The sum of the minor and the cofactor of the element 6 in the determinant \(\Delta=\left|\begin{array}{lll}2 & 3 & 1 \\ 4 & 5 & 6 \\ 7 & 8 & 9\end{array}\right|\) is:

If \(x=\frac{a}{1+t}\) and \(y=\frac{a}{(1+t)^2}\) where \(a>0\), then \(\frac{d^2 y}{d x^2}\) at \(t=1\) is:

Difference between the maximum and minimum value of the objective function \(Z=5 x+3 y\), subject to the constraints: \(3 x+5 y \leq 15 ; 5 x+2 y \leq 10 ; x, y \geq 0\) is:

Area of the region bounded by the curve \(y^2=4 x, y\)-axis and the line \(y=3\) is equal to:

A machine has been producing steel tubes of mean inner diameter of 2 cm.
A sample of 10 tubes gives an inner diameter of 2.01 cm and a standard deviation of 0.063 cm.
Test the hypothesis that the machine is working in the proper order at 5% level of significance and answer, which of the following statements are correct?
[Given that \(t_{0.05}=2.262\)]
(A) The value of the test statistic is t = 0.476
(B) The null hypothesis is rejected at \(5 \%\) level of significance.
(C) The null hypothesis is accepted at \(5 \%\) level of significance.
(D) The degree of freedom is 10
Choose the correct answer from the options given below:

If \(\vec{a}=5 \hat{i}-\hat{j}-3 \hat{k} \& \vec{b}=\hat{i}-3 \hat{j}+5 \hat{k}\) the angle between \(\vec{a}+\vec{b}\) and \(\vec{a}-\vec{b}\) is:

The solution of LPP :
Min. \(z=100 x+400 y\)
s.t. \(x+2 y \geq 8\)
\(2 x+5 y \leq 20\)
\(x \geq 0, y \geq 0\)
occurs at :

Arrange the stages of HIV infection in humans sequentially.
(A) Introduction of viral DNA in the cell
(B) Production of multiple viruses
(C) Infection of human cell by virus
(D) Incorporation of viral DNA into host genome
Choose the correct answer from the options given below:

Answer the questions from the figure given below:

If the reaction starts with one molecule of DNA, the number of cycles required to produce one billion amplified products is:

Select the correct statement.

To avoid the unfavourable conditions, the zooplanktons enter into :

Which of the following does not show symbiotic association?

If the potential difference across a capacitor is changed from 12 V to 24 V, the work done is W. How much work will be done if the potential difference is changed from 24 V to 48 V?