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CBSE Class 10 Maths Question Paper 2017 2018 2019 2020 Solved All Sets

Here we are providing CBSE Previous Year Question Papers Class 6 to 12 solved with soutions CBSE Class 10 Maths Question Paper 2017 2018 2019 2020 Solved all Sets class 10 Maths sample paper 2020 solved, sample paper class 10 Maths, cbse class 10 Maths question paper 2018, sample paper class 10 Maths 2019, Maths question paper for class 10, cbse previous year question papers class 10 Maths, cbse sample paper f Practice of previous year question papers and sample papers protects each and every student to score bad marks in exams.If any student of CBSE Board continuously practices last year question paper student will easily score high marks in tests. Fortunately earlier year question papers can assist the understudies with scoring great in the tests. Unraveling previous year question paper class 10 Maths is significant for understudies who will show up for Class 10 Board tests.

Class 10 Subject Maths Paper Set 1 with Solutions

SECTION A

Q. Nos. 1 to 10 are multiple choice questions. Select the correct option.


Question 1: (Marks 1)

HCF of 144 and 198 is

(a) 9

(b) 18

(c) 6

(d) 12


Answer :

(b) 18


Question 2: (Marks 1)

The median and mode respectively of a frequency distribution are 26 and 29. Then its mean is

(a) 27.5

(b) 24.5

(c) 28.4

(d) 25.8


Answer :

(b) 24.5


Question 3: (Marks 1)

In Fig. 1, on a circle of radius 7 cm, tangent PT is drawn from a point P such that PT = 24 cm. If 0 is the centre of the circle, then the length of PR is

In Fig. 1, on a circle of radius 7 cm, tangent PT is drawn from

(a) 30 cm

(b) 28 cm

(c) 32 cm

(d) 25 cm


Answer :

(c) 32 cm


Question 4: (Marks 1)

225 can be expressed as

(a) 5 × 32

(b) 52 × 3

(c) 52 × 32

(d) 53 × 3


Answer :

(d) 52 × 32


Question 5: (Marks 1)

The probability that a number selected at random from the numbers


Answer :

The probability that a number selected at random from the numbers


Question 6: (Marks 1)

If one zero of a quadratic polynomial


Answer :

If one zero of a quadratic polynomial


Question 7: (Marks 1)

ncert solution 10th math 430-1-1 Question 7

Answer :

(b) a rational number


Question 8: (Marks 1)

The graph of a polynomial is shown in Fig. 2, then the number of its zeroes is

The graph of a polynomial is shown in

(a) 3

(b) 1

(c) 2

(d) 4


Answer :

(a) 3


Question 9: (Marks 1)

Distance of point P(3, 4) from x-axis is

(a) 3 units

(b) 4 units

(c) 5 units

(d) 1 unit


Answer :

(b) 4 units


Question 10: (Marks 1)

If the distance between the points A(4, p) and B(1, 0) is 5 units, then the value(s) of p is (are)

(a) 4 only

(b) –4 only

(c) ±4

(d) 0


Answer :

(c) ±4

Q. Nos. 11 to 15, fill in the blanks.

Question 11: (Marks 1)

If the point C(k, 4) divides the line segment joining two points A(2, 6) and B(5, 1) in ratio 2 : 3, the value of k is _______.

OR

If points A(&nndash;3, 12), B(7, 6) and C(x, 9) are collinear, then the value of x is_______. Sol. 2


Answer :

If the point C(k, 4) divides the line segment joining two poin

OR

2


Question 12: (Marks 1)

If the equations kx – 2y = 3 and 3x + y = 5 represent two intersecting lines at unique point, then the value of k is _______.

OR

If quadratic equation 3x – 4x + k = 0 has equal roots, then the value of k is _______.


Answer :

. ≠ –6

OR

If quadratic equation


Question 13: (Marks 1)

The value of (sin 20° cos 70° + sin 70° cos 20°) is _______.


Answer :

1


Question 14: (Marks 1)

If tan(A + B) =

Answer :

45°


Question 15: (Marks 1)

The perimeters of two similar triangles are 25 cm and 15 cm respectively. If one side of the first triangle is 9 cm, then the corresponding side of second triangle is _______.


Answer :

The perimeters of two similar triangles are 25 cm and 15 cm respectively

In Q. Nos. 16 to 20, answer the following.

Question 16: (Marks 1)

 If 5 tan θ = 3, then what is the value of


Answer :

 If 5 tan θ = 3, then what is the value of


Question 17: (Marks 1)

The areas of two circles are in the ratio 9 : 4, then what is the ratio of their circumferences?


Answer :

The areas of two circles are in the ratio 9 : 4, then what is the ratio of their circumferences


Question 18: (Marks 1)

If a pair of dice is thrown once, then what is the probability of getting a sum of 8?


Answer :

Favourable outcomes are (3, 5); (4, 4); (5, 3); (2, 6); (6, 2) i.e., 5

If a pair of dice is thrown once, then what is


Question 19: (Marks 1)

In Fig. 3, in ΔABC, DE || BC such that AD = 2.4 cm, AB = 3.2 cm and AC = 8 cm, then what is the length of AE?

In Fig. 3, in ΔABC, DE || BC such that AD


Answer :

In Fig. 3, in ΔABC, DE || BC such that AD


Question 20: (Marks 1)

The nth term of an AP is (7 – 4n), then what is its common difference?


Answer :

T1 = 3, T2 = –1

d = –4

SECTION B

Q. Nos, 21 to 26 carry two marks each.


Question 21: (Marks 2)

A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball at random from the bag is three times that of a red ball, find the number of blue balls in the bag.


Answer :

 A bag contains 5 red balls and some blue balls


Question 22: (Marks 2)

Prove that

OR

Prove that


Answer :

Prove that

OR

Prove that


Question 23: (Marks 2)

Two different dice are thrown together, find the probability that the sum of the numbers appeared is less than 5.

