If \(A=\left[\begin{array}{ccc}a & 1 & -1 \\ 0 & b & 4 \\ 4 & 4 & c\end{array}\right]\) and \(a b c=12, b=4 a\), find the value of \(|A(\operatorname{adj} A)|\)

The probability distribution of a random discrete variable is given

X	-1	0	1	2	3
P(X)	0.1	p	0.3	q	r

If it is known that \(P(X=1)\) is the mean of \(P(X=0)\) and \(P(X=2)\).Then the value of \(r\) is :

Three magnetic materials : (A) Paramagnetic, (B) Diamagnetic, (C) Ferromagnetic. The correct order of increasing magnetic susceptibility is :

The function \(f(x)=\tan x-x\) for \(x \in\left(0, \frac{\pi}{2}\right)\) is :

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

Which of the following are correct?
(A) If \(a \equiv b(\bmod n)\), then \(-a \equiv-b(\bmod n)\)
(B) If \(a+b=c\), then \(a(\bmod n)+b(\bmod n) \equiv(a+b+c)(\bmod n)\)
(C) If \(a \equiv b(\bmod n)\), then \(k a \equiv k b(\bmod n), \forall k \in I\)
(D) If \(a \equiv b(\bmod n)\), then \((a+k) \equiv(b+k)(\bmod n), \forall k \in I\)
Choose the correct answer from the options given below :

For \(x>1, \int \frac{e^{7 \log x}-e^{5 \log x}}{e^{5 \log x}-e^{4 \log x}} d x\) equals.

Let \(A =\left[a_{i j}\right]_{n \times n}\) be a matrix. Then
Match List-I with List-II

List-I	List-II
(A) \(A^T=A\)	(I) A is a singular matrix
(B) \(A^T=-A\)	(II) A is a non-singular matrix
(C) \(|A|=0\)	(III)  A is a skew symmetric matrix
(D) \(|A| \neq 0\)	(IV) \(A\) is a symmetric matrix

Choose the correct answer from the options given below:

Predict the order of decreasing reactivity of the following compounds towards SN1 reaction.
(A) \(\mathrm{C}_6 \mathrm{H}_5 \mathrm{CH}_2 \mathrm{Br}\)
(B) \(\mathrm{C}_6 \mathrm{H}_5 \mathrm{CH}\left(\mathrm{C}_6 \mathrm{H}_5\right) \mathrm{Br}\)
(C) \(\mathrm{C}_6 \mathrm{H}_5 \mathrm{CH}\left(\mathrm{CH}_3\right) \mathrm{Br}\)
(D) \(\mathrm{C}_6 \mathrm{H}_5 \mathrm{C}\left(\mathrm{CH}_3\right)\left(\mathrm{C}_6 \mathrm{H}_5\right) \mathrm{Br}\)

Read the passage carefully and answer the questions based on the passage:
Species diversity on earth is not uniformly distributed. It is generally highest in the tropics and decreases towards the poles.Earth's fossil history reveals the incidences of mass extinctions in the past. Earth's rich biodiversity is vital for the very survival of mankind. It is believed that communities with high diversity tend to be less variable and more productive. The reasons of conserving biodiversity are narrowly utilitarian, broadly utilitarian and ethical. Biodiversity conservation may be in-situ as well as ex-situ.
Which of the following is not included in in-situ conservation?

Read the passage carefully and answer the given questions.
Recombinant DNA Technology
Asexual reproduction preserves the genetic information, while sexual reproduction permits variation. Traditional hybridization procedures used in plants and animals breeding very often lead to inclusion and multiplication of undesirable genes along with the desired genes. The techniques of genetic engineering, which include creation of recombinant DNA, use of gene cloning and gene transfer, overcome this limitation and allow us to isolate and introduce only one or a set of desirable genes without introducing genes into the target organism.
Which one of the following is not used as a vector in recombinant DNA
technology?

Which of the following haloalkanes reacts with aqueous \(\text{KOH}\) most easily ?

A small piece of metal wire is dragged in the region of magnetic flux \( 8 \times 10^{-4} \, \text{Wb} \) in 0.5 s. The length of the wire is perpendicular to the magnetic field. The emf induced in the wire would be: