The area (in sq. units) of the region bounded by \(y=2 x+3\), the \(x\)-axis, and the ordinates \(x=-2, x=2\) is equal to

Points at which normal to the curve \(y=x^3-3 x\) is parallel to \(y\)-axis are:

In a 100 metre race, \(A\) beats \(B\) by 10 metres and \(C\) by 13 metres. By how many meters will \(B\) beat \(C\) in a 180 metre race?

The integral \(\int \frac{2 x+x^3}{1+x^2} d x\) is equal to :

The derivative of \(f(\cot x)\) with respect to \(g(cosec x)\) at \(x=\frac{\pi}{4}\) (where \(\left.f^{\prime}(1)=2, g^{\prime}(\sqrt{2})=4\right)\) is:

The area bounded by the curve y = 3 cos x and the x-axis between x = 0 and \(x=2 \pi\) is:

For the given \(5\) values, \(15, 18, 21, 27, 39;\) the three year moving averages are:

Which of the following is NOT a sexually transmitted disease?

If \(\left|\begin{array}{ccc}1 & -2 & 5 \\ 2 & a & -1 \\ 0 & 4 & 2a\end{array}\right|=86\), then product of all values of \(a\) is :

Which of the following will not give iodoform reaction?

If the interval in which the function \(f(x)=4 x^3-6 x^2-72 x+30\) is strictly decreasing, is \(( a , b )\) then \(a + b\) is equal to

\(\Delta G = \Delta H – T\Delta S\)
When \(\Delta H = -ve\) and \(\Delta S = -ve\), then the value of \(\Delta G\) will :

If the corner points of the bounded feasible region for a linear programming problem (LPP) are (0, 2), (3, 0), (6, 0), (6, 8) and (0, 5), then which of the following are correct for the objective function \(Z=4 x+6 y \) ?
(A) The minimum value of the objective function occurs at (0, 2) and (3, 0) only.
(B) The minimum value of the objective function occurs at the mid-point of the line segment joining the points (0, 2) and (3, 0) only.
(C) The minimum value of the objective function occurs at every point of the line segment joining the points (0, 2) and (3,0).
(D) The difference between the maximum value and minimum value of the objective function is 60.
Choose the correct answer from the options given below :