Combination of n Different Things Taken One or More at a Time

Q. Number of divisors of the form (4n + 2), n ≥ 0 of the integer 240 is ?

1. 4
2. 8
3. 10
4. 3

Q. Calculate the value of k.
$(\frac{2}{3}{)}^4\times (\frac{2}{3}{)}^2=(\frac{4}{9}{)}^{(2k-3)}$

1. 7
2. 6
3. 3
4. 2

Q.

Carry out the following division.

$8$ by $-2$

Q. How many $3$ digit even numbers between can be formed with the digit $0,1,2,3,4,5$ and $6$ with no repetition.

1. $105$
2. $57$
3. $51$
4. None of these

Q. Find the sum of the infinite series $1+(1+a)b+(1+a+a^2)b^2+(1+a+a^2+a^3)b^3+....b$ and a being proper fractions.

Q. Total number of four digit odd numbers that can be formed by using $0,1,2,3,5,7$ are

1. $216$
2. $375$
3. $400$
4. $720$

Q. The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that each person gets at least one ball is

1. 75
2. 150
3. 210
4. 243

Q. A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are ladies and 4 are men. Assume X and Y have no common friend. Number of ways in which X & Y together can throw a party inviting 3 ladies and 3 men, so that 3 friends of each of X and Y are in this party, is ?

1. 485
2. 468
3. 484
4. 469

Q. There is a group of boys facing south and standing in a row. Deepak ranks $9^{th}$ from left of shubham who is ${17}^{th}$ from right end. If harsh, the ${16}^{th}$ from the left end is 6th to the right of Deepak. How many boys are there in a row ?

1. $30$
2. $35$
3. $42$
4. Cant be determined

Q. A can do a piece of work in $5$ days and B can do the same work in $20$ days. In the same assignment, they work together for $2$ days. Due to some emergency, they opted out from this assignment after working together for $2$ days. Then to complete the pending work, C joined who is half as efficient as A. How many days C will take to finish the remaining work ?

1. $5$
2. $7$
3. $4$
4. $10$

Q. Let S = {1, 2, 3, ………, 9}. For k = 1, 2, ……..5, let $N_k$ be the number of subsets of S, each containing five elements out of which exactly k are odd. Then $N_1+N_2+N_3+N_4+N_5=$

1. 210
2. 252
3. 126
4. 125

Q. The simplified value of $(5^{-1}÷4^{-1}{)}^3$ is given by $\frac{a}{b}$, where $a$ and $b$ are co-primes, then find the value of $2a-b$.

Q. Carry needs to open a box with a numeric password. The incomplete password written on the box is 427_64_ along with a hint. In how many ways can the box be opened?
(Hint: The password is divisible by 15.)

1. 6
2. 9
3. 15
4. 8

Q. The sum of all the numbers that can be formed by writing all the digits $3,2,3,4$ only once is

1. $39996$
2. $49996$
3. $57776$
4. None of these