Let A = { z ∈ C : |z − 2| ≤ 4 } and B = { z ∈ C : |z − 2| + |z + 2| = 5 }
Let A = { z ∈ C : |z − 2| ≤ 4 } and B = { z ∈ […]
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Statement I : � is divisible by 7. Statement II : The integral part of � is an odd number.
Given below are two statements on divisibility and integral part of an expression Q. Given below are two statements :
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An ellipse has its center at (1, −2), one focus at (3, −2) and one vertex at (5, −2). Then the length of its latus rectum is :
An ellipse has its center at (1, −2), one focus at (3, −2) and one vertex at (5, −2) Q.
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Let P be a point in the plane of the vectors � and � such that P is equidistant from the lines AB and AC. If �, then the area of the triangle ABP is :
Let P be a point in the plane of the vectors AB = 3i + j − k and AC
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Given below are two statements : Statement I : The function f : ℝ → ℝ defined by f(x) = x / (1 + |x|) is one-one. Statement II : The function f : ℝ → ℝ defined by f(x) = (x² + 4x − 30) / (x² − 8x + 18) is many-one.
Given below are two statements on one-one and many-one functions Q. Given below are two statements : Statement I :
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Let the arithmetic mean of 1/a and 1/b be 5/16, a > 2. If α is such that a, 4, α, b are in A.P., then the equation αx² − ax + 2(α − 2b) = 0 has :
Let the arithmetic mean of 1/a and 1/b be 5/16, a > 2 Q. Let the arithmetic mean of 1/a
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Considering the principal values of inverse trigonometric functions, the value of the expression is equal to :
Considering the principal values of inverse trigonometric functions, the value of the expression Q. Considering the principal values of inverse
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Let Q(a, b, c) be the image of the point P(3, 2, 1) in the line �. Then the distance of Q from the line � is
Let Q(a, b, c) be the image of the point P(3, 2, 1) in the line and find the distance
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Let y = y(x) be the solution of the differential equation x dy/dx − y = x² cot x, x ∈ (0, π). If y(π/2) = π/2, then 6y(π/6) − 8y(π/4) is equal to :
Let y = y(x) be the solution of the differential equation x dy/dx − y = x² cot x Q.
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Let the circle x² + y² = 4 intersect x-axis at the points A(a, 0), a > 0 and B(b, 0). Let P(2 cos α, 2 sin α), 0 < α < π/2 and Q(2 cos β, 2 sin β) be two points such that (α − β) = π/2. Then the point of intersection of AQ and BP lies on :
Let the circle x² + y² = 4 intersect x-axis and find the locus of intersection point Q. Let the