppm?
(iii) What is the mean concentration of SO2 in air? OR
Find the median value concentration of SO2 in the air.
30) The following are the ages of 300 patients getting medical treatment in a hospital on a particular day:
Age (in years) 10-20 20-30 30-40 40-50 50-60 60-70
Number of students 1 2 1 5 7 2
Form the “Less than Type” cumulative frequency distribution table: OR
The mean of 10 observations is 15.3. If two observations 6 and 9 are replaced by 8 and 14 respectively. Find the new mean.
31) Find the unknown entries a, b, c, d, e, f in the following distribution of heights the students in a class.
Height (in cm) Frequency Cumulative Frequency
150−155 12 a
155-160 b 25
 160-165 10 c
165-170 d 43
170-175 e 48
175-180 2 f

32). Calculate the average daily income (in Rs.) of the following data about men working in a company.
Daily income (in Rs) < 100 < 200 < 300 < 400 < 500
Number of men 12 28 34 41 50
OR
The weight of coffee in 70 packets are shown in the following table:
Weight (in grams) Number of packets
200-201 12
201-202 26
202-203 20
203-204 9
204-205 2
205-206 1
Determine the modal weight.
33) A health officer took an initiative organizing a medical camp in a remote village. The medical check-up of 35 students of the
age group of 10 year and their weights were recorded as follows:
Weight in kg 38-40 40-42 42-44 44-46 46-48 48-50 50-52
No.of students 3 2 4 5 14 4 3
 (i) Find the mean weight of the students using assumed mean method.
(ii) Calculate the median of the given data. OR
If the median of the distribution given below is 28.5. Find the values of and .

Class interval Frequency

0-10 5
10-20
20-30 20

30-40 15

40-50
5
50-60
Total 60
34) Traffic Management: A traffic enforcement camera is a camera which may be mounted beside or over a road or installed in an
enforcement vehicle to detect motoring offenses, including speeding, vehicles going through a red traffic light. A worldwide
review of studies found that speed cameras led to a reduction of 11% to 44% for fatal and serious injury crashes. The British
Medical Journal recently reported that speed cameras were effective at reducing accidents and injuries in their vicinity and
recommended wider deployment.

In order to monitor reckless driving on Mumbai road, special cameras have been installed at many traffic light. The
following table shows a frequency distribution table for the speed of 100 vehicles passing through a particular spot on a
day.
 Speed in 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100
km/h
Number of 1 3 7 16 35 29 7 2
vehicles
Based on the above information, answer the following questions:
(i) Find the number of vehicles whose speed is more than .
(ii) Find the number of vehicles whose speed is less than .
(iii) What is the mode value of speed? OR
What is the median value of speed?
35) Transport department of a Jaipur wants to buy some Electric buses for the city. For which they wants to analyse the distance
travelled by existing public transport buses in a day.

The following data shows the distance travelled by 60 existing public transport
buses in a day.

Distance travelled 200-209 210-219 220-229 230-239 240-249

in km
Number of buses 4 14 26 10 6

(i) Find the median class of the daily distance travelled.

(ii) What is the cumulative frequency of the class preceeding the median class?
 (iii) Find the median of the distance travelled. OR

Find the mean of the distance travelled.

36) On the occasions of `Diwali' a rectangular plot have been allotted for 'Diwali Mela' to students of secondary school in
Hyderabad. In order to reduce smog and pollution they decided to keep little leaf linden plant on the boundary at a
distance of 1 m from each other. Four air purifier machines have also been set up at points L, M, N, O. (Answer the
following questions considering A as origin).

(i) What are the coordinate of L and N?

(ii) Find the distance between the points L and O.
(iii) Find the point which divides the line segment joining the points M and N in the ratio of 3 : 4 OR
In parallelogram LMNO, L(3, 1), M(5, 1), N(a, b) and O(4, 3) are the vertices, then find the vertex N(a, b).
37) The Class X students of a secondary school in Krishinagar have been allotted a rectangular plot of land for their gardening

activity. Sapling of Gulmohar are planted on the boundary at a distance of 1m from each other. There is a triangular grassy

lawn in the plot as shown in the below figure. The students are to sow seeds of flowering plants on the remaining area of

the plot.
 (i) Taking A as origin, find the coordinates of the vertices of the triangle ∆PQR.

(ii) What is the midpoint of side PQ, when A is the origin?

(iii) Taking A as the origin find the distances PQ and QR. OR

Find the coordinates of the point which divides the line segments joining the points Q and R in ratio of 2 : 3. (Consider

points Q and R, taking A as origin).

38) Junk food is unhealthful food that is high in calories from sugar or fat, with little dietary fiber, protein, vitamins, minerals or

other important forms of nutritional value. A sample of few students have taken. If be the number of students who take

junk, be the number of students who take healthy food such that and are the zeroes of the quadratic

polynomial , then

answer the following questions:

(i) Find the number of students who take the junk food.

(ii) Find the number of students who take healthy food.

(iii) Find the quadratic polynomial whose zeroes are -3 and -4. OR
 If one of the zeroes of the polynomial is 2, find the other zero.

39) ABC Construction Company got the contract of making speed humps on roads. Speed humps are parabolic in shape and

prevents over speeding, minimize accidents and gives a chance of pedestrians to cross the road. The mathematical

representation of a speed hump is shown in the given graph.

Based on the above information, answer the following questions.

(i) What is the type of polynomial represented by the graph?

(ii) What are the zeroes of the polynomial represented by the graph?

(iii) What shall be the sum of the zeroes and product of the zeroes of the polynomial represented by the graph? OR

If are the zeroes of the polynomial represented by the graph such that then, find the value of .

40) A Maths teacher gave a banana to his child to eat. When the child

was eating banana there were some observations made by the teacher. She observed that the shape of the

banana was parabolic. Please give answers to the following questions:

(i) If the parabola touches the X-axis at zero, then how many zeroes of the polynomial will be there.

(ii) Find the polynomial, if the two zeroes of the polynomial representing the given curve are 5 & -2.

(iii) Find the zeroes of the polynomial . OR

If are the zeroes of the polynomial , then the find the value of

41) Kumbh Mela is a major pilgrimage and festival in Hinduism. It is celebrated in a cycle of approximately 12 years at four river-
bank pilgrimage sites: the Prayagraj (Ganges-Yamuna Sarasvati rivers confluence), Haridwar (Ganges), Nashik (Godavari),
and Ujjain (Shipra).

The festival is marked by a ritual dip in the waters. The seekers believe that bathing in these rivers is a means to prayascitta
for past mistakes, and that it cleanses them of their sins.

Government of UP is planning to procure tent for the pilgrims during Kumbh Mela. The specification of tent is given below.
(1) Lower cylindrical part must have a white colored thick fabric whose cost is ` 60 per square meter.
(2) Top conical part must have PVC coated blue fabric whose cost is ` 70 per square meter

The front view of tent is given below with dimension.

 (i) How much blue PVC coated fabric is required?
(ii) How much white fabric is required?
(iii) If labour charge for the construction of tent Rs.15 per sq. meter. What is the total cost of the tent? OR
A cylinder, a cone and a hemisphere have same base and same height. Find the ratio of their total surface areas.
42) In a toys manufacturing company, wooden parts are assembled and painted to prepare a toy. For the wood processing activity
center, the wood is taken out of storage to be sawed, after which it undergoes rough polishing, then is cut, drilled and has
holes punched in it. It is then fine polished using sandpaper. For the retail packaging and delivery activity center, the
polished wood sub-parts are assembled together, then decorated using paint.

