Choose the wrong statement from the following :

A bag contains 12 white and 18 red balls. Two balls are drawn in succession without replacement. The probability that the first is red and the second is white is:

If \(2 f(x)+f\left(\frac{1}{x}\right)=x^2+1\), then \(\int f(x) d x\) is : (Here \(C\) is an arbitrary constant)

If \(\frac{1}{|x|-3} \leq \frac{1}{2}\), then the value of \(x\) is:

If \(f: R \rightarrow R\) be given by \(f(x)=\left(3-x^3\right)^{\frac{1}{3}}\), then \((f \circ f)(x)\) is:

Match List-I with List-II

List-I (Matrix Product)	List-II (Order of resultant matrix)
(A) \(\left[a_{i j}\right]_{2 \times 3} \times\left[b_{i j}\right]_{3 \times 4}\)	(I) \(2 \times 4\)
(B) \(\left[a_{i j}\right]_{2 \times 1} \times\left[b_{i j}\right]_{1 \times 3}\)	(II) Not possible
(C) \(\left[a_{i j}\right]_{3 \times 2} \times\left[b_{i j}\right]_{3 \times 2}\)	(III) \(3 \times 3\)
(D) \(\left[a_{i j}\right]_{3 \times 3} \times\left[b_{i j}\right]_{3 \times 3}\)	(IV) \(2 \times 3\)

Choose the correct answer from the options given below :

Let \(f: R \rightarrow R\) be defined as \(f(x)=100 x+1\) where \(R\) is a set of real numbers, then

On which of the following factors angular fringe width does not depend?

Match List-l with List-II

List-l (Terms)	List-ll (Features)
(A) IgE	(I) Formed by yeast
(B) IgA	(II) Cellular barrier
(C) Hepatitis B vaccine	(III) Antibodies due to allergens
(D) Polimorpho- nuclear leucocytes	(IV) Present in colostrum

Choose the correct answer from the options given below:

Although chlorine is an electron-withdrawing group, it is ortho- and para-directing in electrophilic aromatic substitution because:
(A) Chlorine withdraws electrons through inductive effect.
(B) Chlorine stabilizes the intermediate carbocation formed during electrophilic substitution via resonance.
(C) Chlorine donates electrons through resonance.
(D) Chlorine is a deactivating group due to its -1 effect.
Choose the correct answer from the options below:

Read the passage and answer the following
Microbes are organisms that cannot be seen with the naked eye. They include bacteria, archaea, protists, viruses, prions, and fungi. They account for most of the diversity of life on earth. Far more microbes inhabit a single person's body than there are people on the entire planet. Microbes also dominate in terms of their ability to live and thrive in extreme environments, including clouds, deep-sea volcanoes, springs, ice caps, and animal intestines. Most animals, including humans, exhibit numerous associations with microbes. Our "human microbiome" includes our skin, hair, mouth, and gut.
Which of the following microbe is harmful?

If \(\left|\begin{array}{lll}x & x^2 & 1+p x^3 \\ y & y^2 & 1+p y^3 \\ z & z^2 & 1+p z^3\end{array}\right|=\lambda(x-y)(y-z)(z-x)\), then value of \(\lambda\) is :

The area (in square units) of the region bounded by the curve \(x^2=y\) and the straight line \(y=4\) in the first quadrant is equal to