COMEDK 2025 Morning Shift

A line $L_1$ passes through the points $(h, k),(1,2)$ and $(-3,4)$. The points $(4,3)$ and $(h, k)$ lie on the line $L_2$. Given $L_1 \perp L_2$ then $(k-h)$ equals to

Distance of the point $(-2,3)$ from the line $12 x-5 y-2=0$ is $\frac{41}{k}$. Then the value of $k$ is

P is a point on the line joining the points $(3,5,-1)$ and $(6,3,-2)$. If $y$ coordinate of point P is 2 , then $x$ coordinate will be

The value of $\lambda$ for which the angle between lines $\vec{r}=\hat{\imath}+\hat{\jmath}+\hat{k}+p(2 \hat{\imath}+\hat{\jmath}+2 \hat{k})$ and $\vec{r}=(1+q) \hat{\imath}+(1+q \lambda) \hat{\jmath}+(1+q) \hat{k}$ is $\frac{\pi}{2}$

The value of $\frac{1}{2 \sin 10^{\circ}}-2 \sin 70^{\circ}$ is

If $\sin A+\sin B=-\frac{21}{65}, \cos A+\cos B=-\frac{27}{65}$ and $\pi

If $\tan x^{\circ} \tan 2^{\circ} \tan 3^{\circ} \ldots \ldots \ldots \ldots . . \tan 88^{\circ} \tan y^{\circ}=1$ then $\cot (x+y)=$

The magnitude of the projection of the vector $-\hat{\imath}+2 \hat{\jmath}-\hat{k}$ on the z -axis is

A line $L_1$ passing through the point A with position vector $\vec{a}=4 \hat{i}+2 \hat{j}+2 \hat{k}$ is parallel to the vector $\vec{b}=2 \hat{i}+3 \hat{j}+6 \hat{k}$. The length of the perpendicular drawn from a point P with position vect...

If $\vec{a}, \vec{b}, \vec{c}$ are three vectors such that $a \neq 0$ and $\vec{a} \times \vec{b}=2(\vec{a} \times \vec{c}),|\vec{a}|=|\vec{c}|=1,|\vec{b}|=4$ and $|\vec{b} \times \vec{c}|=\sqrt{15}$ if $\vec{b}-2 \vec{c}=\lambda \vec{a}$ t...