10th Maths Chapter 2 - Online Test | Numbers and Sequences

10th Maths Chapter 2 - Online Test | Numbers and Sequences 

1➤ 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 ………………….

1 point(1) 1 < r < b (2) 0 < r < b (3) 0 < r < 6 (4) 0 < r < b

2➤ Using Euclid’s division lemma, if the cube of any positive integer is divided by 9 then the possible remainders are ………………….

1 point(1) 0, 1, 8 (2) 1, 4, 8(3) 0, 1, 3 (4) 1, 3, 5

3➤ If the H.C.F of 65 and 117 is expressible in the form of 65m – 117 , then the value of m is

1 point(1) 4 (2) 2 (3) 1 (4) 3

4➤ The sum of the exponents of the prime factors in the prime factorization of 1729 is …………………….

1 point(1) 1 (2) 2 (3) 3 (4) 4

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

1 point(1) 2025 (2) 5220 (3) 5025 (4) 2520

6➤ 7⁴ᵏ ≡ ______ (mod 100)

1 point(1) 1 (2) 2 (3) 3 (4) 4

7➤ Given F₁ = 1 , F₂ = 3 and Fₙ = Fₙ₋₁ + Fₙ₋₂ then F₅ is ………….

1 point(1) 3 (2) 5 (3) 8 (4) 11

8➤ 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

1 point(1) 4551 (2) 10091 (3) 7881 (4) 13531

9➤ 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 ………..

1 point(1) 0 (2) 6 (3) 7 (4) 13

10➤ 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

1 point(1) 16 m (2) 62 m (3) 31 m (4) `\frac { 31 }{ 2 }` m

11➤ 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?

1 point(1) 6 (2) 7 (3) 8 (4) 9

12➤ A = 2⁶⁵ and B = 2⁶⁴ + 2⁶³ + 2⁶² …. + 2⁰ which of the following is true?

1 point(1) B is 264 more than A (2) A and B are equal (3) B is larger than A by 1 (4) A is larger than B by 1

13➤ The next term of the sequence `\frac { 3 }{ 16 }`,`\frac { 1 }{ 8 }`,`\frac { 1 }{ 12 }`,`\frac { 1 }{ 18 }` is ………..

1 point1) `\frac { 1 }{ 24 }`2) `\frac { 1 }{ 27 }`3) `\frac { 2 }{ 3 }`4 ) `\frac { 1 }{ 81 }`

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

1 point(1) a Geometric Progression (2) an Arithmetic Progression (3) neither an Arithmetic Progression nor a Geometric Progression (4) a constant sequence

15➤ The value of (1³ + 2³ + 3³ + ……. + 15⁵) – (1 + 2 + 3 + …….. + 15) is …………….

1 point(1) 14400 (2) 14200 (3) 14280 (4) 14520

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