The corner points of the feasible region determined by the system of Linear Constraints are \((0,3),(1,2)\) and \((3,0)\). Let \(z=p x+q y\), where \(p, q>0\), be the objective function. Find the condition on \(p\) and \(q\) so that the minimum of \(z\) occurs at \((3,0)\) and \((1,2)\) :

The number of all possible matrices of order \(2 \times 3\) with each entry 0 or 1 is:

If the system of equations
\(x-3 y+5 z=3\)
\(x-2 y+4 z=4\)
\(2 x-7 y+\lambda z=5\)
has infinite number of solutions, then the value of \(\lambda\) is:

Derivative of \(2 x^2\) with respect to \(5 x^4\) is:

Which of the following is not the specification of the Sinking Fund?

Out of the given statement, choose the correct statement.
(A) The direction ratios of the vector \(\vec{a}=3 \hat{i}-\hat{j}+4 \hat{k}\) is \(3,-1,4\).
(B) If \(\theta\) is the angle between two vectors \(\vec{a}\) and \(\vec{b}\), then their cross product is given as \(\vec{a} \times \vec{b}=|\vec{a}||\vec{b}| \cos \theta\).
(C) The unit vector in the direction of vector \(\vec{a}=\hat{i}+2 \hat{j}-2 \hat{k}\) is \(\hat{a}=\frac{1}{3}(\hat{i}+2 \hat{j}-2 \hat{k})\).
(D) If \(\vec{a}=3 \hat{i}\) and \(\vec{b}=4 \hat{j}\) then \(\vec{a} \cdot \vec{b}=12\).
(E) If \(\vec{a}\) and \(\vec{b}\) represent the adjacent sides of a triangle then its area is given of \(\frac{1}{2}|\vec{a} \times \vec{b}|\).
Choose the correct answer from the options given below :

Let \(f(x)=x^2+\frac{250}{x}\) be any function defined on \(R -\{0\}\), where \(R\) is the set of real numbers. Then which of the following are FALSE?

Which of the following formula correctly represents the double salt "Carnallite"?

There is a parallel plate capacitor of capacitance \( 3 \, \mu \text{F} \). The voltage between the plates is changing at the rate of 8 V/s. The displacement current is :

The degradation of humus by microbes to release inorganic nutrients is known as-

When aniline is reacted with benzoyl chloride, the correct product is

Which of the following statements are not correct?
(A) The milk produced during the initial few days of lactation is called colostrum which contain several antibodies
(B) The signals for the parturition originate from the pituitary gland of the mother
(C) Parturition is induced by a complex neuroendocrine mechanism
(D) Oxytocin is released from the ovary of mother and acts on the uterine muscles
Choose the correct answer from the options given below:

Let two independent random samples of sizes \(n_1\) and \(n_2\) respectively have been drawn from the same normal population. Let \(\overline{X_1}\) and \(\overline{X_2}\) be the means and let \(s_1\) and \(s_2\) be their standard deviations. In order to test whether the the two sample means \(\overline{X_1}\) and \(\overline{X_2}\) differ significantly or not, the \(t\)-test statistic is given by