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Rajneetha walks around the circular park in 15 minutes. If she walks at the rate of 5 km/hr, how much distance would she have to travel, at the minimum, to reach the centre of the park from any point on its perimeter?
Time = 15 minutes
= 15 x 60 sec = 900 sec
Speed = 5 km/hr
= 5 x 5/18 m/sec
= 25/18 m/sec
Now Perimeter of the circular park = D
= S x T
= 25/18 x 900
2πR = 1250 metre
R = 1250 x 7/2 x 22 = 8750/44
= 198.86 metres
∴ Required minimum distance to reach the centre of the circle = 200 metre (approx)
x^{4} + x^{2} + 1 = (x^{2}+ x + 1) (x^{2} − x + 1)
tan 6 x = tan 3(2x)
For how long should a force of 100 N act on a body of 20 kg so that it acquires a velocity of 100 m/s?
F = ma, 100 = 20 x a, a = 5 ms^{2} v = 0, v = 100
v = u + at, 100 = 0 + 5 x t, t = 20 s
Onethird of Ramani's saving in National Saving Certificate is equal to onehalf of his savings in Public Provident Fund. If he has Rs 150000 as total saving, how much has he saved in Public Provident Fund?
Let savings in N.S.C and P.P.F. be Rs x and Rs (150000  x) respectively. Then,
1/3 x = 1/2 (150000  x)
⇒ x/3 + x/2 = 75000
⇒ 5x/6 = 75000
⇒ x = 75000x6/5 = 90000
∴ Savings in Public Provident Fund = Rs (150000  90000) = Rs 60000
In questions below, equations have become wrong due to wrong orders of signs. Choose the correct order of signs from the alternative given.
9=3×720
In a class of 300 students, out of which 60 are girls, 20% of the girls pass Mathematics with distinction. The percentage of boys passing mathematics with distinction is twice of the girls. The number of boys passing Mathematics with distinction is
Total students = 300
Girls = 60
⇒ Boys = 240
Number of girls passing with distinction = 60 x 20/100 = 12
⇒ Number of boys passing with distinction = 240 x 40/100 = 96
The ratio of two numbers is 3:8 and their difference is 115. Then the smaller of the two numbers is
Suppose the two numbers are 3x, 8x
By hypothesis, 8x  3x = 115
or 5x = 115
∴ x = 23
Hence, the smaller number = 3x = 3 x 23 = 69
Mr. kalia invested a total amount of Rs. 16500 for two years in two schemes A and B with rate of simple interest 10% per annum and 12% per annum, respectively. If the total amount of interest earned was Rs.3620, what was amount invested in scheme A?
% interest on total amount per annum
Hence, ratio of amount invested in schemes
A and B
Hence, amount invested in
Velocity of sound waves is 330 m/s. The wave length of the sound wave which has frequency 20 Hz, is:
v = 330 n = 20 H z
λ = v/n = 330/20 = 16.5 m
Seven faculty members at a management institute frequent a lounge for strong coffee and conversation. On being asked about the visit to the lounge last Friday we got the following responses :
JC I came in first, and the next two persons to enter were SS and SM. When I left the lounge, JP and VR were present in the lounge DG left with me.
JP When I entered the lounge with VR, JC was siting there. There was someone else, but I Cannot remember who It was.
SM I went to the lounge for a short while, and met JC, SS and DG in the lounge on that day.
SS I left immediately after SM left.
DG I met JC, SS, JP and VR during my first visit to the lounge. I went back to my office with JC. When I went to the lounge second time, JP and VR were there.
PK I had some urgent work, so I did not sit in the lounge that day, but just collected my coffee and left. JP and DG were the only people in the lounge while I was there.
VR No comments.
Q. Based on the responses, which of the two JP or DG, entered the lounge first ?
Seven faculty members at a management institute frequent a lounge for strong coffee and conversation. On being asked about the visit to the lounge last Friday we got the following responses :
JC I came in first, and the next two persons to enter were SS and SM. When I left the lounge, JP and VR were present in the lounge DG left with me.
JP When I entered the lounge with VR, JC was siting there. There was someone else, but I Cannot remember who It was.
SM I went to the lounge for a short while, and met JC, SS and DG in the lounge on that day.
SS I left immediately after SM left.
DG I met JC, SS, JP and VR during my first visit to the lounge. I went back to my office with JC. When I went to the lounge second time, JP and VR were there.
PK I had some urgent work, so I did not sit in the lounge that day, but just collected my coffee and left. JP and DG were the only people in the lounge while I was there.
VR No comments.
Q. Who was sitting with JC when JP entered the lounge ?
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