In a LPP:
If two corner points yield the same maximum value of the objective function of an LPP then :
(A) the LPP has unique solution
(B) the LPP has 2 solutions
(C) the LPP has 3 solutions
(D) the LPP has infinite many solutions
Choose the correct answer from the options given below :

If A and B are symmetric matrices then \((A B+B A)\) is:

The slope of tangent on the curve \(y=6 x^2-x-12\), at the point where curve meets positive \(x\)-axis is ___________ .

If \(X=11\) and \(Y=3\), then \(X \bmod Y=(X+a Y) \bmod Y\) holds:

For the problem \(\max Z=a x+b y, x \geq 0, y \geq 0\), which of the following is NOT a valid constraint to make it a linear programming problem?

If the matrix \(\left[\begin{array}{ll}1 & 2 \\ 3 & x\end{array}\right]\) is a singular matrix, then the value of \(x\) is :

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 :

Identify the regions of the transcription unit.
(A) Promoter
(B) Sigma factor
(C) Terminator
(D) The structural gene
Choose the correct answer from the options given below:

Read the passage carefully and answer the Questions
Molar conductivity \(\left(\Lambda_m\right)\) of a solution at a given concentration (c) is the conductance of volume, V of solution, containing one mole of electrolyte kept between the two electrodes with area of cross-section A and at a distance of unit length. It increases with the decrease in concentration and when the concentration approaches zero, the molar conductivity is called limiting molar conductivity \(\left(\Lambda_m^0\right)\). For a strong electrolyte, \(\Lambda_m\) increases linearly with dilution and is given by \(\Lambda_m=\Lambda_m^0-A c^{1 / 2}\). The value of the constant A for a given solvent depends on the type of electrolyte along with temperature. According to Kohlrausch law, the value of \(\left(\Lambda_m^0\right)\) for an electrolyte is A\(\Lambda_m^0=\nu_{+} \lambda_{+}^0+\nu_{-} \lambda_{-}^0\), where \(\nu_{+}\)and \(\nu_{-}\) are the number of cations and anions, respectively, per molecule of the electrolyte and \(\lambda_{+}^0\) and \(\lambda_{-}^0\) are limiting molar conductivities of cation and anion, respectively. Kohlrausch law
finds many applications, like determining the solubility of a sparingly soluble salt, determining the degree of dissociation\(\left(\Lambda_m / \Lambda_m^0\right)\), and the dissociation constant of a weak electrolyte.
If the equivalent conductivity of 1 M Phthalic acid is \(12.8 S cm ^2 eq ^{-1}\) and the limiting equivalent conductivities of the
hydrogen and Phthalate ions are 42 and \(288.42 S cm ^2 eq ^{-1}\), respectively, the degree of dissociation of Phthalic acid will be :

The reaction which involves dichloro carbene as an electrophile is :

A random sample of 100 individuals provides 25 positive responses.
Then the point estimate of the population proportion with positive responses is:

For the function \(f(x)=e^{-2 x}(2-x)^2\), the point of local maxima is:

If the product of matrices \(\left[\begin{array}{cc}\cos ^2 \theta & \cos \theta \sin \theta \\ \cos \theta \sin \theta & \sin ^2 \theta\end{array}\right]\) and \(\left[\begin{array}{cc}\cos ^2 \beta & \cos \beta \sin \beta \\ \cos \beta \sin \beta & \sin ^2 \beta\end{array}\right]\) is a null matrix, then \(\theta\) and \(\beta\) differ by: