The half life for radioactive decay of C-14 is 5730 years.
A sample of tree had only 80% of C-14 left.
Estimate the age of the tree.
(log 5 = 0.698) (log 4 = 0.602)

Inversion of cane sugar is a pseudo first order reaction
\(C _{12} H _{22} O _{11}+ H _2 O \xrightarrow{ H ^{+}} C _6 H _{12} O _6+ C _6 H _{12} O _6\)
Choose the correct answer from the options given below:

A first order reaction is found to have rate constant \(k=3.0 \times 10^{-1} \mathrm{~s}^{-1}\). The half-life of the reaction will be:

Trivalent lanthanoid ions which do not show any colour are:

Match the complexes given in List-I with their properties given in List-II

List-I (Complex)	List-II (Property)
(A) \(\left[{FeF}_6\right]^{3-}\)	(I) \(d^6\), high spin
(B) \(\left[{CoF}_6\right]^{3-}\)	(II) \(d^5\), high spin
(C) \(\left[{Mn}({CN})_6\right]^{3-}\)	(III) \(d^6\), low spin
(D) \(\left[{Co}({CN})_6\right]^{3-}\)	(IV) \(d^4\), low spin

Choose the correct answer from the options given below:

p-block elements are placed in groups 13 to 18 of the periodic table. Group 15 is nitrogen family.
Nitrogen makes various compounds like \(NH _3, HNO _3, N_2 O , NO _2\) etc. Phosphorus exists in the form of white and red phosphorus. White phosphorus glows in dark. \(PH _3\) gas is used as smoke screen. Group 16 is called oxygen family. Dry air contains \(21\% O_2\) gas by volume. Combined sulphur exists as sulphates such as gypsum, epsome salt, baryte etc. The allotropic forms of sulphur are Rhombic and monoclinic sulphur. \(S_2\) is paramagnetic like \(O_2\) and it stable at high temperature.
Group 17 is Halogen family. \(F_2\) is highly reactive, \(Cl _2\) is greenish yellow gas. Both \(SO _2\) and \(Cl _2\) are used for bleaching. Group 18 is Noble gas family but some noble gases also form compounds.
Complete hydrolysis of \(XeF _6\) gives HF and \(XeO _3\) as main products.
At elevated temperature \((\sim 1000 K)\) the dominant form of sulphur is :

Which of the following pairs of solutions are isotonic?

The distance of a point \((1, -1, 0)\) from the plane \(\vec{r} \cdot (3\hat{i} - 2\hat{j} - 6\hat{k}) = 4\) is:

According to Joule's law of heating, the rate of heat produced in a resistor is
(A) directly proportional to the current for the given resistance
(B) directly proportional to the square of the current for the given resistance
(C) directly proportional to the resistance for a given value of current
(D) inversely proportional to the resistance for a given voltage
Choose the correct answer from the options given below:

The electric field in a copper wire of cross-sectional area \( 2.0 \, \text{mm}^2 \) carrying a current of 1 A is:
(Given: Resistivity of copper \( \rho = 2 \times 10^{-8} \, \Omega\text{.m} \))

The shortest wavelength in the Balmer series of a hydrogen atom is (Given: \(R=1.1 \times 10^7 m^{-1}\) )

Which of the following statement is not true for the electromagnetic waves?

For \(|x|<1\), if \(x=\cos \left(\frac{1}{a} \log y\right)\), then