The number of bond pairs, lone pairs present on the central atom of \(\mathrm{SF}_4\) molecule and its shape respectively are

When ' \(\mathrm{X}\) ' \(\mathrm{g}\) of graphite is completely burnt in a bomb calorimeter in excess of \(\mathrm{O}_2\) at \(298 \mathrm{~K}\) and \(1 \mathrm{~atm}\) pressure as given in the equation
\(\mathrm{C}\) (graphite) \(+\mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{CO}_2(\mathrm{~g})\)
The temperature of calorimeter raised from \(298 \mathrm{~K}\) to \(302 \mathrm{~K}\). If the heat capacity of the calorimeter and molar enthalpy change for the reaction at \(1 \mathrm{~atm}\) and \(298 \mathrm{~K}\) are \(20.7 \mathrm{~kJ} \mathrm{~K}^{-1}\) and \(-248.4 \mathrm{~kJ} \mathrm{~mol}^{-1}\), ' \(\mathrm{X}^{\prime}\) in \(\mathrm{g}\) is

Match the following

List - I (Pollutant concentration limit in water)	List - II (Effect)
\(\mathrm{Pb}>50\ \mathrm{ppb}\)	Brown mottling of teeth
\(\mathrm{SO}_4^{2-}>500\ \mathrm{ppm}\)	'Blue baby' syndrome
\(\mathrm{NO}_3^{-}>50\ \mathrm{ppm}\)	Laxative effect
\(\mathrm{F}^{-}>2\ \mathrm{ppm}\)	Liver damage

The correct answer is

The reaction of benzene diazonium chloride with Cu and HCl is known as

Consider the following reaction


Which of the following statements are correct ?
a. I is the major product of the reaction
b. II is the major product of the reaction
c. Formation of I is in accordance with Saytzeff's rule
d. II is more stable because it is more substituted

What is the osmotic pressure (in atm) of \(0.02 \mathrm{M}\) aqueous glucose solution at \(300 \mathrm{~K}\) ?
\(\left(\mathrm{R}=0.082 \mathrm{~L} \mathrm{~atm} \mathrm{~mol}{ }^{-1} \mathrm{~K}^{-1}\right)\)

Two statements are given below
Statement I: Chlorobenzene on nitration gives 1-chloro4-nitrobenzene as major product
Statement II: Chlorobenzene undergoes nitration slowly than benzene
Identify the correct answer

A proton, a deuteron (nucleus of \({ }_1 \mathrm{H}^2\) ) and an \(\alpha\)-particle with same kinetic energy enter a region of uniform magnetic field moving at right angles to the field. The ratio of the radii of their circular paths is :

If \(m\) and \(\sigma^2\) are the mean and variance of the random variable \(X\), whose distribution is given by


Then

If a message signal of frequency \(10 \mathrm{kHz}\) and peak voltage \(12 \mathrm{~V}\) is used to modulate a carrier wave of frequency \(1 \mathrm{MHz}\), the modulation index is 0.6 . To make the modulation index 0.75 , the carrier peak voltage should be

If \(f(x)=\left\{\begin{array}{cc}\frac{x-|x|}{x}, & \text { when } x < 0 \\ b\left(\frac{5 x^2+a,}{x^2-3 x+2}\right), & \text { when } 0 \leq x \leq 1 \\ -14, & \text { when } x \geq 3\end{array}\right.\) is a continuous function on \(R\), then \((a, b)=\)

If the total electricity required to deposit 1 mole of a metal \(M\) is equal to that of 10.7 amperes of current for 10 hours. The equivalent weight of the metal is (atomic weight \(=M \mathrm{u}\))

The value of the integral \(\int_0^4 \frac{d x}{1+x^2}\) obtained by using Trapezoidal rule with \(h=1\) is