This is final part of our 40 question collection in mathematics subject. For previous parts you should refer to the related post section at the bottom of this post. Post your answers to these questions in the comments section and share this post with the web. Alternatively, you can also follow our blog so that you never miss an update when a new question paper set is posted.
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} $
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