MCQ
${{{d^2}x} \over {d{y^2}}}$=
- A${1 \over {{{(dy/dx)}^2}}}$
- B${{\left( {{d^2}y/d{x^2}} \right)} \over {{{\left( {dy/dx} \right)}^2}}}$
- C${{{d^2}y} \over {d{x^2}}}$
- ✓${{\left( { - {d^2}y/d{x^2}} \right)} \over {{{\left( {dy/dx} \right)}^2}}}$
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$ 3 x+5 y+\lambda z=3 $
$ 7 x+11 y-9 z=2 $
$ 97 x+155 y-189 z=\mu$
has infinitely many solutions, then $\mu+2 \lambda$ is equal to :
$g(x)=\left\{\begin{array}{ccc}0 & \text { if } & x < a, \\ \int_a^x f(t) d t & \text { if } & a \leq x \leq b, \\ \int_a^b f(t) d t & \text { if } & x > b .\end{array}\right.$, Then
$(A)$ $g(x)$ is continuous but not differentiable at a
$(B)$ $g(x)$ is differentiable on $R$
$(C)$ $g(x)$ is continuous but not differentiable at $b$
$(D)$ $g(x)$ is continuous and differentiable at either a or $b$ but not both