OR

Find the probability that 5 Sundays occur in the month of November of a randomly selected year.


Answer :

Two different dice are thrown together, find the probability that the sum of the numbers


Question 24: (Marks 2)

In Fig. 4, a circle touches all the four sides of a quadrilateral ABCD. If AB = 6 cm, BC = 9 cm and CD = 8 cm, then the find length of AD

In Fig. 4, a circle touches all the four sides of a quadrilateral


Answer :

The sides of quadrilateral touches a circle

AB + DC = BC + AD

6 + 8 = 9 + AD ⇒ AD = 5 cm


Question 25: (Marks 2)

The perimeter of a sector of a circle with radius 6.5 cm is 31 cm, then find the area of the sector.


Answer :

The perimeter of a sector of a circle with radius 6.5 cm is


Question 26: (Marks 2)

Divide the polynomial (4x2 + 4x + 5) by (2x + 1) and write the quotient and the remainder.


Answer :

Divide the polynomial

SECTION C

Q. Nos. 27 to 34 carry 3 marks each.


Question 27: (Marks 3)

I f α and β are the zeroes of the polynomial f(x) = x2 – 4x - 5 then find the value of α2 + β2 .


Answer :

I f α and β are the zeroes of the polynomia


Question 28: (Marks 3)

Draw a circle of radius 4 cm. From a point 7 cm away from the centre of circle. Construct a pair of tangents to the circle.

OR

Draw a line segment of 6 cm and divide it in the ratio 3 : 2.


Answer :

Constructing the circle of given radius

Constructing the tangents

OR

Drawing line segment of length 6 cm.

Dividing it in the ratio 3 : 2.


Question 29: (Marks 3)

A solid metallic cuboid of dimension 24 cm × 11 cm × 7 cm is melted and recast into solid cones of base radius 3.5 cm and height 6 cm. Find the number of cones so formed


Answer :

A solid metallic cuboid of dimension


Question 30: (Marks 3)

Prove that (1 + tan A – sec A) × (1 + tan A + sec A) = 2 tan A

OR

Prove that


Answer :

L.H.S. = (1 + tan A)2 – sec2 A

= 1 tan2 A + 2 tan A – sec2 A

= sec2 A + 2tan A – sec2 A

= 2 tan A = R.H.S.

OR

Prove that


Question 31: (Marks 3)

Given that

OR

An army contingent of 612 members is to march behind an army band of 48 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?


Answer :

Given that

OR

612 = 22 × 32 × 17

48 = 24 × 3

HCF (612, 48) = 22 × 3

= 12

Number of column = 12


Question 32: (Marks 3)

Prove that, in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.


Answer :

Correct figure, given, To prove and construction.

Correct Proof

Read the following passage carefully and then answer the questions given at the end.

Question 33: (Marks 3)

 To conduct Sports Day activities, in your rectangular shaped school ground ABCD, lines have


Answer :

To conduct Sports Day activities, in your rectangular shaped school ground ABCD, lines have


Question 34: (Marks 3)

Solve graphically: 2x + 3y = 2, x – 2y = 8


Answer :

Correct graph of 2x + 3y = 2

Correct graph of x – 2y = 8

Point of intersection = (4, –2)

or x = 4, y = – 2

SECTION D

Q. Nos. 35 to 40 carry 4 marks each.


Question 35: (Marks 4)

A two digit number is such that the product of its digits is 14. If 45 is added to the number; the digits interchange their places. Find the number.


Answer :

Let unit digit = x

Tens digit = y

∴ Number = 10y + x

10y + x + 45 = 10x + y

⇒ x – y = 5 ...(i)

and xy = 14 ...(ii)

Solving (i) and (ii)

x = 7, y = 2

∴ Number = 27


Question 36: (Marks 4)

If 4 times the 4th term of an AP is equal to 18 times the 18th term, then find the 22nd term.

OR

How many terms of the AP : 24, 21, 18, ... must be taken so that their sum is 78?


Answer :

Let first term be a and common difference = d

∴ 4(a + 3d) = 18(a + 17d)

⇒ a = –21d 1 22nd term = a + 21d

= –21d + 21d

= 0

OR

How many terms of the AP


Question 37: (Marks 4)

The angle of elevation of the top of a building from the foot of a tower is 30°. The angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 60 m high, find the height of the building.


Answer :

The angle of elevation of the top of a building from the foot of a tower


Question 38: (Marks 4)

In Fig. 6, DEFG is a square in a triangle ABC right angled at A. Prove that

(i) ΔAGF ~ ΔDBG

(ii) ΔAGF ~ ΔEFC

n Fig. 6, DEFG is a square in a triangle ABC right angled at A

OR

In an obtuse ΔABC (∠B is obtuse), AD is perpendicular to CB produced. Then prove that AC2 = AB2 + BC2 + 2BC × BD.


Answer :

In Fig. 6, DEFG is a square in a triangle ABC right angled at A


Question 39: (Marks 4)

An open metal bucket is in the shape of a frustum of cone of height 21 cm with radii of its lower and upper ends are 10 cm and 20 cm respectively. Find the cost of milk which can completely fill the bucket at the rate of ` 40 per litre.

OR

A solid is in the shape of a cone surmounted on a hemisphere. The radius of each of them being 3.5 cm and the total height of the solid is 9.5 cm. Find the volume of the solid.


Answer :

An open metal bucket is in the shape of a frustum of cone of height 21 cm with radii of its


Question 40: (Marks 4)

Find the mean of the following data:

Find the mean of the following data:


Answer :

Find the mean of the following data:

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CBSE Class 10 Maths Question Paper 2017 2018 2019 2020 Solved all Sets

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