The largest open interval, in which the function \(f(x)=\frac{x}{x^2+1}\) increases, is

If \(f: R \rightarrow R\) is defined by \(f(x)=x^2-3 x+2\) then \(f(f(x))\) is :

If A is a square matrix and I is the identity matrix of same order such that \(A^2=I\), then \((A-I)^3+(A+I)^3-3 A\) is equal to:

Let A be any skew-symmetric matrix (where \(A^T\) is Transpose of matrix A ), then which of the following statements are correct?
(A) \(A^2\) is a symmetric matrix
(B) \(A^2\) is a skew-symmetric matrix
(C) \(A^T A=-A^2\)
(D) \(A^T A-A A^T=O\)
Choose the correct answer from the options given below :

Pipes A and B can fill a tank in 5 hours and 6 hours respectively. Another Pipe can empty the full tank in 30 hours. If all three pipes are opened together, then the tank will be filled in:

The value of the integral \(\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\left(x+x^3+x^5\right) d x\) is:

If \(f(x) = sin\) \(x - cos\) \(x\), \(x \in[0,2 \pi]\) then
(A) f(x) is increasing in \(\left(0, \frac{3 \pi}{4}\right)\)
(B) f(x) is decreasing in \(\left(0, \frac{3 \pi}{4}\right)\)
(C) f(x) is decreasing in \(\left(\frac{3 \pi}{4}, \frac{7 \pi}{4}\right)\)
(D) f(x) is decreasing in \(\left(\frac{7 \pi}{4}, 2 \pi\right)\)
Choose the correct answer from the options given below:

\( 10^{18} \) electrons pass from point A to point B in 0.1 s in a conductor. The value of the current is

According to Einstein's photoelectric equation, the plot of the Kinetic Energy of the emitted photoelectrons from a metal versus the frequency of the incident radiation gives a straight line whose slope :

Which of the following statements are correct about the structure of a sperm?
A. It is composed of head, thorax, neck and tail
B. The neck region contains a lot of mitochondria
C. The mitochondria produces energy for the movement of tail
D. The tail facilitate sperm motility essential for fertilisation
Choose the most appropriate answer from the options given below:

The instrument preferred for measuring the emf of a cell more accurately is :

Read the passage carefully and answer the questions
Many halogen containing organic compounds are present in nature and some of them are clinically useful. These classes of organic compounds find a wide range of applications in our daily life as well as in industries. Many of the polyhalogen compounds are useful too in agriculture. However, some of these compounds cannot be easily decomposed and are thus considered to be environmental hazards. These halo compounds are prepared via different synthetic routes where a variety of organic compounds can be used as substrates such as amines, hydrocarbons etc. They are used as solvents for relatively non-polar compounds. These compounds exhibit substitution and elimination reactions, in addition to their reactions with different metals, which leads to the formation of a versatile starting material for others organic compounds.
The reaction of aryl halide with sodium and dry ether is known as

Down's syndrome is a genetic disorder. It is due to: