## Class 10 Maths Sample Paper 2022-23

Class 10 Maths Sample Paper 2022-23

Time Allowed: 3

Hours Maximum Marks: 80

General Instructions:

1. This Question Paper has 5 Sections A, B, C, D, and E.

2. Section A has 20 Multiple Choice Questions (MCQs) carrying 1 mark each.

3. Section B has 5 Short Answer-I (SA-I) type questions carrying 2 marks each.

4. Section C has 6 Short Answer-II (SA-II) type questions carrying 3 marks each.

5. Section D has 4 Long Answer (LA) type questions carrying 5 marks each.

6. Section E has 3 Case Based integrated units of assessment (4 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 2 marks, 2 Qs of 3 marks and 2 Questions of 5 marks has been provided. An internal choice has been provided in the 2 marks questions of Section E.

8. Draw neat figures wherever required. Take Ï€ =22/7 wherever required if not stated.

Class 10 Maths Sample Paper 2022 23

##

Section A

Section A consists of 20 questions of 1 mark each

Q.1.If two positive integers p and q can be expressed as p = abÂ² and q = aÂ³b; a, b being prime numbers, then LCM (p, q) is

(a) ab (b) aÂ²bÂ²

(c) aÂ³bÂ² (d) aÂ³bÂ³

Q.2.What is the greatest possible speed at which a man can walk 52 km and 91 km in an exact

number of hours?

(a) 17 km/hours (b) 7 km/hours

(c) 13 km/hours (d) 26 km/hours

Q.3.If one zero of the quadratic polynomial xÂ² + 3x + k is 2, then the value of k is

(a) 10 (b) -10 (c) 5 (d) â€“5

Q.4.Graphically, the pair of equations given by

6x â€“ 3y + 10 = 0

2x â€“ y + 9 = 0

represents two lines which are

(a) intersecting at exactly one point. (b) parallel.

(c) coincident. (d) intersecting at exactly two points

Q.5. If the quadratic equation xÂ² + 4x + k = 0 has real and equal roots, then

(a) k < 4 (b) k > 4 (c) k = 4 (d) k â‰¥ 4

Q.6. The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is

(a) 5 units (b) 12 units (c) 11 units (d) (7 + âˆš5) units

Q.7.If in triangles ABC and DEF,

AB/DE = BC/FD, then they will be similar, when

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

Q.8. In which ratio the y-axis divides the line segment joining the points (5, â€“ 6) and (â€“1, â€“ 4)?.

(a) 1 : 5 (b) 5 : 1 (c) 1 : 1 (d) 1 : 2

Q.9. In the figure, if PA and PB are tangents to the circle with centre O such that âˆ APB = 50Â°, then âˆ OAB is

equal to

(a) 25Â° (b) 30Â° (c) 40Â° (d) 50Â°

Q.10. If sin A =Â½, then the value of sec A is :

(a) âˆš3/2 (b) 1âˆš3 (c) âˆš3 (d) 1

Q.11. âˆš3 cosÂ²A + âˆš3 sinÂ²A is equal to

(a) 1 (b) 1âˆš3 (c) âˆš3 (d) 0

Q.12. The value of cos1Â° cos2Â° cos3Â° cos4Â°â€¦â€¦â€¦â€¦..â€¦..cos90Â° is

(a) 1 (b) 0 (c) â€“ 1 (d) 2

Q.13. If the perimeter of a circle is equal to that of a square, then the ratio of their areas is

(a) 22 : 7 (b) 14 : 11 (c) 7 : 22 (d) 11: 14

Q.14. If the radii of two circles are in the ratio of 4 : 3, then their areas are in the ratio of :

(a) 4 : 3 (b) 8 : 3 (c) 16 : 9 (d) 9 : 16

Q.15. The total surface area of a solid hemisphere of radius 7 cm is :

(a) 447Ï€ cmÂ² (b) 239Ï€ cmÂ²

(c) 174Ï€ cmÂ² (d) 147Ï€ cmÂ²

Q.16.For the following distribution :

Class 0 â€“ 5 5 â€“ 10 10 â€“ 15 15 â€“ 20 20 â€“ 25

Frequency 10 15 12 20 9

the upper limit of the modal class is

(a) 10 (b) 15 (c) 20 (d) 25

Q.17.If the mean of the following distribution is 2.6, then the value of y is

Variable (x) 1 2 3 4 5

Frequency 4 5 y 1 2

(a) 3 (b) 8 (c) 13 (d) 24

Q.18.A card is selected at random from a well shuffled deck of 52 cards. The probability of its being a red face card is

(a)3/26 (b) 3/13 (c) 2/13 (d) 1/2

Direction for questions 19 & 20: In question numbers 19 and 20, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option.

Q.19.Assertion: If HCF of 510 and 92 is 2, then the LCM of 510 & 92 is 32460

Reason: as HCF(a,b) x LCM(a,b) = a x b

(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.

