Recent questions tagged cat2004

A new flag is to be designed with six vertical stripes using some or all of the colors yellow, green, blue and red. Then the number of ways this can be done such that no ...

Consider the sequence of the numbers $a_1, a_2, a_3, \dots$ to infinity where $a_1 = 81.33$ and $a_2 = -19$, and $a_j = a_{j-1} - a_{j-2}$ for $j \geq 3$. What is the sum...

Answer the questions on the basis of the information given below:$f_{1}(x) = \left\{\begin{matrix} x & 0 \leq x \leq 1 \\ 1 & x \geq 1 \\ 0 & \text{otherwise} \end{matri...

In Nuts and Bolts factory, one machine produces only nuts at the rate of $100$ nuts per minute and needs to be cleaned for five minutes after production of every $1000$ n...

Let $y=\dfrac{1}{2+ \dfrac{1}{3+ \dfrac{1}{2+ \dfrac{1}{3+ \dots } } } }$ what is the value of $y?$$\frac{\sqrt{13} +3} {2}$$\frac{\sqrt{13} -3} {2}$$\frac{\sqrt{15} +3} ...

Suppose $n$ is an integer such that the sum of the digits of $n$ is $2,$ and $10^{10} < n < 10^{11}$. The number of different values for $n$ is$11$$10$$9$$8$

If the sum of first $11$ terms of an arithmetic progression equals that of a first $19$ terms, then what is the sum of the first $30$ terms?$0$$-1$$1$Not unique

Karan and Arjun run a $100$-metre race, where Karan beats Arjun by $10$ metres. To do a favour to Arjun, Karan starts $10$ meters behind the standing line in a second $10...