Maths

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Let $\lambda \ne 0$ be in R. If $\alpha$ and $\beta$ are the roots of the equation, $x^2-x+2\lambda =0$ and $\alpha$ and $\gamma$ are the roots of the equation, $3x^2-10x+27\lambda =0$ , then $\frac{\beta \gamma }{\lambda }$ is equal to:

A plane is parallel to yz-plane so it is perpendicular to:

(a) x  -axis

(b) y -axis

(c) z -axis

(d) None of these

Let $\lambda \ne 0$ be in R. If $\alpha$ and $\beta$ are the roots of the equation, $x^2-x+2\lambda =0$ and $\alpha$ and $\gamma$ are the roots of the equation, $3x^2-10x+27\lambda =0$ , then $\frac{\beta \gamma }{\lambda }$ is equal to:

A plane is parallel to $yz$ -plane so it is perpendicular to:

(a) $x$ -axis

(b) $y$   -axis

(c) $z$   -axis

(d) None of these

The point $\left(2,3,4\right)$ lies in the

(a) First octant

(b) Seventh octant

(c) Second octant

(d) Eighth octant

Equation of $y$ -axis is considered as

(a) $x=0,y=0$  

(b)  $y=0,z=0$

(c)    

(d)   None of these

  $x$ -axis is the intersection of two planes

(a) $xy$  and $xz$

(b) $yz$ and $zx$

(c) $xy$ and $yz$

(d) None of these

If the distance between the points $\left(a,0,1\right)$ and $\left(0,1,2\right)$ is $\sqrt[]{27}$ , then the value of $a$ is

(a) 5

(b) $\pm 5$

(c) –5

(d) None of these

Distance of the point $\left(3,4,5\right)$  from the origin $\left(0,0,0\right)$  is

(a) $\sqrt[]{50}$    

(b)   3

(c)   4

(d)    5