COMEDK 2025 Evening Shift

If the line $(3 x+14 y+7)+k(5 x+7 y+6)=0$ is perpendicular to $x$-axis then the value of ' $k$ ' is

A straight line makes positive intercepts on the coordinate axes whose sum is 5 . If the line passes through the point $P(-3,4)$ then the equation of a line is

Two lines $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}$ and $\frac{x-3}{1}=\frac{y-k}{2}=\frac{z}{1}$ intersect at a point. Then the value of ' $k$ ' is

The equation of a line passing through origin with direction angles $\frac{2 \pi}{3}, \frac{\pi}{4}, \frac{\pi}{3}$ is

The image of a point $P(3,5,3)$ in the line $\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}$ is $P^{\prime}(a, b, c)$. Then $a+b+c=$

If $\sin x+\sin ^2 x=1$ then $\cos ^8 x+2 \cos ^6 x+\cos ^4 x$ is equal to :

If $\tan \alpha=\frac{1}{7}$ and $\sin \beta=\frac{1}{\sqrt{10}}, \quad 0<\alpha, \beta<\frac{\pi}{2}$ then $2 \beta$ is equal to

The value of $\frac{\sin ^2 20^{\circ}+\cos ^4 20^{\circ}}{\sin ^4 20^{\circ}+\cos ^2 20^{\circ}}$ is :

If $\vec{a}$ and $\vec{b}$ are two vectors such that $\vec{a} \cdot \vec{b}=|\vec{a} \times \vec{b}|$ then the angle between $\vec{a}$ and $\vec{b}$ is

For any vector $\vec{p}$, the value of $\left[2\left\{|\vec{p} \times \hat{\imath}|^2+|\vec{p} \times \hat{\jmath}|^2+|\vec{p} \times \hat{k}|^2\right\}\right]$ is