AIEEE 2008 PYQ Mock Test

In a shop there are five types of ice-creams available. A child buys six ice-creams.Statement - 1: The number of different ways the child can buy the six ice-creams is ${}^{10}{C}_5$.Statement - 2: The number of different ways the child can buy the six ice-creams is equal to the number of different ways of arranging $6$ A’s and $4$ B’s in a row.

Let $f(x)=\{\begin{array}{ll}(x-1)\sin \left(\frac{1}{x-1}\right)& \text{if }x\ne 1\\ 0& \text{if }x=1\end{array}$. Then which one of the following is true?

The first two terms of a geometric progression add up to $12$. The sum of the third and the fourth terms is $48$. If the terms of the geometric progression are alternately positive and negative, then the first term is:

Suppose the cube $x^3-px+q$ has three distinct real roots where $p>0$ and $q>0$. Then which one of the following holds?

How many real solutions does the equation $x^7+14x^5+16x^3+30x-560=0$ have?