What is the molar solubility of $Ag_{2}CO_{3}$ $(K_{sp} = 4 \times 10^{-13})$ in $0.1 \ M \ Na_{2}CO_{3}$ solution?

If a normal chord at a point $t$ on the parabola $y^2=4ax$ subtends a right angle at the vertex,then $t^2$ equals to

The silicates which contain $Si_2O_7^{6-}$ units are called

If $P(A \cup B)=0.8$ and $P(A \cap B)=0.3$,then $P(\bar{A})+P(\bar{B})$ is equal to:

Consider the statements given below regarding contraception and answer as directed thereafter:
$(1)$ Medical Termination of Pregnancy $(MTP)$ during the first trimester is generally safe.
$(2)$ Generally,chances of conception are nil until the mother breast-feeds the infant up to two years.
$(3)$ Intrauterine devices like Copper-$T$ are effective contraceptives.
$(4)$ Contraception pills may be taken up to one week after coitus to prevent conception.
Which two of the above statements are correct?

The value of $\int_0^1 {{{\tan }^{ - 1}}\left( {\frac{{2x - 1}}{{1 + x - {x^2}}}} \right)} \,dx$ is