COMEDK 2026 Morning Shift

A straight line passes through the point $P\left(\log _2 16, \log _3 27\right)$ such that the portion of the line intercepted between the co-ordinate axes is divided by $P$ in the ratio $1: 2$ internally (starting from the $x$-axis). Then t...

$$ \begin{aligned} &\text { Find the co-ordinates of the orthocentre of the triangle formed by the lines }\\ &\begin{aligned} & L_1: y-x=2 \\ & L_2: y+2 x=8 \\ & L_3: 3 y-x=18 \end{aligned} \end{aligned} $$

If a straight line passing through a fixed point $(a, b)$, where $\boldsymbol{a}, \boldsymbol{b}>\mathbf{0}$, makes positive intercepts OA and OB on the coordinate axes, then the least value of $\mathbf{O A}+\mathbf{O B}$ is:

Let L be the foot of the perpendicular drawn from the point $P(5,3 k-7,-4)$ to the YZ - plane. If the distance of point L from the origin is $\sqrt{41}$ units, then the possible value of ' $\boldsymbol{k}$ ' is:

The angle between the two lines whose direction cosines satisfy the relations $\boldsymbol{l}+\boldsymbol{m}+\boldsymbol{n}=\mathbf{0}$ and $\boldsymbol{l}^{\mathbf{2}}=\boldsymbol{m}^{\mathbf{2}}+\boldsymbol{n}^{\mathbf{2}}$ is

Let $\mathbf{P}$ be a point on the line $L_1: \frac{x-2}{2}=y+1=\frac{z-1}{2}$ such that its distance from the point $A(2,-1,1)$ is 6 units.
Given that $\boldsymbol{x}$-coordinate of $\mathbf{P}$ is greater than $\mathbf{2}$,
Find the coord...

\(\text { The expression } \frac{1-\tan ^2\left(\frac{\pi}{4}-A\right)}{1+\tan ^2\left(\frac{\pi}{4}-A\right)} \text { equals }\)

If $\sin A+\sin 2 A=x$ and $\cos A+\cos 2 A=y$ then the value of the expression $\left(x^2+y^2\right)\left(x^2+y^2-3\right)$ equals

\(\text { The direction ratios of the vector }(\hat{\imath}+\hat{\jmath}) \times(\hat{\jmath}+\hat{k}) \text { are }\)

Let $\vec{p}$ and $\vec{q}$ be the position vectors of P and Q with respect to the origin. If points R and S divide PQ internally and externally in the ratio 2:3 respectively, then $\overrightarrow{O R}$ and $\overrightarrow{O S}$ are perpe...