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
Q 4. The sum of exponents of prime factors in the prime-factorisation of 196 is
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 x2 – 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
Q 8. The roots of the quadratic equation x2 – 0.04 = 0 are
Q 9. The common difference of the A.P.
Q 10. The nth term of the A.P. a, 3a, 5a, …. Is
B. (2n – 1)a
C. (2n + 1)a
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 O1 and O2 respectively of the object A are ______, ______.
Q 12. In ΔABC, AB=6 cm, AC = 12 cm and BC = 6 cm, then ∠B=______.
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 ______.
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 x2 < 4.
What is the probability that a randomly taken leap year has 52 Sundays?
Q 18. If sin A + sin2 A = 1, then find the value of the expression (cos2 A + cos4 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, 3x2 + 7x + 2, 4x3 + 3x2 + 2, x3 + + 7, 7x + , 5x3 – 7x + 2, 2x2 + 3 – , 5x – , ax3 + bx2 + 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 .
In fig.5, if AD ⊥ BC, then prove that AB2 + CD2 = BD2 + AC2.
Q 24. Prove that
Show that tan4θ + tan2θ = sec4θ - sec2θ
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 cm2. 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.
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 .
Q 32. Which term of A.P. 20, 19, 18, 17,.... is the first negative term.
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.
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.
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 = ).
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