In a linear programming problem, the constraints on decision variables x and y are \(y-2 x \leq 0, y \geq 0,0 \leq x \leq 5\). The feasible region of the above problem :

\(\int\left(e^{x \log a}+e^{a \log x}\right) d x\) is equal to (where \(\left.a>1\right)\)

Year(x)	2011	2012	2013	2014	2015	2016	2017
Sales (in lakh Rs. ) (y)	65	68	70	72	75	67	73

If \(y=70+0.964(x-2014)\) be a straight line trend fitted by the method of the least squares to the above data, then the trend value for the year 2015 is :

If \(A = \mathbb{R} - \left\{\frac{3}{2}\right\}\) and function \(f: A \rightarrow A\) is defined by \(f(x) = \frac{3x-2}{2x-3}\), then

If the matrix \(\left[\begin{array}{ccc}3 & 2 a & -5 \\ 4 & 0 & b \\ -5 & 3 & 10\end{array}\right]\) is symmetric, then the value of \(5 a+2 b\) is :

Cofactor of \(a_{12}\) in \(A=\left[\begin{array}{ccc}1 & 2 & 3 \\ 4 & -5 & 6 \\ 0 & 1 & -1\end{array}\right]\) is:

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?

Single step large mutations causing speciation are called:

Answer the question on the basis of passage given below :
A colloid is a heterogeneous system in which a substance is dispersed (dispersed phase) as fine particles in another substance called dispersion medium.
Their particle size is intermediate between that of pure solutions (less than 1 nm) and suspensions (greater than 1000 nm). They are known for interesting properties such as enormous surface area, Tyndall effect, Brownian motion etc.
They are widely used in industries and day to day life.
Some prominent uses of colloids are those in smoke precipitators, purification of water, medicines, cleansers etc.
Which of the following electrolyte exhibits maximum flocculating power in the coagulation of a positive metal hydroxide sol?

The number of all possible matrices of order \(2 \times 2\) with each entry ' \(a\) ', ' \(b\) ' or ' \(c\) ' is :

Identify the reagent which can be used to convert benzamide into aniline in a single step:

The direction ratios of the line perpendicular to the lines \(\frac{x-5}{2}=\frac{y+11}{-3}=\frac{z+3}{1}\) and \(\frac{x-7}{1}=\frac{y+2}{2}=\frac{z-4}{-2}\) are proportional to :

Angle between tangents to the curve \(y=x^2-5 x+6\) at the points \((2,0)\) and \((3,0)\) is :