For \(x \in R -\{0\}\), the function \(f(x)=\frac{3}{x}+7\) is decreasing when

If \(A=\left[\begin{array}{ll}1 & 0 \\ 0 & 0\end{array}\right], B=\left[\begin{array}{ll}0 & 0 \\ 3 & 0\end{array}\right]\) then

Set A has 3 elements and the set B has 4 elements. Then the number of injective mappings that can be defined from A to B is

The order and degree of differential equation \(\left[1+\left(\frac{d y}{d x}\right)^2\right]^2=\frac{d^2 y}{d x^2}\) respectively, are

If the random variable \(X\) is normally distributed with mean 16 and standard deviation 4,
then the standard normal variable \(Z\) corresponding to \(X=17\) is

The co-ordinates of the point where the line\(\frac{x+3}{3}=\frac{y-1}{-1}=\frac{z-5}{-5}\) cuts the yz--plane are :

A Linear Programming Problem (LPP) consists of which of the following components?
(A) Decision variables
(B) The graphical compliment
(C) The objective function
(D) The linear constraints
Choose the correct answer from the options given below :

Freon-12 is manufactured from tetrachloromethane by :

Arrange the following electrodes in decreasing order of the strength of the respective ions as reducing agent.
(A) \(Cu ^{2+}+2 e^{-} \rightarrow Cu ( s ) \quad E^{\circ}=0.34 V\)
(B) \(Sn ^{2+}+2 e^{-} \rightarrow Sn (s) \quad E^{\circ}=-0.14 V\)
(C) \(AgBr (s)+e^{-} \rightarrow Ag (s)+ Br ^{-} \quad E^{\circ}=0.10 V\)
(D) \(Pb ^{2+}+2 e^{-} \rightarrow Pb (s) \quad E^{\circ}=-0.13 V\)
Choose the correct answer from the options given below:

Ishita is rowing a boat. She takes 24 hours to row 72 km against the stream and she takes 9 hours to return to the starting point in the direction of the stream. The speed of the boat in still water is :

An iron ring of relative permeability \( \mu_r \) is introduced inside a toroidal solenoid having n turns per meter. If the current in the solenoid is I, then the magnetic field in the ring is :

"Answer the question on basis of passage given below :
Carboxylic acids are weaker than mineral acids, but they are stronger acids than alcohols and many simple phenols (\(\text{pKa}\) is ~ 16 for ethanol and 10 for phenol). The higher acidity of carboxylic acids as compared to phenols can be understood similarly. The conjugate base of carboxylic acid, a carboxylate ion, is stabilised by two equivalent resonance structures in which the negative charge is at the more electronegative oxygen atom. The conjugate base of phenol, a phenoxide ion, has non-equivalent resonance structures in which the negative charge is at the less electronegative carbon atom. Further, the negative charge is delocalised over two electronegative oxygen atoms in carboxylate ion whereas it is less effectively delocalised over one oxygen atom and less electronegative carbon atoms in phenoxide ion. Thus, the carboxylate ion is more estabilised than phenoxide ion, so carboxylic acids are more acidic than phenols.
Effect of substituents on the acidity of carboxylic acids: substituents may affect the stabliity of the conjugate base and thus, also affect the acidity of the carboxylic acids. Electron withdrawing group increase the acidity of carboxylic acids by stabilising the conjugate base through delocalisation of the negative charge by inductive and/or resonance effects. Conversely, electron donating groups decrease the acidity by destabilising the conjugate base.
Which of the following compounds would have the smallest value of \(\text{pKa}\)?"

Which one of the following is most widely accepted method of contraception in India?