Class 10 Maths Case Study Based Questions

CASE STUDY BASED QUESTIONS

1. During a health checkup camp three types of patients registered themselves.
60 were suffering from joint problem , 84 were suffering from some type of
fever and 108 were diabetic. The organisers wants to call doctors for this camp.
(i) What is the maximum number of doctors required if each doctor treat same
number of patients of each type of problem.
(a) 64 (b) 14 (c) 16 (d) 12
(ii) How many patients each doctor will treat.
(a) 7 (b) 12 (c) 21 (d) 9
(iii)At the end of the day when the total count was done the number of patients
with joint problems were 48, suffering from fever were 60 and diabetic
patients were 72 only. How many patients each doctor treated.
(a) 21 (b) 15 (c) 14 (d) 12
(iv) If HCF (48, 60, 72) = 7m – 2, what is the value of m
(a) 2 (b) 1 (c) 3 (d) 12
(v) If HCF (60, 108) = 60 a + 108 b what are the values of a & b.
(a) 2, 1 (b) –2, 1 (c) –2, –1 (d) 2, –1
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2. On children's day the supplier of mid day meal supplied packets of biscuits and
chocolates to the students of two schools . One packet of biscuit contains 20
small packets and a packet of chocolate contains 12 pieces of chocolates . He
supplied p packets of biscuit and q packets of chocolate in school A and 2p
packets of biscuits together with some packets of chocolate in the school B.
(i) How many students are there in school A.
(a) 60 (b) 240 (c) 840 (d) 1200
(ii) How many large packets of biscuits were supplied in school A.
(a) 42 (b) 20 (c) 14 (d) 28
(iii)How many packets of chocolate were supplied in school A.
(a) 42 (b) 35 (c) 70 (d) 40
(iv) The number of large packets of biscuits distributed in school B.
(a) 42 (b) 84 (c) 28 (d) 24
(v) What is the total number of students in school B.
(a) 2520 (b) 840 (c) 1680 (d) 420

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3. For a family of three members a cuboidal tank has been made . The volume of
the tank is expressed in the form of a polynomial p(x) = x 3 + 10x2 + 27x + 18
cubic units.
(i) What are the possible dimensions of the tank ,if the largest is the length,
the smallest is the height and the third is the breadth.
(a) (x + 9)(x + 2)(x + 1) (b) (x + 6)(x + 3)(x + 1)
(c) (x – 6)(x + 3)(x – 1) (d) (x – 9)(x – 2)(x + 1)
(ii) If x = 2, what is the quantity of water each member will require.
(a) 120 (b) 40 (c) 30 (d) 56
(iii)Two more members joined the family, how much is the total requirement
of water now.
(a) 180 (b) 200 (c) 80 (d) 50
(iv) If these members are to stay now then how much height of the tank be
increased to fulfill the total requirement without changing length and
breadth.
(a) 5 (b) 2 (c) 3 (d) x
(v) If x remains the same what could be the possible polynomial for the volume
of tank required for these five persons now.
(a) (x + 3)(x + 9)(x + 1) (b) (x + 3)(x + 3)(x + 6)
(c) (x – 6)(x + 3)(x + 3) (d) (x + 6)(x + 3)(x – 3)
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4. Three NCC Cadets, of a college planted some plants. The polynomial p(x) = x3
– 12x2 + 47x – 60 shows the number of plants planted by them. If Akool, one of
cadets planted 5 plants, then
(i) How many plants are planted by the remaining two cadets
(a) 12 (b) 47 (c) 9 (d) 7
(ii) How many plants each of them planted
(a) 3, 4 (b) 5, 4 (c) 5, 3 (d) 12, 5
(iii) Factorise the given polynomial
(a) (x – 5) (x + 4) (x – 3) (b) (x – 5) (x – 4) (x + 3)
(c) (x – 12) (x – 5) (x – 1) (d) (x – 5) (x – 4) (x – 3)
(iv)Instead of 5, if Akool planted 4 plants only what will be the polynomial
(a) x3 – 5x2 + 40x – 48 (b) x3 – 8x2 + 8x – 48
(c) x3 – 11x2 + 40x – 48 (d) x3 – 5x2 + 8x – 48
(v) What is the polynomial corresponding to the total plants planted by the
remaining two cadets.
(a) x2 – x – 12 (b) x2 – x + 12 (c) x2 – 7x + 12 (d) x2 + 7x + 12

