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.
Algebra — High Frequency
- 1Find the roots of the quadratic equation ax² + bx + c = 0 using the quadratic formula
- 2If α and β are roots of 2x² − 5x + 3 = 0, find α + β and αβ without solving
- 3Find the 10th term and sum of first 20 terms of AP: 3, 7, 11, ...
- 4The sum of n terms of an AP is 5n² − 3n. Find the first term and common difference
- 5Solve the pair of linear equations: 3x + 4y = 10 and 2x − y = 5 by elimination method
Geometry — High Frequency
- 1Prove that the tangent to a circle at any point is perpendicular to the radius at that point
- 2In triangle ABC, D and E are points on AB and AC such that DE || BC. Prove that AD/DB = AE/EC
- 3Draw a pair of tangents from an external point to a circle of radius 4 cm, where point is 7 cm from centre
- 4Find the area of a sector with radius 14 cm and angle 60°
- 5A chord of a circle of radius 10 cm subtends an angle of 90° at the centre. Find the area of the minor segment
Trigonometry — High Frequency
- 1Prove: sin²θ + cos²θ = 1 and derive the other two forms
- 2If tan θ = 4/3, find sin θ, cos θ, and verify sin²θ + cos²θ = 1
- 3From the top of a 60 m high building, the angle of depression of a car is 30°. Find the distance of the car from the base
- 4Prove: (sin A + cosec A)² + (cos A + sec A)² = 7 + tan²A + cot²A
- 5A ladder 10 m long makes an angle of 60° with the ground. Find the height it reaches on the wall
Statistics & Probability
- 1Find the mean of the following grouped data using the step-deviation method
- 2Find the median class and hence the median for a given frequency distribution table
- 3Find the mode of the data: frequency table with modal class identified
- 4A bag has 5 red and 3 blue balls. Find the probability of drawing a red ball at random
- 5Two dice are thrown simultaneously. Find the probability that the sum of numbers is 8
Real Numbers & Polynomials
- 1Find the HCF and LCM of 408 and 170 using prime factorisation
- 2Prove that √3 is irrational
- 3Divide the polynomial p(x) = x³ − 3x + 5 by g(x) = x − 1 and find quotient and remainder
- 4If one zero of the polynomial 3x² − kx − 2 is 2, find the value of k and the other zero
- 5Check whether 6ⁿ can end with digit 0 for any natural number n