Let \(f(x)=x^3\) be a function with domain \(\{0,1,2,3\}\) then domain of \(f^{-1}\) is:

If \(A =\left(\begin{array}{cc}2 & 3 \\ 5 & -2\end{array}\right)\), be such that \(A ^{-1}=K A\), then the value of \(K\) is :

For the function \(f(x)=\sin x+\cos x, x \in[0, \pi]\), which one of the following is correct?

A T.V. panel costing Rs 18000 has a useful life of 12 years. If the annual depreciation is Rs 1000, then its scrap value by linear method is :

If \(\sin ^{-1} x+\sin ^{-1} y=\frac{2 \pi}{3}\), then the value of \(\cos ^{-1} x+\cos ^{-1} y\) is:

A car starts from a point at time \(t = 0\) seconds and stops at Q.
The distance \(x\) in meters covered by it in \(t\) seconds is given by
\(x = t^2 \left( 2 - \frac{t}{3} \right)\).
The time taken by it to reach Q is:

For the objective function \(z=p x+q y\), where \(p, q>0\) the corner points of the feasible region determined by the system of linear constraints are \((0,10),(5,5),(15,15)\) and \((0,20)\), condition on \(p\) and \(q\) so that maximum of \(z\) occurs at both the points \((15,15)\) and \((0,20)\) is :

If \(x=a \cos ^3 \theta, y=a \sin ^3 \theta\). The value of \(\frac{d^2 y}{d x^2}\) at \(\theta=\frac{\pi}{6}\) is :

Match List - I with List - II.

LIST I	LIST II
(A) Lymphoid Organ	(I) ELISA
(B) Cancer	(II) Widal Test
(C) HIV	(III) Bone marrow and Thymus
(D) Typhoid	(IV) Carcinogens

Choose the correct answer from the options given below:

Area bounded by the curve \(|x|+|y|=1\) is:

If \(y=x \sin y\), then \(\frac{d y}{d x}\) 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.
Widal test is used to diagnose

\(y=x(x-3)^2\) decreases for the value of \(x\) given by