CBSE Class 10 Mathematics 2020 — Set 5

Questions in this 2020 Mathematics paper (Set 5)

All 40 questions from this set, exactly as asked. Try each one, then open the question-paper PDF above for the complete paper.

1. 1.
   On dividing a polynomial p(x) by x^2 - 4, quotient and remainder are found to be x and 3 respectively. The polynomial p(x) is:

   • (a) 3x^2 + x - 12
   • (b) x^3 - 4x + 3
   • (c) x^2 + 3x - 4
   • (d) x^3 - 4x - 3
2. 2.
   In Figure-1, ABC is an isosceles triangle, right-angled at C. Therefore:

   • (a) AB^2 = 2AC^2
   • (b) BC^2 = 2AB^2
   • (c) AC^2 = 2AB^2
   • (d) AB^2 = 4AC^2
3. 3.
   The point on the x-axis which is equidistant from (-4, 0) and (10, 0) is:

   • (a) (7, 0)
   • (b) (5, 0)
   • (c) (0, 0)
   • (d) (3, 0)
4. 4.
   The value(s) of k for which the quadratic equation 2x^2 + kx + 2 = 0 has equal roots, is:

   • (a) 4
   • (b) +/-4
   • (c) -4
   • (d) 0
5. 5.
   Which of the following is NOT an A.P.?

   • (a) -1.2, 0.8, 2.8, ...
   • (b) 3, 3 + sqrt(2), 3 + 2*sqrt(2), 3 + 3*sqrt(2), ...
   • (c) 4/3, 7/3, 9/3, 12/3, ...
   • (d) -1/5, -2/5, -3/5, ...
6. 6.
   The pair of linear equations 3x/2 + 5y/3 = 7 and 9x + 10y = 14 is:

   • (a) consistent
   • (b) inconsistent
   • (c) consistent with one solution
   • (d) consistent with many solutions
7. 7.
   In Figure-2, PQ is tangent to the circle with centre O, at the point B. If angle AOB = 100 degrees, then angle ABP is equal to:

   • (a) 50 degrees
   • (b) 40 degrees
   • (c) 60 degrees
   • (d) 80 degrees
8. 8.
   The radius of a sphere (in cm) whose volume is 12*pi cm^3, is:

   • (a) 3
   • (b) 3*sqrt(3)
   • (c) 3^(2/3)
   • (d) 3^(1/3)
9. 9.
   The distance between the points (m, -n) and (-m, n) is:

   • (a) sqrt(m^2 + n^2)
   • (b) m + n
   • (c) 2*sqrt(m^2 + n^2)
   • (d) sqrt(2m^2 + 2n^2)
10. 10.
    In Figure-3, from an external point P, two tangents PQ and PR are drawn to a circle of radius 4 cm with centre O. If angle QPR = 90 degrees, then length of PQ is:

