If x = a sin θ - b cos θ, y = a cos θ + b sin θ, then which of the following is true?
D.
x = a sin θ - b cos θ ...(i)
y = a cos θ + b sin θ ...(ii)
On squaring and adding both the equations
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
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