\(\int \frac{(x-1) e^x}{x^2} d x\), \(x > 0\) equals (where C is an arbitrary constant)

If A and B are two independent events then,
Match List I with List II

List - I	List - II
(A) \(P(A \cup B)\)	(I) \(P\left(A^{\prime}\right) P\left(B^{\prime}\right)\)
(B) P(not A or not B)	(II) \(P(A) ; P(B) \neq 0\)
(C) \(P(A / B)\)	(III) \(1-P\left(A^{\prime}\right) P\left(B^{\prime}\right)\)
(D) P(neither A nor B)	(IV) \(1-P(A) P(B)\)

Choose the correct answer from the options given below:

The probability that it will rain on any particular day is \(50 \%\). The probability that it rains only on the first 4 days of the week is :

The function \(f(x)=x^2-4 x+6\) is
(A) Strictly decreasing on \((-\infty, 2) \cup(2, \infty)\)
(B) Strictly increasing on ( \(2, \infty\) )
(C) Strictly increasing on \((-\infty, \infty)\)
(D) Strictly decreasing on \((-\infty, 2)\)
Choose the correct answer from the options given below :

The value of \(k\) for which the system of equations
\(\begin{array}{l}x+y+z=1 \\x-k y+z=1\end{array}\)
\(x-y+z=1\)
has more than one solution is :

The function \(f(x)=6-6 x-2 x^2\)

Consider the lines \(l_1: \frac{x-1}{0}=\frac{y-1}{1}=\frac{2-z}{1}\) and \(l_2: \frac{x}{2}=\frac{y}{0}=\frac{2 z-1}{4}\), then which of the following are correct?
(A) Direction Ratios of \(l_1=\langle 0,1,1\rangle\)
(B) Direction Ratios of \(l_2=\langle 2,0,2\rangle\)
(C) Angle between \(l_1\) and \(l_2=\frac{\pi}{3}\)
(D) Angle between \(l_1\) and \(l_2=\frac{2 \pi}{3}\)
Choose the correct answer from the options given below :

An excess consumption of which of these compounds causes blindness and death?

Read the passage and answer the question given below. When a host is exposed to antigens, which may be in the form of living or dead microbes or other proteins, antibodies are produced in the host body. This type of immunity is called active immunity. Active immunity is slow and takes time to give its full effective response. Injecting the microbes deliberately during immunisation or infectious organisms gaining access into body during natural infection induce active immunity. When antibodies are directly given to protect the body against foreign agents, it is called passive immunity.
which is passive immunisation?

Match List-I with List-II:

List-I (Physical quantity)	List-II (Unit)
(A) Magnetic moment	(I) N A\(^{-2}\)
(B) Magnetic field strength	(II) N m rad\(^{-1}\)
(C) Torsion constant	(III) A m\(^{-1}\)
(D) Magnetic permeability	(IV) A m\(^2\)

choose the correct answer from the options given below:

The complimentary DNA sequence of the DNA strand 5'-GAATTC-3' would be:

If \(f: R \rightarrow R\) is defined by f(x) = sin x + x then f(f(x)) is:

Widal test is used to diagnose: