If \(\int_0^1 \frac{e^x}{1+x} d x=m\), then the value of \(\int_0^1 \frac{e^x}{(1+x)^2} d x\) is :

Let A be a non-singular square matrix of order n, then
Match List - I with List - II

List - I	List - II
(A) A (adj A)	(I) \(\frac{1}{|A|}\)
(B) |adj A|	(II) \(|A|^n\)
(C) \(\left|A^{-1}\right|\)	(III) \(|A| I\)
(D) \(|A(\operatorname{adj} A)|\)	(IV) \(|A|^{n-1}\)

Choose the correct answer from the options given below:

If a function \(f: R _{+} \rightarrow[-5, \infty)\) given by \(f(x)=9 x^2+6 x-5\) is one-one and onto, then \(f^{-1}(y)\) is

Mrs Rathna invested Rs. 2 lakh in an enterprise for 5 years. Her compound annual growth rate (CAGR) turned out to be 20.5%. The end balance would be (given \((1.205)^5=2.54\) ):

The area (in sq. units) of a triangle formed by vertices \(O, A\), and \(B\) where \(\overrightarrow{O A}=\hat{i}+2 \hat{j}+3 \hat{k}\) and \(\overrightarrow{O B}=-3 \hat{i}-2 \hat{j}+\hat{k}\) is

Match List-I with List-II

List-I	List-II
(A) \(\int \frac{d x}{x^2-16}\)	(I) \(\frac{1}{8} \log \left|\frac{4+x}{4-x}\right|+c\)
(B) \(\int \frac{d x}{x^2+16}\)	(II) \(\log \left|x+\sqrt{x^2-16}\right|+c\)
(C) \(\int \frac{d x}{16-x^2}\)	(III) \(\frac{1}{8} \log \left|\frac{x-4}{x+4}\right|+c\)
(D) \(\int \frac{d x}{\sqrt{x^2-16}}\)	(IV) \(\frac{1}{4} \tan ^{-1}\left(\frac{x}{4}\right)+c\)

Choose the Correct answer from the options given below :

The unit vector in the direction of sum of vectors \(\vec{a}=2 \hat{i}-\hat{j}+\hat{k}\) and \(\vec{b}=2 \hat{j}+\hat{k}\) is:

How does the osmotic pressure of a solution vary with the temperature?

Read the following passage carefully and answer the given questions.
Plasmodium, a tiny protozoan is responsible for the disease malaria. Different species of Plasmodium (P. vivax, P. malaria and P. falciparum) are responsible for different types of malaria. Of these, malignant malaria caused by Plasmodium falciparum is the most serious one and can even be fatal. Innate immunity consist of four types of barriers. These are – (i) Physical barriers- skin on our body is the main barrier which prevents entry of the micro-organisms. (ii) Physiological barriers- Acid in the stomach, saliva in the mouth, tears from eyes-all prevent microbial growth. (iii) Cellular barriers- Certain types of leukocytes (WBC) of our body like polymorpho-nuclear leukocytes (PMNL-neutrophils) and monocytes and natural killer (type of lymphocytes) in the blood as well as macrophages in tissues can phagocytose and destroy microbes. (iv) Cytokine barriers- virus-infected cells secrete proteins called interferons which protect non-infected cells from further viral infection. Allergy is due to the release of chemicals like histamine and serotonin from the mast cells. The use of drugs like anti-histamine, adrenalin and steroids quickly reduce the symptoms of allergy. Drugs like barbiturates, amphetamines, benzodiazepines, and other similar drugs, that are normally used as medicines to help patients cope with mental illnesses like depression and insomnia, are often abused.
Which one of the followings is not the example of cellular barrier?

The puffed up appearance of dough is due to the production of:

In the following nuclear reaction,
\( {}^1_0n + {}^{235}_{92}U \rightarrow {}^{140}_{54}Xe + {}^a_bSr + 2{}^1_0n \), we have

The correct order of dipole moment of the different methyl halides is :

Let \(f: R \rightarrow R\) be defined as \(f(x)=10 x\). Then (Where R is the set of real numbers):