Let A be any square matrix of order n, then which of the following are true?
(A) \(|\operatorname{adj} A |=| A |^{n-1}\)
(B) \(\left| A ^{-1}\right|=\frac{1}{| A |}\)
(C) \(|\operatorname{adj} A |=| A |^n\)
(D) \(\left( A ^{ T }\right)^{-1}=\left( A ^{-1}\right)^{ T }\)
Choose the correct answer from the options given below :

The window of the house is in the form of a rectangle surmounted by a semi-circular portion, having a perimeter of 10 m as shown in figure.

If \(x\) and \(y\) represent the length and breadth of rectangular region the whole area of window is maximum, then value of \(x\) is :

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

In a game, a man wins ₹ \( 8\) for getting a number greater than 3 and loses ₹ 3 otherwise, when a fair die is thrown.
The man decided to throw a die 4 times but to quit as and when he gets a number greater than 3.
If \(X\) denotes the amount which the man wins or loses, then which of the following are correct?
(A) All the possible values of \(X\) are \(8,5,2\) and -1 .
(B) The probability distribution of \(X\) is :

X	8	5	2	-1	-12
P(X)	1/2	1/4	1/8	1/16	1/16

(C) The mean value of \(X\) is \(\frac{75}{16}\).
(D) The variance of \(X\) is \(\frac{6615}{256}\).
Choose the correct answer from the options given below :

The area of a triangle having the points \(A (1,1,1), B (1,2,3)\) and \(C (2,3,1)\) as its vertices is :

For the LPP: minimize z = 6x + 3y subject to the constraints
\(4 x+y \geq 80\)
\(x+5 y \geq 115\)
\(3 x+2 y \leq 150\)
\(x \geq 0, y \geq 0\) then the minimum value of z is

The probability distribution of a random variable X is given by

X	0	1	2
P(X)	k	2k	3k

If \(k>0\), then \(P(0 < X \leq 2)\) is equal to

The area bounded by \(y^2=x, y=5\) and the \(y\)-axis is:

Read the passage carefully and answer the questions
The coordination compounds are of great importance. These compounds are widely present in the mineral, plants and animal world and are known to play many important functions in the area of analytical chemistry, metallurgy, biological systems, industry and medicine. For example, coordination compounds find use in many qualitative and quantitative chemical analysis. Some important metal extraction and purification make use of complex formation. Hardness of water can be estimated by stable complex formation of Ca\(^{2+}\) and Mg\(^{2+}\)
Impure nickel is converted to which of its complex to be decomposed to yield pure nickel?

Answer the question on basis of passage given below :
Look at the following chemical reactions and answer the following question:
(A) \(C_7H_8 \xrightarrow{\text{Conc. HNO}_3, 0^\circ C}
(B) \xrightarrow{Sn/HCl}
(C) \xrightarrow{NaNO_2/H_3O^+}
(D) \xrightarrow{H_2O, Heat} (E)\)
(E) \(CH_3I \xrightarrow{KMnO_4/H^+}
(F) \xrightarrow{H_3O^+}
(G) \xrightarrow{NaOH} (H)\)
Which of the following compounds will form dimer ?

If \( \vec{M} \) is magnetic moment and \( \vec{B} \) is magnetic field, then the torque (\( \vec{\tau} \)) is given by

Read the given passage carefully and answer the questions
Salmonella typhi is a pathogenic bacterium which causes typhoid fever in human beings. Sustained high fever (39° to 40°C), weakness, stomach pain, constipation, headache and loss of appetite are some of the common symptoms of this disease. Typhoid fever could be confirmed by Widal test. Plasmodium enters the human body as sporozoites. The parasites initially multiply within the liver cells and then attack the red blood cells (RBCs) resulting in their rupture. The rupture of RBCs is associated with release of a toxic substance, haemozoin, which is responsible for the chill and high fever recurring every three to four days. There is lymphoid tissue also located within the lining of the major tracts (respiratory, digestive and urogenital tracts) called mucosa-associated lymphoid tissue (MALT). In our body, cell growth and differentiation is highly controlled and regulated. In cancer cells, there is breakdown of regulatory mechanisms. Normal cells show a property called contact inhibition by virtue of which contact with other cells inhibits their uncontrolled growth. Cancerous cells just continue to divide giving rise to masses of cells called tumors. Tumors are of two types: benign and malignant. Cannabinoids are a group of chemicals, which interact with cannabinoid receptors present principally in the brain. Generally taken by inhalation and oral ingestion, these are known for their effects on cardiovascular system of the body.
Which one of the following structures constitute about 50 percent of the lymphoid tissue in the human body?

Match List-l with List-ll
Let A and B be any two events

List-l	List-ll
(A) \(P \left( A ^{\prime}\right)\)	(I) \(\frac{P(A \cap B)}{P(A)} ; P(A) \neq 0\)
(B) \(P (\Phi)\)	(II) \(\frac{P(A \cap B)}{P(B)} ; P(B) \neq 0\)
(C) \(P ( A \mid B )\)	(III) \(1-P(A)\)
(D) \(P ( B \mid A )\)	(IV) \(0\)

Choose the correct answer from the options given below :