COMEDK 2024 Evening Shift

The area of the triangle whose vertices are \((-2, a)(2,-6)\) and \((5,4)\) is 35 sq units then the value of '\(\mathrm{a}\)' is

The points on the \(x\)-axis whose perpendicular distance from the line \(\frac{x}{3}+\frac{y}{4}=1\) is 4 units are

If the straight lines \(\frac{x-2}{1}=\frac{y-3}{1}=\frac{z-4}{-t}\) and \(\frac{x-1}{t}=\frac{y-4}{2}=\frac{z-5}{1}\) are intersecting then \(t\) can have

The measure of the angle between the lines \(x=k+1, \quad y=2 k-1, \quad z=2 k+3, \quad k \in R \quad\) and \(\quad \frac{x-1}{2}=\frac{y+1}{1}=\frac{z-1}{-2}\) is

The co-ordinate of the foot of the perpendicular from \(P(1,8,4)\) on the line joining \(R(0,-1,3)\) and \(Q(2,-3,-1)\) is

\(\text { Value of } \cos 105^{\circ} \text { is }\)

\(\sqrt{2+\sqrt{2+\sqrt{2+2 \cos 8 \theta}}} \text { where } \theta \in\left[-\frac{\pi}{8}, \frac{\pi}{8}\right] \text { is equal to }\)

\(\text { If } \frac{\cos x}{\cos (x-2 y)}=\lambda \text { then } \tan (x-y) \tan y=\)

\(\text { If } \hat{\imath}+\hat{\jmath}-\hat{k} \quad \&~ 2 \hat{\imath}-3 \hat{\jmath}+\hat{k} \text { are adjacent sides of a parallelogram, then length of its diagonals are }\)

Find the value of '\(b\)' such that the scalar product of the vector \(\hat{\imath}+\hat{\jmath}+\hat{k}\) with the unit vector parallel to the sum of the vectors \(2 \hat{\imath}+4 \hat{\jmath}-5 \hat{k}\) and $$b \hat{\imath}+2 \hat{\jmat...