71.

If x⁴ + 2x³ + ax² + bx + 9 is a perfect square, where a and b are positive real numbers, then the values of a and b are

• a = 5,  b = 6

• a = 6,  b = 7

• a = 7,  b = 6

• a = 7,  b = 6

If a² + b² + c² = 16,  x² + y² + z² = 25  and ax + by + cz = 20, then the value of  is

The value of x which satisfies the equation 
is

• (a² + b² + c²)

• - (a² + b² + c²)

• (a² + 2b² + c²)

• (a² + 2b² + c²)

If a³ = 117 + b³  and a = 3 + b, then the value of (a + b) is

If  then the value of  is

• 2

• 0

• 1

• 1

Δ ABC is similar to ΔDEF. If the area of ΔABC is 9 sq. cm. and the area of ΔDEF is 16 sq. cm. and BC = 2.1 cm, then the length of EF will be

• 5.6 cm

• 2.8 cm.

• 3.7 cm.

• 3.7 cm.

A chord of a circle is equal to its radius. The angle subtended by this chord at a point on the circumference is

• 80°

• 60°

• 30°

• 90°

Let two chords AB and AC of the larger circle touch the smaller circle having same centre at X and Y. Then XY = ?

• BC

• 1/2 BC

• 1/3 BC

• 2/3 BC

Let G be the centroid of the equilateral triangle ABC of perimeter 24 cm. Then the length of AG is

• 2√3 cm

• 8⁄√3 cm

• 8√3 cm

• 3√8 cm

A and B are the centres of two circles with radii 11 cm and 6 cm respectively. A common tangent touches these circles at P and Q respectively. If AB  = 13 cm, then the length of PQ is

• 13 cm

• 17 cm

• 8.5 cm

• 12 cm