Q1. In the figure (not drawn to scale) given below. If AD = CD = BC and ∠BCE = 96°, how much is the value of ∠DBC ?
(d) can’t be determined
Q2. A rectangular sheet of paper, when halved by folding it at the mid-point of its longer side, results in a rectangle, whose longer and shorter sides are in the same ratio as of the original rectangle. If the shorter side of the original rectangle is 2, what is the area of the smaller rectangle ?
Q3. Find the area of the shaded region given that all three circular arcs and are of equal radii ‘r’ and A, B and C are the centre C1 , C2 and C₃ respectively.
Q4. A sphere of radius 25 cm is cut by a plane whose distance from the centre of the sphere is 15 cm. What is the circumference of the plane circular section?
(a) 10π cm
(b) 24π cm
(c) 42π cm
(d) 40π cm
Q5. A sphere of radii 14 cm is melted. Molten metal is further utilized to make a cone of radii 21 cm. Find the height of the cone?
Q6. The minimum value of 2^sinx +2^cosx , is
Q7. The top of the hill observed from the top and bottom of a building of height ‘h’ is at angles of elevation p and q respectively. The height of the hill is
Q8. An aeroplane flying at a height of 300 meters above the ground passes vertically above another plane at an instant when the angles of elevation of the two planes from the same point on the ground are 60° & 45° respectively. The height of the lower plane from the ground (in meters) is
Q9. The midpoints of the sides of a ∆ABC are D(6, 1) E(3, 5) and F(–1, –2) then the coordinates of the vertex opposite to D are:
(a) (–4, 2)
(b) (–4, 5)
(c) (2, 5)
(d) (10, 8)
Q10. If C(1, 4) is the centroid of triangle ABC having its two vertices A and B at (4, –3) and (–9, 7) respectively then area of the triangle ABC in square units is :