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5. The consumption of water in a family is divided into two parts one is fixed
consumption used for various activities like cleaning, washing etc. and the
other is individual consumption. For a family of 6 persons the water required is
445 cubic units and for a family of 8 members the total requirement of the
water is 575 cubic units . full form of pair of linear equations for the above
situation
(i) What type of lines are these
(a) parallel (b) intersecting
(c) coincident (d) inconsistent.
(ii) What is the individual and fixed consumption.
(a) 55,65 (b) 65, 55 (c) 55, 55 (d) 65, 65
(iii)If we draw the graph of the pair of equations then what is the distance of
the point of intersection from y axis
(a) 55 (b) 65 (c) 45 (d) 50
(iv)How much water is required for a family of 4 members,
(a) 260 (b) 315 (c) 265 (d) 245
(v) Form a linear equation for the total consumption of a family of four members.

(a) x + 4y = 265 (b) y + 4x = 315
(c) x + 4y = 315 (d) y + 4x = 265
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6. On Diwali occasion two rocket cracers were launched at the same time from
two different places opposite to each other and the path followed by them are
along the lines 3x – 2y = 6 and x + y =12.
(i) What type of set of lines they are representing
(a) Intersecting (b) Parallel
(c) Coincident (d) cannot say.
(ii) What is the point of start i.e. the point of intersection of the first line with x
-axis.
(a) (0, 2) (b) (2, 0) (c) (3, 0) (d) (0,3)
(iii)At what point the second line intersect y-axis.
(a) (0, 12) (b) (12, 0) (c) (6, 0) (d) (0,6)
(iv) What is the point of intersection of the two rockets,
(a) (6,0) (b) (6,6) (c) (0,6) (d) (–6, –6)
(v) If both are launched from x-axis,at what height they cross each other,
(a) 6 (b) 12 (c) 4 (d) 24

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7. In junior forms, we learnt that numbers which can be arranged in a compact
triangular pattern are called triangular numbers

1 3 6 10

n(n  1)
A triangular number p can be expressed as p = where n is a positive
2
integer.
It can be rewritten as n2 + n – 2p = 0, which is called a quadratic equation in n
(i) Consider the quadratic equation x2 + 5x – 6 = 0. Try to substitute the
following values of x into the equation and find which one satisfies it.
(a) x = – 6 (b) x = –3 (c) x = 0 (d) x = 1
(ii) What will be the roots of 2x2 – 3x = 0

3
(a) 0, 2 (b) 2, 3 (c) 3, 0 (d) 0,
2
(iii)What is the condition for a quadratic equation to have equal roots?
(a) D < 0 (b) D = 0 (c) D  0 (d) D > 0
(iv) What will be the sum of roots of the equation 3x 2 + 4x – 5 = 0

2 –2 –5 –4
(a) (b) (c) (d)
3 3 3 3
(v) If ax2 + bx + c = 0 is a quadratic equation what is the must have condition?
(a) a = 0 (b) b  0 (c) a  0 (d) c = 0

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8. A farmer wants to make a rectangular pen for his sheep in the garden near his
house. To make the pen the farmer planned to make it with wooden fencing to
cover the three sides. He has 60m fencing material to cover three sides and the
other side being a brick wall.
(i) If the width be x, then the length of the pen
(a) 60 – 2x (b) 2x + 6 (c) 6x + 20 (d) 20 – 6x
(ii) According to the given conditions area of the pen is (Hint: use length as
calculated in (i))
(a) 60x2 – 2x (b) 60x + 2x2
(c) 6x – 20x2 (d) 60x – 2x2
(iii) If the area of the pen is 250 then the quadratic equation will be
(a) x2 – 30x + 250 = 0 (b) 2x2 – 30x + 250 = 0
(c) x2 – 30x + 125 = 0 (d) 2x2 – 60x + 125 = 0
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(iv)Now let’s sketch a graph for the quadratic equation obtained in question(iii).
Which is as follows:

The area is maximum when
(a) the width = 20m (b) the width = 15m
(c) the width = 25m (d) the width = 35m
(v) If the area of pen is 400, then its width is
(a) 10 or 20 (b) 40 or20
(c) 20 or 20 (d) 40 or 40
9. As we know a tree or a plant needs both soil and water along with sunlight to
grow. It will have the necessary nourishment in both water and sun to make its
leaves green and fruit to grow. A rural Indian school Gardner planted some
trees on his school at certain distances from the water body following a sequence.
There are 25 trees at equal distances of 5 meters in a line with a well, the
distance of the well from the nearest tree being 10 meters. A gardener waters
all the trees separately starting from the well and he returns to the well after
watering each tree to get water for the next.

