Class 10 Maths Unit 2 Test Question Paper with Answers

Evaluate your preparation and build real exam confidence with this dedicated 10th Maths Unit 2 Test Question Paper. Focused entirely on Numbers and Sequences, this model test paper is structured according to the latest public exam blueprint. It provides comprehensive coverage of key concepts, including Arithmetic Progression (AP), Geometric Progression (GP), Euclid's Division Lemma, and Modular Arithmetic. Designed with a balanced mix of basic concepts, challenging application problems, and mandatory questions, this paper is the perfect tool for self-assessment and scoring full marks in your unit tests.

CLASS: 10 MATHEMATICS MARKS: 50

TIME: 1.30 Hrs LESSON - 2

I. CHOOSE THE BEST ANSWER 7 × 1 = 7

1. The first term of an arithmetic progression is unity and the common difference is 4. Which of the following will be a term of this A.P.

(A) 4551

(B) 10091

(D) 13531

2. If 6 times of 6th term of an A.P. is equal to 7 times the 7th term, then the 13th term of the A.P. is

(A) 0

(B) 6

(D) 13

3. An A.P. consists of 31 terms. If its 16th term is m, then the sum of all the terms of this A.P. is

(A) 16 m

(B) 62 m

(D) ³¹/₂ m

4. In an A.P., the first term is 1 and the common difference is 4. How many terms of the A.P. must be taken for their sum to be equal to 120?

(A) 6

(B) 7

(D) 9

5. If the sequence t₁, t₂, t₃, ... are in A.P. then the sequence t₆, t₁₂, t₁₈, ... is

(A) a Geometric Progression

(B) an Arithmetic Progression

(D) a constant sequence

6. The value of (1³ + 2³ + 3³ + ... + 15³) - (1 + 2 + 3 + ... + 15) is

(A) 14400

(B) 14200

(D) 14520

7. If 3, x, 6.75 are in G.P. then x is

(A) 4.5

(B) 5.5

(D) 3.5

II. ANSWER THE FOLLOWING QUESTIONS (Q.NO.13 COMPULSORY) 5 × 2 = 10

8. Find the number of terms in the A.P. 3, 6, 9, 12, ..., 111.

9. If 3 + k, 18 - k, 5k + 1 are in A.P. then find k.

10. Find the 8th term of the G.P. 9, 3, 1, ...

11. How many terms of the series 1 + 4 + 16 + ... make the sum 1365?

12. Find the average of first 100 natural numbers.

13. Find the 12th term from the last term of the A.P. -2, -4, -6, ..., -100. (Compulsory)

III. ANSWER THE FOLLOWING QUESTIONS (Q.NO.19 COMPULSORY) 5 × 5 = 25

14. Find the sum of all natural numbers between 300 and 600 which are divisible by 7.

15. A mother divides ₹207 into three parts such that the amounts are in A.P. and gives it to her three children. The product of the two least amounts that the children had 4623. Find the amount received by each child.

16. Find the sum to n terms of the series 3 + 33 + 333 + ...

17. Rekha has 15 square colour papers of sizes 10 cm, 11 cm, 12 cm, ..., 24 cm. How much area can be decorated with these colour papers?

18. If a, b, c are three consecutive terms of an A.P. and x, y, z are three consecutive terms of a G.P. then prove that x^{b - c} × y^{c - a} × z^{a - b} = 1.

19. The product of three consecutive terms of a Geometric Progression is -1 and their sum is ¹³/₁₂. Find the three terms. (Compulsory)

IV. GEOMETRY 8 × 1 = 8

20. Construct a triangle similar to a given triangle PQR with its sides equal to ³/₅ of the corresponding sides of the triangle PQR (scale factor ³/₅ < 1).