Aptitude · all questions

Number System
practice.

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Q61

The total number of 3 digit numbers which have two or more consecutive digits identical is:

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Q62

A magazine publisher publishes a monthly magazine of 84 pages. One I found that in a magazine 4 pages was missing. One out of them was page number 29 it is known that the page number of the last page of the magazine is 84, (including the cover pages). The numbers printed on the missing pages were :

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Q63

The remainder when 6^{6^{6^{6^{.^{.^∞}}}}} is divided by 10 is :

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Q64

\frac{[ ( 888 \times 888 \times 888 ) - ( 222 \times 222 \times 222 ) ]}{[ ( 888 \times 888 ) + ( 888 \times 222 ) + ( 222 \times 222 ) ]} = ?

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Q65

The remainder of

\frac{32 ^{32^{32}}}{7} :

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Q66

The Remainder of

\frac{888 ^{222} + 222 ^{888}}{3} is :

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Q67

Find the remainder when
10 + 10² + 10³ + 10⁴ + ........ + 10⁹⁹ is divided by 6.

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Q68

The remainder of (3)^67! divided by 80 is :

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Q69

The remainder of

\frac{39 ^{97!}}{40}

is :

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Q70

The remainder of

\frac{2 ^{59}}{255}

is:

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Q71

The number of prime factors in the expressions 6⁴ × 8⁶ × 10⁸ × 12¹⁰ is:

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Q72

x is five digit number. The digit in ten thousands place is 1. the number formed by its digits in units and ten places is divisible by 4. The sum of all the digits is divisible by 3. If 5 and 7 also divide x, then x will be.

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Q73

A man sells chocolates which are in the boxes. Only either full box or half a box of chocolates can be purchased from him. A customer comes and buys half the number of boxes which the seller had plus half box more. A second customer comes and purchases half the remaining number of boxes plus half a box. After this the seller is left with no chocolate boxes. How many chocolate boxes the seller had initially?

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Q74

If x + y + z = 0, then x³ + y³ + z³ is equal to :

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Q75

To write all the page numbers of a book, exactly 136 times digit 1 has been used. Find the number of pages in the book.

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Q76

Given, N = 98765432109876543210 ..... up to 1000 digits, find the smallest natural number n such that N + n is divisible by 11.

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Q77

The remainder when 4⁰ + 4¹ + 4² + 4³ + ........ + 4⁴⁰ is divided by 17 is:

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Q78

The remainder when 3⁰ + 3¹ + 3² + 3³ + . . . . . . . + 3²⁰⁰ is divided by 13 is:

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Q79

The distance between the house of Rajan and Raman is 900 km and the house of former is at 100^th milestone where as the house of Raman is at 1000^th milestone. There are total 901 milestone at a regular interval of 1 km each. When you go to Raman's house from the house of Rajan which are on same highway, you will find that if the last digit (i.e. unit digit) of 3 digit number on every milestone is same as the first (i.e. hundreds digit) of the number on the next milestone is same, then these milestones must be red colour and rest will be of black. Total number of red colour milestone is:

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Q80

Half way through the journey from Delhi to Lahore Atalji began to look out of the window of the Samjhauta Express and continued it until the distance which was remained to cover was half of what he has covered. Now at this time how much distance he has to cover?

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