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Practice Test - Mathematics 18
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Question 1
The radius of the circle in which the sphere x2 + y2 + z2 + 2x − 2y − 4z − 19 = 0 is cut by the plane x + 2y + 2z + 7 = 0 is
Question 2
Consider the function f(x) = |x – 2| + |x – 5|, x ∈ R.
Statement 1: f’(4) = 0
Statement 2: f is continuous in [2, 5], differentiable in (2, 5) and f(2) = f(5)
Statement 1: f’(4) = 0
Statement 2: f is continuous in [2, 5], differentiable in (2, 5) and f(2) = f(5)
Question 3
The area (in sq. units) of the region described by {(x, y); y2 ≤ 2x and y ≥ 4x – 1} is
Question 4
If the coefficient of x3 and x4 in the expansion of (1 + ax + bx2) (1 – 2x)18 in powers of x are both zero, then (a, b) is equal to
Question 5
If the two circles (x − 1)2 + (y − 3)2 = r2 and x2 + y2 − 8x + 2y + 8 = 0 intersect at two distinct points, then
Question 6
If z1 and z2 are two non-zero complex numbers such that |z1 + z2| = |z1| + |z2| then argz1 – argz2 is equal to
Question 7
The eccentricity of the hyperbola whose length of the latus rectum is equal to 8 and the length of its conjugate axis is equal to half of the distance between its foci, is :
Question 8
equals Question 9
The population p(t) at time t of a certain mouse species satisfies the differential equation
. If p(0) = 850, then the time at which the population becomes 0 is -
Question 10
If 
, then 
is equal to
, then is equal to- 647 attempts
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Sep 18JEE & BITSAT
