Number system: practice set 3

For 1/3 < x < y < 2, which of the following statements is/are always correct?

1. I.x + 1/x < y + 1/y
2. II.√(1 + y²)/y < √(1 + x²)/x

Select the answer using the code given below.

If x and y are two digits and the number 4x5y790 is divisible by 11, then what is the remainder, if x + y is divided by 11?

What is the unit digit in the multiplication of 1 × 3 × 5 × 7 × 9 × ... × 999?

If N² = 12345678987654321, then how many digits does the number N have?

Let p + q = 10, where p, q are integers.

1. Value-I: Maximum value of p × q when p, q are positive integers.
2. Value-II: Maximum value of p × q when p ≥ −6, q ≥ −4.

Which one of the following is correct?

What is the rightmost digit preceding the zeros in the value of 30³⁰?

What is the sum of the first 28 terms in the following sequence?

1, 1, 2, 1, 3, 2, 1, 4, 3, 2, 1, 5, 4, 3, 2, ⋯

If ABC and DEF are both 3-digit numbers such that A, B, C, D, E and F are distinct non-zero digits such that ABC + DEF = 1111, then what is the value of A + B + C + D + E + F?

If p, q, r and s are distinct single digit positive numbers, then what is the greatest value of (p + q)(r + s)?

There are three traffic signals. Each signal changes colour from green to red and then from red to green. The first signal takes 25 seconds, the second signal takes 39 seconds and the third signal takes 60 seconds to change the colour from green to red. The durations for green and red colours are same. At 2:00 p.m, they together turn green. At what time will they change to green next, simultaneously?

Which number amongst 2⁴⁰, 3²¹, 4¹⁸ and 8¹² is the smallest?

Consider the following statements in respect of two natural numbers p and q such that p is a prime number and q is a composite number:

1. 1.p × q can be an odd number.
2. 2.q/p can be a prime number.
3. 3.p + q can be a prime number.

Which of the above statements are correct?

Consider all 3-digit numbers (without repetition of digits) obtained using three non-zero digits which are multiples of 3. Let S be their sum.

Which of the following is/are correct?

1. 1.S is always divisible by 74.
2. 2.S is always divisible by 9.

Select the correct answer using the code given below:

How many zeroes are there at the end of the following product?

1 × 5 × 10 × 15 × 20 × 25 × 30 × 35 × 40 × 45 × 50 × 55 × 60

One page is torn from a booklet whose pages are numbered in the usual manner starting from the first page as 1. The sum of the numbers on the remaining pages is 195. The torn page contains which of the following numbers?

What is the remainder when 51 × 27 × 35 × 62 × 75 is divided by 100?

The ratio of a two-digit natural number to a number formed by reversing its digits is 4: 7. The number of such pairs is

Consider two statements S1 and S2 followed by a question:

1. S1.p and q both are prime numbers.
2. S2.p + q is an odd integer.
3. Question: Is pq an odd integer?

Which one of the following is correct?

A number consists of three digits of which the middle one is zero and their sum is 4. If the number formed by interchanging the first and last digits is greater than the number itself by 198, then the difference between the first and last digits is

There are certain 2-digit numbers. The difference between the number and the one obtained on reversing it is always 27. How many such maximum 2-digit numbers are there?