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1.

The solution of the differential equation  $(x+2y^{3})\frac{dy}{dx}=y$ is

A) $x=y^{3}+c$

B) $x=y^{3}+cy$

C) $y=x^{3}+c$

D) $y=x^{3}+cx+d$

2.

The area (in square units) of the region bounded by the curve y=|sin 2x|  and X-axis  in [0, $2 \pi$] is

A) 0

B) 1

C) 3

D) 4

3.

If the minimum  value of  f(x)= $2x^{2} +\alpha x+8$ is the same as the maximum value of g(x)=$-3x^{2}-4x+\alpha^{2}$ ,  then $\alpha^{2}$=

A) $\frac{150}{27}$

B) $\frac{160}{27}$

C) $\frac{170}{27}$

D) $\frac{181}{27}$

4.

Electric current is measured by tangent galvanometer, the current being proportional to the tangent of the angle $\theta$ of deflection. If the deflection is read as $45^{0}$ and  an error of 1%  is made  in reading it.then  the percentage error in the current  is

A) $\pi$

B) $\frac{\pi}{2}$

C) $\frac{\pi}{3}$

D) $\frac{\pi}{4}$

5.

The coordinates of a a point on the curve  $x=a(\theta +\sin \theta), y =a(1-\cos \theta)$   where the tangent is inclined at an angle $\frac{\pi}{4}$  to the positive X-axis , are

A) $\left(a\left(\frac{\pi}{2}-1\right)a\right)$

B) $\left(a\left(\frac{\pi}{2}+1\right)a\right)$

C) $\left(a \frac{\pi}{2},a\right)$

D) (a,a)

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