One specific toy is in the shape of a cone mounted on a cylinder. The total height of the toy is 110 mm and the height of its
conical part is 77 mm. The diameters of the base of the conical part is 72 mm and that of the cylindrical part is 40 mm.
Based on the above information, answer the following questions:
(i) If its cylindrical part is to be painted red, what is the surface area need to be painted red?
(ii) If its conical part is to be painted blue, what is the surface area need to be painted blue?
(iii) If the cost of painting the toy is 2 paise for mm2, then what is the cost of painting of a box of 100 toys?
OR
A cone, a hemisphere and a cylinder stand on equal bases of radius R and have the same heights H. What is the ratio of
their whole surface area?
43) A wooden article as shown in the figure was made from a cylinder by scooping out a hemisphere from one end and a cone
from other end, given that total height of the wooden article is 10cm and diameter is 6cm, meanwhile the height of the
conical part is 7cm.

(i) Find the C.S.A of cone.

(ii) Find the C.S.A of hemisphere.
(iii) Find the total surface area of the article. OR
The radii of two right circular cylinders are in the ratio of 2 : 3 and their heights are in the ratio of 5 : 4. Calculate the ratio of
their curved surface area
44) India is competitive manufacturing location due to the low cost of manpower and strong technical and engineering
capabilities contributing to higher quality production runs. The production of TV sets in a factory increases uniformly by a
fixed number every year. It produced 16000 sets in 6th year and 22600 in 9th year.

Based on the above information answer the following questions:

(i) Find the production during the 1st year.

(ii) Find the production during 8th year.

(iii) Find the production during first 3 years. OR

Find the difference of the production during 7th year and 4th year.
45) A seminar is being conducted by an Educational Organisation, where the participants will be educators of different subjects.
The number of participants in Hindi, English and Mathematics are 60, 84 and 108 respectively.

(i) In each room the same number of participants are to be seated and all of them being in the same subject, hence find the

maximum number participants that can accommodated in each room.

(ii) What is the minimum number of rooms required during the event?

(iii) Find the LCM of 60, 84 and 108. OR

Find the product of HCF and LCM of 60, 84 and 108.

46)In an online test, Ishita comes across the statement-If a tangent is drawn to a circle from an external point, then the square of
the length of the tangent drawn is equal to difference of squares of distance of the tangent from the centre of the circle and
the radius of the circle.

Help Ishita, in answering the following questions based on the above statement.
(i) If AB is a tangent to a circle with centre O at B such that AB = 10cm and OB = 5cm, then find OA.
(ii) In the adjoining figure, find the radius of the circle.

(iii) In the adjoining figure, find the length of the tangent.

 OR
In given figure, if AT is a tangent to the circle with centre O, such that OT = 4 cm and , then find the length of AT.

47) Traditional Japanese Fans: Japanese fans are made of paper on a bamboo frame, usually with a design painted on them. A
Japanese Fan symbolises friendship, respect and good wishes and are given on special occasions, as well as to help cool you
down in hot weather. The fan is an immediately recognizable icon of Japanese culture. Today they remain an important
artistic medium and stylish fashion accessory.

Lavanya hold a Japanese folding fan in her hand as shown in figure. It is shaped like a sector of a circle. The inner and outer
radii are 14 cm and 21 cm. The fan has three colour material.

(i) If the region containing the pink colour makes an angle of θ 2 = 720 at the centre, then find the area of the region having pink
colour.
(ii) If the region containing the orange colour makes an angle of θ 1 = 540 at the centre, then find the area of the region having
orange colour.
(iii) If the region containing the red colour makes an angle of θ 3 = 450 at the centre, then find the perimeter of the region having
 red colour. OR
Find the total area of the region having radius 14 cm.
48) Your elder brother wants to buy a car and plans to take loan from a bank for his car. He repays his total loan of ₹ 118000 by
paying every month starting with the first installment of ₹ 1000. If he increases the instalment by ₹100 every month, answer
the following:

(i) What is the amount paid by him in 30th installment?

(ii) What is the amount paid by him in the 30 installments?

(iii) If total installments are 40, then what is the amount paid by him in the last installment? OR

What is the ratio of 1st installment to the last installment?

49) A Mathematics Exhibition is being conducted in your school and one of your friends is making a model of a factor tree. He has
some difficulty and asks for your help in completing a quiz for the audience. Observe the following factor tree and answer
the following.

(i) What will be the value of ?

