If \(A=\left[\begin{array}{ccc}0 & x^2-6 & -3 \\ -x & 0 & -8 \\ x^2-2 x & 8 & 0\end{array}\right]\) is a skew symmetric matrix, then the value(s) of \(x\) is/ are -
(A) 3
(B) -3
(C) -2
(D) -1
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The shortest distance between the following lines :
\(\vec{r}=(\hat{i}+\hat{j}-\hat{k})+s(2 \hat{i}+\hat{j}+\hat{k})\)
\(\vec{r}=(\hat{i}+\hat{j}+2 \hat{k})+t(4 \hat{i}+2 \hat{j}+2 \hat{k})\), where \(s\) and \(t\) are scalars, is :

If a person \(A\) speaks the truth in \(80 \%\) cases and the person \(B\) speaks the truth in \(75 \%\) cases, then the probability that they contradict each other in a statement is:

The corner points of the feasible region determined by the system of linear constraints are \((0,3),(1,1)\) and \((3,0)\).
Let \(Z=p x+q y\), where \(p, q>0\), be the objective function.
Then the condition on \(p\) and \(q\) so that the minimum of \(Z\)
occurs at \((3,0)\) and \((1,1)\) is:

Solution of \(\frac{d y}{d x}=\left(1+x^2\right)\left(1+y^2\right)\) is :

The function \(f:[-1,1] \rightarrow R\) is given by \(f(x)=\frac{x}{x+2}\)

If \(A X=B\) where \(A , X\) and B are matrices and \(A^{-1}, B^{-1}\) exist, then matrix X is

The core of a transformer is laminated, so as to

Match List - I with List - II.

List - I	List - II
(A) Convergent evolution	(I) Adaptive radiation
(B) Thorns of Bougainvillea and tendrils of cucurbits	(II) Analogous Structures
(C) Darwin's finches	(III) Use and disuse of organs
(D) Lamarck	(IV) Homologous organs

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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

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Molecular nitrogen is very little reactive chemically. During lightning discharge, atmospheric nitrogen and oxygen combines to form nitric oxide which also combines with oxygen to form nitrogen dioxide. Both NO and \(NO _2\) constitute smog which is very poisonous. It can cause burning sensation in the eyes and adversely affect respiratory system.
What are the constituents of photo chemical smog ?

\(\int \frac{d x}{x^3 \sqrt{\left(1+x^4\right)}}=\)

A pure inductor of 70 mH is connected to a source of 220 V. The frequency of the source is 50 Hz. The current in the circuit is: