Class 10th Pre-board question paper {SQP}

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So Today in This post I'm going to give you Pre-board Mathematic question paper for your practice.

This is the Exam had recently conducted in Army public School Golconda.

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This is Standered mathematics pre-board Question paper




This is Basic mathematics pre-board Question paper

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Part – A
Section-I

All questions are compulsory. In case of internal choices, attempt anyone.

1. 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?
2. Find a quadratic polynomial, the sum and product of whose zeroes are 2 and – 8 respectively.

OR
If one of the zeroes of the quadratic polynomial x

2 + 3x + k is 2, then find the value of k ?
3. What is the probability that a non leap year selected at random will contain 53 sundays ?
4. If a marble of radius 2.1 cm is put into a cylindrical cup full of water of radius 5cm and height 6 cm, then how
much water flows out of the cylindrical cup?

OR

A cone of height 24 cm and radius of base 6 cm is made up of modeling clay. A child reshapes it in the
form of a sphere. Find the radius of the sphere.
5. If the volumes of two spheres are in the ratio 64:27. Find the ratio of their surface areas ?
6. Find the area of the circle that can be inscribed in a square of side 6 cm ?
7. In the given Figure, if O is the centre of a circle, PQ is a chord and the tangent PR at P makes an angle of 50° with
PQ, then find < POQ.

8. Check whether 301 is a term of the list of numbers 5, 11, 17, 23, . . . ?
9. If sin A = 1/ 2 , then find the value of cot A ?

OR
Find the value of (sin30° + cos30°) – (sin60° + cos60° )
10. Without actually performing the long division, find if 987
10500
will have terminating or non-terminating (repeating)

decimal expansion. Give reasons for your answer.
11. If ∆ABC is right angled at C, then find the value of cos (A+B) ?
12. A pole 6 m high casts a shadow 2√3 m long on the ground, then what is the Sun’s elevation ?

OR

The ratio of the length of a rod and its shadow is 1:√3 , then find the angle of elevation of the sun ?
13. For what values of k will the following pair of linear equations 3x + y = 1 and kx + 2y – 1= 0 have
infinitely many solutions?
14. It is given that ∆ ABC ̴∆ PQR, with BC
QR
=
1
3
. Then, find the value of ar (PQR)
ar (ABC)
?

15. If the common difference of an AP is 5, then what is a18 – a13 ?
OR
Find the sum of first 16 terms of the AP: 10, 6, 2,..... ?
16. A tangent PQ at a point P of a circle of radius 7 cm meets a line through the centre O at a point Q so
that OQ = 25 cm. Find the length of tangent PQ ?

Part – A
Section-II

Case study questions are compulsory. Attempt any four sub-parts of each questions.

Each sub-parts carries 1 marks each

17. Kerala is a region of great natural beauty. Indias most verdant state ,rated by National Geographic Traveller as
one of the worlds 50 must-see destinations, is a paradisiacal landscape of palm-lined beaches, steamy jungles,

plantation-covered hills, and tropical rivers and lakes.
This map of the Indian province of kerala shows its area can be approximated using a simple straight – sided
triangular shape. The shape has two parallel sides 561 km and 216 km long. The other sides are 180 km and 211 km
long. Its parallel sides are 100 km apart. Rohan observed the shape formed by four straight lines and explored it on
her note book in different ways shown below:

Shape-I Shape-II
Refer to Shape-I:
(i) Let ABCD is a trapezium with AB ׀׀ DC, E and F are the points on non-parallel sides
AD and BC respectively such that EF ׀׀ AB. Then AE
ED
=

(a) BF
CD
(b) AB
CD
(c) BF
FC
(d) none of these
(ii) Here, AB ׀׀ DC. If DO = 3x-19, OB = x-5, CO = x-3 and AO = 3, the value of x is
(a) 5 or 8 (b)8 or 9 (c)10 or 12 (d) none of these

(iii) Again, AB ׀׀ DC. If DO = 3x-1, OB = 5x-3, AO = 6x-5 and OC = 2x+1, the value of x is
(a) 0 (b) 1 (c) 2 (d) 3
Refer to Shape-II:
(iv) In ∆ABC, PQ ׀׀ BC. If AP = 2.4 cm, AQ = 2 cm, QC = 3 cm and BC = 6 cm, then find
the value of AB and PQ respectively ,
(a) 6 cm , 2.4 cm (b) 4.8cm , 8.2 cm (c) 4cm , 5.3cm (d) 8.4cm , 2.8 cm
(v) In ∆DEF, RS ׀׀ EF. If DR = 4x-3, DS = 8x-7 and ER = 3x-1and FC = 5x-3, then the value of x is
(a) 1 (b) 2 (c) 8 (d) 10
18. Neon glow lamps are a sort of miniature gas discharge lamps. The lamp is composed by a sealed glass bulb
containing two electrodes and a low pressure noble gas mixture.

When current flows through the lamp, the
gas immediately surrounding the negative electrode glows. This glow is usually orange in color and not very
bright. These lamps glow with a very low current and a relatively high voltage. This makes them ideal for
running on mains voltage with just an additional resistor.

Neon glow lamps last a very long time: they can burn continuously for decades. As the metal grows thicker and
thicker, the glass becomes less and less transparent: the bulb blackens and gradually becomes less bright.
The following table gives the life times of 400 neon lamps:

Life time
(in hrs.)

300-400 400-500 500-600 600-700 700-800 800-900 900-1000

No. of neon
lamps

14 56 60 86 74 62 48

i)While computing the mean of grouped data, we assume that the frequencies are
(a)evenly distributed over all the classes
(b)centred at the class marks of the classes
(c)centred at the upper limits of the classes
(d)centred at the lower limits of the classes
ii)The upper limit of the median class is
(a) 500 (b) 600 (c) 700 (d) 800
iii) The lower limit of the modal class is
(a) 900 (b) 600 (c) 700 (d) 800
iv) The number of neon lamps having life times range (in hrs.) from 600 to 800 is
(a) 14 (b) 26 (c) 12 (d) 16
v)The difference of the upper limit of modal class and lower limit of median class is
(a) 10 (b) 100 (c) 200 (d) 300

19. Cricket is a famous game played in many countries of the world like England, India and Australia. The team that
bats must score runs while the bowling team should stop them by taking wickets. The game is played on a field with a
rectangular pitch on which batsmen play. The Captain sets the field according to a plan. He instructs the players to
take a position at a particular place. There are two reasons to set a cricket field-to take wickets and to stop runs
being scored. The following graph shows the position of players during a cricket match:

i) If the distance between the points showing the players at Gully A(1,0) and as
wicketkeeper B(4,p) is 5m, then the value of p is
(a) 4 m (b) 8 m (c) 6 m (d) 9 m
ii) Suppose the length of a line segment joining the players of Mid-Off and Mid-On be 10 units.If the
coordinates of its one end are (2,-3) and the abscissa of the other end is 10 units,then its ordinate is
(a) (9,6) (b) (3,-9) (c) (-3,9) (d) (9,-6)
iii) The coordinate of point on x-axis which are equidistant from the points representing the
players at Cover P(-3,4) and the Mid-wicket Q(2,5) are
(a) (20,0) (b) (-23,0) (c) (4
5
,0) (d) none of these

iv) The ratio in which (4,5) divides the line segment joining the points Extra Cover S(2,3) and Fine Leg (7,8) is
(a) 4:3 (b) 5:2 (c) 3:2 (d) 2:3
v) If the points (4,3) and (x,5) are on the circular field with centre (2,4), the the value of x is
(a) 0 (b) 1 (c) 2 (d) 3
20. The state governments revise the auto and taxi fares from time to time based on various factors such as
inflation,fuel price, demand from various quarters, etc. The government notifies different fares for different types of
vehicles like Auto –rickshaw, Taxis, Radio cab, etc. The auto charges in a city comprises of a fix charge together with
the charges for the distance covered.

