1
Class X
Mathematics
Sample Question Paper 2018

19
Time allowed
:
3
Hours
Max. Marks
:
8
0
General Instructions:
1.
All the questions are compulsory.
2.
The questions paper consists of 30 questions divided into 4 sections A,
B, C and D.
3.
Section A comprises of 6 questions of 1 mark each. Section B comprises of 6 questions of 2
marks each. Section C comprises of 10 questions of 3 marks each. Section D comprises of 8
questions of 4 marks each.
4.
There is no overall choice. However
, an internal choice has been provided in two questions of 1
mark each, two questions of 2 marks each, four questions of 3 marks each and three questions
of 4 marks each. You have to attempt only one of the alternatives in all such questions.
5.
Use of calcul
ators is not permitted.
Section

A
1.
Find the value of a, for which point P
(
ୟ
ଷ
, 2) is the mid

point of the line segment joining the
points Q(

5,4) and R(

1,0).
1
2.
Find the value of k, for which one roo
t of the quadratic equation
kx
2

14x+8 = 0
is 2.
1
OR
Find the value(s) of k for which the equation
ݔ
ଶ
+
5
ݔ݇
+
16
=
0
has real and equal roots.
3.
Write the value of
cot
ଶ
θ
−
ଵ
ୱ୧୬
మ
1
OR
If
ߠ݊݅ݏ
=
ߠݏܿ
, then find the value of
2tan
θ
+
cos
ଶ
θ
4.
If nth term of an A.P. is (2n+1),
what is the sum of its first three terms?
1
5.
In figure if AD= 6cm, DB=9cm, AE = 8cm and EC = 12cm and
ADE = 48
0
. Find
ABC
1
6.
After how many decimal places will the decimal expansion of
ଶଷ
ଶ
ర
×
ହ
య
terminate?
1
2
Section

B
7.
The HCF and LCM of
two numbers are 9 and 360 respectively. If one number is 45, find
the other number.
2
OR
Show that
7
−
√
5
is irrational, give that
√
5
is irrational.
8.
Find the 20
th
term from the last term of the AP
3,8,13,....,253
2
OR
If 7 times the 7
th
term of an A.P is equal to 11 times its 11
th
term, then find its 18
th
term.
9.
Find the coordinates of the point P which divides the join of A(

2,5) and B(3,

5) in the ratio
2:3
2
10.
A card is drawn at random from a well shuffled deck of 52 cards.
Find the probability of
getting neither a red card nor a queen.
2
11.
Two dice are thrown at the same time and the product of numbers appearing on them is
noted. Find the probability that the product is a prime number
2
12.
For what value of p will the
following pair of linear equations have infinitely many
solutions
(p

3)x+3y = p
px+py = 12
2
Section

C
13.
Use Euclid’s Division Algorithm to find the HCF of 726 and 275.
3
14.
Find the zeroes of the following polynomial:
5
√
5
x
2
+30x+8
√
5
3
15.
Places A and B are 80 km apart from each other on a highway. A car starts from A and
another from B at the same time. If they move in same direction they meet in 8 hours and if
they move towards each other they meet in 1 hour 20 minutes. Find the speed of
cars.
3
16.
The points A(1,

2) , B(2,3), C (k,2) and D(

4,

3) are the vertices of a parallelogram. Find
the value of k.
3
OR
Find the value of k for which the points (3k

1,k

2), (k,k

7
) and
(k

1,

k

2) are collinear.
17.
Prove that
ࣂ
−
ࣂ
=
ࣂ
ି
ࣂࣂ
3
OR
Prove that
ࣂ
(
+
ࣂ
)
+
ࣂ
(
+
ࣂ
)
=
ࣂ
+
ࣂ
18.
The radii of two concentric circles are 13 cm and 8 cm. AB is a diameter of the bigger circle
and BD is a tangent
to the smaller circle touching it at D and intersecting the larger circle at
P on producing. Find the length of AP.
3