\(\cos ^{-1}\left(\cos \frac{7 \pi}{6}\right)\) equals:

If y = - 4 a root of \(\left|\begin{array}{lll}y & 2 & 3 \\ 1 & y & 1 \\ 3 & 2 & y\end{array}\right|=0\), then the product of the other two roots is

The solution set of the inequation \(4x + 3y > 5\) is

If the corner points of the bounded feasible region for a Linear Programming Problem (LPP) are \(A(0,2), B(3,0), C(2,3)\) and \(D(3,1)\), then the maximum value of the objective function \(Z=4 x+2 y\) occurs at

Corner points of the feasible region for a linear programming problem are \((0,2),(3,0),(6,0)\) and \((0,5)\). Let \(F=4 x+6 y\) be the objective function. The minimum value of \(F\) occurs at:

If \(\left[\begin{array}{cc}4 x & 5 x-7 \\ 4 x & 2 x+y\end{array}\right]=\left[\begin{array}{cc}x+6 & y \\ 7 y-13 & 7\end{array}\right]\) then the value of \(2 x+y\) is:

The value of \(\int_{\frac{-\pi}{2}}^{\pi / 2}\left(x^5+x^3 \cos x\right) d x\) is :

Two point charges of 2 C each are separated from each other by a distance of 1 m in water (K = 80). The force between the charges is:

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

For the reaction, \(R \rightarrow P\), the \(\log \left([ R ]_0 /[ R ]\right)\) verses time \(( t )\) plot is given below. What is the order of reaction and what are the units of rate constant ? 

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 :

The value of \(\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}(\sin |x|-\cos |x|) d x\) is :

The side of an equilateral triangle increases at the rate of \(3 cm / sec\), then the rate at which the area of the triangle increases when the side is 4 cm , is :