(ii) What will be the value of ?
(iii) Write the prime factorisation of 13915. OR
Given that HCF(252, 594) = 18, find LCM(252, 594).
50) In a maths class, the teacher draws two circles that touch each other externally at point K with centres A and B and radii 5cm
and 4cm respectively as shown in the figure.

(i) Find the length of PA.

(ii) Find the length of BQ.
(iii) What are the values of PK and QY. OR
In the given figure, find .

51) Pendulum Clock: It is a clock that uses a pendulum, a swinging weight, as its
time keeping element. From its invention in 1656 by Christiaan Huygens, the
pendulum clock was the world’s most precise timekeeper, accounting for its widespread use. Their greater accuracy
allowed for the faster pace of life which was necessary for the Industrial Revolution. The home pendulum clock was
replaced by less-expensive, synchronous, electric clocks in the 1930s and 40s. Pendulum clocks are now kept mostly for
their decorative and antique value.

Dhriti bought a pendulum clock for her living room. the clock contains a small pendulum of lenght 45 cm. the minute hand
 and hour hand of the clock are 9 cm and 6 cm long respectively.

(i) Find the area swept by the minute hand in 14 minutes.

(ii) Find the angle described by hour hand in 10 minutes.

(iii) Find the distance covered by the tip of hour hand in 3.5 hours OR

If the tip of pendulum covers a distance of 66 cm in complete oscillation, then find the angle described by pendulum at the

centre.

52) A hockey field is the playing surface for the game of hockey.. It is rectangular in shape - 100 yards by 60 yards. Goals consist

of two upright posts placed equidistant from the centre of the backline, joined at the top by a horizontal crossbar. The

inner edges of the posts must be 3.66 metres (4 yards) apart, and the lower edge of the crossbar must be 2.14 metres (7

feet) above the ground. Each team plays with 11 players on the field during the game including the goalie. Positions you

might play include-  Forward: As shown by players A, B, C and D.  Midfielders: As shown by players E, F and G.  Fullbacks:

As shown by players H, I and J.  Goalie: As shown by player K. Using the picture of a hockey field below, answer the

questions that follow: a) Write the coordinates which represents the position of the goalie?
a) Write the coordinates which represents the position of the goalie?

b) Find the point on the y axis equidistant from B and C.

c) Find the coordinates of the centroid of ΔEHJ. (OR) If points K, Q and E are to be collinear, then, what should be the position of

a player Q such that his distance from K is twice his distance from E

53) India is a competitive manufacturing location due to the low cost of manpower and strong technical and engineering

capabilities contributing to higher quality production runs. The production of TV sets in a factory increases uniformly by a

fixed number every year. It produced 16000 sets in 6th year and 22600 in 9th year. Based on the above information,

answer the following questions:

a) What was the production in the 1st year? b) What is the increase in production every year?

c) In which year, will the production be 29,200. (OR) Find the difference of the production during the 7th year and 4th year.

54) There are two temples on each bank of a river .One temple is 50m high. While doing a renovation work, a man standing on
 the top of the 50m tall temple, observes that the angle of depression of the top and bottom of the other temple are 300

and 600 respectively. [us 3 =1.73

Based on the above information, answer the following questions: a) Find the measure of ACB .

b) What is the height (DC) of the other temple? (OR) Find the width of the river.

c) Find the difference in the heights of the two temples?

55) To conduct Sports Day activities, in your rectangular school ground ABCD, lines have been drawn with chalk powder at a

distance of 1 m each. 100 flower pots have been placed at a distance of 1 m from each other along AD, as shown in Figure.

Niharika runs 1/ 4 th the distance AD on the 2nd line and posts a green flag. Preet runs 1/ 5 th distance AD on the eighth

line and posts a red flag. i) Write the coordinates of green flag. ii) Find the position of red flag.

iii) If Rashmi has to post a blue flag exactly half way between the line segments joining the two flags, where should she post

the blue flag? OR If Joy has to post a flag at one-fourth distance from green flag, in the line segment joining the
 green and red flags, then where should he post his flag?

56) Amit was playing a number card game. In the game, some number cards (having both +ve or –ve numbers) are arranged in a

row such that they are following an arithmetic progression. On his first turn, Amit picks up 6th and 14th card and finds their

sum to be –76. On the second turn he picks up 8th and 16th card and find their sum to be – 96.

i) What is the difference between the numbers on any two consecutive cards?

ii) What is the number on the first card?

iii) What is the sum of 9th and 15th card? OR What is the difference of 10th and 18th card?

57) A group of students of class X visited India Gate on an education trip. The teacher and students had interest in history as well.

The teacher narrated that India Gate, official name Delhi Memorial, originally called All-India War Memorial, monumental

sandstone arch in New Delhi, dedicated to the troops of British India who died in wars fought between 1914 and 1919.The

teacher also said that India Gate, which is located at the eastern end of the Rajpath (formerly called the Kingsway), is about

138 feet (42 metres) in height.

 i) What is the angle of elevation if they are standing at a distance of 42m away from the monument?

ii) They want to see the tower at an angle of 600. So, they want to know the distance where they should stand and hence find

the distance. iii) If the altitude of the sun is at 600 then what is the height of the vertical tower that will cast a shadow of

length 20 m? OR What is the angle of elevation of the Sun, if the ratio of length of a rod and its shadow is 1:1?

58) Conical tank: The advantages of cone bottom tanks are found in nearly every industry, especially where getting every last

drop from the tank is important. This type of tank has excellent geometry for draining, especially with high solids content

slurries as these cone tanks provide a better full-drain solution. The conical tank eliminates many of the problems that flat

base tanks have as the base of the tank is sloped towards the centre giving the greatest possible full-drain system in vertical

tank design. Rajesh has been given the task of designing a conical bottom tank for his client. Height of the conical part is

equal to its radius. Length of the cylindrical part is 3 times of its radius. Tank is closed from the top. The cross section of the

conical tank is given below.

(i) If the radius of the cylindrical part is taken as 3 meter, what is the volume of the cylindrical part of the tank?
 (ii) What is the area of the metal sheet used to make this conical tank? Assume that tank is covered from top?

(iii) What is the ratio of volume of cylindrical part to the volume of the conical part? OR

The cost of the metal sheet is Rs. 2000 per square meter and fabrication cost is Rs. 1000 per square meter. What is the total

cost of the tank?

59) 100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of

letters in the English alphabets in the surnames was obtained as follows:

Number of letters 1-4 4-7 7-10 10-13 13-16 16-19

Number of surnames 6 30 40 16 4 4

(i) What is the upper limit of the median class? (ii) Determine the median number of letters in the surnames. OR

Determine the mean number of letters in the surnames

(ii) What is the average of upper limit of median class and lower limit of modal class?

60) A carpenter made a wooden pen stand. It is in the shape of a cuboid with four conical depressions to hold pens. The

dimensions of cuboid are 15cm by 10cm by 3.5cm. The radius of each of depressions is 0.5cm and depth is 1.4cm (see below

figure).

(i) What is the volume of the cuboid? (ii) What is the volume of the conical depression?

(iii) What is the volume of wood in the entire stand? OR

A heap of rice in the form of a cone of base diameter 24m and height 3.5m. How much canvas cloth is required to cover the

heap? 61) 100 Metres Race: The 100 metres is a sprint race in track and field competitions. The shortest common outdoor

running distance, it is one of the most popular and prestigious events in the sport of athletics. It has been contested at the

summer Olympics since 1896 for men and since 1928 for women. The World Championships 100 metres has been contested since

1983. The reigning 100 m Olympic or world champion is often named “the fastest man or woman in the world”. A stop watch was

used to find the time that it took for a group of students to run 100m.

Time in sec 0-20 20-40 40-60 60-80 80-100

No.of students 8 10 13 6 3

Based on the above information answer the following questions: (i) Estimate the mean time taken by a student to finish the race.

(ii) What will be the upper limit of the modal class? (iii) What is the sum of the lower limits of the median class and modal class ?

OR How many students finish the race within 1 minute?