    • (a) 3 cm
    • (b) 4 cm
    • (c) 2 cm
    • (d) 2*sqrt(2) cm
11. 11.
    The probability of an event that is sure to happen, is ________.
12. 12.
    Simplest form of (1 + tan^2 A) / (1 + cot^2 A) is ________.
13. 13.
    AOBC is a rectangle whose three vertices are A(0, -3), O(0, 0) and B(4, 0). The length of its diagonal is ________.
14. 14.
    In the formula x_bar = a + (Sum(f_i * u_i) / Sum(f_i)) * h, u_i = ________.
15. 15.
    All concentric circles are ________ to each other.
16. 16.
    Find the sum of the first 100 natural numbers.
17. 17.
    In Figure-4, the angle of elevation of the top of a tower from a point C on the ground, which is 30 m away from the foot of the tower, is 30 degrees. Find the height of the tower.
18. 18.
    The LCM of two numbers is 182 and their HCF is 13. If one of the numbers is 26, find the other.
19. 19.
    Form a quadratic polynomial, the sum and product of whose zeroes are (-3) and 2 respectively.
20. 20.
    Evaluate: (2 * tan 45 * cos 60) / sin 30.
21. 21.
    In the given Figure-5, DE || AC and DF || AE. Prove that BF/FE = BE/EC.
22. 22.
    Show that 5 + 2*sqrt(7) is an irrational number, where sqrt(7) is given to be an irrational number.
23. 23.
    If A, B and C are interior angles of a triangle ABC, then show that cos((B + C)/2) = sin(A/2).
24. 24.
    In Figure-6, a quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB + CD = BC + AD.
25. 25.
    Find the mode of the following distribution: Marks: 0-10, 10-20, 20-30, 30-40, 40-50, 50-60 Number of Students: 4, 6, 7, 12, 5, 6
26. 26.
    2 cubes, each of volume 125 cm^3, are joined end to end. Find the surface area of the resulting cuboid.
27. 27.
    A fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to its denominator. Find the fraction.
28. 28.
    Use Euclid Division Lemma to show that the square of any positive integer is either of the form 3q or 3q + 1 for some integer q.
29. 29.
    Find the ratio in which the y-axis divides the line segment joining the points (-4, -6) and (2, -7). Also find the point of intersection.
30. 30.
    Prove that: sqrt((1 + sin A) / (1 - sin A)) = sec A + tan A.
31. 31.
    In an A.P., it is given that the first term

    • (a) = 5, common difference
    • (d) = 3, and the n-th term (a_n) = 50. Find n and sum of first n terms (S_n) of the A.P.
32. 32.
    Construct a triangle ABC with sides BC = 6 cm, AB = 5 cm and angle ABC = 60 degrees. Then construct a triangle whose sides are 3/4 of the corresponding sides of triangle ABC.
33. 33.
    Diwali Fair: A game in a booth at a Diwali Fair involves using a spinner first. Then, if the spinner stops on an even number, the player is allowed to pick a marble from a bag. Prizes are given when a black marble is picked. Shweta plays the game once.

    • (i) What is the probability that she will be allowed to pick a marble from the bag?
    • (ii) Suppose she is allowed to pick a marble from the bag…
34. 34.
    In Figure-9, a square OPQR is inscribed in a quadrant OAQB of a circle. If the radius of the circle is 6*sqrt(2) cm, find the area of the shaded region.
35. 35.
    Obtain other zeroes of the polynomial p(x) = 2x^4 - x^3 - 11x^2 + 5x + 5, if two of its zeroes are sqrt(5) and -sqrt(5).
36. 36.
    Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
37. 37.
    Sum of the areas of two squares is 544 m^2. If the difference of their perimeters is 32 m, find the sides of the two squares.
38. 38.
    A solid toy is in the form of a hemisphere surmounted by a right circular cone of same radius. The height of the cone is 10 cm and the radius of the base is 7 cm. Determine the volume of the toy. Also find the area of the coloured sheet required to cover the toy. (Use pi = 22/7 and sqrt(149) = 12.2)
39. 39.
    A statue 1.6 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60 degrees and from the same point the angle of elevation of the top of the pedestal is 45 degrees. Find the height of the pedestal. (Use sqrt(3) = 1.73)
40. 40.
    For the following data, draw a 'less than' ogive and hence find the median of the distribution. Age (in years): 0-10, 10-20, 20-30, 30-40, 40-50, 50-60, 60-70 Number of persons: 5, 15, 20, 25, 15, 11, 9

Class 10 Mathematics exam pattern (80 marks)

The theory paper carries 80 marks over 3 hours (38 questions, with internal choice in some). Section-wise structure:

Structure per the CBSE 2023-24 sample-paper design; question wording varies by set.

Prepare with

How to use these papers

1. 1Start chapter-wise early in the year — solve only the Mathematics questions from a chapter you have just finished.
2. 2Switch to full timed papers 2–3 months before the exam: one complete set in the real time limit, no notes.
3. 3Self-mark against the marking scheme, then fix every mistake with our free NCERT solutions.
4. 4Re-attempt your weakest chapters until the recurring question types feel routine.

CBSE Class 10 Mathematics 2020 paper — FAQ