SSC CGL 20191)The graphs of the equations 3x + y - 5 = 0 and 2x - y - 5 = 0 intersect at the point P(\({\alpha,\beta}\)). What is the value of (\({3\alpha+\beta}\)) ?

Correct Option: D

5

When graphs of the equations intersect at the point

\( P(\alpha, \beta) then,; 3\alpha + \beta - 5 = 0; 2\alpha - \beta - 5 = 0; \alpha = 2; \beta = -1; (3\alpha + \beta) = 3 \times 2 - 1 = 6 - 1 = 5 \)

SSC CGL 20192)The graph of the equation x - 7y = -42, intersects the y-axis at \(P\left(\alpha,\beta\right)\) and the graph of 6x + y - 15 = 0, intersects the x-axis at \( Q\left(\gamma,\delta\right)\) , What is the value of \(\alpha+\beta+\gamma+\delta\)?

Correct Option: A

\(17\over2\)

The

graph of the equation x — 7y = —42, intersects the y-axis at \(P\left(\alpha,\beta\right)\);

So, x = 0;

0 - 7y = -42;

y = 6;

\(\alpha\) = 0;

\(\beta\) = 6;

graph of 6x + y - 15 = 0, intersects the x-axis at\( Q\left(\gamma,\delta\right)\);

So, y = 0;

6x - 15 = 0;

x = 5/2;

\(\gamma\) = 5/2;

\(\delta \)= 0;

Now,

\(\alpha+\beta+\gamma+\delta = 0 + 6 + 5/2 + 0 = \frac{17}{2}\)

SSC CGL 20193)What is the area (in square units) of the triangular region enclosed by the graphs of the equations x + y = 3, 2x + 5y= 12 and the x-axis?

Correct Option: B

3

x + y = 3;

2x + 2y = 6 ---(1);

2x + 5y = 12 ---(2);

From eq (1) and eq (2), 3y = 6; y=2; so height = 2; put the value of y in eq(1) and (2), x = 3; and x = 6; Area = \({1\over2}\times base\times height\)= \({1\over2}\times(6-3)\times2=3\) square units

SSC CGL 20194)The graph of the equations 5x - 2y + 1 = 0 and 4y - 3x +5 = 0 , intersect at the point P (\(\alpha, \beta\) ). What is the value of \((2\alpha - 3\beta)\)?

Correct Option: A

4

SSC CGL 20195)The point of intersection of the graphs of the equations 3x - 5y = 19 and 3y - 7x + 1 =0 is P\((\alpha,\beta)\) . What is the value of \((3\alpha-\beta)\)?

Correct Option: B

-1

SSC CGL 20196)The graphs of the equations 2x+3y=11 and x-2y+12=0 intersects at P (\(x_1,y_1\)) and the graph of the equations x-2y+12=0 intersects the x-axis at \(Q(x_2,y_2)\). What is the value of \((x_1-x_2+y_1+y_2)\)?

Correct Option: C

15

2x+3y=11 and x-2y+12=0 intersects at P (\(x_1,y_1\)) ; x-2y+12=0 intersects the x-axis at \(x_2,y_2\).

therefore \(x_1=-2,y_1=5 \)

Also, when a line intersect x-axis the y cordinate is 0.

therefore \(x_2=-12,y_2=0\)

\((x_1-x_2+y_1+y_2) = \) 15

showing 1 - 6 results of 6 results