# NIELIT 2019 Feb Scientist C - Section D: 10

743 views

Let $(x_{1},4),(-2,y_{1})$ lies on the line joining the points $(2,-1),(5,-3)$ then the point  $P(x_{1},y_{1})$ lies on the line:

1. $6(x+y)-25=0$
2. $2x+6y+1=0$
3. $2x+3y-6=0$
4. $6(x+y)+25=0$

Equation of line joining the points ($x_{1}$, $y_{1}$) and ($x_{2}$, $y_{2}$) is $\frac{y-y_{1}}{y_{2}-y_{1}} =\frac{x-x_{1}}{x_{2}-x_{1}}$

Here, two points are (2, -1) and (5, -3), so equation of the line will be $\frac{y+1}{-3+1} =\frac{x-2}{5-2}$

2x+3y-1=0 is the equation of line. ($x_{1},4$) and $(-2,y_{1})$ lies on this line, so

2*$x_{1}$ + 3*4 -1 = 0 → On solving, we get $x_{1}$ = $-\frac{11}{2}$. Similarly,

2*-2+3*$y_{1}$ -1 = 0 → On solving, we get $y_{1}$ = $\frac{5}{3}$. So point is ($x_{1}$,$y_{1}$) = ($-\frac{11}{2}$, $\frac{5}{3}$)

Only option B 2x + 6y + 1 = 0 satisfies the point ($x_{1}$,$y_{1}$).

2*$-\frac{11}{2}$ + 6*$\frac{5}{3}$ + 1 = 0

The line $x+y=4$ divides the line joining $\text{(-1,1) & (5,7)}$ in the ratio $\lambda : 1$ then the value of $\lambda$ is:$2$$3$$\dfrac{1}{2}$$1 0 votes 2 answers 2 1,002 views If P$$\left (x, y \right)$ is any point on the line joining the points $A$$\left (a, 0 \right) and B$$\left(0, b \right)$ then the value of $bx+ay-ab$ is :$1$$-1$$0$$2... 0 votes 1 answer 3 629 views The image of the point \left (3, 8 \right) in the line x+3y=7 is :\left (1, 4 \right)$$\left (4, 1 \right)$$\left (-1, -4 \right)$$\left (-4, -1 \right)$
The minute hand is $10$ cm long. Find the area of the face of the clock described by the minute hand between $9$ a.m and $9:35$ a.m.${183.3\ cm^{2}}$${366.6\ cm^{2}}$${24... 0 votes 1 answer 5 715 views Determine$a+b$such that the following system of equations:$2x-(a-4)y=2b+1 \text{ and }4x-(a-1)y=5b-1$infinite solutions.$11$$9$$108\$