If `ax+by+c=0` is a normal to hyperbola `xy=1`, then (A) `alt0, blt0` (B) `alt0, bgt0` (C) `agt0, bgt0` (D) `agt0, blt0`

If the line ax+by+c=0 is normal to the xy+5=0 , then a and b have

If parabola y^2 = 4ax touches circle x^2 + y^2 + 2gx = 0 externally, then (A) agt0, ggt0 (B) agt0, glt0 (C) alt0,ggt0 (D) alt0, glt0

If the line a x+b y+c=0 is a normal to the curve x y=1, then a >0,b >0 a >0,b >0 (d) a<0,b<0 none of these

If the line a x+b y+c=0 is a normal to the curve x y=1, then a >0,b >0 a >0,b >0 (d) a<0,b<0 none of these

The direction cosines of any normal to the xy-plane are (A) 1,0,0 (B) 0,1,0 (C) 1,1,0 (D) 0,01

For a gt b gt c gt 0 , if the distance between (1,1) and the point of intersection of the line ax+by-c=0 and bx+ay+c=0 is less than 2sqrt2 then, (A) a+b-cgt0 (B) a-b+clt0 (C) a-b+cgt0 (D) a+b-clt0

Consider f(x)=ax^(4)+cx^(2)+dx+e has no point of inflection. Then which of the following is/are possible? (a) agt0,clt0 (b) alt0,cgt0 (c) a,clt0 (d) a,cgt0

Figure 2.23 shows the graph of the polynomial f(x)=a x^2+b x+c for which (FIGURE) (a) a<<0,\ \ b>>0\ a n d\ c >0 (b) a<0, blt0 and cgt0 (c) a<0,\ b<0\ a n d\ c<0 (d) a >0,\ b >0\ a n d\ c<0

If a=int_(1/2)^2 1/x cot^7(x-1/x)dx , then (A) a=0 (B) 0ltalt1 (C) agt0 (D) none of these

Let a=int_0^(pi/2) sinx/xdx , then (A) 0ltalt1 (B) agt2 (C) 1ltaltpi/2 (D) none of these