If `x=m x+c` touches the parabola `y^2=4a(x+a),` then (a)`c=a/m` (b) `c=a m+a/m` (c)`c=a+a/m` (d) none of these

The locus of the midpoint of the segment joining the focus to a moving point on the parabola y^2=4a x is another parabola with directrix (a) y=0 (b) x=-a (c) x=0 (d) none of these

If a!=0 and the line 2b x+3c y+4d=0 passes through the points of intersection of the parabolas y^2=4a x and x^2=4a y , then (a) d^2+(2b+3c)^2=0 (b) d^2+(3b+2c)^2=0 (c) d^2+(2b-3c)^2=0 (d)none of these

If y=m_1x+c and y=m_2x+c are two tangents to the parabola y^2+4a(x+a)=0 , then

The lines which intersect the skew lines y=m x ,z=c ; y=-m x ,z=-c and the x-axis lie on the surface: (a.) c z=m x y (b.) x y=c m z (c.) c y=m x z (d.) none of these

Statement 1: The line y=x+2a touches the parabola y^2=4a(x+a) Statement 2: The line y=m x+a m+a/m touches y^2=4a(x+a) for all real values of mdot

Parabola y^2=4a(x-c_1) and x^2=4a(y-c_2) , where c_1a n dc_2 are variable, are such that they touch each other. The locus of their point of contact is (a) x y=2a^2 (b) x y=4a^2 (c) x y=a^2 (d) none of these

The value of lim_(m->oo)(cos(x/m))^("m") is 1 (b) e (c) e^(-1) (d) none of these

Let h(x)=x^(m/n) for x in R , where +m and n are odd numbers and 0 less than m less than n Then y=h(x) has a)no local extremums b)one local maximum c)one local minimum d)none of these

Normal drawn to y^2=4a x at the points where it is intersected by the line y=m x+c intersect at P . The foot of the another normal drawn to the parabola from the point P is (a) (a/(m^2),-(2a)/m) (b) ((9a)/m ,-(6a)/m) (c) (a m^2,-2a m) (d) ((4a)/(m^2),-(4a)/m)

The straight lines represented by (y-m x)^2=a^2(1+m^2) and (y-n x)^2=a^2(1+n^2) from a (a) rectangle (b) rhombus (c) trapezium (d) none of these