Circles `x^2 + y^2 = 1 and x^2 + y^2 - 8x + 11=0` cut off equal intercepts on a line through the point `(-2, 1/2)`. The slope of the line is : (A) `(-1 + sqrt(29))/14` (B) `(1+sqrt(7)/4` (C) `(-1-sqrt(29))/14` (D) none of these

Solution set of inequation ( cos^-1x)^2-(sin^-1x)^2gt0 is (A) [0, 1/sqrt(2)) (B) [-1, 1/sqrt(2)) (C) (-1,sqrt2) (D) none of these

A(1/sqrt(2), 1/sqrt(2)) is a point on the circle x^2 + y^2 = 1 and B is another point on the circle such that AB = pi/2 units. Then coordinates of B can be : (A) (1/sqrt(2), - 1/sqrt(2)) (B) (-1/sqrt(2), 1/sqrt(2)) (C) (-1/sqrt(2), - 1/sqrt(2)) (D) none of these

The length of perpendicular from the poit (1,-1,2) on the line (x+1)/2=(2-y)/3=(z+2)/4 is (A) 0 (B) sqrt(6) (C) sqrt(21) (D) none of these

The image of the centre of the circle x^2 + y^2 = 2a^2 with respect to the line x + y = 1 is : (A) (sqrt(2), sqrt(2) (B) (1/sqrt(2) , sqrt(2) ) (C) (sqrt(2), 1/sqrt(2)) (D) none of these

The line x-y+2=0 touches the parabola y^2 = 8x at the point (A) (2, -4) (B) (1, 2sqrt(2)) (C) (4, -4 sqrt(2) (D) (2, 4)

The length of the perpendicular drawn from the point (3,-1,11) to the line x/2=(y-2)/3=(z-3)/4 is (A) sqrt(33) (B) sqrt(53 (C) sqrt(66) (D) sqrt(29)

The value of lim_(x rarr2)(sqrt(1+sqrt(2+x))-sqrt(3))/(x-2) is (1)/(8sqrt(3))(b)(1)/(4sqrt(3)) (c) 0 (d) none of these

The distance between the parallel planes x+2y-3z=2 and 2x+4y-6z+7=0 is (A) 1/sqrt(14) (B) 11/sqrt(56) (C) 7/sqrt(56) (D) none of these

The direction cosines of line joining (1,-1,1) and (-1,1,1) are (A) 2,-2,0 (B) 1,-1,0 (C) 1/sqrt(2)-1/sqrt(2),0 (D) none of these