SATHYAM INTERNATIONAL SCHOOL – CBSE

SR.SEC.SCHOOL, AFFILIATED TO CBSE, NEW DELHI

AFFILIATION NO: 1930707

VELLAKOVIL

SUBJECT: MATHEMATICS MARKS: 80

GRADE: X 50 % TEST -2 (ch: 1,2,7,9,10,14,15)

DURATION: 3 HRS

General Instructions:
1. This Question Paper has 5 Sections A-E.
2. Section A has 20 MCQs carrying 1 mark each
3. Section B has 5 questions carrying 02 marks each.
4. Section C has 6 questions carrying 03 marks each.
5. Section D has 4 questions carrying 05 marks each.
6. 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.
7. All Questions are compulsory. However, an internal choice in 2 Qs of 5 marks, 2 Qs
of 3 marks and 2 Questions of 2 marks has been provided. An internal choice has
been provided in the 2marks questions of Section E
8. Draw neat figures wherever required. Take π =22/7 wherever required if not stated.

SECTION A 20 X 1=20

Section A consists of 20 questions of 1 mark each.

1. The HCF of smallest 2 digit composite number and the largest two digit prime number is
(a)2 (b)0 (c)10 (d)1
2.HCF of 52 X 32 and 35 X 53 is
(a) 53 X 35 (b) 5 X 33 (c) 53 X 32 (d) 52 X 32
3. If the LCM (a,18) = 36 and the HCF (a,18) = 2, find a.
(a)1 (b) 2 (c)3 (d)4
4. A quadratic polynomial, whose zeroes are -3 and 4, is
(a) x2 - x + 12 (b) x2 + x + 12 (c) x²/2 - x/2 – 6 (d) 2x2 + 2x -24
5. If α and β are the zeroes of f(x) = 2x2 + 8x – 8, then prove that α + β – αβ = 0
(a) α + β + αβ = 0 (b) α + β = αβ (c) α + β < αβ (d) α + β > αβ
6. A ladder leans a wall making an angle of 60owith the ground. The foot a the ladder is 2 m away
from the wall. The length of the ladder is:
(a)8 cm (b)6 cm (c)4 cm (d)2cm
7. A pole 6m high casts a shadow 2√ 3 m long on the ground, then the Sun’s elevation is

(a) 60∘ (b) 45∘ (c) 30∘ (d) 90∘

8. In the following figure, AB is a chord of the circle and AOC is its diameter such that ACB = 50°.
If AT is the tangent to the circle at the point A, then BAT is equal to

(a) 65° (b) 60° (c) 50° (d) 40°

9. In given figure, CP and CQ are tangents to a circle with centre O. ARB is another tangent touching
the circle at R. If CP = 11 cm and BC = 6 cm then the length of BR is

(a) 6 cm (b) 5 cm (c) 4 cm (d) 3 cm

10.If TP and TQ are the two tangents to a circle with centre O so that ∠POQ = 110°, then ∠PTQ is
equal to

(a) 60° (b) 70° (c) 80° (d) 90°

11. If the distance between the points A(2, -2) and B(-1, x) is equal to 5, then the value of x is:

(a) 2 (b) -2 (c) 1 (d) -1

12. The distance of the point P(–6, 8) from the origin is

(a) 8 units (b) 2√7 units (c) 10 units (d) 6 units

13.Two cubes have their volumes in the ratio 1 :27, find the ratio of their surface areas.
(a)1 :2 (b)1:3 (c)1 :4 (d)1 :9
14. Consider the following frequency distribution of the heights of 60 students of a class:
Height (in 150 – 155 155 – 160 160– 165 165 – 170 170 – 175 175 – 180
cm)
Number of 15 13 10 8 9 5
students
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
15. If the mean of frequency distribution is 7.5 and ∑fi xi = 120 + 3k, ∑fi = 30, then k is equal to:
 (a) 40 (b) 35 (c) 50 (d) 45
16.The mean and median of a same data are 24 and 26 respectively. Find the mode of same data.
(a)30 (b) 31 (c)40 (d)41

17. If a number x is chosen at random from the numbers -2, -1, 0, 1, 2. What is the probability that x2<2 ?
(a) 1/5 (b)2/5 (c)3/5 (d)4/5
18.Two unbiased dice are thrown. The probability that the total score is more than 5 is:
(a)1/18 (b)5/18 (c)7/18 (d)13/18
19.Assertion: Anvi and Manvi were born in the year 2000. The probability that they have same
birthday is 1/ 366.
Reason: Leap year has 366 days.
(a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of
assertion(A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of
assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true
20.Assertion: The distance of the point (2, 11) from the x -axis is 11 units.
Reason: The distance of the point (x ,y ) from the x -axis is its ordinate, i.e, y -axis.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of
assertion(A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of
assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true

SECTION B 5 x 2 = 10
Section B consists of 5 questions of 2 marks each.
21. M and N are positive integers such that M = p2 q³r and N=p³ q2, where p,q,r are prime numbers.
Find LCM(M, N) and HCF(M, N).

