# HSC +2 Maths Important Questions AA4 - Part 5

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Questions from 33-40 of 40 - AA4 Series
33) The curves $2x^2+3y^2=1$ and $3x^2-ky^2=1$ cut orthogonally. Then the value of k is:

a) 2          b) -4          c) 6          d) –6

34) If $u=x.f(\frac{y}{x})$, then $x\frac{\partial u}{\partial x}+y\frac{\partial u}{\partial y}$

is equal to:

a) 0          b) 1          d) u          d) 2u

35) $\int_{0}^{\pi}sin^3 \: x \: dx$ is equal to:

a) $\frac{2}{3}$           b) $\frac{4}{3}$

c) $\frac{\pi}{2}$           d) $\pi$

36) Integrating factor of $\frac{\mathrm{d} y}{\mathrm{d} x}-x \: cot \:y=y^2$ is:

a) $cot \: y$              b) $-cot \: y$

c) $sin \: y$               d) $cosec \: y$

37) (R   ; +) is a:

a) group           b) ableian group           c) semigroup           d) monoid

38) $a\ast b=a^2+b^2$, then $(2\ast 3)\ast 5$ is equal to:

a) 184            b) 194            c) 174            d) 204

39) In a poisson distribution, moment of order two about origin is 30, then the parameter of the distribution is:

a) 6           b) 5           c) –6           d) 30

40) $\overrightarrow{a}.\overrightarrow{b}=|\overrightarrow{a} \times \overrightarrow{b}|$,

then the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is:

a) $\frac{\pi}{2}$              b) $\frac{\pi}{4}$

c) $\frac{\pi}{3}$              d) $\frac{\pi}{6}$