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TS SSC · Class 10

Mathematics Important Questions

High-frequency problems from BSE Telangana Class 10 Maths public exam — algebra, geometry, trigonometry, and statistics questions that appear almost every year.

Ch. 1 Real Numbers & Logarithms — Important Questions

  1. 1Find HCF and LCM of 408 and 170 using prime factorisation. Verify: HCF × LCM = product of numbers.
  2. 2Prove that √3 is irrational. State the theorem you use in your proof.
  3. 3Check whether 6ⁿ can end with digit 0 for any natural number n. Give reason.
  4. 4Find the HCF of 96 and 404 by Euclid's Division Lemma. Hence find their LCM.
  5. 5Without actual division, state whether 17/8 has terminating or non-terminating decimal expansion. Justify.
  6. 6Simplify: log 125 + log 8 − log 1000. (Use laws of logarithms.)
  7. 7If log 2 = 0.3010, find the value of log 50 without using tables.
  8. 8Prove that log(xy) = log x + log y using the definition of logarithms.
  9. 9Solve for x: log₂ x + log₂(x − 6) = 4.

Ch. 2 Sets — Important Questions

  1. 1In a class of 60 students, 35 play cricket, 30 play football, and 15 play both. Find how many play neither.
  2. 2If A = {1, 2, 3, 4, 5} and B = {3, 4, 5, 6, 7}, find A∪B, A∩B, A−B, and B−A. Draw a Venn diagram.
  3. 3In a survey of 100 people, 60 read newspaper A, 50 read B, and 20 read both. Find n(A∪B) and those who read neither.
  4. 4Verify n(A∪B) = n(A) + n(B) − n(A∩B) for given sets A and B.
  5. 5If n(A) = 20, n(B) = 28, n(A∪B) = 36, find n(A∩B). Draw a Venn diagram to illustrate.

Ch. 3, 4, 5 Polynomials & Equations — Important Questions

  1. 1If one zero of the polynomial 3x² − kx − 2 is 2, find the value of k and the other zero.
  2. 2Find a quadratic polynomial whose sum of zeros is 4 and product is 1.
  3. 3Solve: 2x + 3y = 11 and 2x − 4y = −24. Find the value of m if the pair has infinitely many solutions.
  4. 4Find the roots of 3x² − 5x + 2 = 0 by factorisation method.
  5. 5Find the discriminant and nature of roots: 2x² − 3x + 5 = 0 and x² − 4x + 4 = 0.
  6. 6The product of two consecutive positive integers is 306. Find them using a quadratic equation.

Ch. 6 Progressions — Important Questions

  1. 1Find the 10th term and sum of first 20 terms of AP: 3, 7, 11, ...
  2. 2How many terms of the AP 3, 5, 7, ... must be taken so that the sum is 120?
  3. 3The sum of n terms of an AP is 5n² − 3n. Find the AP and its 20th term.
  4. 4Find which term of the GP 2, 4, 8, 16, ... is 512.
  5. 5The 4th term of a GP is 54 and the 7th term is 1458. Find the GP.

Ch. 7, 8, 9 Geometry — Important Questions

  1. 1Prove the Basic Proportionality Theorem (Thales Theorem): If a line is parallel to one side of a triangle, it divides the other two sides proportionally.
  2. 2Prove that the tangent drawn to a circle at any point is perpendicular to the radius at the point of tangency.
  3. 3Prove that the lengths of the two tangents drawn from an external point to a circle are equal.
  4. 4In ΔABC, D and E are on AB and AC respectively such that DE ∥ BC. If AD/DB = 3/4 and AC = 14 cm, find AE.
  5. 5Find the area of a triangle whose vertices are (2, 3), (−1, 0), and (2, −4) using the coordinate formula.
  6. 6Two tangents are drawn from external point P to a circle of radius 5 cm. If length of each tangent is 12 cm, find the distance OP.

Ch. 11, 12 Trigonometry — Important Questions

  1. 1Prove: sin²θ + cos²θ = 1. Hence derive 1 + tan²θ = sec²θ and 1 + cot²θ = cosec²θ.
  2. 2If tan θ = 4/3, evaluate (sin θ + cos θ) and verify sin²θ + cos²θ = 1.
  3. 3Prove: (sin A + cosec A)² + (cos A + sec A)² = 7 + tan²A + cot²A.
  4. 4From the top of a 75 m high tower, the angles of depression of two cars on either side are 30° and 45°. Find the distance between the two cars.
  5. 5A ladder 10 m long makes an angle of 60° with the ground. Find: (i) height reached on wall (ii) distance of foot from wall.

Ch. 10, 13, 14 Mensuration, Probability & Statistics

  1. 1A solid is in the form of a cone mounted on a hemisphere with same radius 7 cm. If height of cone is 14 cm, find total surface area and volume.
  2. 2A vessel is in the form of a hollow hemisphere mounted on a cylinder. The diameter is 14 cm, hemisphere height 7 cm, cylinder height 13 cm. Find inner surface area.
  3. 3Find the mean of the following frequency distribution using the step-deviation method (table with class intervals).
  4. 4Find the median from a given ogive or frequency distribution table. Show the cumulative frequency table.
  5. 5Two dice are rolled simultaneously. Find the probability that: (i) sum is 8 (ii) difference is 2 (iii) both show same number.

More for Mathematics

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