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HALF YEARLY MODEL QUESTION PAPER -4
10th Standard
Maths

Exam Time : 03:00 Hrs Total Marks : 100

CHOOSE THE BEST ANSWER 14 x 1 = 14
1)
Let A = {1, 2, 3, 4} and B = {4, 8, 9, 10}. A function f: A ⟶ B given by f = {(1, 4), (2, 8), (3, 9),
(4,10)} is a
(a) Many-one function (b) Identity function (c) One-to-one function (d) Into function
2)
Euclid’s division lemma states that for positive integers a and b, there exist unique integers q and r
such that a = bq + r , where r must satisfy
(a) 1 < r < b (b) 0 < r < b (c) 0 ≤ r < b (d) 0 < r ≤ b
3) The next term of the sequence 3
,
1
,
1
,
1
, ..... is
16 8 12 18

(a) 1

24
(b) 1
(c) 2
(d) 1

27 3 81

4)
The solution of (2x - 1)2 = 9 is equal to
(a) -1 (b) 2 (c) -1, 2 (d) None of these
5) 1 3 5 7
⎛ ⎞
For the given matrix A = ⎜ 2 4 6 8 ⎟ the order of the matrix AT is
⎝ ⎠
9 11 13 15

(a) 2 x 3 (b) 3 x 2 (c) 3 x 4 (d) 4 x 3

6)
In ∆LMN, ∠L = 60o, ∠M = 50o. If ∆LMN ~ ∆PQR then the value of ∠R is
(a) 40o (b) 70° (c) 30° (d) 110°
7)
A man walks near a wall, such that the distance between him and the wall is 10 units. Consider
the wall to be the Y axis. The path travelled by the man is
(a) x = 10 (b) y = 10 (c) x = 0 (d) y = 0
8)
If (5, 7), (3, p) and (6, 6) are collinear, then the value of p is
(a) 3 (b) 6 (c) 9 (d) 12
9)
Two persons are standing ‘x’ metres apart from each other and the height of the first person is
double that of the other. If from the middle point of the line joining their feet an observer finds the
angular elevations of their tops to be complementary, then the height of the shorter person (in
metres) is
x x
(a) √2 x (b) 2√2
(c) √2
(d) 2x
10)
If two solid hemispheres of same base radius r units are joined together along their bases, then
curved surface area of this new solid is
(a) 4πr2 sq.units (b) 6πr2 sq.units (c) 3πr2 sq.units (d) 8πr2 sq.units
11)
The height of a right circular cone whose radius is 5 cm and slant height is 13 cm will be
(a) 12 cm (b) 10 cm (c) 13 cm (d) 5 cm
12)
Which of the following is incorrect?
(a) P(A) > 1 (b) 0 ≤ P(A) ≤ 1 (c) P(ф) = 0 (d) P(A) + P(A
¯
)=1
13)
If triangle PQR is similar to LMN such that 4PQ = LM and QR = 6 cm, then MN is equal
to ____________
(a) 12 cm (b) 24 cm (c) 10 cm (d) 36 cm
14)
The angle of elevation and depression are usually measured by a device called
(a) Theodolite (b) Kaleidoscope (c) Periscope (d) Telescope
ANSWER ANY 10 QUESTIONS 10 x 2 = 20
QUESTION NUMBER 28 IS COMPULSORY
15)
The distance S an object travels under the influence of gravity in time t seconds is given by S(t)
= gt2 + at + b where, (g is the acceleration due to gravity), a, b are constants. Verify whether the
1

function S(t) is one-one or not.

16)
Find k if f o f(k) = 5 where f(k) = 2k - 1.
17) Find the first four terms of the sequences whose nth terms are given by
a n = n3 - 2
18) 5 4 −2 −7 4 −3
⎡ ⎤ ⎡ ⎤

If A = ⎢ ,B=⎢ , find 4A - 3B.

1 3 1 7
√2 ⎥ 3 ⎥
2 4 4 2

⎣ ⎦ ⎣ ⎦
1 9 4 5 −6 9

19)
Find the LCM of the given expressions.
-9a3b2, 12a2b2c
20) In △ ABC, D and E are points on the sides AB and AC respectively. For each of the following
cases show that DE||BC
AB = 12 cm, AD = 8 cm, AE = 12 cm and AC = 18 cm.
21)
Find the length of the tangent drawn from a point whose distance from the centre of a circle is 5
cm and radius of the circle is 3 cm.

