DON BOSCO SCHOOL - ALAKNANDA- NEW DELHI- 110 019

Pre- Boards MATHEMATICS- 041 (Standard) MM-80

Time: 3hrs CLASS10 13-01-2023

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 subparts of the value of 1, 1 and 2 marks each respectively.
7. All Questions are compulsory.
8. Draw neat figures wherever required. Take π =22/7 wherever required if not stated.

SECTION A

Q 1- Q 20 are multiple choice questions. Select the most appropriate answer from the given options.

Q1) The LCM of the smallest two digit prime number and smallest composite number is
a) 11 b) 4 c) 22 d) 44

Q2) Let p be a prime number. The quadratic equation having its roots as factors of p is
a) x2 –px +p=0 b) x2 –(p+1)x +p=0 c) x2+(p+1)x +p=0 d) x2 –px+p+1=0

Q3) For what value of k , the equation 9x2 + 6kx + 4 =0 has equal roots?
a) k = 2 b) k = -2 c) k = 0 d) Both (a) and (b)

Q4) For which value of k, will the lines represented by the following pair of linear
equations be parallel: 8x + k y = 10 and 4x + 2y =20
a) 4 b) 1 c) 5/2 d) ½

Q5)The point which divides the line segment joining the points (8, – 9) and (2, 3) in
ratio 1 : 2 internally lies in the
a) Ist quadrant b) IInd quadrant c) IIIrd quadrant d) IVth quadrant

Q6) ∆ABC~∆PQR. If AM and PN are altitudes of ∆ABC and ∆PQR respectively

and AB2: PQ2 = 4 : 9, then AM : PN =
(a) 3:2 (b) 16:81 (c) 4:9 (d) 2:3

Q7) If triangle ABC is right angled at C, then the value of sin (A+B) is
a) 0 b) 1 c) not defined d) none of the above
Q8) tan x + cot x = 2 then tan2 x + cot2 x = ……………………………
a) 2 b) 4 c) 0 d) 6

Q9) Two ………………….. triangles are always similar

a) scalene b) isosceles c) right angled d) equilateral

Q10) ABCD is a trapezium in which AB is parallel to CD and DC = 3 AB.

If the diagonals intersect at O then AO: OC is
a) 3:1 b) 3:4 c) 1:3 d) 1:4

Q11) The angle between radius and tangent at the point of contact is
a) 45 degrees b) 90 degrees c) 180 degrees d) 360 degrees

Q12) The area of the circle that can be inscribed in a square of 6cm is
a) 36π cm2 b) 18π cm2 c) 12 π cm2 d) 9π cm2

Q13) If the diagonal of a cube is √3 cm then volume of the cube is …………..

a)3cm3 b) 3√3cm3 c) 1 cm3 d)9cm3

Q14) Q2) Median= 3 , Mean = 2.5 then Mode =

a) 2.5 b) 3.0 c) 3.5 d) 4.0

Q15) length of arc of sector 90⸰ and radius 14cm is …………………..

a)22cm b) 44cm c) 88cm d) 11cm

Q16) The modal class is ………………………………………

CI 10-20 20-30 30-40 40-50 50-60

fi 6 16 11 18 3

a)50-60 b) 20-30 c) 30-40 d) 40-50

Q17) The probability of getting atmost (2 Heads) on tossing 2 coins is

a)0 b) 1 c) 2 d) 1/2

Q18) If sin x = √3cos x the x in degrees is …………………

a)0 b) 30 c) 45 d)60
DIRECTION: In the question number 19 and 20, a statement of assertion (A) is followed
by a statement of Reason (R). Choose the correct option

Q19) Statement A (Assertion): If product of two numbers is 5780 and their HCF is 17, then
their LCM is 340. Statement R( Reason) : HCF is always a factor of LCM

(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 and 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.

Q 20) Statement A (Assertion): If the co-ordinates of the mid-points of the sides AB and AC of
∆ABC are D(3,5) and E(-3,-3) respectively, then BC = 20 units. Statement R( Reason) : The
line joining the mid points of two sides of a triangle is parallel to the third side and equal to half
of it.

(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 and 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

Section B consists of 5 questions of 2 marks each.

Q21) 2x + 3y = 6 and 3x + 2y = 5 find x and y

Q22) Using converse of Basic Proportionality Theorem, prove that the line joining the mid
Points of any 2 sides of a triangle is parallel to the third side.

Q23) If the angle between two tangents drawn from an external point ‘P’ to a circle of radius ‘r’
and centre O is 60 degrees, then find the length of OP.
Q24) The wheels of a car are of diameters 80cm each. How many complete revolutions does each wheel

make in 10 minutes when the car is travelling at a speed of 66 km per hour.

1
Q25) sin x = then find the value of cos (x + 60)
2

SECTION C
Section C consists of 6 questions of 3 marks each.

Q26) Prove that √7 is an irrational number

Q27) Find the zeroes of the polynomial x2 – 18 and verify the relation between the zeroes
and the coefficients
Q28) Find the roots of the of the quadratic equation: 5√5x2 + 30x + 8√5 = 0
Q29) Prove: (sin A + cosec A)2 + (cos A + sec A)2 = 7 + tan2A + cot2A
Q30) Prove that a parallelogram circumscribing a circle is a rhombus.
Q31) One card is taken at random from a pack of 52 cards.
Find a) P(red king) b) P(ace) c) P(spade)

SECTION D
Section D consists of 4 questions of 5 marks each.

Q32) A train covers a distance of 360 km at a uniform speed. Had the speed been 5km/hr more, it would
have taken 48 minutes less for the journey. Find the original speed of the train.
Q33) Prove that if a line is drawn parallel to one side of a triangle intersecting the other two sides
in distinct points, then the other two sides are divided in the same ratio
Q34) Due to heavy floods in a state, thousands were rendered homeless. 50 schools collectively
decided to provide place and the canvas for 1500 tents and share the whole expenditure
equally. The lower part of each tent is cylindrical with base radius 2.8 m and height 3.5 m
and the upper part is conical with the same base radius, but of height 2.1 m. If the canvas
used to make the tents costs ₹120 per m2
Find the amount shared by each school to set up the tents.

Q35) Find the mean, mode and median number of letter in the surnames.

Number of 1-4 4 -7 7 - 10 10 - 13 13 - 16 16 - 19
letters

Number of 6 30 40 16 4 4
surnames
 SECTION E
Case study based questions

Q36) In a class, the teacher asks every student to write an example of A.P. Two friends Geeta
and Madhuri writes their progressions as -5, -2, 1,4, ... and 187, 184, 181, .... respectively. Now,
the teacher asks various students of the class the following questions on these two progressions.
Help students to find the answers of the questions.

(a) Find the 34th term of the progression written by Madhuri.

(b) Find the sum of common difference of the two progressions.

(c) Which term of the two progressions will have the same value?

Q37) 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.
Based on the above information answer the following questions using the map given

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)

Q38) A Satellite flying at height h is watching the top of the two tallest mountains in
Uttarakhand and Karnataka, them being Nanda Devi(height 7,816m) and Mullayanagiri (height
1,816 m). The angles of depression from the satellite, to the top of Nanda Devi and
Mullayanagiri are 30° and 60° respectively. If the height of the satellite from the ground is
9816m then answer the following questions.

a)What is the angle of elevation if a man is standing at a distance of 7816m from Nanda Devi?
b) Find the distance of the satellite from the top of Nanda Devi
c) Find the distance of the satellite from the top of Mullayanagiri