Let R be the real line. Consider the following subsets of the plane `RxxR` . `S""=""{(x ,""y)"":""y""=""x""+""1""a n d""0""<""x""<""2},""T""=""{(x ,""y)"":""x-y""` is an integer }. Which one of the following is true?

Prove that the following sets of three lines are concurrent: x/a+y/b=1, x/b+y/a=1\ a n d\ y=x

Let S be non-empty subset of R. consider the following statement: P: There is a rational number x ne S " such that " x gt 0 Which of the following statements is the negation of the statement P ?

Find the angles between each of the following pairs of straight line: 3x+y+12=0\ a n d\ x+2y-1=0

Find the angles between each of the following pairs of straight line: 3x-y+5=0\ a n d\ x-3y+1=0

Let P=0 be the equation of a plane passing through the line of intersection of the planes 2x-y=0a n d3z-y=0 and perpendicular to the plane 4x+5y-3z=8. Then the points which lie on the plane P=0 is/are a. (0,9,17) b. (1//7,2,1//9) c. (1,3,-4) d. (1//2,1,1//3)

Let P=0 be the equation of a plane passing through the line of intersection of the planes 2x-y=0a n d3z-y=0 and perpendicular to the plane 4x+5y-3z=8. Then the points which lie on the plane P=0 is/are a. (0,9,17) b. (1//7,21//9) c. (1,3,-4) d. (1//2,1,1//3)

Prove that the following sets of three lines are concurrent: 15 x-18 y+1=0,\ 12 x+10 y-3=0\ a n d\ 6x+66 y-11=0.

Let x, y in R . Then x + i y is a non real complex number if

Let the straight lines x+y-2=0, 2x-y+1=0 and px+qy-r=0 be concurrent and l_1 and l_2 be the two members of the family of lines 2px+2qy+4r=0 which are nearest and farthest from origin : Now answer the following questions : The eqation of line l_1 is : (A) y=5x (B) y=3x (C) 5y=x (D) none of these

Consider the lines x=y=z and line 2x+y+z-1=0=3x+y+2z-2 , then