KCET 2017

If coefficient of variation is 60 and standard deviation is 24 , then Arithmetic mean is

Equation of line passing through the point $(1,2)$ and perpendicular to the line $y=3 x-1$

Reflexion of the point $(\alpha, \beta, \gamma)$ in $X Y$-plane is

The plane $2 x-3 y+6 z-11=0$ makes an angle $\sin ^{-1}(\alpha)$ with $X$-axis, the value of $\alpha$ is equal to

The perpendicular distance of the point $P(6,7,8)$ from $X Y$-plane is

The distance of the point $(-2,4,-5)$ from the line $\frac{x+3}{3}=\frac{y-4}{5}=\frac{z+8}{6}$ is

The value of $\cos ^2 45^{\circ}-\sin ^2 15^{\circ}$ is

If $\mathbf{a}=2 \hat{\mathbf{i}}+\lambda \hat{\mathbf{j}}+\hat{\mathbf{k}}$ and $\mathbf{b}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}$ are orthogonal, then value of $\lambda$ is

If $\mathbf{a}, \mathbf{b}, \mathbf{c}$ are unit vectors such that $a+b+c=0$, then the value of $\mathbf{a} \cdot \mathbf{b}+\mathbf{b} \cdot \mathbf{c}+\mathbf{c} \cdot \mathbf{a}$ is equal to

If $a$ and $\mathbf{b}$ are unit vectors, then angle between $\mathbf{a}$ and $\mathbf{b}$ for $\sqrt{3} \mathbf{a}-\mathbf{b}$ to be unit vector is