The area of a triangle whose vertices are (-3,0), (3, 0) and (0, k) is 6. Then the value (or the values) of k will be:

If A is a square matrix such that \(A^2=A\), then \(|A|\) equals :

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 :

If the order of matrix \(A\) is \(4 \times 3\), order of matrix \(B\) is \(4 \times 5\) and order of matrix \(C\) is \(5 \times 3\), then the order of matrix \((B \cdot C) A^{\prime}\) is :

A machine costing Rs.50,000 has a useful life of 4 years .The estimated scrap value is Rs 10,000. The rate of depreciation per annum is :

A vector of magnitude 9, which is perpendicular to both the vectors \((4 \hat{i}-\hat{j}+8 \hat{k})\) and \((-\hat{j}+\hat{k})\) is

The sum of order and degree of the differential equation \(y=x \frac{d y}{d x}+2 \sqrt{1+\left(\frac{d y}{d x}\right)^2}\) is

The unit vector in the direction of sum of vectors \(\vec{a}=2 \hat{i}-\hat{j}+\hat{k}\) and \(\vec{b}=2 \hat{j}+\hat{k}\) is:

Resolving power of a telescope can be increased by increasing :

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 statements is not true?

A molecule X associates in a given solvent as per the following equation: \(X \rightleftharpoons(X) n\). For a given concentration of \(X\), the van't Hoff factor was found to be \(0 . 8 0\), and the fraction of associated molecules was \(0 . 3\). The correct value of ' \(n\) ' is:

Match List - I with List - II.

List - I (Use/product)	List - II (Micro-organism)
(A) Immuno suppressive agent	(I) Streptococcus
(B) Clot buster	(II) Aspergillus niger
(C) Biofertiliser	(III) Trichoderma polysporum
(D) Citric acid	(IV) Azotobacter

Choose the correct answer from the options given below:

Amongst the following ions which one has the highest magnetic moment value?