CLASS X MATHEMATICS FULL LENGTH TEST
TIME ALLOWED: 3 hours
MM: 90
GENERAL INSTRUCTIONS:
1.
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3.
4.
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2.
3.
4.
5.
6.
7. The circumference of two concentric circles
forming a ring are 88 cm and 66 cm respectively:
All questions are compulsory.
The width of the ring is:
The paper consists of 34 questions divided into
(a) 14 cm
(b) 7 cm
(c) 3.5 cm (d) 21 cm
four sections A, B, C and D.
8. Two cubes each of volume 8 cm3 are joined end
(i) Section A contains 8 MCQs of 1 mark each.
to end, then the surface area of the resulting
(ii) Section B contains 6 questions of 2 marks
cuboid is:
each.
(a) 80 cm2 (b) 64 cm2 (c) 40 cm2 (d) 8 cm2
(iii) Section C contains 10 questions of 3 marks
SECTION – B
each.
9. Which term of the A.P. 6, 13, 20, 27, ………. is 98
(iv) Section D contains 10 questions of 4 marks
more than its 24th term?
each.
10. Two concentric circles are of radii 5 cm and 3 cm
Use of calculator is not permitted.
respectively. Find the length of a chord of the
larger circle which touches the smaller circle.
SECTION – A
11. A card is drawn at random from well shuffled
deck of playing cards. Find the probability that
Which of the following equations has the product
card drawn is:
of its roots as 4?
2
2
(a) A card of spade.
(a) x  4x  4  0
(b) x  4x  4  0
(b) A red king.
(c)  x 2  4x  4  0
(d) x 2  4x  2 4  0
12. If the vertices of ∆ABC
Which term of the A.P. 113, 108, 103, ………. is the
are A(5, -1), B( - 3, - 2),
first negative term?
C (-1, 8), find the length
(a) 22nd term
(b) 24th term
of median through A.
(c) 26th term
(d) 28th term
13. A paper is in the form of a rectangle ABCD in
The probability of a sure event is:
which AB = 20 cm, BC = 14 cm. A semi – circular
(a) 0
(b) 1
portion with BC as diameter is cut off. Find the
(c) Between 0 and 1
(d) greater than 1
22 

A girl calculate the probability of her winning the
area of the remaining part.  use    .
7 

game in a match and finds it 0.08. What is the
14. A hemispherical bowl of internal radius 9 cm is
probability of her losing the game?
full with a liquid. This liquid is to be filled into
(a) 91%
(b) 8%
(c) 92%
(d) 80%
cylindrical shaped bottles of diameter 3 cm and
The perpendicular distance of A(5, 12) from the y
height 4 cm. How many bottles are necessary to
– axis) is:
empty the bowl?
(a) 13 units
(b) 5 units
SECTION – C
(c) 12 units
(d) 17 units
15. One fourth of a herd of camels was seen in forest.
In fig., the area
Twice of square root of the herd had gone to
of triangle ABC
mountains and remaining 15 camels were seen
(in sq. units)
on the bank of a river. Find the total number of
is:
camels.
(a) 15
16.
The sum of ages (in years) of a son and his father
(b) 10
is 35 years and product of their ages is 150 years.
(c) 7.5
Find their ages.
(d) 2.5
ALL THE BEST
17. The sum of 4th and 8th terms of an A.P. is 24 and
sum of 6th and 10th terms is 44. Find the first
three terms of an A.P.
18. How many multiples of 4 lie between 11 and
266?
19.
20.
21.
22.
23.
24.
25.
26.
27.
cm and altitude 3.5 cm then another triangle
whose sides are
4
times the corresponding order
7
of the isosceles triangle.
28. Draw a circle of radius 5 cm. Mark a point A
1
which is 8cm away from its centre O, construct
Find the number of terms of the A.P. 18, 15 ,
2
the tangents AB and AC. Measure the lengths of
1
AB and AC.
13,………, 49 .
2
29. From the top of a tower the angle of depression
PQ is a chord of length 8 cm of a circle of radius 5
of an object on the horizontal ground is found to
cm. The tangents PT and QT intersect at a point T.
be 60˚. On descending 20 m vertically
find the length of TP.
downwards from the top of the tower, the angle
Find the point of the x – axis which is equidistant
of depression of the object is found to be 30˚.
from the points (5, 4) and (–2, 3). Also find the
Find the height of the tower.
area of a triangle formed by these points.
30. A man on a cliff observes a boat at an angle of
AB and CD are two
depression of 30˚ which is approaching the shore
diameters of a circle
to the point immediately beneath the observer
perpendicular to each
with a uniform speed. Six minutes later, the angle
other and OD is the
of depression of the boat is found to be 60˚.
diameter of the
(a) Find the time taken by the boat to reach the
smallest circle. If OA =
shore.
7 cm, find the area of
(b) Which mathematical concept is used in above
the shaded region.
problem?
A bicycle wheel makes 75 revolutions per
(c) What is its value?
minute to maintain a speed of 8.91 km/hour.
31. One die and one coin are tossed simultaneously.
Find the diameter of the wheel.
Write the sample space. Find the probability of
The circumference of the base of a conical tent is
getting:
44m. If the height of the tent is 24 m, find the
(a) Prime number on die.
length of the canvas used in making the tent, if
(b) Head
22 

(c) Head and even number.
the width of the canvas is 2 m.  Use   
7


32. Find the area of the triangle PQR formed by
joining the mid points of the sides of the triangle
SECTION – D
whose vertices are A(1, – 2), B(3, 2) and C(–1, 4).
A passenger train takes 3 hours less for a journey
Also find area of ∆ABC.
of 360 km if its speed is increased by 10 km/hr
33. A bucket is in the form of a frustum of a cone
from the usual speed. What is its usual speed?
whose radii of bottom and top are 7 cm and 28
A circle is inscribed in a
cm respectively. If the capacity of the bucket is
∆ABC, with sides AC, AB
21560 cm3 , find the whole surface area of bucket.
and BC are 8 cm, 10 cm
34. If the radii of the ends of a bucket 24 cm high are
and 12 cm respectively.
5 cm and 15 cm, find the surface area of the
Find the lengths of AD, BE
bucket provided it is closed from the smaller end.
and CF.
Construct an isosceles
triangle whose base is 7.5
ALL THE BEST