The simple interest on a sum of money is  of the sum. If the number of years is numerically half the rate percent per annum, then the rate percent per annum is

• 5

• 8

• 
• 

If x² + y² + z² = xy + yz + zx, then the value of
   is

• 2

• 1

• 0

• 0

If  and  then the value of  is

• 0

• 1

• 3

• 3

Two places P and Q are 162 km apart. A train leaves P for Q and simultaneously another train leaves Q for P. They meet at the end of 6 hours. If the former train travels 8 km/hr faster than the other, then speed of train from Q is

•  km/hour
• 
• 
• 

If  then the relation between a, b and c is

The radii of two solid iron spheres are 1 cm and 6 cm respectively. A hollow sphere is made by melting the two spheres. If the external radius of the hollow sphere is 9 cm, then its thickness (in cm) is

• 2

• 1.5

• 0.5

• 0.5

In an examination average marks obtained by the girls of a class is 85 and the average marks obtained by the boys of the same class is 87. If the girls and boys are in the ratio 4 : 5, average marks of the whole class (approximately) is closest to

• 85.9

• 86.1

• 86.4

• 86.4

88.

If sin A + sin²A = 1,  then the value of cos²A + cos⁴A is

• 2

• 
• 
• 

The marked price of a tape recorder is Rs. 12,600. A festival discount of 5% is allowed on it. Further for a cash payment, a second discount of 2% is given. The cash payment, is to be made for buying it, is

• Rs. 11,703.60

• Rs. 11,730.60

• Rs. 11,370.60

• Rs. 11,370.60

Let x be the least number, which when divided by 5, 6, 7 and 8 leaves a remainder 3 in each case but when divided by 9 leaves no remainder. The sum of digits is

• 21

• 22

• 18

• 18