Problem 1
A unit tangent vector to the surfiace \(x=t, y=t^{2}, z=t^{3} \operatorname{at} t=1\) is .....
Problem 9
If \(\mathrm{A}\) is such that \(\mathrm{V} \times \mathrm{A}=0\), then \(\mathrm{A}\) is called
Problem 11
If \(\nabla, F=0\), then \(\mathbf{F}\) is called......
Problem 12
The directional derivative of \(\phi(x, y, z)=x^{2} y z+4 x^{2}\) at the point \((1,-2,-1)\) in the direction \(F Q\) where \(P=(1,2,-1)\) and \(Q=(-1,2,3)\) is
Problem 16
If \(F\) is at conservstive foree field then curl \(\mathbf{F}\) is
Problem 19
Workdone by a particle along the equare formed by the linen \(y=\pm 1\) and \(x=\pm 1\) under the force $$ \mathbf{F}=\left(x^{2}+x y\right) I+\left(x^{2}+y^{2}\right) J \text { is. } $$
Problem 26
Maximum value of the directional derivative of \(\phi=x^{2}-2 y^{2}+4 z^{2}\) at the point \((1,1,-1)\) is
Problem 31
The value of curl (grad \(f\), where \(f=2 x^{2}-3 y^{2}+4 x^{2}\) is (a) \(4 x-6 y+8 z\) (b) \(4 r I-6 y \mathrm{~J}+\mathrm{8r} \mathbf{K}\) (c) 0 (d) 8 .
Problem 32
The value of \(\int \operatorname{grad}(x+y-z)\) dR from \((0,1,-1)\) to \((1,2,0)\) is (a) 0 (b) 3 (c) \(-1\) (d) not obtainable.
Problem 33
If \(\mathbf{F}=\alpha x \mathbf{I}+b y \mathbf{J}+c \boldsymbol{K}\), then \([\mathbf{F}-d \mathbf{S}, S\) being the surface of a unit sphere, is \(\begin{array}{llll}\text { (c) }(4 / 3) \mathrm{x}(a+b+c)^{2} & \text { (b) } 0 & \text { (c) } 4 \pi / 3(a+b+c) & (d) \text { none of these. }\end{array}\)
