If x =  a sin θ - b cos θ,  y = a cos θ + b sin θ, then which of the following is true?

32.

A man sells an article at 5% above its cost price. If he had bought it at 5% less than what he had paid for it and sold it at Rs. 2 less, he would have gained 10%. The cost price of the article is

• Rs. 200

• Rs. 400

• 300

• 300

P and Q together can do a job in 6 days. Q and R can finish the same job in  P started the work and worked for 3 days. Q and R continued for 6 days. Then the difference of days in which R and P can complete the job is

• 15

• 10

• 8

• 8

The H.C.F. and L.C.M. of two numbers are 21 and 84 respectively. If the ratio of the two numbers is 1 : 4, then the larger of the two numbers is

• 12

• 108

• 48

• 48

If 60% of A = 30% of B, B = 40% of C, C = x% of A, then value of x is

• 200

• 500

• 800

• 800

In an office, 40% of the staff is female. 70% of the female staff and 50% of the male staff are married. The percentage of the unmarried staff in the office is

• 64

• 60

• 54

• 54

ABCD is a cyclic quadrilateral. AB and DC when produced meet at P, If PA = 8 cm, PB = 6 cm, PC = 4 cm, then the length (in cm) of PD is

• 8 cm

• 6 cm

• 10 cm

• 12 cm

A and B are centres of two circles of radii 11 cm and 6 cm, respectively. PQ is a direct common tangent to the circles. If , then length of  will be

• 8.5 cm

• 13 cm

• 12 cm

• 10 cm

The diameter of each wheel of a car is 70 cm. If each wheel rotates 400 times per minute, then the speed of the car (in km/hr) is 

• 0.528

• 528

• 52.8

• 52.8

Water tax is increased by 20% but its consumption is decreased by 20%. Then the increase or decrease in the expenditure of the money is

• 5% decrease

• 4% decrease

• No change

• No change