Mathematics Test 241

The coefficient of x¹⁸ in the product (1 + x) (1 – x)¹⁰ (1 + x + x²)⁹ is :

The tangent and the normal lines at the point (√3, 1) to the circle x² + y² = 4 and the x-axis form a triangle. The area of this triangle (in square units) is :

The angle of elevation of the top of vertical tower standing on a horizontal plane is observed to be 45° from a point A on the plane. Let B be the point 30 m vertically above the point A. If the angle of elevation of the top of the tower from B be 30°, then the distance (in m) of the foot of the tower from the point A is:

The solutions of the equation

sin x + 3sin 2x + sin 3x = cosx + 3cos2x + cos3x in the interval 0 ≤ x ≤ 2π, are ;

If the straight lines joining the origin and the points of intersection of the curve

5x² + 12xy – 6y² + 4x – 2y + 3 = 0 and

x + ky – 1 = 0 are equally inclined to the co-ordinate axis, then the value of k -

If a straight line passing through the point P(–3, 4) is such that its intercepted portion between the coordinate axes is bisected at P, then its equation is :

Consider the circle S ≡ x² + y² – 4x – 4y + 4 = 0. If another circle of radius ‘r’ less than the radius of the circle S is drawn, touching the circle S and the coordinate axes, then the value of ‘r’ is

An equilateral triangle is inscribed in the parabola y² = 4ax, such that one vertex of this triangle coincides with the vertex of the parabola. Side length of this triangle is