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(i) Distance travelled to water nearest tree and back to the well is:
(a) 10m (b) 15m (c) 20m (d) 25m
(ii) Progression so formed in the above condition is
(a) 20, 30, 40, 50, ... (b) 15, 30, 45, 60,...
(c) 10, 15, 20, 25,... (d) 25, 35, 45, 55
(iii) To find the total distance we have to use the formula
(a) an = a + (n + 1) (b) an = a + (n –1)

n n
(c) Sn = (2a + (n + 1) d) (d) Sn = (20 + (n – 1)d)
2 2

(iv)Distance travelled to water 25th tree
(a) 250 m (b) 260 m (c) 270 m (d) 280 m
(v) The total distance the gardener will cover in order to water all the trees.
(a) 3000 m (b) 3500 m (c) 3800 m (d) 4000 m
10. A construction company will be penalized each day of delay in the construction
of the bridge. The penalty will be ` 4000 for the first day and will increase by
` 1000 for each following day. Based on its budget, the company can afford to
pay a maximum of ` 165000 toward penalty.

Mathematics-X 257

(i) The penalty amount paid by the construction company from the first day as
a sequence
(a) 4000, 8000, 12000,... (b) 4000,5000,6000,...
(c) 5000, 6000, 7000,... (d) 1000,5000,9000
(ii) First-term and difference respectively of the above series is
(a) 4000 and 4000. (b) 5000 and 1000
(c) 4000 and 1000 (d) 1000 and 4000
(iii) Find the maximum number of days by which the completion of work
can be delayed (take Sn = 165000)
(a) 10 days (b) 20 days (c) 15 days (d) 25 days
(iv)The penalty will be charged on the tenth day
(a) ` 16000 (b) ` 15000 (c) ` 14000 (d) ` 13000
(v) If (x + 1), 3x, and (4x + 2) are the first three terms of an AP, then its 5th
term is:
(a) 14 (b) 19 (c) 24 (d) 28
11. Rahul is studying in X Standard. He is making a kite to fly it on a Sunday. Few
questions came to his mind while making the kite. Give answers to his questions
by looking at the figure.

(i) Rahul tied the sticks at what angles to each other?
(a) 30° (b) 60° (c) 90° (d) 60°

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(ii) Which is the correct similarity criteria applicable for smaller triangles at
the upper part of this kite?
(a) RHS (b) SAS (c) SSA (d) AAS
(iii) Sides of two similar triangles are in the ratio 4:9. Corresponding medians
of these triangles are in the ratio:
(a) 2 : 3 (b) 4 : 9 (c) 81 : 16 (d) 16 : 81
(iv)In a triangle, if the square of one side is equal to the sum of the squares of
the other two sides, then the angle opposite the first side is a right angle.
This theorem is called:
(a) Pythagoras theorem
(b) Thales theorem
(c) The converse of Thales theorem
(d) The converse of Pythagoras theorem
(v) What is the area of the kite, formed by two perpendicular sticks of length 6
cm and 8 cm?
(a) 48 cm2 (b) 14 cm2 (c) 24 cm2 (d) 96 cm2
12. There exist a tower near the house of Shankar. The top of the tower AB is tied
with steel wire and on the ground, it is tied with string support.
One day Shankar tried to measure the longest of the wire AC using Pythagoras
theorem.

(i) In the figure, the length of wire AC is: (take BC = 60 ft)
(a) 75 ft (b) 100 ft (c) 120 ft (d) 90 ft
(ii) What is the area of ABC?
(a) 2400 ft2 (b) 4800 ft2 (c) 6000 ft2 (d) 3000 ft2
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(iii)What is the length of the wire PC?
(a) 20 ft (b) 30 ft (c) 25 ft (d) 40 ft
(iv)What is the length of the hypotenuse in ABC?
(a) 100 ft (b) 80 ft (c) 60 ft (d) 120 ft
(v) What is the area of a POC?
(a) 100 ft2 (b) 150 ft2 (c) 200 ft2 (d) 250 ft2
13. The ECO Club of a senior secondary school in Rohini have to make a Herbal
Garden in a rectangular plot of a land (See figure). Saplings of Tulsi are planted
on the boundary at a distance of 1 m from each other. There is a square land
inside the plot as shown in the figure for planting ‘ALOEVERA’. The students
are to sow seeds of other herbal pants on the remaining area of the plot.
Answer the questions given below the diagram:

(i) Considering A as the origin, what are coordinates of M?
(a) (4, 0) (b) (4, 2) (c) (4, 1) (d) (0, 4)
(ii) What are the coordinates of D?
(a) (0, 23) (b) (22, 0) (c) (23, 0) (d) (23, 1)
(iii)What is the distance MO?
(a)2 units (b) 3 3 units (c) 5 2 units (d) 6 2 units
(iv) The mid point of PN is
(a) (7, 5) (b) (14, 10) (c) (4, 8) (d) (10, 2)

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(v) If we join diagonals of square MNOP, in what ratio Q divides diagonals PN
and MO?
(a) 2 : 1 (b) 1 : 1 (c) K : 1 (d) m : n
14. RPVV, Suraj Mal organised Sports Day in which one of the event is 100 m
race. Participants have to run in the rows which are marked at a distance of 1
metre as shown in the figure. At one time the participants are at position A, B,
1
C, D. A has covered half the distance PQ, B has covered th distance PQ, C
4
has covered the distance PQ, D has covered half the distance PQ.
Considering P as origin, answer the questions given below the diagram.

Q

P

(i) On joing A, B, C, D which figure you will get
(a) Square (b) Rectangle
(c) Rhombus (d) Quadrilateral

Mathematics-X 261

(ii) What area is enclosed by ABCD ?
(a) 250 sq units (b) 275 sq units (c) 225 sq units (d) 300 sq units
(iii)If another participant at E could not run due to some shoe problem, what
are the co-odinates of E
(a) (0, 5) (b) (5, 10) (c) (5, 0) (d) (5, 5)
(iv) What is the distance CE?
(a) 10 units (b) 100 units (c) 50 units (d) 70 units
(v) In what ratio B divides AE?
(a) 2 : 1 (b) 1 : 2 (c) 3 : 2 (d) 1 : 1
15. An electrician has to repair an electric fault on a pole of height 5 m. He needs
to reach a point 1.3 m below the top of the pole to undertake the repair work.
The ladder is inclined at an angle of 45° to the horizontal.
(you may use 2 = 1.41)

(i) What is the length of RB?
(a) 3.7 m (b) 1.3 m (c) 7.4 m (d) 2.6 m
(ii) What is the distance between the foot of the pole and the foot of the ladder?
(a) 1.3 m (b) 3.7 m (c) 7.4 m (d) 3.7 2 m
(iii)What is the length of the ladder ?
(a) 3.7 m (b) 7.4 m (c) 5.217 m (d) 7.05 m

262 Mathematics-X

(iv) What is the measure of LRB?
(a) 90° (b) 30° (c) 60° (d) 45°
(v) What type of LRB is ?
(a) Scalene triangle (b) Obtuse angled triangle
(c) Equilateral triangle (d) Isosceles triangle
16. Suresh was going to his school on his bicycle. Suddenly his bicycle chain got
stuck on the chians wheel. He decided to take it to the nearest cycle repairer.
There he carefully observed the chain wheels of the cycle. He found that both
chain wheel were almost of the shape of circles.

(i) If both chain wheels are considered as circles then the total number of
tangents are
(a) 1 (b) 2 (c) 3 (d) 4
(ii) If both chain wheels are kept side by touching each other and their diameters
are 42 cm and 14 cm, the distance between their centres is
(a) 7 cm (b) 14 cm (c) 28 cm (d) 56 cm
(iii)The common point of tangent and the circle is called
(a) point of tangent (b) point of circle
(c) point of radius (d) point of contact
(iv) Distance between two parallel tangents of a circle is always equal to its
(a) radius (b) chord (c) diameter (d) secant
(v) In a circle of radius 14 cm, length of tangent PT = 48 cm, drawn from a
point P to the circle of centre O. Then length of OP is
(a) 62 cm (b) 50 cm (c) 25 cm (d) 34 cm
17. A horse is tied to a peg at one corner of a square shaped grass field of sides 15
m by means of a 5 m long rope. Use  = 3.14 to answer the following questions.

Mathematics-X 263

(i) What is the area of the grass field?
225
(a) 225 m (b) 225 m2 (c) 225 m2 (d) m2
4
(ii) The area of that part of the field in which the horse can graze is :
(a) 19.625 m2 (b) 78.5 m2 (c) 196.25 m2 (d) 19.265 m2
(iii)If the length of rope is 10 m, the grazing area is :
(a) 7.85 m2 (b) 78.5 m2 (c) 225 m2 (d) 785 m2
(iv) The increase in the grazing area if the rope were 10 m long instead of 5 m
is:
(a) 58.875 m2 (b) 58 m2 (c) 58.758 m2 (d) 78.5 m2
(v) The angle made by the horse in grazing the grass field is is :
(a) 45° (b) 90° (c) 60° (d) 360°
18. On a square handkerchief, nine circular designs each of radius 7 cm are made
as shown in the figure.

(i) What is the side of the square?
(a) 7 cm (b) 21 cm (c) 42 cm (d) 84 cm
(ii) What is the area of square?
(a) 1764 cm2 (b) 441 cm2 (c) 49 cm2 (d) 7056 cm2
(iii)What is the area of one circle ?
(a) 49 cm2 (b) 7 cm2 (c) 9 cm2 (d) 14 cm2

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(iv) What is the area of nine circles ?
(a) 154 cm2 (b) 1386 cm2 (c) 1836 cm2 (d) 451 cm2
(v) What is the area of the remaining portion of square handkerchief?
(a) 378 cm2 (b) 783 cm2 (c) 738 cm2 (d) 387 cm2
19. Uttar Bantra Sarbojanin Durgotsav Committee had started planning for their
Durga puja a year in advance with a mega budget in mind.
Bholeram Tents is given a contract by municipal corporation of Budaun (Uttar
Pradesh), India to setup a mega function pandal (tent). The architect has designed
a tent of height 7.7 m in the form of a right circular cylinder of diameter 36 m
and height 4.4 m surmounted by a right circular cone. This tent is setup in a
rectangular park of dimensions 70 m × 60 m as shown below. The tent is made
up of canvas. (Take  = 3.14)

On the basis of the above information, answer any four of the following
questions:
(i) For the workers to finalise the purchase of material, the height of the conical
part is :
(a) 2.3 m (b) 6.3 m (c) 3.3 m (d) 12.1 m
(ii) The slant height of the conical part is :
(a) 18.3 m (b) 18.7 m (c) 19.1 m (d) 19.4 m

Mathematics-X 265

(iii)To purchase the canvas, the area of the canvas to be used approximate in
making the tent, is :
(a) 1353 m2 (b) 1386 m2 (c) 1406 m2 (d) 1533 m2
(iv) The cost of canvas at ` 4.50 per m2 is:
(a) ` 6327 (b) ` 6237 (c) ` 6898.50 (d) ` 6088.50
(v) The area of the rectangular park outside the tent is :
(a) 1883 m2 (b) 2864.64 m2 (c) 3182.64 m2 (d) 4200 m2
20. In a toys manufacturing company, wooden parts are assembled and painted to
prepare a toy. One specific toy is in the shape of a cone mounted on a cylinder.
For the wood processing activity center, the wood is taken out of storage to be
saved, after which it undergoes rought polishing, then is cut, drilled and has
holes punched in it. It is then fine polished using sand paper.

For the retail packaging and delivery activity center, the polished wood sub-
parts are assembled together, then decorated using paint.
The total height of the toy is 26 cm and the height of its conical part is 6 cm.
The diameters of the base of the conical part is 5 cm and that of the cylinderical
part is 4 cm.
On the basis of the above information, answer any four the following questions:
(i) If its cylinderical part is to be painted yellow, the surface area need to be
painted is :
(a) 80  cm2 (b) 82  cm2 (c) 84  cm2 (d) 88  cm2
(ii) If its conical part is to be painted green, the surface area need to be painted
is :
(a) 26.5  cm2 (b) 22.5  cm2 (c) 20.5  cm2 (d) 18.5  cm2

266 Mathematics-X

(iii)The volume of the wood used in making this toy, is
(a) 92.5  cm3 (b) 89.5  cm3 (c) 85.5  cm3 (d) 72.5  cm3
(iv) If the cost of painting the toy is 3 paise per cm2, then the cost of painting
the toy is : (Use  = 3.14)
(a) r` 10 (b) r` 9.65 (c) r` 9.84 (d) r` 10.25
(v) The paint company gives a discount of 5% if the number of toys to be
painted is 100 or more. The cost of painting of 200 toys will be :
(a) ` 1900.50 (b) ` 1869.50 (c) ` 1833.50 (d) ` 1805.50
21. As part of the ‘Swachh Bharat Abhiyan’, some houses of a locality in Delhi
decided to clean up and beautify a school of their locality by planting a number
of plants. They involved the school kids and the local community in doing so.

Here is the data indicating the number of plants contributed by different houses:
Number of Plants 1–3 4–6 7–9 10 – 12 13 – 15 16 – 18
contributed
Number of houses 10 8 x 7 12 4
On the basis of the above information, answer any four of the following
questions:
(i) If the mean number of plants contributed be 8.9, then how many houses
contributed 7 to 9 plants?
(a) 6 houses (b) 7 houses (c) 8 houses (d) 9 houses

Mathematics-X 267

(ii) How many houses of the locality came forward to beautify the school?
(a) 50 houses (b) 49 houses (c) 48 houses (d) 47 houses
(iii)The mode of the frequency distribution is :
(a) 11.5 (b) 12.65 (c) 13.25 (d) 13.65
(iv) Calculate the median of the frequency distribution, using empirical relation
among mean, median and mode.
(a) 9.77 (b) 10.48 (c) 10.35 (d) 10.15
(v) The median class of the frequency distribution is :
(a) 3.5 – 6.5 (b) 6.5 – 9.5 (c) 9.5 – 12.5 (d) 12.5 – 15.5
22. 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
On the basis of the above information, answer any four of the following
questions:
(i) What is the upper limit of median class?
(a) 10 (b) 13 (c) 16 (d) 19
(ii) Determine the median number of letters in the sur names.
(a) 8.5 (b) 8 (c) 7.88 (d) 8.32
(iii)What is the upper limit of modal class?
(a) 13 (b) 19 (c) 10 (d) 16

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(iv) Sum of lower limits of median and modal class is
(a) 10 (b) 12 (c) 20 (d) 14
(v) Cumulative frequency of median class is
(a) 36 (b) 76 (c) 92 (d) 96
23. In a club, men are playing the card game. A man named Ramesh draw a card
from a well-shuffled deck of cards.

On the basis of the above information, answer any four of the following
questions:
(i) Find the probability of getting a king of red colour.
1 3 3 1
(a) (b) (c) (d)
26 13 26 52
(ii) Find the probability of getting a face card.
1 3 3 1
(a) (b) (c) (d)
26 13 26 52
(iii)Find the probability of getting a jack of hearts.
1 3 1 1
(a) (b) (c) (d)
26 13 52 4
(iv) Find the probability of getting a spade card.
1 3 1 1
(a) (b) (c) (d)
26 13 52 4

Mathematics-X 269

(v) Find the probability of getting a queen of diamonds.
1 3 1 1
(a) (b) (c) (d)
26 13 52 4
24. A game of chance consists of spinning an arrow which comes of rest pointing
at one of the numbers 1, 2, 3, 4 5, 6, 7, 8 (see figure) and these are equally
likely outcomes

:

On the basis of the above information, answer any four of the following
questions:
(i) What are the total number of possible outcomes?
(a) 8 (b) 1 (c) 36 (d) 4
(ii) What is the probability that spinning arrow will point at 8?
1 1 3
(a) (b) (c) (d) 1
8 2 4
(iii)What is the probability that spinning arrow will point at a number greater
than 2?
1 1 3
(a) (b) (c) (d) 1
8 2 4
(iv) What is the probability that spinning arrow will point at an odd number ?
1 1 3
(a) (b) (c) (d) 1
8 2 4
(v) What is the probability that spinning arrow will point at a number less
than 9 ?
1 1 3
(a) (b) (c) (d) 1
8 2 4
270 Mathematics-X

ANSWERS AND HINTS

1. (i) (d) No. of doctors = 12
(ii) (c) 21
(iii) (b) 15
(iv) (a) m = 2
(v) (d) 2, – 1
2. (i) (c) 840
(ii) (a) 42
(iii) (c) 70
(iv) (b) 84
(v) (c) 1680
3.
(i) (b) (x + 6), (x + 3), (x + 1)
(ii) (b) 40 cubic units
(iii) (b) 200
(iv) (b) 2
(v) (b) (x + 3) (x + 3) (x + 6)
4.
(i) (d) 7
(ii) (a) 3, 4
(iii) (d) (x – 5) (x – 4) (x – 3)
(iv) (c) x3 – 11x2 + 40x – 48
(v) (c) x2 – 7x + 12
5. (i) (b) Intersecting
(ii) (b) 65, 55
(iii) (a) 55
(iv) (b) 315
(v) (c) x + 4y = 315

Mathematics-X 271

6.
(i) (a) Intersecting
(ii) (b) (2, 0)
(iii) (d) (0, 6)
(iv) (b) (6, 6)
(v) (a) 6
7. (i) (d) x = 1
3
(ii) (d) x = 0,
2
(iii) (b) D = 0
4
(iv) (d) –
3
(v) (c) a  0
8. (i) (a) 60 – 2x
(ii) (d) 60x – 2x2
(iii) (c) x2 – 30x + 125 = 0
(iv) (b) the width = 15 m
(v) (a) 10 or 20
9. (i) (c) 20 m
(ii) (a) 20, 30, 40, 50 .....
n
(iii) (d) Sn = (2a + (n – 1)d)
2
(iv) (b) 260 m
(v) (b) 3500 m
10. (i) (b) 4000, 5000, 6000
(ii) (c) 4000 and 1000
(iii) (c) 15 days
(iv) (d) 13000
(v) (d) 28

272 Mathematics-X

11. (i) (c) 90°
(ii) (b) SAS
(iii) (b) 4 : 9
(iv) (d) Converse of Pythagoras theorem
(v) (a) 48 cm 2
12. (i) (b) 100 ft
(ii) (a) 2400 ft2
(iii) (c) 25 ft
(iv) (a) 100 ft
(v) (b) 150 ft2
13. (i) (b) M (4, 2)
(ii) (c) (23, 0)

(iii) (d) 6 2
(iv) (a) (7, 5)
(v) (b) 1 : 1
14. (i) (d)
(ii) (c)
(iii) (c)
(iv) (b)
(v) (d)
15. (i) (a)
(ii) (b)
(iii) (c)
(iv) (d)
(v) (d)
16. (i) (b)
(ii) (c)

Mathematics-X 273

(iii) (d)
(iv) (c)
(v) (b)
17. (i) (b)
(ii) (a)
(iii) (b)
(iv) (a)
(v) (b)
18. (i) (c)
(ii) (a)
(iii) (a)
(iv) (b)
(v) (a)
19. (i) (c) 3.3 m
(ii) (a) 18.3 m
(iii) (d) 1533 m2
(iv) (c) r` 6898.50
(v) (c) 3182.64 m2
20. (i) (c) 84  cm2
(ii) (d) 18.5  cm2
(iii) (a) 92.5  cm3
(iv) (b) ` 9.65
(v) (c) ` 1833.50
21. (i) (d) 9 houses
(ii) (a) 50 houses
(iii) (c) 13.65
(iv) (b) 10.48
(v) (b) 6.5 – 9.5

274 Mathematics-X

22. (i) (a) 10
(ii) (a) 8.5
(iii) (c) 10
(iv) (d) 14
(v) (b) 76
1
23. (i) (a)
26
3
(ii) (b)
13
1
(iii) (c)
52
1
(iv) (d)
4
1
(v) (c)
52
24. (i) (a) 8

1
(ii) (a)
8

3
(iii) (c)
4

1
(iv) (b)
2
(v) (d) 1

Mathematics-X 275