Numbers and Sequences One Mark

10th Standard EM

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Maths

Time : 00:45:00 Hrs
Total Marks : 15
    15 x 1 = 15
  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

    (a)

    1 < r < b

    (b)

    0 < r < b

    (c)

    \(\le\) r < b

    (d)

    0 < r \(\le\) b

  2. 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)

    0, 1, 3

  3. 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

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

    (a)

    1

    (b)

    2

    (c)

    3

    (d)

    4

  5. 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

  6. 74k \(\equiv \) ________ (mod 100)

    (a)

    1

    (b)

    2

    (c)

    3

    (d)

    4

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

    (a)

    3

    (b)

    5

    (c)

    8

    (d)

    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.

    (a)

    4551

    (b)

    10091

    (c)

    7881

    (d)

    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

    (a)

    0

    (b)

    6

    (c)

    7

    (d)

    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

    (a)

    16 m

    (b)

    62 m

    (c)

    31 m

    (d)

    \(\frac { 31 }{ 2 } \)

  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?

    (a)

    6

    (b)

    7

    (c)

    8

    (d)

    9

  12. If A = 265 and B = 264+263+262+...+20 Which of the following is true?

    (a)

    B is 264 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

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

    (a)

    \(\frac { 1 }{ 24 } \)

    (b)

    \(\frac { 1 }{ 27 } \)

    (c)

    \(\frac { 2 }{ 3 } \)

    (d)

    \(\frac { 1 }{ 81 } \)

  14. 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

    (c)

    neither an Arithmetic Progression nor a Geometric Progression

    (d)

    a constant sequence

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

    (a)

    14400

    (b)

    14200

    (c)

    14280

    (d)

    14520

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