If the line joining the points `(0,3)a n d(5,-2)` is a tangent to the curve `y=C/(x+1)` , then the value of `c` is 1 (b) `-2` (c) 4 (d) none of these

The value of int_0^1e^(x^2-x)dx is (a) 1 (c) > e^(-1/4) (d) none of these

If a tangent of slope 2 of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 is normal to the circle x^2+y^2+4x+1=0 , then the maximum value of a b is 4 (b) 2 (c) 1 (d) none of these

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

The slope of the tangent to the curve y=sqrt(4-x^2) at the point where the ordinate and the abscissa are equal is -1 (b) 1 (c) 0 (d) none of these

The minimum value of 2^(x^2-3)^(3+27) is a) 2^(27) (b) 2 (c) 1 (d) none of these

The line joining the points (-2,1,-8)a n d(a ,b ,c) is parallel to the line whose direction ratios are 6,2,a n d3. Find the values of a ,b and c

Show that the line joining the points A(2, 3, 1) and B(4, 6, 2) is perpendicular to the line joining the points C(6, -2, -9) and D(4, -1, -8).

The number of real solutions of the (log)_(0. 5)|x|=2|x| is (a) 1 (b) 2 (c) 0 (d) none of these