Let \(L_1\) and \(L_2\) be two lines, represented as, \(L_1: \vec r=\hat i+\hat j+\lambda(2\hat i-\hat j+\hat k)\) and \(L_2: \vec r=2\hat i+\hat j-\hat k+\mu(4\hat i-2\hat j+2\hat k)\), where \(\lambda\) and \(\mu\) are scalars. Then which of the following are true? (A) \(L_1\) is perpendicular to \(L_2\) (B) \(L_1\) is parallel to \(L_2\) (C) \(L_1\) passes through the point (1,1,0) (D) \(L_2\) passes through the point (2,1,-1) Choose the correct answer from the options given below:

For the LPP: minimize \(z=6x+3y\) subject to the constraints \(4x+y\ge80\) \(x+5y\ge115\) \(3x+2y\le150\) \(x\ge0,\ y\ge0\) then the minimum value of z is

Which of the following statements are true? (A) The vector joining the points P(2,3,0) and Q(-1,-2,-4) directed from P to Q is \(\overrightarrow{PQ}=-3\hat i-5\hat j-4\hat k\) (B) Projection of a vector \(\vec a\) on other vector \(\vec b\) is…

If \(A\) and \(B\) square matrices of order 3 such that \(|A|=-1\), \(|B|=5\), then the value of \(|2AB|\) is :

If \(c_{ij}\) denotes the cofactor of element \(a_{ij}\) of the matrix \(A=\begin{bmatrix}1&2&-1\\0&-3&2\\4&2&3\end{bmatrix}\), then the value of \(c_{21}\cdot c_{33}\) is

If \(y=\sqrt{\sin x+\sqrt{\sin x+\sqrt{\sin x+\cdots+\infty}}}\) then \(\frac{dy}{dx}\) equals to

The solution of the differential equation \((x^2+xy)dy=(x^2+y^2)dx\) is

The function \(f:\mathbb{R}\to[-1,1]\) defined by \(f(x)=\cos x\) is:

The following system of equations: \(x+y-z=7\) \(4x+\lambda y-\lambda z=3\) \(3x+2y-4z=5\) does not possess a solution if the value of \(\lambda\) is: