The angle between lines joining the origin to the point of intersection of the line x + y = 2 and the curve y2 - x2 = 4 is
If the area of the triangle on the complex plane formed by the points z, z + iz and iz is 200, then the value of 3lz I must be equal to
20
40
60
80
Equation of the chord of the hyperbola 25x2 - 16y2 = 400 which is bisected at the point (6, 2), is
6x - 7y = 418
75x - 16y = 418
25x - 4y = 400
None of these
A four-digit number is formed by the digits 1, 2, 3, 4 with no repetition. The probability that the number is odd, is
zero
None of these
The equation of normal to the curve y = (1 + x)y +sin-1(sin2(x)) at a = 0 is
x + y = 1
x - y = 1
x + y = - 1
x - y = - 1
The value of cfrom the Lagrange's mean value theorem for which f(x) = in [1, 5], is
5
1
None of these
C.
It is clear that f(x) has a definite and unique value for each x [1, 5].
Thus, for every point in the interval [1, 5], the value of f(x) exists.
So, f(x) is continuous in the interval [1, 5].
Also, f'(x) = , hich clearly exists for all x in an open interval (1,5).
Hence, f'(x) is differentiable in (1, 5).
So, there must be a value c [1, 5] such that
If there is an error of h % in measuring the edge of a cube, then the per cent error in estimating its volume is
k
3k
None of these
If the system of equations x + ky - z = 0, 3x - ky - z = 0 and x - 3y + z =0, has non-zero solution, then k is equal to
- 1
0
1
2