The corner points of the feasible region determined by the system of linear inequalities are \((0,0)\), \((2,4),(7,3)\) and \((5,0)\). If the maximum value of \(z=p x+q y\), where \(p, q>0\) occurs at both \((2,4)\) and \((7,3)\), then :

A letter is known to have come from either TATAPUR or from CHAKRATA. On the envelope, only two letters "TA" are visible consecutively. The probability that the letter has come from CHAKRATA is :

The value of \(\int_{-3}^2 x^2|2 x| d x\) is :

For some constant 'k', if the system of linear equations
\(2 x-y+3 z=1\)
\(x-2 y+z=3\)
\(k x+y-z=0\)
has a unique solution, then

One root of the equation \(\left|\begin{array}{ccc}3 x-8 & 3 & 3 \\ 3 & 3 x-8 & 3 \\ 3 & 3 & 3 x-8\end{array}\right|=0\) is:

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:

The unit vector in the xy-plane, making an angle of \(60^{\circ}\) with the positive direction of x-axis is:

Endosperm is completely consumed during embryo development in the seed of -

The presence of additional copy of X chromosome in humans lead to

An emf \( E = 200 \sin 300t \text{ volt} \) is applied across an inductor coil having a resistance of \( 1.0 \text{ } \Omega \). If the maximum current is found to be 10 A, then the value of inductance is approximately:

Which one of the following statements is not correct regarding the DNA?

A glass prism of angle 60° has an angle of minimum deviation of 30° for a given colour of light. The refractive index of glass for that colour of light is :

Forward bias applied to a p-n junction diode