Consider the lines \(l_1: \frac{x-1}{0}=\frac{y-1}{1}=\frac{2-z}{1}\) and \(l_2: \frac{x}{2}=\frac{y}{0}=\frac{2 z-1}{4}\), then which of the following are correct?
(A) Direction Ratios of \(l_1=\langle 0,1,1\rangle\)
(B) Direction Ratios of \(l_2=\langle 2,0,2\rangle\)
(C) Angle between \(l_1\) and \(l_2=\frac{\pi}{3}\)
(D) Angle between \(l_1\) and \(l_2=\frac{2 \pi}{3}\)
Choose the correct answer from the options given below :

If \(f(x)=\left\{\begin{array}{cl}\frac{k \cos x}{\pi-2 x}, & x \neq \frac{\pi}{2} \\ 3, & x=\frac{\pi}{2}\end{array}\right.\) is continuous at \(x=\frac{\pi}{2}\), then \(k\) is :

Let \(f(x)=x^3-6 x^2+9 x-8\) be a function, then which of the following statements are TRUE?
(A) \(f^{\prime}(x)=3(x-1)(x-3)\)
(B) The critical points of the function are \(x=1\) and \(x=3\)
(C) \(x=1\) is the point of local minimum
(D) The local maximum value is -4
Choose the correct answer from the options below :

The matrix \(X\) in the equation \(A X=B\), such that \(A=\left[\begin{array}{ll}1 & 3 \\ 0 & 2\end{array}\right]\) and \(B=\left[\begin{array}{cc}1 & -1 \\ 0 & 2\end{array}\right]\) is given by

If the matrix \(A =\left(\begin{array}{ll}1 & 3 \\ 2 & 1\end{array}\right)\), then the value of \(\operatorname{det}\left( A ^2-2 A \right)\) is equal to

The value of the determinant \(\left|\begin{array}{lll}a-b & b+c & a \\b-c & c+a & b \\c-a & a+b & c\end{array}\right| \text { is : }\)

Which of the following statements are correct?
(A) If elements of a row (or column) of a determinant are multiplied with cofactors of any other row (or column), then their sum is zero.
(B) The value of determinant is equal to the sum of the product of elements of any row (or column) with their corresponding cofactors.
(C) If any two rows (or columns) of a determinant are interchanged, their sign of determinant does not change.
(D) The value of determinant remains unchanged if its rows and columns are interchanged.
(E) A square matrix A has inverse if and only if A is singular.
Choose the correct answer from the options given below:

Two electric bulbs of 60 W and 100 W powers, respectively are connected in series across a 220 V supply. The current is :

Antibodies are secreted by:

If \(\left|\begin{array}{cc}2 x & 2 \\ 4 & x\end{array}\right|=10\), then \(x\) is:

Which one of the following enzymes acts as molecular scissors?

The unit of molar conductivity is

The isotope \({ }^{42} K\) has a half life of about 12 hours. What fraction of the initial concentration remains after 48 hours?