If \(A=\left[\begin{array}{lll}a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & a\end{array}\right], a \neq 0\) then \(|\operatorname{adj} A|\) is equal to

Let A be a non-singular square matrix of order 3 and |adj A| = 5 then |A| is equal to

The relation \(R\) on the set \(N \times N\) defined by \((a, b) R(c, d) \Longleftrightarrow a+d=b+c\), \(\forall(a, b),(c, d) \in N \times N\), where N is the set of natural numbers, is:

\(\int \frac{\sin x-x \cos x}{x(x+\sin x)} d x=\) (where \(C\) is an arbitrary constant)

The present value of a perpetuity of ₹2,500 payable at the end of each year, if money is worth 10% compounded annually, is:

Assuming the same rate of change continues for the following data :

Year(X)	2019	2020	2021	2022	2023
Profit in Percentage (y)	38	40	65	72	69

The equation of the straight line trend using the least square method is :

The distance of the plane \(\vec{r} \cdot(2 \hat{i}-\hat{j}+\hat{k})=3\) from the origin is :

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.
In which organ of the human body, cannabinoid receptors are principally present?

Match List-l with List-ll

List-l (Term)	List-II (Feature)
(A) Multiple alleles	(I) Variation in DNA
(B) Mendelian disorder	(II) Non segregation of chromatids during cell division
(C) Chromosomal disorder	(III) Pedigree analysis
(D) Mutation	(IV) Population study

Choose the correct answer from the options given below:

For \(x \in\left(0, \frac{\pi}{2}\right), \int \frac{1}{\sin ^2 x+\sin 2 x} d x\) is equal to

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?

Area bounded between the parabola \(y=x^2-2\) and the line \(y=x\) in square units is:

The area of the region bounded by the curve y = x + 1, x-axis and the lines x = 2 and x = 3 is