Study the following situations :
Situation-I: In a city A, for a journey of 10 km, the charge paid is Rs.75 and for a journey of 15 km, the charge paid
is Rs.110.
Situation-II: In a city B, for a journey of 8 km, the charge paid is Rs.91 and for a journey of 14 km, the charge paid
is Rs.145.
Refer Situation-I:
i) If the fixed charges of auto rickshaw be Rs.x and the running charges be Rs. y km/hr, the pair of
linear equations representing the situation is
(a) x + 10y = 110, x + 15y = 75 (b) x + 10y = 75, x + 15y = 110
(c) 10x + y = 110, 15x + y = 75 (d) 10x + y = 75, 15x + y = 110
ii) What will a person have to pay for travelling a distance of 25 km ?
(a) Rs.160 (b) Rs.280 (c) Rs.180 (d) Rs.260
iii) A person travels a distance of 50 km. The amount he has to pay is
(a) Rs.155 (b) Rs.255 (c) Rs.355 (d) Rs.455
Refer Situation-II:

iv) What will a person have to pay for travelling a distance of 30 km ?
(a) Rs.185 (b) Rs.289 (c) Rs.275 (d) Rs.305
v) The graph of the lines representing the conditions are

Part–B

All questions are compulsory. In case of internal choices, attempt anyone.
21. Construct an isosceles triangle whose equal sides are 6 cm each and angle between them is 600 and
then another triangle whose sides are 7
5
of the corresponding sides of the isosceles triangle.

22. In sports Day activities of a school, three cyclists start together and can cycle
48 km, 60 km and 72 km a day round the field. The field is circular, whose circumference is 360 km.
After how many rounds they will meet again?
OR

In a flower bed, there are 23 rose plants in the first row, 21 in the second, 19 in the third, and so on. There
are 5 rose plants in the last row. How many rows are there in the flower bed?
23. Prove that 3 - √3 a irrational number.
24. Two different dice are tossed together. Find the probability:
(i) of getting a doublet
(ii) of getting a prime number on both the dice.
25. If sin θ + cos θ = p and sec θ + cosec θ = q, then prove that q (p2 – 1) = 2p.

OR
If sin θ + cos θ = √3 , then prove that tan θ + cot θ = 1
26. The frequency distribution table of agricultural holdings in a village is given below :

Find the modal agricultural holdings of the village.

Part–B

All questions are compulsory. In case of internal choices, attempt anyone.

27. In the figure, ABC is a triangle right angled at A. Semicircles are drawn on AB, AC and BC as diameters. Find the
area of the shaded region.

28.Prove that :

cosÓ¨ –sinÓ¨ + 1
sinÓ¨+cosÓ¨− 1
=
1
cosecÓ¨ – cot Ó¨

29. If the remainder on division of x3+ 2x2 + kx +3 by x – 3 is 21, find the quotient and the value of k.
Also find the relationship between the zeroes and the coefficients of the cubic polynomial x3 + 2x2 + kx – 18.
30. The sum of the third and seventh term of an AP is 6 and their product is 8. Find the sum of first sixteen
terms of the AP.

OR

A manufacturer of TV sets produced 600 sets in the third year and 700 sets in the seventh year. Assuming that the
production increases uniformly by a fixed number every year, find :
(i) the production in the 1st year,
(ii) the production in the 10th year and
(iii) the total production in first 7 years
31. Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same
time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel
towards each other, they meet in 1 hour. What are the speeds of the two cars?

OR

A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it
would have taken 3 hours more to cover the same distance. Then, find the speed of the train.
32. Prove that the lengths of the tangents drawn from an external point to a circle are equal. Using the above
theorem, prove that: If quadrilateral ABCD is circumscribing a circle, then AB + CD = AD + BC.
33. Graphically, solve the following pair of equations: 2x + y = 6 and 2x – y + 2 = 0 .
Find the ratio of the areas of the two triangles formed by the lines representing these
equations with the x-axis and the lines with the y-axis.
Part–B

All questions are compulsory. In case of internal choices, attempt anyone.

34. (a) State and prove Pythagoras theorem.
(b) In given Fig, O is a point in the interior of a triangle ABC,
OD ┴ BC, OE ┴ AC and OF ┴ AB.

Show that:
(i) OA2 + OB2 + OC2 – OD2 – OE2 – OF2 = AF2 + BD2 + CE2
(ii) AF2 + BD2+ CE2 = AE2 + CD2 + BF2