If triangle PQR is similar to triangle LMN such that 4PQ = LM and QR = 6 cm then MN is equal to ____________

(a)

12 cm

(b)

24 cm

(c)

10 cm

(d)

36 cm

I the given figure DE||AC which of the following is true.

(a)

\(x=\frac { ay }{ b+a } \)

(b)

\(x=\frac { a+b }{ ay } \)

(c)

\(x=\frac { ay }{ b-a } \)

(d)

\(\frac { x }{ y } =\frac { a }{ b } \)

S and T are points on sides PQ and PR respectively of \(\Delta PQR\) If PS = 3cm, AQ = 6 cm, PT = 5 cm, and TR = 10 cm and then QR

(a)

4 ST

(b)

5 ST

(c)

3 ST

(d)

3 QR

In the given figure DE||BC:BD = x - 3, BA = 2x,CE = x- 2, and AC = 2x + 3, Find the value of x.

(a)

3

(b)

6

(c)

9

(d)

12

The ratio of the areas of two similar triangles is equal to ____________

(a)

The ratio of their corresponding sides

(b)

The cube of the ratio of their corresponding sides

(c)

The ratio of their corresponding attitudes

(d)

The square of the ratio of their corresponding sides

If ABC is a triangle and AD bisects A, AB = 4cm, BD = 6cm, DC = 8cm then the value of AC is ____________

(a)

\(\frac { 16 }{ 3 } cm\)

(b)

\(\frac { 32 }{ 3 } cm\)

(c)

\(\frac { 3 }{ 16 } cm\)

(d)

\(\frac { 1 }{ 2 } cm\)

In a triangle, the internal bisector of an angle bisects the opposite side. Find the nature of the triangle.

(a)

right angle

(b)

equilateral

(c)

scalene

(d)

isosceles

The height of an equilateral triangle of side a is

(a)

\(\frac { a }{ 2 } cm\)

(b)

\(\sqrt { 3a } \)

(c)

\(\frac { \sqrt { 3 } }{ 2 } a\)

(d)

\(\frac { \sqrt { 3 } }{ 4 } a\)

The perimeter of a right triangle is 36 cm. Its hypotenuse is 15 cm, then the area of the triangle is ____________

(a)

108 cm²

(b)

54 cm²

(c)

27 cm²

(d)

216 cm²

A line which intersects a circle at two distinct points is called ____________

(a)

Point of contact

(b)

secant

(c)

diameter

(d)

tangent

If the angle between two radio of a circle is ^o, the angle between the tangents at the end of the radii is ____________

(a)

50^o

(b)

90^o

(c)

40^o

(d)

70^o

In figure \(\angle OAB={ 60 }^{ o }\) and OA = 6cm then radius of the circle is ____________

(a)

\(\frac { 3 }{ 2 } \sqrt { 3 } cm\)

(b)

2 cm

(c)

\(3\sqrt { 3 } cm\)

(d)

\(2\sqrt { 3 } cm\)

In the given figure if OC = 9 cm and OB = 15 cm then OB + BD is equal to ____________

(a)

23 cm

(b)

24 cm

(c)

27 cm

(d)

30 cm

Two concentric circles if radii a and b where a>b are given. The length of the chord of the circle which touches the smaller circle is ____________

(a)

\(\sqrt { { a }^{ 2 }-{ b }^{ 2 } } \)

(b)

\(\sqrt { { a }^{ 2 }-{ b }^{ 2 } } \)

(c)

\(\sqrt { { a }^{ 2 }+{ b }^{ 2 } } \)

(d)

\(2\sqrt { { a }^{ 2 }+{ b }^{ 2 } } \)

Three circles are drawn with the vertices of a triangle as centres such that each circle touches the other two if the sides of the triangle are 2cm,3cm and 4 cm. find the diameter of the smallest circle.

(a)

1 cm

(b)

3 cm

(c)

5 cm

(d)

4 cm