**Class – X (Session: 2023-24)**

**Subject- Mathematics (Standard-041)**

**Time Allowed: 3Hrs Maximum Marks:80**

__General Instructions__ for Class 10 Maths Sample Paper 2023-24

__General Instructions__for Class 10 Maths Sample Paper 2023-24

**This Question Paper has 5 Sections A-E****Section A has 20 MCQs carrying 1 mark each****Section B has 5 questions carrying 02 marks each.****Section C has 6 questions carrying 03 marks each.****Section D has 4 questions carrying 05 marks each.****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.****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****Draw neat figures wherever required. Take π =22/7 wherever required if not stated.**

** SECTION A**

** Class 10 Maths Sample Paper 2023-24**

**Section A consists of 20 questions of 1mark each**

1. | ‘a’ and ‘b’ are two positive integers, where a >b and ‘b’ is a factor of ‘a’, then HCF (a,b) is : b (b) a (c) ab (d) |

2. The product of three consecutive positive integers is divisible by

(a) 4 (b) 6 (c) 2 (d) 3

3. Three farmers have 490 kg, 588 kg and 882 kg of wheat respectively. Find the maximum capacity of a bag so that the wheat can be packed in exact number of bags.

(a) 98 kg (b) 290 kg (c) 200 kg (d) 350 kg

4. | The number of zeroes that the polynomial f(x) = (x-2)^{2} + 4 can have is 1 (b) 0 (c) 2 (d) 3 | ||

5. | The value of k for which the system of equations (k-3)x + 3y = k kx + ky = 12 has infinite number of solutions is (b) 4 (d) 6 | ||

6. The (n – 1)^{th} term of the A.P. 7,12,17, 22,……. is

(a) 5n + 2 (b) 5n + 3 (c) 5n – 5 (d) 5n – 3

- 7. In ∆ ABC, DE || AB. If CD = 3 cm, EC = 4 cm, BE = 6 cm, then DA is equal to

(a) 7.5 cm (b) 3 cm (c) 4.5 cm (d) 6 cm

- 8. If in ∆ABC and ∆DEF, = , then they will be similar, if

(a) ∠B = ∠E (b) ∠A = ∠D (c) ∠B = ∠D (d) ∠A = ∠F

- 9. ABCD is a trapezium in which AB|| DC and P, Q are points on AD and BC respectively such that PQ || DC. If PD = 18 cm, BQ = 35 cm and QC = 15 cm, find AD.

(a) 55cm (b) 57cm (c) 60cm (d) 62cm

10. The line segment joining the points (3, -1) and (-6, 5) is trisected. The coordinates of one of the points of trisection is

(a) (3, 3) (b) (- 3, 3) (c) (3, – 3) (d) (-3,-3)

11. If (a/3, 4) is the mid-point of the line segment joining the points P(-6, 5) and R(-2, 3), then the value of ‘a’ is

(a) 12 (b) -6 (c) -12 (d) -4

12. | If cot = ,then the value of is _{} (a) (b) (c) 3 (d) |

13. 5 tan² A – 5 sec² A + 1 is equal to

(a) 6 (6) -5 (c) 1 (d) -4

14. **AB is a chord of the circle and AOC is its diameter such that angle **∠**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°

15. The volumes of two spheres are in the ratio 27 : 8. The ratio of their curved surface areas is:

(a) 9 : 4 (b) 4 : 9 (c) 3 : 2 (d) 2 : 3

16. The relationship between mean, median and mode is

(a) mode = median – 2 mean (b) mode = 3 median – 2 mean

(c) mode = 2 median – 3 mean (d) mode = median – mean

17. If the probability of an event is P, the probability of its complementary event will be:

(a) P – 1 (b) P (c) 1 – P (d) -1 – P

18. The probability that a non-leap year selected at random will contain 53 Sundays is:

(a) 1/7 (b) 2/7 (c) 3/7 (d) 5/7

DIRECTION: In the question number 19 and 20, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as: (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.

19. **Assertion: AB and CD are two parallel chords of a circle whose diameter is AC. Then AB = CD.**

**Reason : Perpendicular from the centre of a circle does not bisects the chord.**

20. **Assertion: Frequency is the number of times a particular observation occurs in data.**

**Reason: Data can be grouped into class intervals such that all observations in that range belong to that class.**

** SECTION B Class 10 Maths Sample Paper 2023-24 **

** Section B consists of 5 questions of 2 marks each.**

21. Solve the following pair of linear equations in two variables.

ax+ by+ a=0

bx+ay +b=0

22. If 5 tanA= 4, find the value of

OR

Find the value of A , if + = 4 , A 90^{0}

23. If AB is a diameter of a circle with centre O and AT is a tangent. If 58^{0} , find ATQ.

24. The length of the minute hand of a clock is 14cm. Find the area swept by minute hand in 10 mins.

25. Two different dice are tossed together.Find the probability

(i) of getting a doublet

(ii) of getting a sum 10 of the numbers on the two dice.

**OR**

A card is drawn at random from a well shuffled deck of playing cards . Find the probability that the card drawn is

- a card of spade or an ace
- either a king or a queen

**SECTION C**

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

26. Prove that 2- 3 is irrational.

27. A part of monthly Hostel charge is fixed and the remaining depends on the number of days one has taken food in the mess. When Swati takes food for 20 days, she has to pay Rs.3000 as hostel charges whereas, Mansi who takes food for 25 days pays Rs.3500 as hostel charges. Find the fixed charges and the cost of food per day.

28. A train travels 180 km at a uniform speed . If the speed had been 9km/hr more, it would have been taken 1 hour less for the same journey. Find the speed of the train.

OR

The speed of boat in still water is 15 km/h. It can go 30 km upstream and return downstream to the original point in 4 hours and 30 minutes. Find the speed of the stream.

29. A girl of height 90 cm is walking away from the base of a lamp-post at a speed of 1.2 m/s. If the lamp is 3.6 m above the ground, find the length of her shadow after 4 seconds.

30. Prove that (1+cotA-cosecA) (1+tanA+ secA) =2

OR

If secA + tanA= p, prove that sin A =

31. A tent is in the shape of a right circular cylinder up to a height of 3 m and conical above it.The total height of the tent is 13.5 m and radius of bases is14 m .Find the cost of cloth required to make the tent at the rate of rupees 80 per metre square.

**SECTION D** Class 10 Maths Sample Paper 2023-24

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

32. A Manufacturer of TV sets produced 600 sets in the third year and 700 sets in the 7^{th} year assuming that the production increases uniformly by a fixed number every year,find

(i) the production in the first year

(ii) production in the 10^{th} year.

(iii)The total production in first 7 years.

OR

If the sum of first four terms of an AP is 40 and that of first 14 terms is 280, find the sum of its first n terms.

33. Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of ∆PQR (see in given figure). Show that ∆ABC ~ ∆PQR.

34. The angle of elevation of an aeroplane from a point on the ground is 60 degree. After a flight of 30 seconds the angle of elevation becomes 30 degree. If the aeroplane is flying at a constant height of 3000√3 metres.Find the speed of the aeroplane

OR

At a point A, 20 m above the level of water in a lake ,the angle of elevation of a cloud is 30 degree. The angle of depression of the reflection of the cloud in the lake, at A is 60 degree. Find distance of the cloud from A.

35. The following table gives the daily income of 50 workers of a factory.Find the mode and median of the data.

Daily income(Rs) | 100-120 | 120-140 | 140-160 | 160-180 | 180-200 |

No. of workers | 12 | 14 | 8 | 6 | 10 |

**SECTION E**

** Case study based questions are compulsory**

36. Students of a DAV school are standing in a rows and columns in their playground for a drill practice . A,B,C and D are the positions of 4 students as shown in figure.

On the basis of above information, answer the following questions.

- Find the mid point of BD
- Find the distance between A and D.
- If the point P divides the line segment AC in the ratio 1:2 , then find the coordinates of P.

OR

Find the position of Jaspal standing in such a way that he is equidistant from each of the 4 boys A,B,C and D

37. Basketball and soccer are played with a spherical ball. Even though an athlete dribbles the ball in both sports, a basketball player uses his hands and a soccer player uses his feet. Usually, soccer is played outdoors on a large field and basketball is played indoor on a court made out of wood. The projectile (path traced) of soccer ball and basketball are in the form of parabola representing quadratic polynomial.

(i) What is the shape of the path traced shown in figures ?

(ii) In polynomial ax ^{2}+bx +c , what ^{ }is the condition that the graph of parabola open upwards ?

- Find the zeroes of the quadratic polynomial .

OR

are the zeroes of the quadratic polynomial 2 then find the value of k .

38. **A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a 5 m long rope. **(Use π=3.14) find

(i) the area of that part of the field in which the horse can graze.

(ii) The area of remaining field where horse can not graze.

(iii) The increase in the grazing area if the rope were 12 m long instead of 5m.

OR

Find length of an arc if radius is 3.5m and sector angle is 54^{0}

Solutions Class 10 Maths Exercise 1.1 https://10thmathsguide.com/exercise-11-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 1.2

Ncert Solutions Class 10 Maths Exercise 2.1 https://10thmathsguide.com/exercise-21-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 2.2

Ncert Solutions Class 10 Maths Exercise 3.1 https://10thmathsguide.com/exercise-31-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 3.2 https://10thmathsguide.com/exercise-32-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 3.3 https://10thmathsguide.com/exercise-33-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 4.1 https://10thmathsguide.com/exercise-41-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 4.2 https://10thmathsguide.com/exercise-42-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 4.3 https://10thmathsguide.com/exercise-43-class-10-maths/

MCQ VIDEOS ALL CHAPTERS CLASS 10 MATHShttps://www.youtube.com/watch?v=-eBlHyBxjLg&list=PL2uPMjJCHErQZZNipbsnagBqPrCU_WRN8