Practice questions 17-24 are provided in this section. Refer here for questions 1-8 and 9-16. Prepare the questions well and send your answers through the comments section of this post..
17) If the point of intersection of the tangents at $ t_{1}=t $ and $ t_{2}=3t $ to the parabola $ y^2=8x$ is:
a) $ (6t^2, 8t) $
b) $ (8t, 6t^3) $
c) $ (t^2, 4t) $
d) $ (4t, t^2) $
18) The straight line 2x-y+c = 0 is a tangent to the ellipse $ 4x^2+8y^2=32 $, if c is:
a) $ \pm 2\sqrt3 $
b) $ \pm 6 $
c) 36
d) $ \pm 4 $
19) The angle between the curves $ \frac{x^2}{25}+\frac{y^2}{9}=1 $ and $ \frac{x^2}{8}-\frac{y^2}{8}=1 $ is:
a) $ \frac{\pi}{4} $
b) $ \frac{\pi}{3} $
c) $ \frac{\pi}{6} $
d) $ \frac{\pi}{2} $
20) The least possible perimeter of a rectangle of area $ 100m^2 $ is:
a) 10
b) 20
c) 40
d) 60
21) The curve $ y=ax^3+bx^2+cx+d $ has a point of inflexion at x = 1, then
a) 3a+b = 0
b) 3a+b = 1
c) a+b = 0
d) a+3b = 0
22) If $ s=t^3-4t^2+7 $, the velocity when the acceleration is zero is:
a) $ \frac{-16}{3} m/Sec $
b) $ \frac{32}{3} m/Sec $
c) $ \frac{16}{3} m/Sec $
d) $ \frac{-32}{3} m/Sec $
23) If u = y sinx, then $ \frac{\partial^2 u}{\partial x\partial y}= $
a) cos x
b) cos y
c) sin x
d) 0
24) The curve $ a^2y^2 = x^2(a^2-x^2) $ has
a) one loop between x = 0 and x = a
b) two loops between x = 0 and x = a
c) two loops between x = –a and x = a
d) no loop
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