Practice Paper-I

Time Allowed: 3 Hrs Maximum Marks : 80

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 Questions of 5 marks,
2 Questions 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.
22
8. Draw neat figure wherever required. Take π = wherever required if not stated.
7
SECTION A

Section A consists of 20 questions of 1 mark each.

S.No Marks
1 The HCF of k and 93 is 32, where k is a natural number. 1
Which of these can be true for some values of k?
(i) K is a multiple of 31
(ii) K is a multiple of 93
(iii) K is an even number
(iv) K is an odd number
(a) Only (ii and (iii) (b) only (i) (ii) and (iii)
(b) Only (i), (iii) and (iv) (d) all
2 𝐴𝐵 𝐵𝐶 𝐶𝐴 1
If in triangles ABC and PQR, = = , then
𝑄𝑅 𝑃𝑅 𝑃𝑄
(a)∆ PQR ~ ∆ CAB (b) )∆ PQR ~ ∆ ABC
(c) )∆CBA ~ ∆ PQR (d) )∆ BCA ~ ∆ PQR
3 In the figure below, DE || AC and DF || AE, Which of these is equal to 1
BF
?
FE

DF BE BA FE
(𝑎) AE (b) EC (c) AC (d) EC

4 If the nth term of an A.P : -1, 4, 9, 14,….. is 129, find the value of n. 1

(a)25 (b) 27 (c) 28 (d) 26

5 If x = 2sin2𝜃 and y = 2cos2𝜃 + 1, then find the value of x + y. 1
(a)1 (b) 2 (c) 3 (d) 4
6 If the discriminant of the equation 6x2 + bx + 2 = 0 is 1, then the value of b: 1
is:
(A)7 (B)-7 (C)±7 (D) √7

7 If am ≠bl, then the system of equations ax + by = c and lx + my = n 1

(a)has a unique solution (b) has no solution
(c)has infinitely many solutions (d) may or may not have a solution
8 The vertices of a parallelogram in order are A(1 ,2), B(4 , y) , C(x , 6) and 1
D(3 , 5). Then (x ,y) is:
(a) (6 , 3) (b) (3 , 6) (c) (5 , 6) (d) (1 , 4)
9 If the equation ax2 + 2x + a = 0 has two distinct roots, if 1
(a)a = ±1 (b) a = 0 (c) a = 0, 1 (d) a = -1, 0
10 The angle of depression of a car parked on the road from the top of a 150m 1
high tower is 300. The distance of the car from the tower (in metres) is:
(a)50√3 (b) 150√3 (c) 150√2 (d) 75
11 ABC is a triangle such that AB:BC = 1:2. Point A lies on the y-axis and the 1
coordinates of B and C are known:
Which of the following can definitely be used to find the coordinates of A?
(i) section formula
(ii) distance formula
(a)only (i) (b) only (ii)
(c) both (i) and (ii) (d) neither (i) or (ii)
12 If one zero of the polynomial f(x) = (k2 + 4)x2 + 13x + 4k is reciprocal of the 1
other, then k =
(a)2 (b) -2 (c) 1 (d) -1
13 For what value of k will k + 9, 2k – 1 and 2k + 7 are the consecutive terms 1
of an A.P?
(a)14 (b) 2 (c) 18 (d) 8
14 If an event that cannot occur, then its probability is: 1
3 1
(a)1 (b) 4 (c) 2 (d) 0
15 The value of k for which the system of equations x + 2y = 5 and 3x + ky + 1
15 = 0 has no solution is
3
(a)6 (b) -6 (c) 2 (d) None
16 Which of the following cannot be the probability of an event? 1

16 17
(a)0.01 (b) 3% (c) 17 (d) 16
17 If the product of zeroes of the polynomial f(x) = ax3 - 6x2 + 11x – 6 is 4, then 1
value of a is:
3 −3 2 −2
(a)2 (b) 2 (c) 3 (d) 3
18 The value(s) of k for which the quadratic equation 2x2 + kx + 2 = 0 has equal 1
roots, is
(a)4 (b)±4 (c)-4 (d) 0
19 DIRECTION: In the question number 19 and 20, a statement of 1
Assertion(A) is followed by a statement of Reason (R).
 Choose the correct option.
(a) Both Assertion(A) and Reason (R)are true and Reason (R)is a correct
explanation of Assertion(A)
(b) Both Assertion(A) and Reason (R)are true and Reason (R)is not a correct
explanation of Assertion(A)
(c) Assertion (A) is true and Reason (R ) is false.
(d) Assertion (A) is false and Reason (R ) is true.

Statement A (Assertion): The line of sight is the line drawn from the eye
of an observer to the point in the object viewed by the observer.

Statement R (Reason) :Trigonometric ratios are used to find height or

length of an object or distance between two distant objects.
20* Statement A (Assertion): If Sn is the sum of the first n terms of an A.P , 1
then its nth term is given by an = Sn – Sn-1.

Statement R (Reason) : The 10th term of the A.P 7, 10, 13, 16,….. is 37.

SECTION B

Section B consists of 5 questions of 2 marks each.

S.No Marks
21 Find the point on X-axis which is equidistant from the points (2, -2) and 2
(-4, 2).
22 Determine the values of p and so that the prime factorisation of 2520 2
expressible as 23 × 3p × q× 7
23 The King, Queen and Jack of clubs are removed from a pack of 52 cards 2
and then the remaining cards are well shuffled. A card is selected from the
remaining cards. Find the probability of getting a card
(i) of spade
(ii)of Black King
24 Solve : 99x + 101 y = 499 ; 101x + 99y = 501 2
(OR)
Find the values of p for the lines represented by the following pair of
equations -3x + 5y = 7 and 2px – 3y = 1 are intersecting at a unique point.
25 Find the sum of the first 20 terms of the A.P 1, 4, 7, 10,…… 2
(OR)
Find the sum of first 8 multiples of 3.

SECTION C
S.No Section C consists of 6 questions of 3 marks each. Marks
26 Two right triangles ABC and DBC are drawn on the same hypotenuse BC 3
and on the same side of BC. If AC and BD intersect at P, prove that
AP × PC = BP × DP
27 Ten years ago, father was twelve times as old as his Son and ten years 3
hence, he will be twice as old as his Son will be. Find their present ages.
 28 The line segment joining the points A(2, 1) and B(5, -8) is trisected at the 3
points P and Q such that P is nearer to A. If P also lies on the line given by
2x – y + k = 0 , find the value of k.
(OR)
If the point C(-1, 2) divides internally the line segment joining A(2,5) and
B(x,y) in the ratio 3:4, find the coordinates of B.
29 In similar triangles ABC and PQR, AD and PM are the medians 3
AD AB
respectively. Prove that PM = PQ
30 Prove that 7 – 2√3 is an irrational number 3
(OR)
In a seminar, the number of participants in Hindi, English and Maths are
60, 84 and 108 respectively. Find the minimum number of rooms required,
if in each room the same number of participants are to be seated and all of
them being in the same subject.
31* Prove that (sin4𝜃 –cos4𝜃+1) cosec2𝜃 =2 3

SECTION D

S.No Section D consists of 4 questions of 5 marks each Marks

32 The shadow of a tower standing on a level ground is found to be 40m 5
longer when the Sun’s altitude is 300 than when it was 600. Find the height
of the tower.[√3 = 1.732].

(OR)
As observed from the top of a light house, 100m high above sea level, the
angles of depression of a ship, sailing directly towards it, changes from 300
to 600. Find the distance travelled by the ship during the period of
observations.{√3 = 1.73]

33 Sides AB and BC and median AD of a triangle ABC are respectively 5

proportional to sides PQ and QR and median PM of ∆PQR . Show that
∆ABC~∆PQR.

34 The denominator of a fraction is one more than twice the numerator. If 5

16
the sum of the fraction and its reciprocal is 221, find the fraction.
(OR)
A shop keeper buy certain number of books for 80. If he buy 4 more books
then new cost price of each book is reduced by 1. Find the number of books
initially be buy.

35* The sum of four consecutive numbers in an A.P is 32 and the ratio of the 5
product of the first and the last term to the product of two middle terms is
7:15. Find the numbers.
 SECTION E

S.No Case study based questions are compulsory Marks

36 Rohan is very intelligent in Maths. He always try to relate the concept of
Maths in daily life. One day he is walking away from the base of a lamp
post at a speed of 1m/s. Lamp is 4.5m above the ground.

(i) If after 2 seconds, the length of shadow is 1 metre, what is the

height of Rohan? 1
(ii) What is the maximum time after his shadow will become larger
than his original height? 2
(iii) What is the distance of Rohan from pole at this point?
(OR) 1
What will be the length of his shadow after 4 seconds ?
37 Two aeroplanes leave an airport,
one after the other. After moving
on runway, one flies due North and
the other flies due South. The speed
of two aeroplanes are 400 km/hr
and 500 km/hr respectively.
Considering PQ as runway and A
and B are any two points in the
path followed by two planes, then
answer the following questions.
(i) Find tan 𝜃 if <APQ = 𝜃
(ii) Find cot B
(iii) If 𝜃 = 300, find the value of: 1
𝜃 𝜃 1
sin 𝜃 cos – cos 𝜃 sin
2 2 2

38* The Chief Minister of Delhi launched the

“Swatch Delhi” an electric vehicle mass
awareness campaign in the National Capital.
The Government has also issued tenders for
setting up 100 charging stations across the city.
Each station will have five charging points.
Charging station is set up along a straight line
and has charging points at:
 −7 7
A( 3 , 0) , B (0 , 4 )(), C(3 , 4) , D(7 , 7) and E (x , y). Also the distance
between C and E is 10 units.
Based on the above information, answer the following questions.
(i) Find the distance DE
(ii) Find the value of x + y
(iii) Find the ratio in which B divides AC.
(OR) 1
Find the ratio in which C divides AE. 1
2