22. In what ratio is the line joining (2,−3) and (5,6) divided by the x-axis.

23. An observer 1.7 m tall, is 20√3 away from a tower. The angle of elevation from the eye of observer to
the top of tower is 30◦. Find the height of tower. (OR)

A kite is flying at a height of 60m above the ground. The string attached to the kite is temporarily tied to
a point on the ground. The inclination of the string with the ground is 60o. Find the length of the string
assuming that there is no slack in the spring.

24.Find the mean of the following distribution:

CLASS 3 -5 5 -7 7 -9 9 -11 11 -13
FREQUENCY 5 10 10 7 8
25. A game consists of tossing a one rupee coin 3 times and noting its outcome each time. Hanif wins if all
the tosses give the same result i.e., three heads or three tails, and loses otherwise. Calculate the probability that
Hanif will lose the game. (OR)

A bag contains 5 red, 8 white and 7 black balls. A ball is drawn at random from the bag. Find the probability
that the drawn ball is (i) red or white (ii) not black (iii) neither white nor black.

SECTION - C 6 x 3 =18
consists of 6 questions of 3 marks each
26. Show that 5 + 2 √7 is an irrational number, where √7 is given to be an irrational number.

27. If one root of the quadratic equation 3x2 + px + 4 = 0 is 2 /3, then find the value of p and the
other root of the equation. (OR)
The roots α and β of the quadratic equation x2−5x+3(k−1)=0 are such that α−β=11 Find the value
of k.

28. Find the ratio in which P(4, m) divides the line segment joining the points A(2, 3) and B(6, –3).
Hence find m.
29.From a point P outside a circle having a circle centre at O , tangents PQ and PR are drawn to a
circle . Prove that OP is the right bisector of line segment QR. (OR)
Prove that tangents drawn from an external point to a circle are equal in lengths.

30. The mode of the following distribution is 55, then find the value of x.

CLASS FREQUENCY
0-15 10
15 -30 7
30 -45 x
45 -60 15
60 -75 10
75- 90 12

31. A piggy bank contains hundred 50p coins, fifty Rs1 coins, twenty Rs.2 coins and ten Rs.5
coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down,
what is the probability that the coin (i) will be a 50p coin ? (ii) will not be a Rs.5 coin? (iii) will be
RS. 2 coin.

SECTION - D 4 x 5 = 20
Section D consists of 4 questions of 5 marks each.

32. If α, β are the zeros of the quadratic polynomial f(x)=2x2−5x+7. Find a polynomial whose zeros
are 2α+3β and 3α+2β.
33. As observer from the top of a lighthouse 100m high observe sea level, the angle of depression of
a ship sailing directly towards it, changes from 30◦ to 60◦. Determine the distance travelled by the
ship during the period of observation. (OR)
A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the ground, the angle of
elevation of the top of the statue is 60° and from the same point the angle of elevation of the top of
the pedestal is 45°. Find the height of the pedestal.

34. Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the
centre of the circle.

35. If the median of the distribution given below is 28.5, find the values of x and y.

(OR)
If the mean of the following frequency distribution is 91, and sum of frequencies is 150, find the
missing frequency x and y:
CLASS FREQUENCY
0-30 12
30 -60 21
60-90 x
90 -120 52
120 -150 y
150 -180 11
TOTAL 150

SECTION E 3 X 4 = 12

Case study based questions are compulsory.

Section E consists of 3 questions of 4 marks each.

36. Aditi plantations have two rectangular fields of the same. width but different lengths. They are
required to plant 168 trees in the smaller field and 462 trees in the larger field. In both fields, the
trees will be planted in the same number of rows but in different number of columns.
(a) What is the maximum number of rows in which the trees can be planted in each of the fields?
(b) If the trees are planted in the number of rows obtained in part (i), how many columns will each
fields have?
(c) If total cost of planted trees in one column is ₹500, then find the cost to plant the trees in smaller
field. (or)
If total cost of planted trees in one column is ₹ 500, then find the cost to plant the trees in larger
field.
37. In a GPS, The lines that run east-west are known as lines of latitude, and the lines running north-
south are known as lines of longitude. The latitude and the longitude of a place are its coordinates
and the distance formula is used to find the distance between two places. The distance between two
parallel lines is approximately 150 km. A family from Uttar Pradesh planned a round trip from
Lucknow (L) to Puri (P) via Bhuj (B) and Nashik (N) as shown in the given figure below.

(a)Find the distance between Lucknow (L) to Bhuj(B).

(b)If Kota (K), internally divide the line segment joining Lucknow (L) to Bhuj (B) into 3 : 2 then
find the coordinate of Kota (K).
(c)Name the type of triangle formed by the places Lucknow (L), Nashik (N) and Puri (P) (or)
Find a place (point) on the longitude (y-axis) which is equidistant from the points Lucknow (L) and
Puri (P).
38. Ram Gopal has 20 tickets on which numbers are written from 1 to 20. He mixed thoroughly all
the tickets and then a ticket is drawn at random out of them.
a) Find the probability that drawn ticket bears a number, which is multiple of 3.
(b) Find the probability of drawing a prime number ticket.
c)Find the probability of getting a perfect square number ticket.
d) Find the probability of getting an even number.