Statement 1 : The line `(x-12) cos theta + (y-3) sin theta = 1` touches a fixed circle for all values of `theta`. Statement 2 : `y-beta = m (x-alpha) +- asqrt(1+m^2)` is tangent to the circle `(x-alpha)^2 + (y-beta)^2 = a^2` for all values of `m`. (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not a correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true

Show that the line (x-2)costheta+(y-2)sintheta=1 touches a circle for all values of theta .Find the circle.

Statement 1 : The circle x^2 + y^2 - 8x - 6y + 16=0 touches x-axis. Statement : 2 : y-coordinate of the centre of the circle x^2 + y^2 - 8x -6y+16=0 is numerically equal to its radius. (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not a correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true

Statement-1: The area bounded by the curves y=ln|x| , y-axis and y=1-|x| is 2 sq. units.Statement-2: Both the curves y=log|x| and y=1-|x| are symmetric about y-axis. (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true

Statement-1: The area of the region R={(x,y) : |x| le |y| and x^2+y^2 le 1} is pi/4 sq. units.Statement-2: Curves |y|=|x| and x^2+y^2=1 symmetric about both x and y-axis. (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true

Statement-1: Solution of the differential equation dy/dx tany=sin(x+y)+sin(x-y) is secy+2cosx=c .Statement-2: The differential equation dy/dx tany=sin(x+y)+sin(x-y) is (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true

Statement-1: The solution of the differential equation (x^2+y^2)dx=2xydy satisfying y(1)=0 is x^2-y^2=x .Statement-2: The differential equation (x^2+y^2)dx=2xydy can be solved by putting y=vx . (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true

The line (x-1) cos theta + (y-1) sin theta =1, for all values of theta touches the circle

x-y+b=0 is a chord of the circle x^2 + y^2 = a^2 subtending an angle 60^0 in the major segment of the circle. Statement 1 : b/a = +- sqrt(2) . Statement 2 : The angle subtended by a chord of a circle at the centre is twice the angle subtended by it at any point on the circumference. (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not a correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true

Statement 1. If sin^-1 x=cos^-1 x, then x= 1/sqrt(2) , Statement 2. sin^-1 x+cos^-1 x= pi/2, 1lexlarr1 (A) Both Statement 1 and Statement 2 are true and Statement 2 is the correct explanation of Statement 1 (B) Both Statement 1 and Statement 2 are true and Statement 2 is not the correct explanatioin of Statement 1 (C) Statement 1 is true but Statement 2 is false. (D) Statement 1 is false but Statement 2 is true

The straight line x cos theta+y sin theta=2 will touch the circle x^(2)+y^(2)-2x=0, if