CBSE Std-10 Mathematics — Practice Paper
CBSE Std 10 · Mathematics
General instructions: Attempt all questions. Marks for each question are shown in the right margin. Internal choice, where given, is indicated by “OR”.
Section A
- 1.
Two positive integers have HCF 6 and LCM 60. If one integer is 12, the other is:
[1]- (a)20
- (b)30
- (c)60
- (d)15
- 2.
If α and β are zeroes of p(x) = x² − 5x + 6, then α + β equals:
[1]- (a)5
- (b)6
- (c)−5
- (d)−6
- 3.
The system of linear equations 2x + 3y = 7 and 4x + 6y = 14 has:
[1]- (a)Unique solution
- (b)No solution
- (c)Infinite solutions
- (d)Two solutions
- 4.
The discriminant of 3x² − 4x + 2 = 0 is:
[1]- (a)16
- (b)−8
- (c)8
- (d)24
- 5.
In an AP with first term a = 2 and common difference d = 3, the 5th term is:
[1]- (a)14
- (b)11
- (c)17
- (d)10
- 6.
If ΔABC ~ ΔPQR and AB/PQ = 3/4, then Area(ΔABC)/Area(ΔPQR) =
[1]- (a)3/4
- (b)9/16
- (c)4/3
- (d)16/9
- 7.
The distance between points A(3, 4) and B(0, 0) is:
[1]- (a)7
- (b)5
- (c)25
- (d)√7
- 8.
If sin θ = 3/5 and θ is acute, then cos θ =
[1]- (a)4/5
- (b)5/4
- (c)3/4
- (d)4/3
- 9.
Using the Euclidean algorithm, HCF(135, 225) =
[1]- (a)15
- (b)45
- (c)5
- (d)225
- 10.
If α and β are zeroes of x² + 3x − 4, then αβ =
[1]- (a)3
- (b)−4
- (c)4
- (d)−3
Section B
- 11.
Solve x² − 5x + 6 = 0 by factorization.
[2] - 12.
Find the sum of the first 20 terms of the arithmetic progression: 2, 5, 8, ...
[2] - 13.
Find the coordinates of the midpoint of the line segment joining A(3, 4) and B(7, 8).
[2]
Section C
- 14.
(Choice A) Solve the following system of linear equations graphically: x + y = 5 and 2x − y = 4
[3] - 14.
(Choice B) Solve the following system of linear equations by the elimination method: 3x + 2y = 11 and 2x + 3y = 9
[3] - 15.
(Choice A) State and prove the Basic Proportionality Theorem (Thales' Theorem).
[3] - 15.
(Choice B) In ΔABC, DE || BC where D is on AB and E is on AC. If AD/DB = 2/3 and AC = 15 cm, find the length of AE.
[3] - 16.
(Choice A) Prove the following trigonometric identity: (sin θ + cos θ)² + (sin θ − cos θ)² = 2
[3] - 16.
(Choice B) Find the value of: sin 60° − cos 30° + tan 45°
[3]
Section D
- 17.
(Choice A) Divide x⁴ + 1 by x² − 1 using the polynomial long division algorithm and write the quotient and remainder.
[5] - 17.
(Choice B) Find all the zeroes of p(x) = x³ − 6x² + 11x − 6.
[5] - 18.
(Choice A) The sum of the first n terms of an arithmetic progression is Sₙ = 5n² + 3n. Find the AP and hence find its 15th term.
[5] - 18.
(Choice B) In an arithmetic progression, the sum of the first 10 terms is 120 and the sum of the first 20 terms is 480. Find the first term and the common difference.
[5]
Section E
- 19.
A school library has 432 Hindi books and 360 English books. The librarian wants to arrange these books in equal piles where each pile contains only one type of book and all piles have the same number of books. (a) Find the maximum number of books in each pile. (b) How many piles of Hindi books will be formed? (c) How many piles of English books will be formed? (d) What is the total number of piles?
[4] - 20.
A city park is designed in the shape of a quadrilateral with vertices at A(0, 0), B(4, 0), C(6, 3), and D(0, 3). Using coordinate geometry concepts: (a) Find the length of the diagonal AC. (b) Find the distance from vertex B to vertex D. (c) Find the coordinates of the midpoint of diagonal BD. (d) Verify whether ABCD forms a trapezium by checking if any pair of opposite sides is parallel.
[4]