\(\int e^x\left(\frac{1-x}{1+x^2}\right)^2\) \(dx\) is equal to

\(\int \frac{d x}{9 x^2-16}\) is equal to:

For \(x>e\),\(\int \frac{d x}{x-\sqrt{x}}\) is equal to

The equation of tangent line to \(y=2 x^2+7\) which is parallel to the line \(4 x-y+3=0\) is :

The matrix \(\left[\begin{array}{lll}2 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]\) is a

The value of \(\sin ^{-1} \frac{3}{5}-\sin ^{-1} \frac{8}{17}\) is :

The relation \(R\) on the set of real numbers defined by \(R=\left\{(a, b): a \leq b^2\right\}\) is

Inlet pipe A can fill a tank in 30 minutes and outlet pipes B and C can empty the tank in 2 hours each. If all three pipes operate together, the tank will be filled in

Choose the correct statements from the following:
A. Displacement current is due to time varying magnetic field.
B. The frequency of the electromagnetic wave naturally equals the frequency of oscillation of the charge.
C. Light carries energy from the Sun to the Earth.
D. Electromagnetic wave does not exert pressure.
E. Electromagnetic wave contains both electric and magnetic field.
Choose the correct answer from the options given below:

The distance between two point charges \(q_1 = 5\) mC and \(q_2 = -10\) mC in vacuum so that electrostatic force of attraction between them is 50 kN is :

Read the passage carefully and answer the questions:
Optically active polyhydroxy aldehydes or ketones or molecules which provide such units on hydrolysis are called carbohydrates. They can be broadly classified as monosaccharides, disaccharides and polysaccharides depending on their behavior towards hydrolysis. They are also classified as reducing or non-reducing sugars. Another class of biomolecules is proteins which are polymers of twenty different amino acids linked by peptide bonds. Amino acids can be classified as acidic, basic or neutral depending on the relative number of amino and carboxyl groups in their
molecule. The essential amino acids cannot be synthesized by our body and hence must be provided through diet. Nucleic acids are the polymers of nucleotides which in turn consist of a base, pentose sugar and phosphate. There are two types of nucleic acids namely, DNA and RNA which differ in the composition of sugar and a base
The sugar moiety in DNA and RNA molecules, respectively, are

The area of region bounded by the curve \(y = x^2\) and the line \(y = 4\) is:

Read the following statements regarding energy levels, and identify the correct statements.
(A) The energy of an atom is least when its electron is revolving in an orbit closest to the nucleus
(B) the energy levels of the excited states come closer and closer together as principal quantum number increases
(C) ionisation energy of the hydrogen atom is the minimum energy required to free the electron from the ground state of the hydrogen atom
(D) as the excitation of hydrogen atom increases, the value of minimum energy required to free the electron from the excited atom decreases.
Choose the correct answer from the options given below: