How many distinct 8-digit numbers can be formed by rearranging the digits of the number 11223344 such that odd digits occupy odd positions and even digits occupy even positions?

Questions: Is p greater than q?

Statement-1: $p \times q$ is greater than zero. Statement-2: $p^2$ is greater than $q^2$.

Which one of the following is correct in respect of the above Question and the Statements?

125 identical cubes are arranged in the form of cubical block. How many cubes are surrounded by other cubes from each side?

A, B, C working independently can do a piece of work in 8, 16 and 12 days respectively. A alone works on Monday, B alone works on Tuesday, C alone works on Wednesday; A alone, again works on Thursday and so on. consider the following statements:

1. The work will be finished on Thursday.
2. The work will be finished in 10 days.

Which of the above statements is/are correct?

In how many ways can a batsman score exactly 25 runs by scoring single runs, fours and sixes only, irrespective of the sequence of scoring shots?

Questions: Is $(p + q - r)$ greater than $(p - q + r)$, where p, q and r are integers? Statement-1: $(p - q)$ is positive. Statement-2: $(p - r)$ is negative.

Which one of the following is correct in respect of the above Question and the Statements?

A cuboid of dimensions $7\text{cm} \times 5\text{cm} \times 3\text{cm}$ is painted red, green and blue colour on each pair of opposite faces of dimensions $7\text{cm} \times 5\text{cm}$, $5\text{cm} \times 3\text{cm}$, $7\text{cm} \times 3\text{cm}$ respectively. Then the cuboid is cut and separated into various cubes each of side length $1\text{cm}$. Which of the following statements is/are correct?

1. There are exactly 15 small cubes with no paint on any face.
2. There are exactly 6 small cubes with exactly two faces, one painted with blue and the other with green.

Select the correct answer using the code given below:

Consider a 3-digit number.

Question: What is the number? Statement-1: The sum of the digits of the number is equal to the product of the digits. Statement-2: The number is divisible by the sum of the digits of the number.

Which one of the following is correct in respect of the above Question and the Statements?

There are large number of silver coins weighing $2$gm, $5$gm, $10$gm, $25$gm, $50$gm each. Consider the following statements:

1. To buy $78$ gm of coins one must buy at least $7$ coins.
2. To weigh $78$ gm using these coins one can use less than $7$ coins.

Which of the statements given above is/are correct?

If today is Sunday, then which day is it exactly on $10^{10}$th day?

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 $A + B + C + D + E + F$?

How many natural numbers are there which given a remainder of 31 when 1186 is divided by these natural numbers?

D is a 3-digit number such that the ratio of the number to the sum of its digits is least. What is the difference between the digit at the hundred's place and the digit at the unit's place of D?

What is the number of selections of 10 consecutive things out of 12 things in a circle taken in the clockwise direction?

ABCD is a square. One point on each of AB and CD; and two distinct points on each of BC and DA are chosen. How many distinct triangles can be drawn using any three points as vertices out of these six points?

For any choices of values of X, Y and Z, the 6 digit number of the form $XYZXYZ$ is divisible by:

Consider the following in respect of prime number p and composite number c.

1. $\frac{(p + c)}{(p - c)}$ can be even.
2. $2p + c$ can be odd.
3. $pc$ can be odd.

Which of the statements given above are correct?

What is the unit digit in the expansion of $57242^{9 \times 7 \times 5 \times 3 \times 1}$?

A rectangular floor measures 4 m in length and 2.2m in breadth. Tiles of size 140 cm by 60 cm have to be laid such that the tiles do not overlap. A tile can be placed in any orientation so long as its edges are parallel to the edges of the floor. What is the maximum number of tiles that can be accommodated on the floor?

What is the remainder when $85 \times 87 \times 89 \times 91 \times 95 \times 96$ is divided by 100?

There are five persons, P, Q, R, S and T each one of whom has to be assigned one task. Neither P nor Q can be assigned Task-1. Task-2 must be assigned to either R or S. In how many ways can the assignment be done?

Let $pp$, $qq$ and $rr$ be 2 digit numbers where $p < q < r$. If $pp + qq + rr = tt0$, where $tt0$ is a 3-digit number ending with zero, consider the following statements:

1. The number of possible values of $p$ is 5.
2. The number of possible values of $q$ is 6

Which of the above statements is/are correct?

A 3-digit number ABC, on multiplication with D gives 37DD where A, B, C and D are different non-zero digits. What is the value of $A + B + C$?

AB and CD are 2-digit numbers. Multiplying AB with CD results in a 3-digit number DEF. Adding DEF to another 3-digit number GHI results in 975. Further A, B, C, D. E, F, G, H, I are distinct digits. If E = 0, F = 8, then what is A + B + C equal to?

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?

A box contains 14 black balls, 20 blue balls, 26 green balls, 28 yellow balls, 38 red balls and 54 white balls.

Consider the following statements:

1. The smallest number n such that any n balls drawn from the box randomly must contain one full group of at least one colour is $175$.
2. The smallest number m such that any m balls drawn from the box randomly must contain at least one ball of each colour is $167$.

Which of the above statements is/are correct?

What is the sum of all digits which appear in all the integers from 10 to 100 ?

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

What is the sum of all 4-digit numbers less than 2000 formed by the digits 1, 2, 3 and 4, where none of the digits is repeated?

There are four letters and four envelopes and exactly one letter is to be put in exactly one envelope with the correct address. If the letters are randomly inserted into the envelopes, then consider the following statements:

1. It is possible that exactly one letter goes into an incorrect envelope.
2. There are only six ways in which only two letters can go into the correct envelopes.

Which of the statements given above is/are correct?

A principal $P$ is lent in 1 year when compounded half-yearly with $R\%$ annual rate of interest. If the same principal $P$ is lent in 1 year when compounded annually with $S\%$ annual rate of interest, then which one of the following is correct?

Each digit of a 9-digit number is 1. It is multiplied by itself. What is the sum of the digits of the resulting number?

A number N is formed by writing 9 for 99 times. What is the remainder if N is divided by 13?

Let x be a positive integer such that $7x + 96$ is divisible by x. How many values of x are possible?

In an examination, the maximum marks for each of the four papers namely P, Q, R and S are 100. Marks scored by the students are in integers. A student can score 99% in n different ways. What is the value of n? Let $p$, $q$, $r$, and $s$ be the marks scored in papers P, Q, R, and S respectively. Since the maximum marks for each paper is 100, we have $0 \le p, q, r, s \le 100$. The total marks is $p+q+r+s$. The maximum possible total marks is $4 \times 100 = 400$. 99% of the maximum marks is $0.99 \times 400 = 396$. We need to find the number of integer solutions to the equation $p+q+r+s = 396$, subject to the constraint $0 \le p, q, r, s \le 100$.

Without the upper bound restriction, the number of non-negative integer solutions is given by $\binom{396+4-1}{4-1} = \binom{399}{3}$. However, we have the constraint $p, q, r, s \le 100$. Let $p' = 100 - p$, $q' = 100 - q$, $r' = 100 - r$, $s' = 100 - s$. Then $0 \le p', q', r', s' \le 100$. $p+q+r+s = 396$ $(100-p')+(100-q')+(100-r')+(100-s') = 396$ $400 - (p'+q'+r'+s') = 396$ $p'+q'+r'+s' = 400-396 = 4$ The number of non-negative integer solutions to $p'+q'+r'+s'=4$ is $\binom{4+4-1}{4-1} = \binom{7}{3} = \frac{7 \times 6 \times 5}{3 \times 2 \times 1} = 35$. Thus, $n = 35$.

Final Answer: The final answer is $\boxed{35}$

Three of the five positive integers p, q, r, s, t are even and two of them are odd (not necessarily in order). Consider the following:

1. $p + q + r – s - t$ is definitely even.
2. $2p + q + 2r - 2s + t$ is definitely odd.

Which of the above statements is/are correct?

40 children are standing in a circle and one of them (say child-1) has a ring. The ring is passed clockwise. Child-1passes on the child-2, child-2 passes on to child-4, child-4 passes on to child-7 and so on. After how many such changes (including child-1) will the ring be in the hands of child-1 again?

In a party, 75 persons took tea, 60 persons took coffee and 15 persons took both tea and coffee. No one taking milk takes tea. Each person takes at least one drink.

Question: how many persons attended the party? Statement-1: 50 persons took milk. Statement-2: Number of persons who attended the party is five times the number of persons who took milk only.

Which one of the following is correct in respect of the above Question and the Statements?

What is the remainder if $2^{192}$ is divided by 6?