Find ∂2y/∂y∂x for the function u = x/y2 - y/x2
2/y2 + 2/x2
2/y3 + 2/x3
-2/y3 + 2/x3
The largest value of ax3 - 3x2 - 12x = 5 for -2 ≤ x ≤ 4 occurs at x =
-2
If y = a log | x | + bx2 + x has its extreme value at x = -1 and x = 2 then:
a = 2, b = -1
a = 2, b = -1/2
a = -2, b = 1/2
None of these
The equation of the normal to the curve y (x - 2 ) (x - 3) 0 x + 7 = 0 at the point where it cuts the x axis is:
x - 20y = 7
20 x - y = 7
20x + y = 140
20x - y = 140
If u = x2y + y2z + z2x then ux + uy + uz =
x + y + z
3(x2y + y2z + z2x)
(x + y + z)2
The length of the subnormal to the parabola y2 = 4dx at any point is equal to:
√2 a
2√2 a
a/√2
2a
If a particle moves according to the law s = t3/3 - 3t2 + 8t then the distance covered before it first comes to rest is.
16/3
8
10/3
20/3
A man is walking at the rate of 8 kmph towards the foot of a tower 60 metres high.The rate at which he is approaching the top when he is 80 metres from the foot of the tower is.
6.4 kmph
32/3 kmph
6 kmph
For the curve x = t2 - 1, y = t2 - t tangent is parallel to x - axis where
t = 0
t = 1/√3
1/2
- 1/√3
The side of an equilateral triangle is 2 cm and is increasing at the rate of 8 cm/hr.The area of the triangle is increasing at the rate of
8√3 sq.cm/hr
4√3 sq.cm/hr
√3/8 sq cm/hr