Q.20. Assertion (A): The ratio in which the line segment joining (2, -3) and (5, 6) internally divided by x axis is 1:2.

Reason (R): as formula for the internal division is

(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.

## Class 10 Maths Sample Paper 2022 23

Section B

Section B consists of 5 questions of 2 marks each.

Q.21. For what values of k will the following pair of linear equations have infinitely many solutions?

kx + 3y â€“ (k â€“ 3) = 0

12x + ky â€“ k = 0

Q.22. In the figure, altitudes AD and CE of Î” ABC intersect each other at the point P. Show that:

(i) Î”ABD ~ Î”CBE

(ii) Î”PDC ~ Î”BEC

[OR]

In the figure, DE || AC and DF || AE. Prove that BF/FE= BE/EC

Q.23.Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.

Q.24. If cot Î¸ =7/8, evaluate (1 + sin Î¸) (1âˆ’ sin Î¸) / (1 + cos Î¸) (1âˆ’ cos Î¸)

Q. 25 Find the perimeter of a quadrant of a circle of radius 14 cm.

[OR]

Find the diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm.

Maths Class 10 Sample Paper 2022 23:

## Section C

Section C consists of 6 questions of 3 marks each.

Q.26. Prove that âˆš5 is an irrational number.

Q.27. Find the zeroes of the quadratic polynomial 6xÂ² â€“ 3 â€“ 7x and verify the relationship between the zeroes and the coefficients.

Q.28.A shopkeeper gives books on rent for reading. She takes a fixed charge for the first two days, and an additional charge for each day thereafter. Latika paid Rs 22 for a book kept for six days, while Anand paid Rs 16 for the book kept for four days. Find the fixed charges and the charge for each extra day.

[OR]

Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?

Q.29.In the figure, PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q intersect at point T. Find the length TP.

Q.30.Prove that, tan Î¸ / (1 âˆ’ cot Î¸) + cot Î¸ / (1 âˆ’ tan Î¸) = 1 + sec Î¸ cosec Î¸

[OR]

If sin Î¸ + cos Î¸ = âˆš3, then prove that tan Î¸ + cot Î¸ = 1

Q.31. Two dice are thrown at the same time. What is the probability that the sum of the two numbers appearing on the top of the dice is

(i) 8

(ii) 13

(iii) less than or equal to 12?

Class 10 Maths Sample Paper 2022-23

Section D

Section D consists of 4 questions of 5 marks each

Q.32.An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore (without taking into consideration the time they stop at intermediate stations). If the average speed of the express train is 11km/h more than that of the passenger train, find the average speed of the two trains.

[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.

Q.33. Prove that If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.

Q.34.A pen stand made of wood is in the shape of a cuboid with four conical depressions to hold pens. The

dimensions of the cuboid are 15 cm by 10 cm by 3.5 cm. The radius of each of the depressions is 0.5 cm

and the depth is 1.4 cm. Find the volume of wood in the entire stand.

[OR]

Ramesh made a bird-bath for his garden in the shape of a cylinder with a hemispherical depression at one

end. The height of the cylinder is 1.45 m and its radius is 30 cm. Find the total surface area of the bird-bath.

Q.35.A life insurance agent found the following data for distribution of ages of 100 policy holders. Calculate the median age, if policies are given only to persons having age 18 years onwards but less than 60 years.

Class 10 Maths Sample Paper 2022-23

## Section E

Case study-based questions are compulsory.

Q.35.Case Study â€“ 1

In the month of April to June 2022, the exports of passenger cars from India increased by 26% in the corresponding quarter of 2021â€“22, as per a report. A car manufacturing company planned to produce 1800 cars in 4th year and 2600 cars in 8th year. Assuming that the production increases uniformly by a fixed number every year.

Based on the above information answer the following questions

1 Find the production in the 1st year. 1

II. Find the production in the 12th year. 1

III. Find the total production in first 10 years.

[OR]

In which year the total production will reach to 15000 cars? 3

Q.37. Case Study â€“ 2

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 coordinate geometry.

I Find the distance between Lucknow (L) to Bhuj(B). 1

II If Kota (K), internally divide the line segment joining Lucknow (L) to Bhuj (B) into

3 : 2 then find the coordinate of Kota (K). 1

III 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).

2

Q.38. Case Study â€“ 3

Lakshaman Jhula is located 5 kilometers northeast of the city of Rishikesh in the Indian state of Uttarakhand.

The bridge connects the villages of Tapovan to Jonk. Tapovan is in Tehri Garhwal district, on the west bank of the river, while Jonk is in Pauri Garhwal district, on the east bank. Lakshman Jhula is a pedestrian bridge also used by motorbikes. It is a landmark of Rishikesh.

Based on the above information answer the following questions.

Find the distance PA. 1

II. Find the distance PB 1

III. Find the width AB of the river.

[OR]

Find the height BQ if the angle of the elevation from P to Q be 30Â° 2

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Class 10 Maths Sample Paper 2022-23

Class 10 Maths Sample Paper 2022-23