Let $f(0)=1, f(0.5)=\frac{5}{4}, f(1)=2, f(1.5)=\frac{13}{4}$ and $f(2)=5$. Using Simpson's rule,$\int_0^2 f(x) dx$ is equal to

Four resistors $A, B, C$ and $D$ form a Wheatstone bridge. The bridge is balanced when $C = 100 \ \Omega$. If $A$ and $B$ are interchanged,the bridge balances for $C = 121 \ \Omega$. The value of $D$ is (in $Omega$)

If $A$ and $B$ are mutually exclusive events with $P(B) \neq 1$,then $P(A \mid \bar{B})$ is equal to (Here $\bar{B}$ is the complement of the event $B$)

$A$ parallel beam of white light falls on a convex lens. Images of blue,red,and green light are formed on the other side of the lens at distances $x, y,$ and $z$ respectively from the pole of the lens. Then:

Which of the following is not a synthetic polymer?

Which of the following statements are correct?
$I$. $P_4$ molecule is very reactive because of angular strain.
$II$. The basicity of $H_3PO_3$ is $3$.
$III$. In gas phase,all $P-Cl$ bonds of $PCl_5$ have same bond length.
$IV$. In solid state,$PCl_5$ exists as an ionic solid,in which anion $[PCl_6]^-$ has octahedral and cation $[PCl_4]^+$ has tetrahedral shape.