#Welcome to Educbse-The Platform of Learning#

Maths Sample Paper 3 (standard)-Class 10th

 Mathematics Sample Paper 

Part- A 

Section -I

Direction:-(Q.nos-1-16) Section-I has 16 questions of 1 marks each.Internal choice is provided in 5 questions.

1.∆ABC and ∆DEF are similar such that 2 AB=DE and BC=8cm,then find the value of EF.

2. 12 sphere of the same size are made from melting a solid cylinder of 16 cm diameter and 2cm height .Find the diameter of each sphere.

3.ABC is a right- angle triangle with BC =6 and and AB= 8 cm of a circle with centre O and radius xcm has been inscribed in a ∆ABC as shown in figure.Then find the value of x.
4.If the circumference of a circle exceeds its diameter by 30 ,then find the radius of circle.

You are watching this sample paper on Educbse (The platform of learning)


5.To divide a line segment ABAB  the ratio of 6:7, a ray  AX is drawn first such that angle BAX an acute angle and then points A1,A2, ...located at equal distances on the ray AX, find the point on the ray AX, which point B is join.

6.If the first term of an Ap is 2 and common difference is 4, then find the sum of its 40 terms.

Or
What is the common difference of an AP in which T18-T14=32?

7.If P(-1,1) is the mid-point of the line segment joining A(-3,b) and B (1,b+4)
then find the value of b.

8.In figure, AT is a tangent to the circle with centre O such that OT = 4 cm and angle OTA= 30°.Then find the value of AT.
Or
Find the length of a tangent drawn to a circle with radius 5 cm from a point 13 cm away from the centre of the circle.

9.In a lottery ticket, there are 10 prizes and 25 blanks, find the probability of not getting a prize.

10. If the graph of quadratic polynomial does not intersect the X-axis ,then find the number of zeroes.

11. If the mean of first n natural number is 5/ 9, then find the value of n.

12.Find the centroid of triangle PQR whose vertices are P (- 8,0) Q(5,5) and R(- 3 - 2)


You are watching this sample paper on Educbse (The platform of learning)

13.The material of a cone is converted into the shape of cylinder of equal radius.If the height of the cylinder is 6cm, then find the height of the cone.

14.What is the value of 2 tan^2∅+cos^2∅-2.
If ∅ is an acute angle and sin∅=cos∅.

Or
In a rectangle ABCD, AB=40cm,and angle BAC=30°,then find the side of BC.

15.If alpha and bita are the zeroes of polynomial 3x^2 +4x+2,then find alpha bita^2 + Bita alpha square.
Or
If alpha and bita are the zeroes of polynomial f(x^2)=x^2-5x+k such that alpha- bita=1 ,then find the value of 4k.

16.Find the  HCF of 96 and 404 by prime factorization method.
Or
If 17/25 is a rational number, find the decimal expansion of it.

Section-II
Direction(Q nos - 17-20) 
Case study based questions are compulsory. Attempt any four sub parts of each question. Each sub part carries 1marks.

17.Case Study I
Pollution
Sulpher dioxide (SO2) can cause respiratory problems such as branchitis and can irritate your nose, throat and lungs. It may cause cough, whearing,phlegm and asthma attacks. The effects are worse when you are exercising. SO2 has been linked to cardiovascular disease.
To find out the concentration of SO2 in the air (in parts per million,i.e.ppm).

A student collect the data for 30 localities in a certain city and is presented below

Concentration of SO2.                 Frequency
(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


a)Suppose mean of n observations is x bar ,if we multiply each observation by 5 then you mean will be.
I)5 xbar
II)xbar/5
III)x bar + 5
IV)x bar - 5

b) Class with the maximum frequency is said to be
I) Median
II) Mean
III) Mode
IV) None of these.

c) Find mean concentration of SO2 in the air.
I)0.0750ppm
II)0.085ppm
III)0.0999ppm
IV)0.087 ppm

d) Find the median class of the given data.
I)0.04-0.08
II)0.08-0.12
III)0.12-0.16
IV) None of these 

e) Find the number of localities, which have more than 0.12PPM
I)7
II)8
III)6
IV)5
.
18.Case study II
Satellite Tower in Himalayas 
The satellite image of Himalaya mountain is shown below .In this image there are many signal towers are standing.
The angle of elevation of the top of a hill from the foot of a tower is 60 ° and the angle of elevation of the top of the tower with height 50 m from the foot of the hill is 30°
a) find the horizontal distance between hill and tower.
I)50m
II)50√3m
III)40√3m
IV)45√3m

b) find the height of the hill.
I) 150 m
II)145 m
III)155m
IV)160m

c)Find the distance from foot of tower to top of the hill.
I)100√3 m
II)150√3 m
III)120m
IV)100m

d)Find the distance from foot of the hill to the top of the tower.
I)100m 
II)100√3m 
III)120m 
IV)140m

e) Suppose a person is sitting on the top of the tower and see the object on the ground at point A, and angle of depression made by person to objects is ∅.

 If the object way from the tower then the angle of depression make by person is
I)increasing 
II)decreasing
III)increasing or decreasing
IV)None of the above 


You are watching this sample paper on Educbse (The platform of learning)

19.Case study III
Fun game
 Oneday children invite some friends in their house and they want to play some fun game.
So,they consider block in the shape of cube with one letter / number written on each face as shown below.
While through the cube,they want to know the change of getting some particular number of alphabet.
  2.           3 .         5 .          7 .           A .             B

a) Find the probability of getting an alphabet .
I)1
II)1/3
III)2)3
IV)5/7
 
b) Find the probability of getting a prime number .
I)2/3
II) 1/3
III)1
IV)None of the above.

c) Find the probability of getting a constant.
I)1/3
II)1/6
III)5/6
IV)2/3

d).When we have no reason to believe that one is more likely to occur than the other, then it is said to be
I)Simple event 
II)Compound  event 
III)Equally likely events 
IV)None of the above.

e) If  the probability of any event is one , then in percentage we can say that it is 
I)0%
II)20%
III)50%
IV)100%

20.Case study IV
Number of tangents on a circle 
The number of tangents  drawn from a point on a circle depends upon the position of the point with respect to the circle.
Suppose O is the centre radius 5cm.T is a point such that OT=13cm and OT intersects the circle at E and AB is the tangent to the circle at E.

a) fiFi the length of a tangent at point T.
I)12 m
II)14 cm 
III)13 cm 
IV)15cm

b)Find the length of the tangent AB .
I)20/7cm
II)20/3cm
III)10/3 cm 
IV) None of the above 

c)How many tàngents can be drawn from point O.
I)0
II)1
III)2
IV)3

d)Find the area of the traingle ABT.
I)80/7cm^2 
II)80/3cm^2
III)80/11cm^2
IV)None of the above.

e) If two tangents are drawn to a circle from an external point, than the substend equal angles  at
I)inside the circle 
II) chord
III) centre
IV) None of the above.

You are watching this sample paper on Educbse (The platform of learning)


Thank You very much

By Anuranjan Gadekar.
               *********************





Post Comment

1 comment: