| 2023-07-03 | Suppose \( m \) and \( n \) are positive integers and let \( \mathrm{S}=\sum_{\mathrm{k}=0}^{\ma... |
| 2023-07-03 | The value of \( \sum_{\substack{r=0}}^{s} \sum_{\substack{s=1 \\ r \leq s}}^{n} C_{s}^{s} C_{r} ... |
| 2023-07-03 | The largest real value for \( x \) such that \( -\sum_{\mathrm{k}=0}^{4}\left(\frac{5^{4-\mathrm... |
| 2023-07-03 | Let \( S_{1}=\{(i, j, k): i, j, k \in\{1,2, \ldots, 10\}\} \)
\( S_{2}=\{(i, j): 1 \leq \mathrm{... |
| 2023-07-03 | Consider 4 boxes, where each box contains 3 red balls and 2 blue balls. Assume that all 20 balls... |
| 2023-07-03 | Let \( x=(5 \sqrt{2}+7)^{19} \), then \( \mathrm{x}\{\mathrm{x}\}\{ \).\( \} .denotes the fracti... |
| 2023-07-03 | The number of natural numbers lying between 1012 and 23421 that can be formed using the digits \... |
| 2023-07-03 | The number of 4-digit integers in the closed interval \( [2022,4482] \) formed by using the digi... |
| 2023-07-03 | In the expansion of \( \left(1+3 x+2 x^{2}\right)^{6} \) the coefficient of \( x^{11} \) is
(a) ... |
| 2023-07-03 | How many different nine-digit numbers can be formed from the number 223355888 by rearranging its... |
| 2023-07-03 | Number of divisors of the form \( (4 n+2), n \geq 0 \) of the integer 240 is
(a) 4
(b) 8
(c) 10
... |
| 2023-07-03 | Let \( S \) be the set of all passwords which are six to eight characters long, where each chara... |
| 2023-07-03 | Let \( n \) and \( k \) be positive integers such that \( n \geq \frac{k(k+1)}{2} \). The number... |
| 2023-07-03 | The letters of the word MANKIND are written in all possible orders and arranged in serial order ... |
| 2023-07-03 | A class contains \( b \) boys and \( g \) girls. If the number of ways of selecting 3 boys and 2... |
| 2023-07-03 | Number are to formed between 1000 and 3000 , which are divisible by 4 , using the digits \( 1,2,... |
| 2023-07-03 | The number of one-one functions \( f:\{a, b, c, d\} \rightarrow\{0,1 \), \( 2, \ldots ., 10\} \)... |
| 2023-07-03 | The number of 5-digit natural numbers, such that the product of their digits is 36 , is |
| 2023-07-03 | Let \( b_{1} b_{2} b_{3} b_{4} \) be a 4-element permutation with bi \( \in\{1,2,3 \), ...., 100... |
| 2023-07-03 | The total number of four digit numbers such that each of the first three digits is divisible by ... |
| 2023-07-03 | Let \( A \) be a matrix of order \( 2 \times 2 \), whose entries are from the set \( \{0,1,2,3,4... |
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