# CBSE Class 10 Mathematics Previous Year Question Paper 2020 Delhi Set - 3

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**Question numbers 1 to 10 are multiple choice questions of 1 mark each.**

Select the correct option.

**Q 1.** The point P on x-axis equidistant from the points A(–1, 0) and B(5, 0) is

A. (2, 0)

B. (0, 2)

C. (3, 0)

D. (2, 2)

**Q 2.** The co-ordinates of the point which is reflection of point (–3, 5) in x-axis are

A. (3, 5)

B. (3, -5)

C. (-3, -5)

D. (-3, 5)

**Q 3.** If the point P(6, 2) divides the line segment joining A(6, 5) and B(4, y) in the ratio 3:1, then the value of y is

A. 4

B. 3

C. 2

D. 1

**Q 4.** The sum of exponents of prime factors in the prime-factorisation of 196 is

A. 3

B. 4

C. 5

D. 2

**Q 5.** Euclid’s division Lemma states that for two positive integers a and b, there exists unique integer q and r satisfying a = bq + r, and

A. 0 < r < b

B. 0 < r < b

C. 0 ≤ r < b

D. 0 ≤ r ≤ b

**Q 6.** The zeroes of the polynomial x^{2} – 3x – m(m+3) are

A. m, m+3

B. –m, m+3

C. m, –(m+3)

D. –m, –(m+3)

**Q 7.** The value of k for which the system of linear equations x + 2y = 3, 5x + ky + 7 = 0 is inconsistent is

A.

B.

C. 5

D. 10

**Q 8.** The roots of the quadratic equation x^{2} – 0.04 = 0 are

A. ±0.2

B. ±0.02

C. 0.4

D. 2

**Q 9.** The common difference of the A.P.

A. 1

B.

C. -1

D. 2

**Q 10.** The n^{th} term of the A.P. a, 3a, 5a, …. Is

A. na

B. (2n – 1)a

C. (2n + 1)a

D. 2na

**In Q. Nos. 11 to 15, fill in the blanks. Each question carries 1 mark:**

**Q 11.** In fig. 1, the angles of depressions from the observing positions O_{1} and O_{2} respectively of the object A are ______, ______.

**Q 12. **In ΔABC, AB=6 cm, AC = 12 cm and BC = 6 cm, then ∠B=______.

**OR**

Two triangles are similar if their corresponding sides are ______.

**Q 13. **In given Fig. 2, the length PB=______cm.

**Q 14.** In fig. 3, MN || BC and AM : MB =1 : 2, then

**Q 15. **The value of sin 32° cos 58° +cos 32° sin 58° is ______.

**OR**

The value of is ______.

**Q Nos. 16 to 20 are short answer type questions of 1 mark each.**

**Q 16.** A die is thrown once. What is the probability of getting a prime number?

**Q 17.** If a number x is chosen at random from the numbers –3, –2, –1, 0, 1, 2, 3, then find the probability of x^{2 }< 4.

**OR**

What is the probability that a randomly taken leap year has 52 Sundays?

**Q 18.** If sin A + sin^{2} A = 1, then find the value of the expression (cos^{2} A + cos^{4} A).

**Q 19.** Find the area of the sector of a circle of radius 6 cm whose central angle is 30°. (Take π =3.14).

**Q 20.** Find the class marks of the classes 20 – 50 and 35 – 60.

**Q.Nos.21 to 26 carry 2 marks each.**

**Q 21.** A teacher asked 10 of his students to write a polynomial in one variable on a paper and then to handover the paper.

The following were the answers given by the students:

2x + 3, 3x^{2} + 7x + 2, 4x^{3} + 3x^{2} + 2, x^{3} + + 7, 7x + , 5x^{3} – 7x + 2, 2x^{2} + 3 – , 5x – , ax^{3 }+ bx^{2} + cx + d, x + .

Answer the following questions:

- How many of the above ten, are not polynomials?
- How many of the above ten, are quadratic polynomials?

**Q 22 **.A child has a die whose six faces show the letters as shown below:

The die is thrown once. What is the probability of getting (i) A, (ii) D?

**Q 23.** In fig. 4, ABC and DBC are two triangles on the same base BC. If AD intersects BC at O, show that .

**OR**

In fig.5, if AD ⊥ BC, then prove that AB^{2} + CD^{2} = BD^{2} + AC^{2}.

**Q 24.** Prove that

**OR**

Show that tan^{4}θ + tan^{2}θ = sec^{4}θ - sec^{2}θ

**Q 25.** Find the mode of the following frequency distribution:

**Q 26. **From a solid right circular cylinder of height 14 cm and base radius 6 cm, a right circular cone of same height and same base radius is removed. Find the volume of the remaining solid.

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

**Q 27.** If a circle touches the side BC of a triangle ABC at P and extended sides AB and AC at Q and R, respectively, prove that .

**Q 28.** The area of a circular play ground is 22176 cm^{2}. Find the cost of fencing this ground at the rate of Rs. 50 per metre.

**Q 29.** If the mid – point of the line segment joining the points A (3, 4) and B (k, 6) is P(x, y) and x + y – 10 = 0, find the value of k.

**OR**

Find the area of triangle ABC with A (1, –4) and the mid-points of sides through A being (2, –1) and (0, –1).

**Q 30.** If Fig.6, if ΔABC ~ ΔDEF and their sides of lengths (in cm) are marked along them, then find the lengths of sides of each triangle.

**Q 31.** If 2x + y = 23 and 4x – y = 19, find the value of (5y – 2x) and .

**OR**

Solve for

**Q 32.** Which term of A.P. 20, 19, 18, 17,.... is the first negative term.

**OR**

Find the middle term of the A.P. 7, 13, 19, …., 247.

**Q 33.** Water in a canal, 6m wide and 1.5m deep, is flowing with a speed of 10 km/h. How much area will it irrigate in 30 minutes, if 8cm standing water is required?

**Q 34.** Show that:

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

**Q 35.** The mean of the following frequency distribution is 18. The frequency f in the class interval 19 – 21 is missing. Determine f.

**OR**

The following table gives production yield per hectare of wheat of 100 farms of a village:

Change the distribution to a ‘more than’ type distribution and draw its ogive.

**Q 36.** From a point on the ground, the angles of elevation of the bottom and the top of a tower fixed at the top of a 20m high building are 45° and 60° respectively. Find the height of the tower.

**Q 38. **Prove that is an irrational number.

**Q 39. **Draw a circle of radius 3.5cm. From a point P, 6cm from its centre, draw two tangents to the circle.

**OR**

Construct a ΔABC with AB=6cm, BC=5cm and ∠B=60°. Now construct another triangle whose sides are times the corresponding sides of ΔABC.

**Q 40.** A solid is in the shape of hemisphere surmounted by a cone. If the radius of hemisphere and base radius of cone is 7cm and height of cone is 3.5cm, find the volume of the solid. (Take π = ).