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CBSE Class 10 Maths Standard 2020 Question Paper

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CBSE Class 10 Maths Standard 2020 Question Paper

CBSE Class 10 Maths Standard 2020 Question Paper

This question paper comprises four sections - A, B, C and D. This question paper carries 40 questions. All questions are compulsory.
Section A: Question no. 1 to 20 comprises of 20 questions of one mark each.
Section B: Question no. 21 to 26 comprises of 6 questions of two marks each.
Section C: Question no. 27 to 34 comprises of 8 questions of three marks each.
Section D: Question no. 35 to 40 comprises of 6 questions of four marks each.

Section A

Question numbers 1 to 10 are multiple choice questions of 1 mark each. Select the correct option.

  1. The sum of exponents of prime factors in the prime-factorisation of 196 is
    1. 3
    2. 4
    3. 5
    4. 2
  2. 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
    1. 0 < r < b
    2. 0 < r ≤ b
    3. 0 ≤ r < b
    4. 0 ≤ r ≤ b
  3. The zeroes of the polynomial x² – 3x – m(m + 3) are
    1. m, m + 3
    2. –m, m + 3
    3. m, –(m + 3)
    4. –m, –(m + 3)
  4. The value of k for which the system of linear equations x + 2y = 3, 5x + ky + 7 = 0 is inconsistent is
    1. –14/3
    2. 2/5
    3. 5
    4. 10
  5. The roots of the quadratic equation x² – 0.04 = 0 are
    1. ± 0.2
    2. ± 0.02
    3. 0.4
    4. 2
  6. The common difference of the A.P. whose general term an = 2n + p is
    1. 1
    2. 1/p
    3. –1
    4. –1/p
  7. The nth term of the A.P. a, 3a, 5a, …… is
    1. na
    2. (2n – 1)a
    3. (2n + 1)a
    4. 2na
  8. The point P on x-axis equidistant from the points A(–1, 0) and B(5, 0) is
    1. (2, 0)
    2. (0, 2)
    3. (3, 0)
    4. (2, 2)
  9. The co-ordinates of the point which is reflection of point (–3, 5) in x-axis are
    1. (3, 5)
    2. (3, –5)
    3. (–3, –5)
    4. (–3, 5)
  10. 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
    1. 4
    2. 3
    3. 2
    4. 1

In Q. Nos. 11 to 15, fill in the blanks. Each question is of 1 mark.

  1. In figure, MN || BC and AM : MB = 1 : 2, then ar(Δ AMN)/ar(Δ ABC) = _________.
    (Figure not shown)
  2. In given Figure, the length PB = _________ cm.
    (Figure not shown)
  3. In ΔABC, AB = 6√3 cm, AC = 12 cm and BC = 6 cm, then ∠B = _________.
    OR
    Two triangles are similar if their corresponding sides are _________.
  4. The value of (tan 1º tan 2º …… tan 89º) is equal to _________.
  5. In figure, the angles of depressions from the observing positions O1 and O2 respectively of the object A are _________, _________.
    (Figure not shown)

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

  1. If sin A + sin² A = 1, then find the value of the expression (cos² A + cos⁴ A).
  2. In figure is a sector of circle of radius 10.5 cm. Find the perimeter of the sector. (Take π = 22/7)
    (Figure not shown; sector angle not specified in text)
  3. 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.
    OR
    What is the probability that a randomly taken leap year has 52 Sundays?
  4. Find the class-marks of the classes 10-25 and 35-55.
  5. A die is thrown once. What is the probability of getting a prime number.

Section B

  1. 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:
    (List of polynomials not shown in text extract)
    Answer the following questions:
    1. How many of the above ten, are not polynomials?
    2. How many of the above ten, are quadratic polynomials?
  2. In figure, ABC and DBC are two triangles on the same base BC. If AD intersects BC at O, show that ar(Δ ABC)/ar(Δ DBC) = AO/DO
    (Figure not shown)
    OR
    In figure, if AD ⊥ BC, then prove that AB² + CD² = BD² + AC².
    (Figure not shown)
  3. Prove that [specific identity not fully shown].
    OR
    Show that tan⁴ θ + tan² θ = sec⁴ θ – sec² θ
  4. The volume of a right circular cylinder with its height equal to the radius is 25 1/7 cm³. Find the height of the cylinder. (Use π = 22/7)
  5. A child has a die whose six faces show the letters as shown below: A B C D E A
    (Die figure not shown)
    The die is thrown once. What is the probability of getting (i) A, (ii) D?
  6. Compute the mode for the following frequency distribution:
    (Table not shown)

Section C

  1. If 2x + y = 23 and 4x – y = 19, find the value of (5y – 2x) and (y/x - 2).
    OR
    Solve for x: [equation not fully specified]
  2. Show that the sum of all terms of an A.P. whose first term is a, the second term is b and the last term is c is equal to (a + c)(b + c – 2a)/2(b – a)
    OR
    Solve the equation: 1 + 4 + 7 + 10 + … + x = 287.
  3. In a flight of 600 km, an aircraft was slowed down due to bad weather. The average speed of the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. Find the duration of flight.
  4. 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).
  5. In Figure, if Δ ABC ~ Δ DEF and their sides of lengths (in cm) are marked along them, then find the lengths of sides of each triangle.
    (Figure not shown)
  6. 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 AQ = 1/2 (BC + CA + AB)
  7. If sin θ + cos θ = √2, prove that tan θ + cot θ = 2.
  8. 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.

Section D

  1. Prove that √5 is an irrational number.
  2. It can take 12 hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for four hours and the pipe of smaller diameter for 9 hours, only half of the pool can be filled. How long would it take for each pipe to fill the pool separately?
  3. Draw a circle of radius 2 cm with centre O and take a point P outside the circle such that OP = 6.5 cm. From P, draw two tangents to the circle.
    OR
    Construct a triangle with sides 5 cm, 6 cm and 7 cm and then construct another triangle whose sides are 3/4 times the corresponding sides of the first triangle.
  4. 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 20 m high building are 45° and 60° respectively. Find the height of the tower.
  5. Find the area of the shaded region in figure, if PQ = 24 cm, PR = 7 cm and O is the centre of the circle.
    (Figure not shown)
    OR
    Find the curved surface area of the frustum of a cone, the diameters of whose circular ends are 20 m and 6 m and its height is 24 m.
  6. The mean of the following frequency distribution is 18. The frequency f in the class interval 19 - 21 is missing. Determine f.
    (Table not shown)
    OR
    The following table gives production yield per hectare of wheat of 100 farms of a village:
    (Table not shown)
    Change the distribution to a ‘more than’ type distribution and draw its ogive.

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