The water and milk in two vessels are in the ratio 1:1 and 3: 8 respectively. In what ratio, the mixtures in the vessels be mixed to obtain a new mixture containing water and milk in the ratio 4 : 7?

\(\tan ^{-1} 3+\tan ^{-1} \lambda=\tan ^{-1}\left(\frac{3+\lambda}{1-3 \lambda}\right)\) is valid for which values of \(\lambda\) ?

The function \(f: R \rightarrow R, f(x)=x^2\) is :

The area of the region enclosed by \(y=x+2\) and \(y=x^2+x-2\) is:

"The random variable \(X\) has a probability distribution \(P ( X )\) of the following form, where \(k\) is some number.
\(P(X=x)=\left\{\begin{array}{ll}k, & \text { if } x=0 \\2 k, & \text { if } x=1 \\3 k, & \text { if } x=2 \\0, & \text { otherwise }\end{array}\right.\)
Then \(P(x \leq 2)\) is :"

If \(y=\left(x+\sqrt{x^2+1}\right)^m\), then \(\frac{d y}{d x}\) is

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

Alcohol is a depressant, which means that even small amounts of alcohol slow down the actions of parts of the brain, so alcohol lengthens the time you take to respond to a stimulus.
Different people react differently to alcohol. In some people, it increase their feelings of aggression, and releases their inhibitions so that they are more likely to be violent or commit other crimes.
An alcoholic needs to drink quite large quantities of alcohol regularly. This causes many parts of the body to be damaged, because alcohol is poisonous to cells. Probably, there are many factors which decide whether or not a person becomes alcoholic. Over a long period of time, it can cause loss of memory and confusion. One way in which the damage is done is that alcohol in the body fluids draws water out of cells by osmosis.
Identify the measure which is not useful for prevention and control of alcohol abuse among adolescents.

Which phenomena proves the particle nature of photon?

Unit of rate constant for sero order reaction is:

MTP is considered safe up to _________ weeks of pregnancy.

Read the passage carefully and answer the Questions
Haloalkanes undergo nucelophilic substitution reactions owing to the polarity of CX bond. The nucleophile reacts with the haloalkane on the carbon possessing a partial positive charge holding the halogen atom. The halogen atom \(X\) is replaced by a nucleophile. Depending on the kinetics and mode of bond breaking, the mechanism can be either SN1 or SN2 reaction. The rate of SN1 reaction is governed by the stability of carbocation and in SN2 reaction, the rate of reaction is governed by steric factor. Chirality is the main factor in both SN1and SN2. In SN1 reaction, the chirality of alkyl halide is accompanied by racemization of the product, while in SN2 reaction, the product is characterized by inversion of configuration. The structure of alkyl halide and the nature of the solvent also governs the mechanism of the substitution.
Which of the following compound will undergo \(S_N 1\) reaction readily?

The flowers which do not open at all are known as: