Maths Sample Paper 4 (Part A), class 10th

 Maths Sample Paper 

Part A

Section - I

1. Find the nth term of the AP 

1/1·2, 1/2·3, 1/3·4

2. If 2x² + bx + 8 = 0 to have non - real roots 

-8 < b < 4, then find the interval for b.

3. If ∆ADE ~ ∆ACB, DEC = 105° and angle ECB = 65°, then find the value of x.

4. In a right angle triangle ∆ABC, right angle at C, if tanA = 1, then find 2sinA cosA 

Or

Evaluate

1 - tan² 30° / 1 + cot² 30°

5. A die is thrown once, what is the probability of not getting a prime number?

Or

If a box contains 3 red and 5 blue balls, find the probability of drawing one blue ball.

6. If ∆ABC is an isosceles triangle, right angle at C, with AC = 2cm, then find the hypotenuse.

7. Find the distance between two parallel tangents to a circle of radius 7 cm.

8. Find the area of shaded portion.

Or

Check whether the following statement is true or false.

'If a semi - circle is rolled along a diameter, then the figure formed is cylindrical.' 

9. Find the length of the tangent drawn form a point, which is 5cm away from the centre of circle of radius 3 cm.

Or

In the given figure, if DE \\BC, then find the value of x.

10. It is true, that if the height of tower is doubled and the distance between the observer and foot of tower is also doubled, then the angle of elevation remains the same.

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11. Suppose mean of 10 observation is 20, if we add 5 in each observation, then find the new mean.

12. For what value(s) of a, the system of linear equations 2x + 3y = 7 and (a - 1 )x +

 (a + 1)y = 3a +1 represent parallel lines?

Or

Write the value of k for which the system of equation x + ky = 0, 2x - y = 0 has unique solution.

14. A parallelogram has vertices P(1,4), Q(7,11), R(a,4 ) and S(1,-3). Find the value of a.

15. Gayatri was making a mathematical model, in which she placed 4 cubes each of edge 20cm one above another. Find the surface area of the resulting cuboid.

16. sin∅ and cos∅ are equal, when 0 ≤ ∅, ∅≤ 90°.

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Section - II

Case Study

Balloon Seller

A balloon seller, sells packet of colourful balloon. Each packet has two different shapes. After filling the air in the balloon, two different shapes can be shown below.

One of them is a spherical shape and another is conical shape.

i. Find the air capacity of spherical balloon.

a) 930.2 m³

b) 904.32 m³

c) 905.2 m³

d) 906.50 m³

ii. Find the slant height of the conical balloon shape.

a) 6.30 m

b) 6.50 m

c) 6.10 m

d) 6.75 m

iii. Find the total surface area of the conical balloon.

a) 105.50 m²

b) 106.7 m²

c) 107.2 m²

d) 108 m²

iv. If the air of spherical balloon is transferred into the shape of cylindrical container having radius 4m, then the height of container is

a) 18 m

b) 16 m

c) 15 m

d) 14 m

v. A cone is formed by revolving plane figure of 

a) rectangle

b) triangle

c) parallelogram 

d) circle

18. 

Traffic light signal

In our daily life we all see traffic lights. A traffic controller set the timings of traffic lights in such a way that all lights are not been at the same time or specially not in rush hour. It may create problem in an hour because lights are for few minutes only. So, he take the timings of nearby places in same area and calculate 1 cm of all traffic stops and he easily manage the traffic by increase the duration or set at different times. There are two traffic lights on a particular highway which shows green light on time of 90 seconds and 144 seconds respectively.

i. Find the HCF between two green lights.

a) 18

b) 16

c) 20

d) 22

ii. Find the LCM between two green lights.

a) 720

b) 710

c) 730

d) 740

iii. Factor tree is used for determining the 

a) HCF

b) LCM

c) prime factor

d) None of these

iv. Identify the correct option.

a) HCF (a, b) × LCM (a, b) = a/b

b) HCF (a, b) / LCM (a, b) = a / b

c) HCF (a, b) × LCM (a, b) = a - b

d) HCF (a, b) × LCM (a, b) = a × b

v. A number which do not have any factor other than 1, is

a) coprime

b) prime number

c) coprime or prime number

d) None of the above.

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19. 

Horse Tied with Peg

A horse is tied to a peg at one corner of a square shaped grass field of side 15 metre by means of a 5 metre long rope.

Due to this, a horse can eat he grass only one particular corner of the field.

i. Find the area of the field.

a) 220 m²

b) 225 m²

c) 227 m²

d) 229 m²

ii. Choose the correct formula for determining the area of sector of a circle.

a) ∅/ 360° × πr²

b) ∅/ 360° × 2πr

c) 5∅ / 360° × πr²

d) ∅/ 180° × πr²

iii. Find the area of the part of the field in which horse can graze.

a) 19.625 m²

b) 18.70 m²

c) 19.80 m²

d) 19.30 m²

iv. Find the increase in the grazing area if the rope were 10m long instead of 5 metre.

a) 58.875 m²

b) 58.5 m²

c) 58 m²

d) 58.7 m²

v. Find the arc length of the circle.

a) 7.4 m²

b) 7.3 m²

c) 7.85 m²

d) 7.95 m²

20.

Bridge Game

In a bridge Game, there are four persons play and make a pair of two - two persons as a partner. In a deck of 52 playing cards, distributed around the table clockwise in such a way that each person get 14 cards.

i. Find the probability that the card drawn is a queen of black colour.

a) 25 / 26

b) 3 / 26

c) 1/ 26

d) 5/ 26

ii. Find the probability that the card drawn is a card with number 5 or 6.

a) 2/13

b) 11/13

c) 1/13

d) 12/13.

iii. Find the probability that the card drawn is a card with number less than 8.

a) 6/13

b) 5/13

c)7/13

d) None of these

iv. Find the probability that the card drawn is a card with number between 2 and 9.

a) 7/13

b) 5/13

c) 6/13

d) 3/13

v. What is the probability that any one person get Queen of Spade.

a) 1/2

b) 1/3

c) 1/4

d) 1

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Posted by - Anuranjan Gadekar

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