COMEDK 2023 Morning Shift

3 and 5 are intercepts of a line \(L=0\), then the distance of \(L=0\) from \((3,7)\) is

The place \(x-2 y+z=0\) is parallel to the line

The lines \(\frac{x-1}{2}=\frac{y-4}{4}=\frac{z-2}{3}\) and \(\frac{1-x}{1}=\frac{y-2}{5}=\frac{3-z}{a}\) are perpendicular to each other, then \(a\) equals to

If two lines \(L_1: \frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}\) and \(L_2: \frac{x-3}{1}=\frac{y-k}{2}=z\) intersect at a point, then \(2 k\) is equal to

The general solution of \(2 \cos 4 x+\sin ^2 2 x=0\) is

If \(\cos A=m \cos B\) and \(\cot \left(\frac{A+B}{2}\right)=\lambda \tan \left(\frac{B-A}{2}\right)\), then \(\lambda\) is equal to

The expression \(\frac{2 \tan A}{1-\cot A}+\frac{2 \cot A}{1-\tan A}\) can be written as

The angle between the vectors \(\mathbf{a}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}\) and \(\mathbf{b}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}\) is

If the vectors \(\mathbf{a}=2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}} ; \mathbf{b}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}\) and \(\mathbf{c}=m \hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}}\) are coplanar,...

\(\mathbf{a}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}-\hat{\mathbf{j}}\) and \(\mathbf{c}=5 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}\), then unit vector parallel to $$\mathbf{a}+\mathbf{b}-...