The length of shadow of a tower on the plane ground is 3 times the height of the tower. The angle of elevation of sun is

• 45⁰

• 30⁰

• 60⁰

• 90⁰

If the area of a circle is equal to sum of the areas of two circles of diameters 10 cm and 24 cm, then the diameter of the larger circle (in cm) is

• 34

• 26

• 17

• 14

If the radius of the base of a right circular cylinder is halved, keeping the height the same, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is

• 1 : 2

• 2 : 1

• 1 : 4

• 4 : 1

Two dice are thrown together. The probability of getting the same number on both dice is:

• $\frac{1}{2}$

• $\frac{1}{3}$

• $\frac{1}{6}$

• $\frac{1}{12}$

5.

The coordinates of the point P dividing the line segment joining the points A(1, 3) and B(4, 6) in the ratio 2 : 1 are

• ( 2, 4 )

• ( 3, 5 )

• ( 4, 2 )

• ( 5, 3 )

If 1 is a root of the equations ay2 + ay + 3 = 0 and y2 + y + b = 0, then ab equals

• 3

• $-\frac{7}{2}$

• 6

• -3

In Fig., the sides AB, BC and CA of a triangle ABC, touch a circle at P, Q and R respectively. If PA = 4 cm, BP = 3 cm and AC = 11 cm, then the length of BC (in cm) is

• 11

• 10

• 14

• 15

In Fig., a circle touches the side DF of $\angle$EDF at H and touches ED and EF produced at K and M respectively. If EK = 9 cm, then the perimeter of $\angle$EDF (in cm) is:

• 18

• 13.5

• 12

• 9

If a point A(0, 2) is equidistant from the points B(3, p) and C(p, 5) then find the value of p.

A number is selected at random from first 50 natural numbers. Find the probability that it is a multiple of 3 and 4.