22)
Check whether the given lines are parallel or perpendicular : 5x + 23y + 14 = 0 and 23x − 5y + 9
=0
23) Among the six trigonometric quantities, as the value of angle θ increase from 0° to 90° , which of
the six trigonometric quantities has undefined values?
24)
The slant height of a frustum of a cone is 5 cm and the radii of its ends are 4 cm and 1 cm. Find
its curved surface area.
25)
The radius of a sphere increases by 25%. Find the percentage increase in its surface area.
26)
If the standard deviation of a data is 4.5 and if each value of the data is decreased by 5, then find
the new standard deviation.
27)
The mean of a data is 25.6 and its coefficient of variation is 18.75. Find the standard deviation.
28)
Find the values of k if the straight line 2x + 3y + 4 + k(6x - y + 12) = 0 is perpendicular to the line
7x + 5y - 4 = 0.
ANSWER ANY 10 QUESTIONS 7 x 5 = 35
QUESTION NUMBER 42 IS COMPULSORY
29)
The data in the adjacent table depicts the length of a person forehand and her corresponding
height. Based on this data, a student finds a relationship between the height (y) and the forehand
length(x) as y = ax + b, where a, b are constants.
(i) Check if this relation is a function.
(ii) Find a and b.
(iii) Find the height of a woman whose forehand length is 40 cm.
(iv) Find the length of forehand of a woman if her height is 53.3 inches.
Length ‘x’ of forehand (in cm)Height 'y' (in inches)
35 56
45 65
50 69.5
55 74
30)
What is the smallest number that when divided by three numbers such as 35, 56 and 91 leaves
remainder 7 in each case?
31)
In an A.P., sum of four consecutive terms is 28 and their sum of their squares is 276. Find the
four numbers.
32)
Solve the following system of linear equations in three variables 3x – 2y + z = 2, 2x + 3y – z =
5, x + y + z = 6.
33) a b 1 0
If A = [ ] and I = [ ] show that A2 - (a + d) A = (bc - ad)I2
c d 0 1

34)
In △ ABC , points D,E,F lies on BC, CA, AB respectively. Suppose AB, AC and BC have lengths
13, 14 and 15 respectively. If =
AF
=
FB
. Find BD an DC
2

5
CE

EA
5

35)
Find the area of a triangle formed by the lines 3x + y− 2 = 0 , 5x + 2y − 3 = 0 and 2x − y − 3 = 0
36)
A(-3, 0) B(10, - 2) and C(12, 3) are the vertices of ΔABC. Find the equation of the altitude
through A and B.
37)
An aeroplane at an altitude of 1800 m finds that two boats are sailing towards it in the same
direction. The angles of depression of the boats as observed from the aeroplane are 60° and 30°
respectively. Find the distance between the two boats.(√3 = 1.732)
38)
A cylindrical glass with diameter 20 cm has water to a height of 9 cm. A small cylindrical metal of
radius 5 cm and height 4 cm is immersed it completely. Calculate the raise of the water in the
glass?
39) As shown in figure a cubical block of side 7 cm is surmounted by a hemisphere. Find the surface
area of the solid.

40)
The marks scored by the students in a slip test are given below.
x 4 6 8 10 12
f 7 3 5 9 5
Find the standard deviation of their marks.
41)
Two customers Priya and Amuthan are visiting a particular shop in the same week (Monday to
Saturday). Each is equally likely to visit the shop on any one day as on another day. What is the
probability that both will visit the shop on
(i) the same day
(ii) different days
(iii) consecutive days?
42) The sum of two numbers is 15. If the sum of their reciprocals is 3
, find the numbers.
10

8 Marks 2 x 8 = 16
43) a)
Draw the graph of y = x2 - 4 and hence solve x2 - x - 12 = 0
(OR)

b)
The following table shows the data about the number of pipes and the time taken to till the
same tank.
No of pipes (x) 2 3 6 9

Time Taken (in min) (y) 45 30 15 10

Draw the graph for the above data and hence

(i) find the time taken to fill the tank when five pipes are used
(ii) Find the number of pipes when the time is 9 minutes.
44) a)
Construct a △PQR which the base PQ = 4.5 cm, ∠R = 35oand the median RG from R to PG
is 6 cm
(OR)

b)
Draw a tangent to the circle from the point P having radius 3.6 cm, and centre at O. Point P is
at a distance 7.2 cm from the centre.

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