0 votes
50
How many positive integers are factors of 2310?
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52
A thin piece of metal of length $20$ cm and width $16$ cm is to be used to construct an open-topped box. A square will be cut from each corner and the sides will be folde...
0 votes
53
Let $p(x)$ be a polynomial with integer coefficients. Let $n$ be a positive integer and suppse $a$ and $b$ are two integers such that $a \equiv b(\text{mod}\;n)$. Is it t...
0 votes
54
Show that among any set of $7$ distinct integers there must exist $2$ integers whose sum or difference is divisible by $10$.
0 votes
55
A small circular fire is spreading with its radius increasing at the rate of $1.5$ meters per minute. When the radius of the fire is $5$ metres, how fast is the burned ar...
0 votes
58
If the lines $2x+y=2,-5x+3y=4$ and $ax+by=1$ are concurrent then prove that the line $9x-10y=1$ passes through $(a,b).$
0 votes
59
Four friends attending an opera leave their coats at the checkroom. When they return each one is handed a coat that does not belong to her. In how many ways can this happ...
0 votes
60
Suppose $X$ is a continuous distribution with probability density function$$f(x)=k(x-x^2),\;0\leq x\leq 1,$$where $k$ is the normalizing constant. Find the value of $k$ a...