AIEEE 2005 Maths Question Paper Mock Test

A particle is projected from a point $O$ with velocity $u$ at an angle of $60^{\circ }$ with the horizontal. When it is moving in a direction at right angles to its direction at $O$, its velocity then is given by:

If both the roots of the quadratic equation $x^2-2kx+k^2+k-5=0$ are less than $5$, then $k$ lies in the interval:

If $a_1,a_2,a_3,\dots ,a_n,\dots$ are in G.P., then the determinant $\Delta =\left|\begin{array}{ccc}\log a_n& \log a_{n+1}& \log a_{n+2}\\ \log a_{n+3}& \log a_{n+4}& \log a_{n+5}\\ \log a_{n+6}& \log a_{n+7}& \log a_{n+8}\end{array}\right|$ is equal to:

A real valued function $f(x)$ satisfies the functional equation $f(x-y)=f(x)f(y)-f(a-x)f(a+y)$ where $a$ is a given constant and $f(0)=1$. Then $f(2a-x)$ is equal to:

If the equation $a_n{x}^n+a_{n-1}{x}^{n-1}+\cdots +a_{1}x=0,a_1\ne 0,n\ge 2$, has a positive root $x=\alpha$, then the equation $n{a}_n{x}^{n-1}+(n-1)a_{n-1}{x}^{n-2}+\cdots +a_1=0$ has a positive root, which is: