**CBSE Sample Question Papers for Class 10 Maths Standard 2020**

Class X

Mathematics -Standard (041)

Sample Question Paper 2019-20

Duration : 3 hrs Duration: 3 hrs.

General Instructions:

- All the questions are compulsory.
- The question paper consists of 40 questions divided into 4 sections A, B, C, and D.
- Section A comprises of 20 questions of 1 mark each. Section B comprises of 6 questions of 2 marks each.
- Section C comprises of 8 questions of 3 marks each. Section D comprises of 6 questions of 4 marks each.
- There is no overall choice. However, an internal choice has been provided in two questions of 1 mark each, two questions of 2 marks each, three questions of 3 marks each, and three questions of 4 marks each. You have to attempt only one of the alternatives in all such questions.
- Use of calculators is not permitted.

**SECTION A**

Practice **MCQ Questions for Class 10 Maths With Answers** for 2020 Board Exams.

Q 1 – Q 10 are multiple choice questions. Select the most appropriate answer from the given options.

Question 1.

The decimal representation of 11/23×5 will** [1]**

a) terminate after 1 decimal place

b) terminate after 2 decimal places

c) terminate after 3 decimal places

d) not terminate

Question 2.

Consider the following frequency distribution of the heights of 60 students of a class

^{Height (in cm)} |
150-155 | 155-160 | 160-165 | 165-170 | 170-175 | 175-180 |

^{No of students } |
15 | 13 | 10 | 8 | 9 | 5 |

The upper limit of the median class in the given data is** [1]**

a) 165

b) 155

c) 160

d) 170

Question 3.

The LCM of smallest two digit composite number and smallest composite number is** [1]**

a) 12

b) 4

c) 20

d) 44

Question 4.

For which value(s) of p, will the lines represented by the following pair of linear equations be parallel** [1]**

3x – y – 5 = 0

6x – 2 y – p = 0

a) all real values except 10

b) 10

c) 5/2

d) 1/2

Question 5.

If triangle ABC is right angled at C, then the value of sec (A+B) is** [1]**

a) 0

b) 1

c) 2/√3

d) not defined

Question 6.

If sinθ + cosθ = √2cosθ, (θ ≠ 90°) then the value of tanθ is** [1]**

a) √2 – 1

b) √2 + 1

c) √2

d) -√2

Question 7.

Given that sinα = √3/2 and cosβ = 0, then the value of β – α is** [1]**

a) 0°

b) 90°

c) 60°

d) 30°

Question 8.

The point which divides the line segment joining the points (8,-9) and (2,3) in ratio 1 : 2 internally lies in the** [1]**

a) I quadrant

b) II quadrant

c) III quadrant

d) IV quadrant

Question 9.

The distance of the point P (-3, -4) from the x-axis (in units) is** [1]**

a) 3

b) -3

c) 4

d) 5

Question 10.

If A(m/3, 5)is the mid-point of the line segment joining the points Q (-6, 7) and R (-2, 3), then the value of m is** [1]**

a) -12

b) -4

c) 12

d) -6

(Q 11 – Q 15) Fill in the blanks

Question 11.

The total surface area of the given solid figure is _____.** [1]**

Question 12.

If one root of the equation (k – 1)x^{2} – 10x + 3 = o is the reciprocal of the other, then the value of k is_____.** [1]**

OR

The graph of y = p(x), where p(x) is a polynomial in variable x, is as follows;

The number of zeroes of p(x) is _____.

Question 13.

The perimeters of two similar triangles ∆ABC and ∆PQR are 35cm and 45cm respectively, then the ratio of the areas of the two triangles is_____.** [1]**

Question 14.

Fill the two blanks in the sequence 2, __ , 26, __ so that the sequence forms an A.P.** [1]**

Question 15.

A number is chosen at random from the numbers -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5. Then the probability that square of this number is less than or equal to 1 is ______.** [1]**

(Q 16- Q 20) Answer the following

Question 16.

Write one rational and one irrational number lying between 0.25 and 0.32** [1]**

Question 17.

In the figure, if ∠ACB = ∠CDA, AC = 6 cm and AD = 3 cm, then find the length of AB** [1]**

Question 18.

If the angle between two tangents drawn from an external point ‘P’ to a circle of radius ‘r’ and centre O is 60°, then find the length of OP.** [1]**

OR

If the radii of two concentric circles are 4 cm and 5 cm, then find the length of each chord of one circle which is tangent to the other circle.

Question 19.

If the first three terms of an A.P are b, c and 2b, then find the ratio of b and c.** [1]**

Question 20.

Find the value(s) of k for which the quadratic equation x^{2} + 2√2kx + 18 = 0 has equal roots** [1]**

**Section – B**

Question 21.

Find the number of natural numbers between 102 and 998 which are divisible by 2 and 5 both.** [2]**

Question 22.

Prove that the rectangle circumscribing a circle is a square.** [2]**

Question 23.

In the given figure, DEFG is a square and ∠BAC = 90°. Show that FG^{2 }= BG x FC** [2]**

In an equilateral triangle, prove that three times the square of one side is equal to four times the square of one of its altitudes.

Question 24.

‘Skysails’ is that genre of engineering science that uses extensive utilization of wind energy to move a vessel in the sea water. The ‘Skysails’ technology allows the towing kite to gain a height of anything between 100 metres – 300 metres. The sailing kite is made in such a way that it can be raised to its proper elevation and then brought back with the help of a ‘telescopic mast’ that enables the kite to be raised properly and effectively.

Based on the following figure related to sky sailing, answer the questions:** [2]**

(i) In the given figure, if sin θ = cos (3θ – 30°), where θ and 3θ – 30° are acute angles, then find the value of θ.

(ii) What should be the length of the rope of the kite sail in order to pull the ship at the angle θ (calculated above) and be at a vertical height of 200 m?

Question 25.

Jayanti throws a pair of dice and records the product of the numbers appearing on the dice. Pihu throws 1 dice and records the squares the number that appears on it. Who has the better chance of getting the number 36? Justify?** [2]**

OR

An integer is chosen between 70 and 100, Find the probability that it is

(a) a prime number

(b) divisible by 7

Question 26.

Isha is 10 years old girl. On the result day, Isha and her father Suresh were very happy as she got first position in the class. While coming back to their home, Isha asked for a treat from her father as a reward for her success. They went to a juice shop and asked for two glasses of juice.

Aisha, a juice seller, was serving juice to her customers in two types of glasses. Both the glasses had inner radius 3cm. The height of both the glasses was 10cm.

First type: A Glass with hemispherical raised bottom.

Second type: A glass with conical raised bottom of height 1.5 cm.

Isha insisted to have the juice in first type of glass and her father decided to have the juice in second type of glass. Out of the two, Isha or her father Suresh, who got more quantity of juice to drink and by how much?** [2]**

**Section C**

Question 27.

Given that √5 is irrational, prove that 2√5 – 3 is an irrational number.** [3]**

OR

If HCF of 144 and 180 is expressed in the form 13m – 16. Find the value of m.

Question 28.

If the sum of first m terms of an AP is the same as the sum of its first n terms, show that the sum of its first (m+n) terms is zero.** [3]**

Question 29.

In the figure, ABCDE is a pentagon with BE||CD and BC||DE. BC is perpendicular to CD. AB= 5cm, AE = 5cm, BE = 7cm, BC = x-y and CD = x+y. If the perimeter of ABCDE is 27cm. find the value of x and y, given x, y ≠ 0.** [3]**

OR

Solve the following system of equations:

Question 30.

Obtain all the zeros of the polynomial x^{4} + 4x^{3} – 2x^{2} – 20x -15, if two of its zeroes are √5 and -√5.** [3]**

Question 31.

Two friends Seema and Aditya work in the same office at Delhi. In the Christmas vacations, both decided to go to their hometowns represented by Town A and Town B respectively in the figure given below. Town A and Town B are connected by trains from the same station C (in the given figure)in Delhi.Based on the given situation, answer the following questions:** [3]**

(i) Who will travel more distance, Seema or Aditya, to reach to their hometown?

(ii) Seema and Aditya planned to meet at a location D situated at a point D represented by the mid-point of the line joining the points represented by Town A and Town B. Find the coordinates of the point represented by the point D

(iii) Find the area of the triangle formed by joining the points represented by A, B and C.

Question 32.

If sinθ + cosθ = √3, then prove that tanθ + cotθ = 1** [3]**

OR

Question 33.

Sides of a right triangular field are 25m, 24m and 7m. At the three corners of the field, a cow, a buffalo and a horse are tied separately with ropes of 3.5 m each to graze in the field. Find the area of the field that cannot be grazed by these animals.** [3]**

Question 34.

A TV reporter was given a task to prepare a report on the rainfall of the city Dispur of India in a particular year. After collecting the data, he analyzed the data and prepared a report on the rainfall of the city. Using this report, he drew the following graph for a particular time period of 66 days.** [3]**

Based on the above graph, answer the following questions:

(i) Identify less than type ogive and more than type ogive from the given graph.

(ii) Find the median rainfall of Dispur

(iii) Obtain the Mode of the data if mean rainfall is 23.4cm

**Section – D**

Question 35.

Draw a triangle ABC with side BC=6.5cm, ∠B=30°, ∠A =105°. Then construct another triangle whose sides are 3/4 times the corresponding sides of the triangle ABC.** [4]**

OR

Construct a pair of tangents to a circle of radius 3 cm which are inclined to each other at an angle of 60°.

Question 36.

Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides are divided in the same ratio.** [4]**

Question 37.

A train covers a distance of 360 km at a uniform speed. Had the speed been 5km/hour more, it would have taken 48 minutes less for the journey. Find the original speed of the train.** [4]**

OR

Solve the following equation:

Question 38.

A petrol tank is in the form of a frustum of a cone of height 20 m with diameters of its lower and upper ends as 20 m and 50 m respectively. Find the cost of petrol which can fill the tank completely at the rate of Rs. 70 per litre. Also find the surface area of the tank.** [4]**

OR

Water is flowing at the rate of 15 km/hour through a pipe of diameter 14 cm into a cuboidal pond which is 50 m long and 44 m wide. In what time will the level of water in the pond rise by 21 cm?

Question 39.

The angle of elevation of an airplane from a point on the ground is 60°. After a flight of 30 seconds, the angle of elevation becomes 30°. If the airplane is flying at a constant height of 3000√3 m, find the speed of the airplane.** [4]**

Question 40.

Daily wages of 110 workers, obtained in a survey, are tabulated below:** [4]**

Daily Wages (in Rs.) | 100-120 | 120-140 | 140-160 | 160-180 | 180-200 | 200-220 | 220-240 |

Number of Workers | 10 | 15 | 20 | 22 | 18 | 12 | 13 |

Compute the mean daily wages and modal daily wages of these workers.