15. $\operatorname { Lim } x \rightarrow 1 \sqrt { } ( 1 - \cos 2 ( x - 1 ) ) / ( x - 1 )$ :\\
(A) exists and it equals $\sqrt { } 2$.\\
(B) exists and it equals $- \sqrt { } 2$\\
(C) does not exist because $x - 1 - - > 0$\\
(D) does not exist because left hand limit is not equal to right hand limit

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\section*{III askllTians III}
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\begin{enumerate}
  \setcounter{enumi}{15}
  \item If in a triangle $P Q R , \sin P , \sin Q , \sin R$ are in $A$. $P$., then :\\
(A) the altitudes are in A.P.\\
(B) the altitudes are in H.P.\\
(C) the medians are in G.P.\\
(D) the medians are in A.P.
  \item If $a n = \sum r = 0 n 1 / n \mathrm { Cr }$, then $\sum r = 0 n \mathrm { r } / \mathrm { n }$ Cr equals:\\
(A) (n - 1) an\\
(B) $n$ an\\
(C) $1 / 2$ nan\\
(D) none of these
  \item If the vertices $P , Q , R$ of a triangle $P Q R$ are rational points, which of the following points of the triangle PQR is/(are) always rational point(s).\\
(A) centroid \&\\
(B) incentre\\
(C) circumcentre\\
(D) orthocenter\\
(A rational point is a point both of whose co-ordinates are rational numbers).
  \item The number of values of $c$ such that the straight line $y = 4 x + c$ touches the curve $x 2 / 4 + \mathrm { y } 2 = 1$ is :\\
(A) 0\\
(B) 1\\
(C) 2\\
(D) infinite.
  \item If $x > 1 , y > 1 , z > 1$ are in G.P., then $1 / ( 1 + \operatorname { In } x ) , 1 / ( 1 + \operatorname { In } y ) , 1 / ( 1 + \operatorname { In } z )$ are in :\\
(A) A.P.\\
(B) H.P.\\
(C) G.P.\\
(D) none of these
  \item The number of values of $x$ in the interval $[ 0,5 p ]$ satisfying the equation $3 \sin 2 x - 7 x + 2 = 0$ is:\\
(A) 0\\
(B) 5\\
(C) 6\\
(D) 10
  \item The order of the differential equation whose general solution is given by
\end{enumerate}

$$\begin{aligned}
& y = \left( C _ { 1 } + C _ { 2 } \right) \cos \left( x + C _ { 3 } \right) - C _ { 4 } e ^ { x + C s } \\
& \text { where } C _ { 1 } , C _ { 2 } , C _ { 3 } , C _ { 4 } , C _ { 5 }
\end{aligned}$$

are arbitrary constants, is:

\section*{III askllTians ||}
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(A) 5\\
(B) 4\\
(C) 3\\
(D) 2\\