Vidyamandir Classes: Innovating For Your Success
MATHEMATICS
CLASS-X
PAPER-1
Time allowed: 3 hours
Maximum marks: 80
General Instructions:
(i)
This Question Paper has 5 Sections A-E
(ii)
Section A has 20 MCQs carrying 1 mark each.
(iii)
Section B has 5 questions carrying 02 marks each.
(iv)
Section C has 6 questions carrying 03 marks each.
(v)
Section D has 4 questions carrying 05 marks each.
(vi)
Section E has 3 case based integrated units of assessment (04 marks each) with sub-parts of the values of
1, 1 and 2 marks each respectively.
(vii)
All Questions are compulsory. However, an internal choice in 2 Questions of 5 marks, 2 Question of 3
marks and 2 Questions of 2 marks has been provided. An internal choice has been provided in the 2
marks questions of Section E.
(viii) Draw neat figures wherever required. Take  = 22 / 7 wherever required if not stated.
SECTION-A
Section A consists of 20 questions of 1 mark each.
1.
If HCF (26, 169) = 13 then LCM (26, 169) is:
(a)
26
(b)
52
(c)
338
2.
4.
13
(d)
−m, − ( m + 3)
2
The zeroes of the polynomial x − 3 x − m ( m + 3) are:
m, m + 3
(a)
3.
(d)
(b)
−m, m + 3
(c)
m, − ( m + 3)
The value(s) of k for which the quadratic equation 2 x 2 + kx + 2 = 0 has equal roots, is:
4
−4
4
(a)
(b)
(c)
(d)
0
The value of c for which the pair of equation cx − y = 2 and 6 x − 2 y = 3 will have infinitely many
solutions is:
(a)
3
(b)
−3
(c)
−12
(d)
No value
m 
,5  is the mid-point of the line segment joining the points Q ( −6, 7 ) and R ( −2,3) , then the
3 
5.
If A 
6.
value of m is:
−12
−4
12
(a)
(b)
(c)
(d)
−6
QA and PB are perpendicular on AB , if AO = 10 cm , BO = 6 cm and PB = 9 cm , then measure of
AQ (see figure) is:
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Vidyamandir Classes: Innovating For Your Success
(a)
15 cm
(b)
25 cm
(c)
10 cm
(d)
None of these
(d)
90°
4 − sin 45
is 3.5. What is the value of k?
cot k tan 60
2
7.
The value of
(a)
8.
30°
(b)
45°
(c)
60°
If a a cos  + b sin  = m and a sin  − b cos  = n , then a + b is equal to:
2
(a)
m2 − n 2
(b)
m2 n2
(c)
2
n 2 − m2
(d)
m2 + n 2
(d)
2.7 cm
AD 3
= and AE = 2.7 cm, then EC is equal to:
DB 2
9.
In figure, DE || BC . If
10.
(a)
2.0 cm
(b)
Consider the triangles below.
1.8 cm
(c)
4.0 cm
Which statement is correct?
(a)
For triangles to be similar, the measure of A = 40
(b)
For triangles to be similar, the measure of A = 100
(c)
Triangles are similar as all isosceles triangles are similar
(d)
Triangles are similar as corresponding sides of the triangles are in the ratio 1 : 2
11.
The value of (1 + cot  − cosec )(1 + tan  + sec  ) is:
(a)
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(b)
2
(c)
2
−1
(d)
None of these
Mathematics
Vidyamandir Classes: Innovating For Your Success
12.
13.
14.
15.
16.
17.
18.
In the given figure, if PA and PB are tangents to the circle with centre O such that APB = 50 , then
OAB is equal to:
(a)
25°
(b)
30°
(c)
40°
The area of the shaded region in the given figure is (Take  = 3.14 ).
(d)
50°
(a)
75 cm2
(b)
73 cm2
(c)
70 cm2
(d)
None of these
A wheel has diameter 84 cm. The number of complete revolution it takes to cover 792 m is:
(a)
330
(b)
400
(c)
360
(d)
300
Consider the following frequency distribution of the height of 60 students of a class:
Height (in cm) 150-155 155-160 160-165 165-170 170-175 178-180
No. of students
15
13
10
8
9
5
The sum of the lower limit of the modal class and upper limit of the median class is
(a)
310
(b)
315
(c)
320
(d)
330
Two identical solid cubes of side k units are joined end to end. What is the volume, in cubic units, of the
resulting cuboid?
3k 3
6k 3
2k 3
4k 3
(a)
(b)
(c)
(d)
A girl calculates that the probability of her winning the first prize in a lottery is 0.08. If 6,000 tickets are
sold, how many tickets has she bought?
(a)
40
(b)
240
(c)
480
(d)
750
The table below shows the time taken by a group of students to complete 100 m race.
Time taken (in sec) 18-20 20-22 22-24 24-26 26-28 28-30
No. of students
3
18
26
19
9
5
Which of these is the mean time taken, in sec, by the group of students to complete the 100 m race when
calculated using direct method?
(a)
18.16
(b)
18.96
(c)
23.7
(d)
33.7
DIRECTION: In the question numbers 19 and 20, a statement of assertion (A) is followed by a statement of
Reason (R). Choose the correct option.
(a)
Both A and R are true and R is the correct explanation for A.
(b)
Both A and R are true and R is not the correct explanation for A.
(c)
A is true but R is false.
(d)
A is false but R is true.
19.
Assertion (A): For any two positive integers a and b, HCF (a, b) × LCM (a, b) = a × b.
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Reason (R) :
20.
The HCF of two numbers is 5 and their product is 150. Then their LCM is 40.
Assertion(A): The value of y is 6, for which the distance between the points P ( 2, −3) and Q(10, y)
is 10.
Reason (R):
Distance between two given points A( x1, y1 ) and B( x2 , y2 ) is given by
AB =
( x2 − x1 )2 + ( y2 − y1 )2
SECTION-B
Section B consists of 5 questions of 2 marks each.
21.
In the given figure, ABCD is a rectangle. Find the values of x and y.
BE BC
.
=
EC CP
22.
In the given figure, DE || AC and DC || AP , Prove that
23.
If from an external point P of a circle with centre O, two tangents PQ and PR are drawn such that
QPR = 120 , prove that 2PQ = PO .
24.
A race track is in the form of a ring whose inner circumference is 352 m, and the outer circumference is
396 m. Find the width of the track.
OR
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Vidyamandir Classes: Innovating For Your Success
A piece of wire 22 cm long is bent into the form of an arc of a circle subtending an angle of 60° at its


centre. Find the radius of the circle.  Use  =
25.
22 

7 
If sin  = cos  , then find the value of 2 tan  + cos 2  .
OR
If sin 2 A = 2sin A then find the value of A.
SECTION-C
Section C consists of 6 questions of 3 marks each.
(
)
2 is irrational, prove that 5 + 3 2 is an irrational number.
26.
Given that
27.
Quadratic polynomial 2 x 2 − 3x + 1 has zeros as  and  . Now form a quadratic polynomial whose
zeros are 3 and 3 .
28.
A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream
and 55 km downstream. Determine the speed of the stream and that of the boat in still water.
OR
The present age of a father is three years more than three times the age of his son. Three years hence the
father's age will be 10 years more than twice the age of the son. Determine their present ages.
29.
If sin  + cos  = 3 , then prove that tan  + cot  = 1 .
30.
A quadrilateral ABCD is drawn to circumscribe a circle (see Fig.).
Prove that AB + CD = AD + BC
31.
OR
Prove that the lengths of two tangents drawn from an external point to a circle are equal.
Two different dice are thrown together. Find the probability that the numbers obtained
(i) have a sum less than 7
(ii) have a product less than 16
(iii) is a doublet of odd numbers
SECTION-D
Section D consists of 4 questions of 5 marks each.
32.
Two taps running together can fill a tank in 3
1
hours. If one tap takes 3 hours more than the other to
13
fill the tank, then how much time will each tap take to fill the tank?
OR
A motor boat whose speed is 18 km/h in still water takes 1 hour more to go 24 km upstream than to
return downstream to the same spot. Find the speed of the stream.
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Vidyamandir Classes: Innovating For Your Success
33.
34.
Through the mid-point M of the side CD of a parallelogram ABCD, the line BM is drawn intersecting AC
at L and AD produced to E. Prove that EL = 2BL.
A right triangle with sides 3 cm and 4 cm is revolved around its hypotenuse. Find the volume of double
cone thus generated. (Use  = 3.14).
OR
In the given figure a decorative block is shown which is made of two solids, a cube and a hemisphere.
The base of the block is a cube with edge 6 cm, and the hemisphere fixed on the top has a diameter of
4.2cm. Find.
(i)
the total surface area of the block
(ii)
35.


the volume of the block formed.  Use  =
22 

7 
If the median of the following frequency distribution is 32.5. Find the values of f1 , and f 2 .
Class
0-10 10-20 20-30 30-40 40-50 50-60 60-70 Total
2
40
f2
f1
Frequency
5
9
12
3
SECTION-E
Case study based questions are compulsory.
36.
Your friend Veer wants to participate in a 200 m race. He can currently run that distance in 51 seconds
and with each day of practice it takes him 2 seconds less. He wants to complete it in 31 seconds.
Based on the above information answer the following questions.
(i)
What is the minimum number of days he needs to practice till his goal is achieved?
(ii)
What is the AP formed in this situation?
(iii)
If nth term of an AP is given by an = 2n + 3 , then write its common difference.
OR
Write the value of x, for which 2 x, x + 10,3x + 2 are three consecutive terms of the AP.
37.
Shown below is a town plan on a coordinate grid, where 1 unit = 1 km. Consider the co-ordinates of each
building to be the point of intersection of the respective grid lines.
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Vidyamandir Classes: Innovating For Your Success
38.
Based on the above information answer the following questions.
(i)
What is the distance between the School and House 1 along the path shown?
(ii)
What is the ratio in which House 1 divides the path joining house 3 and the police station?
(iii)
What is the shortest distance between the school and House 3?
OR
Write the shortest distance between House 2 and House 5.
A group of students of class X visited India Gate on an education trip. The teacher and students had
interest in history as well. The teacher narrated that India Gate, official name Delhi Memorial, originally
called All-India War Memorial, monumental sandstone arch in New Delhi, dedicated to the troops of
British India who died in wars fought between 1914 and 1919. The teacher also said that India Gate,
which is located at the eastern end of the Rajpath (formerly called the Kingsway), is about 138 feet (42
metres) in height.
Based on the above information answer the following questions.
(i)
What is the angle of elevation if they are standing at a distance of 42 m away from the
monument?
(ii)
They want to see the tower at an angle of 60°. So, where should they stand?
(iii)
If the altitude of the Sun is at 60° then what is the height of the vertical tower that will cast a
shadow of length 20 m?
OR
If the ratio of the length of a rod and its shadow is 1:1. Then find the angle of elevation of the Sun.
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