Mathematics Test 155

In acute angled triangle ΔABC, there is an interior point P such that ∠PAB = 10°, ∠PBA = 20°, ∠PCA = 30°, ∠PAC = 40°, then ∠ACB = x°, then x is :

If 0 ≤ x ≤ 5π, then equation (3 + cos x)² = 4 – 2 sin⁸x has

Let  (where [x] denotes greatest integer less than or equal to x). If A and B denotes the domain and range of f(x) respectively, then the number of integers in (A ∪ B) is m, then the value of sin^–1(cos 2) – cos^–1(sin 2) + tan^–1(cot 4) – cot^–1(tan 4) + sec^–1(cosec 6) – cosec^–1(sec 6) is :

Consider two lines L₁ and L₂ given by 3x + 4y – 7 = 0 and 4x – 3y – 1 = 0 respectively and a variable point P. Let d(P, L_i), i = 1, 2 represents the perpendicular distance of point P from the line L_i. If point P moves in a certain region R in such a way that 6 ≤ 2d(P, L₁) + 3d(P, L₂) ≤ 12, then the area of the region R :

If two distinct chords, drawn from the point (p, q) on the circle x² + y² = px + qy, where p, q ≠ 0, are bisected by the x-axis, then which of the following is correct :

If the line x + 2y = k is normal to the parabola x² – 4x – 8y + 12 = 0 then the value of k is :

If a tangent to ellipse x² + 4y² = 4, meet the ellipse x² + 2y² = 6 at points P & Q, then angle between tangents at P and Q is :

A circle cuts two fixed perpendicular lines such that each of the non zero intercepts is of given length (but unequal). The eccentricity of locus of the centre of the circle is :

If α is an imaginary fifth root of unity then the value of 

Let f(x) = x² + px + q and g(x) = x² + rx + s where real roots of f(x) = 0 are α, β and real roots of g(x) = 0 are α + δ, β + δ such that minimum value of f(x) be  and least value of g(x) occurs at x = 7/2, then correct option is –