PSEB 10TH CLASS MATHEMATICS SOLVED QUESTION PAPER BOARD SAMPLE PAPER PDF

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PSEB 10TH CLASS MATHEMATICS SOLVED QUESTION PAPER BOARD SAMPLE PAPER PDF

Solution to the Provided Paper

In this blog post, we will walk through the solutions to the questions provided in the paper. The paper is divided into four parts: Part-A, Part-B, Part-C, and Part-D. Each part contains questions of varying difficulty and marks. Let’s dive into the solutions step by step.

Part-A (1 Mark Each)

Choose the correct option:

  1. (i) Which of the following numbers is a rational number?
  • Answer: (d) 2.75
  1. (ii) If α and β are the zeros of quadratic polynomial p(x) = ax² + bx + c, a ≠ 0, then factors of p(x) are:
  • Answer: (a) x – α, x – β
  1. (iii) What is the degree of a linear polynomial?
  • Answer: (a) 1
  1. (iv) What will be the condition of lines when the equations 3x – y = 3; 9x – 3y = 9 are represented by a graph?
  • Answer: (c) Coincide
  1. (v) A quadratic equation ax² + bx + c = 0 has unique real roots, if:
  • Answer: (b) b² – 4ac = 0
  1. (vi) If the first term of an A.P. is a and d be the common difference, then its nth term is:
  • Answer: (c) a + (n – 1)d
  1. (vii) Which of the following is not a criterion for similarity of two triangles?
  • Answer: (d) RHS
  1. (viii) How many tangents can be drawn to a circle from a point lies on it?
  • Answer: (a) 1
  1. (ix) 3 sin²A + 3 cos²A is equal to:
  • Answer: (b) 3
  1. (x) Value of tan 30° is:
    • Answer: (c) 1/√3
  2. (xi) Find the central angle if the area of the corresponding sector is one-fourth of the area of the circle?
    • Answer: (a) 90°
  3. (xii) What is the length of a cuboid by joining the edges of three cubes of side 4 cm each?
    • Answer: (c) 12 cm
  4. (xiii) What is the relation between the volumes of a cylinder and a cone of the same radius and same height?
    • Answer: (a) Volume of a cylinder = 3 × Volume of cone
  5. (xiv) What is the class mark of the class interval 10-25?
    • Answer: (c) 17.5
  6. (xv) If Y, R, and B be the fundamental events of an experiment, then P(Y) + P(B) + P(R) will be:
    • Answer: (d) 1
  7. (xvi) Probability of a sure event will be:
    • Answer: (b) 1
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Choose the true or false answers:

  1. (i) 1/√2 is an irrational number.
  • Answer: True
  1. (ii) If in a system of equations a1/a2 ≠ b1/b2, then the pair of equations is consistent.
  • Answer: True
  1. (iii) If the discriminant of a quadratic equation is equal to 0, then the equation has equal roots.
  • Answer: True
  1. (iv) The tangent of a circle intersects the circle at only one point.
  • Answer: True
  1. (v) The distance of a point (6, 8) from a point (0, 0) is 10 units.
  • Answer: True
  1. (vi) The value of tan A is always less than 1.
  • Answer: False
  1. (vii) The class interval with maximum frequency is called the median class.
  • Answer: False

Fill in the blanks:

  1. (i) If x + y = 5 and x – y = 7, then the value of x is 6.
  2. (ii) The next term of an A.P.: a, a + d, a + 2d will be a + 3d.
  3. (iii) In the given figure DE || BC, the value of AD is 8.
  4. (iv) The mid-point of a line segment joining the points A(2, 3) and B(4, 3) will be (3, 3).
  5. (v) Area of a sector = Area of a corresponding segment – Area of its corresponding triangle.
  6. (vi) Volume of a sphere is (4/3)πr³.
  7. (vii) In a pack of playing cards, cards of king, queen, and jack are called face cards.

Part-B (2 Marks Each)

  1. Find H.C.F. and L.C.M. of 12, 15, and 21 by the prime factorization method.
  • Solution:
    • 12 = 2² × 3
    • 15 = 3 × 5
    • 21 = 3 × 7
    • H.C.F. = 3
    • L.C.M. = 2² × 3 × 5 × 7 = 420
  1. Find zeros of x² – 2x – 8.
  • Solution:
    • x² – 2x – 8 = 0
    • x² – 4x + 2x – 8 = 0
    • x(x – 4) + 2(x – 4) = 0
    • (x – 4)(x + 2) = 0
    • x = 4, x = -2
  1. Find the area of the sector of a circle with a radius of 6 cm and an angle of the sector at the center of the circle is 60°.
  • Solution:
    • Area of sector = (θ/360°) × πr²
    • Area of sector = (60°/360°) × π × 6²
    • Area of sector = (1/6) × π × 36
    • Area of sector = 6π cm²
  1. Savita and Hamida are two friends. Find the probability of their birthday will be:
  • (i) on different days
    • Probability = 364/365
  • (ii) on the same day.
    • Probability = 1/365
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Part-C (4 Marks Each)

  1. Find the nature of the roots of the quadratic equation 2x² – 3x – 5 = 0. If roots are possible, then find them.
  • Solution:
    • Discriminant (D) = b² – 4ac = (-3)² – 4(2)(-5) = 9 + 40 = 49
    • Since D > 0, the roots are real and distinct.
    • 2x² – 5x + 2x – 5 = 0
    • x(2x – 5) + 1(2x – 5) = 0
    • (2x – 5)(x + 1) = 0
    • x = 5/2, x = -1
  1. Find the sum of the A.P. 34 + 32 + 30 + … + 10.
  • Solution:
    • a = 34, d = -2, an = 10
    • an = a + (n – 1)d
    • 10 = 34 + (n – 1)(-2)
    • -24 = -2n + 2
    • -26 = -2n
    • n = 13
    • Sn = n/2 (a + an) = 13/2 (34 + 10) = 13/2 × 44 = 286

Part-D (6 Marks Each)

  1. The length of a rectangular garden is 4 meters more than its breadth, and its perimeter is 36 meters. Find the length and breadth of the garden.
  • Solution:
    • Let the breadth be x meters.
    • Length = x + 4 meters
    • Perimeter = 2(length + breadth)
    • 36 = 2(x + 4 + x)
    • 18 = 2x + 4
    • 14 = 2x
    • x = 7 meters (breadth)
    • Length = 7 + 4 = 11 meters

This concludes the solutions to the provided paper. If you have any questions or need further clarification, feel free to leave a comment below!