Numbers and Sequences One Mark Online Test

Numbers and Sequences One Mark Online Test (10th Standard Mathematics)

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Euclid's division lemma states that for positive integers \(a\) and \(b\), there exist unique integers \(q\) and \(r\) such that \(a = bq + r\), where \(r\) must satisfy:

A.\(1 < r < b\) B.\(0 < r < b\) C.\(0 \le r < b\) D.\(0 < r \le b\)

Using Euclid's division lemma, if the cube of any positive integer is divided by \(9\) then the possible remainders are:

A.\(0, 1, 8\) B.\(1, 4, 8\) C.\(0, 1, 3\) D.\(1, 3, 5\)

If the HCF of \(65\) and \(117\) is expressible in the form of \(65m - 117\), then the value of \(m\) is:

A.4 B.2 C.1 D.3

The sum of the exponents of the prime factors in the prime factorization of \(1729\) is:

A.1 B.2 C.3 D.4

The least number that is divisible by all the numbers from \(1\) to \(10\) (both inclusive) is:

A.2025 B.5220 C.5025 D.2520

\(7^{4k} \equiv\) _____ \(\pmod{100}\):

A.1 B.2 C.3 D.4

Given \(F_1 = 1\), \(F_2 = 3\) and \(F_n = F_{n-1} + F_{n-2}\), then \(F_5\) is:

A.3 B.5 C.8 D.11

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 C.7881 D.13531

If \(6\) times of \(6^{\text{th}}\) term of an A.P. is equal to \(7\) times the \(7^{\text{th}}\) term, then the \(13^{\text{th}}\) term of the A.P. is:

A.0 B.6 C.7 D.13

Q10

An A.P. consists of \(31\) terms. If its \(16^{\text{th}}\) term is \(m\), then the sum of all the terms of this A.P. is:

A.16 m B.62 m C.31 m D.\(\frac{31}{2}\) m

Q11

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 C.8 D.9

Q12

If \(A = 2^{65}\) and \(B = 2^{64} + 2^{63} + 2^{62} + \dots + 2^0\), which of the following is true?

A.B is \(2^{64}\) more than A B.A and B are equal C.B is larger than A by 1 D.A is larger than B by 1

Q13

The next term of the sequence \(\frac{3}{16}, \frac{1}{8}, \frac{1}{12}, \frac{1}{18}, \dots\) is:

A.\(\frac{1}{24}\) B.\(\frac{1}{27}\) C.\(\frac{2}{3}\) D.\(\frac{1}{81}\)

Q14

If the sequence \(t_1, t_2, t_3, \dots\) are in A.P. then the sequence \(t_6, t_{12}, t_{18}, \dots\) is:

A.a Geometric Progression B.an Arithmetic Progression C.neither an Arithmetic Progression nor a Geometric Progression D.a constant sequence

Q15

The value of \((1^3 + 2^3 + 3^3 + \dots + 15^3) - (1 + 2 + 3 + \dots + 15)\) is:

A.14400 B.14200 C.14280 D.14520

Q16

If the HCF of 120 and 45 is expressible in the form \(120x - 225\), then the value of \(x\) is

A.1 B.2 C.3 D.4

Q17

If a positive integer \(n\) is divided by \(7\), the remainder is \(5\). What is the remainder when \(n^2\) is divided by \(7\)?

A.1 B.2 C.3 D.4

Q18

If \(2^a \times 3^b \times 5^c = 3600\), where \(a\), \(b\), and \(c\) are natural numbers, then the value of \(a + b + c\) is

A.6 B.7 C.8 D.9

Q19

The least positive integer value of \(x\) satisfying the congruence \(5x \equiv 4 \pmod{6}\) is

A.2 B.4 C.5 D.8

Q20

If the general term of a sequence is \(a_n = (-1)^n (n^2 + 1)\), then the value of \(a_4 - a_3\) is

A.7 B.17 C.27 D.37

Q21

If the \(7^{\text{th}}\) term of an Arithmetic Progression is \(40\) and the \(13^{\text{th}}\) term is \(76\), then its common difference is

A.4 B.5 C.6 D.8

Q22

The sum of the first \(20\) terms of an Arithmetic Progression with first term \(5\) and common difference \(4\) is

A.800 B.820 C.860 D.900

Q23

If the \(3^{\text{rd}}\) term of a Geometric Progression is \(24\) and the \(6^{\text{th}}\) term is \(192\), then its first term is

A.3 B.4 C.6 D.12

Q24

The sum to infinity of the Geometric Progression \(12, 4, \frac{4}{3}, \dots\) is

A.16 B.18 C.20 D.24

Q25

The sum of the squares of the first \(10\) natural numbers is

A.285 B.330 C.385 D.505

Q26

If the sum of the first \(n\) natural numbers is \(15\), then the sum of their cubes is

A.125 B.225 C.625 D.3375

Q27

Using Euclid's division lemma, when the integer \(-25\) is divided by \(4\), the quotient and remainder are respectively

A.\(-6, -1\) B.\(-6, 1\) C.\(-7, 3\) D.\(-7, 1\)

Q28

The number of distinct prime factors in the prime factorization of \(13824\) is

A.2 B.3 C.5 D.6

Q29

If today is Sunday, then the day of the week \(100\) days from now (excluding today) will be

A.Monday B.Tuesday C.Wednesday D.Thursday

Q30

If the three consecutive terms \(x + 2\), \(2x + 3\), and \(5x - 1\) form an Arithmetic Progression, then the value of \(x\) is

A.2 B.3 C.2.5 D.3.5

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About this Numbers and Sequences test

This free online practice test covers Numbers and Sequences from the 10th Standard Mathematics (Samacheer Kalvi) syllabus. Choose the number of questions and an optional time limit, then answer and submit — everything is checked in your browser, with the correct answers and a worked explanation shown at the end. For the full solutions to every question in this set, see the solved MCQs page.

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