P, Q R are the points so that PR = 3 cm, QR = 5 cm and PQ = 8 cm. The number of circle passing through the points P, Q, R is

• 3

• 2

• 1

• 1

If  where 0° < a < 90°, then the value of a is

• 0°

• 15°

• 45°

• 45°

The average age of 3 friends is 23. Even if the age of 4th friend is added, the average age remains the same. Then the age of the four friend is

• 20 years

• 21 years

• 22 years

• 22 years

The LCM of two prime numbers x and y, (x > y) is 161. The value of (3y - x)

• -2

• -1

• 1

• 1

If , then the value of U₁ + U₂ + U₃ + U₄ + U₅

If , then the value of  is

• 
• 

• 0

• 0

67.

In a ΔABC, if and   then the correct relation is

• CA > AB

• CA = AB

• CA < AB

• CA + AB = CB

Length of a chord PQ of a circle with centre O is 4 cm. If the distance of PQ from the point O is 2 cm, then the length of the diameter is

• 2√2

• 3√2

• 5√2

• 4√2

The shadow of a vertical tower on ground level increases by 10 m when the altitude of the sun changes from 45° to 30°. The height of the tower is

• 5( √3 + 1 ) m

• 10( √3 - 1 ) m

• 9 m

• 13 m

An arc AB of a circle subtends an angle x radius at the centre of the circle. Given that the area of the sector AOB is equal to the square of the length of the arc AB, then the value of x is

• 1/√2

• 1/2

• 1/√3

• 1/3