The straight lines `4a x+3b y+c=0` , where `a+b+c` are concurrent at the point a) `(4,3)` b) `(1/4,1/3)` c) `(1/2,1/3)` d) none of these

The straight lines x+2y-9=0,3x+5y-5=0 , and a x+b y-1=0 are concurrent, if the straight line 35 x-22 y+1=0 passes through the point (a) (a , b) (b) (b ,a) (c) (-a ,-b) (d) none of these

If the straight lines x+y-2-0,2x-y+1=0 and a x+b y-c=0 are concurrent, then the family of lines 2a x+3b y+c=0(a , b , c) are nonzero) is concurrent at (a) (2,3) (b) (1/2,1/3) (c) (-1/6,-5/9) (d) (2/3,-7/5)

The straight lines represented by x^2+m x y-2y^2+3y-1=0 meet at (a) (-1/3,2/3) (b) (-1/3,-2/3) (c) (1/3,2/3) (d) none of these

In A B C , if the orthocentre is (0,0) and the circumcenter is (1,2), then centroid of A B C) is (a) (1/2,2/3) (b) (1/3,2/3) (c) (2/3,1) (d) none of these

If 6a^2-3b^2-c^2+7ab-ac+4bc=0 then the family of lines ax+by+c=0,|a|+|b| != 0 can be concurrent at concurrent (A) (-2,3) (B) (3,-1) (C) (2,3) (D) (-3,1)

The value of 3^((log)_4 5)-5^((log)_4 3) is 0 (b) 1 (c) 2 (d) none of these

If the lines ax + 2y + 1 = 0, bx + 3y + 1 = 0, cx + 4y + 1 = 0 are concurrent, then a, b, c are in

If f(x)=sin^6x+cos^6x , then range of f(x) is [1/4,1] (b) [1/4,3/4] (c) [3/4,1] (d) none of these

Line a x+b y+p=0 makes angle pi/4 with xcosalpha+ysinalpha=p ,p in R^+ . If these lines and the line xsinalpha-ycosalpha=0 are concurrent, then (a) a^2+b^2=1 (b) a^2+b^2=2 (c) 2(a^2+b^2)=1 (d) none of these

In A B C , the coordinates of B are (0,0),A B=2,/_A B C=pi/3, and the middle point of B C has coordinates (2,0)dot The centroid o the triangle is (a) (1/2,(sqrt(3))/2) (b) (5/3,1/(sqrt(3))) (c) (4+(sqrt(3))/3,1/3) (d) none of these