[[x]+V{x} x <1 60. If f(x) = 1 ; then {where [.) and [x]+{x}? {-} represents greatest integer part and fractional part respectively.] (a) f(x) is continuous at x = 1 but not differentiable (b) f(x) is not continuous at x = 1 (c) f(x) is differentiable at x = 1 (d) lim f(x) does not exist

Which of the following are examples of the singleton set? (i) {x:x in Z, x^2=4} (ii) {x:x in Z, x +5 =0} (iii) {x:x in Z, |x| =1} (iv) {x :x in N, x^2=16} (v) {x:x " is an even prime number "}

The potential energy of a system under the influence of conservative force at position x is V(x) =[3x^(2)+4x+5] .At x = 2 m the conservative force acting on the system is ……….

Find the polynomials u(x) and v(x) such that (x^(4) -1) * u(x) + (x^(7) -1) * v(x) = (x-1) .

Convert the following polar coordinates to its equivalent Cartesian coordinates. (i) ( i i ) (iii)2,pi)( i v ) (v) (ii) ( v i ) (vii)(( v i i i ) (ix)sqrt(( x )2( x i ))( x i i ) , (xiii)pi/( x i v )6( x v ) (xvi) (xvii))( x v i i i ) (xix) (iii) ( x x ) (xxi)(( x x i i ) (xxiii)-3,-( x x i v )pi/( x x v )6( x x v i ) (xxvii) (xxviii))( x x i x ) (xxx)

Differentiate w.r.t x y = x(x^(2) - 2x) . Here u = x, v=x^(2) - 2x