Q5. If a^2+b^2+c^2=2(a-b-c)-3, then the value of 4a-3b+5c is
(a) 2
(b) 3
(c) 5
(d) 6
Q6. A man riding his bicycle covers 150 m in 25 second. What is his speed in km per hour?
(a) 25
(b) 21.6
(c) 23
(d) 20
Q7. A train passes two bridges of lengths 800 m and 400 m in 100 seconds and 60 seconds respectively. The length of the train is:
(a) 80 m
(b) 90 m
(c) 200 m
(d) 150 m
Q8. A train is 125 m long. If the train takes 30 seconds to cross a tree by the railway line, then the speed of the train is:
(a) 14 km/hr.
(b) 15 km/hr.
(c) 16 km/hr.
(d) 12 km/hr.
Q9. A 120 m long train takes 10 seconds to cross a man standing on a platform. What is the speed of the train?
(a) 12 m/sec
(b) 10 m/sec
(c) 15 m/sec
(d) 20 m/sec
Q10. A 75 m long train is moving at 20 km/h. It will cross a man standing on the platform in
(a) 12 seconds
(b) 14 seconds
(c) 13.5 seconds
(d) 15.5 seconds
Solutions
S5. Ans.(a)
Sol. a^2+b^2+c^2=2(a-b-c)-3
a^2+1-2a+b^2+1+2b+c^2+2c+1
(a-1)^2+(b+1)^2+(c+1)^2 = 0
that means
⇒ a – 1 = 0, ⇒ a = 1
⇒ b + 1 = 0, ⇒ b = -1
⇒ c + 1 = 0, ⇒ c = -1
⇒ 4a – 3b + 5c
⇒ 4 + 3 – 5 = 2
S6. Ans.(b)
Sol. Speed of bicycle =150/25 m/sec =6×18/5km/hr
= 21.6 km/hr
S7. Ans.(c)
Sol. Distance covered in 100 sec = 800 + l
Distance covered in 60 sec = 400 + l
So, Distance covered in 40 sec
= (800 + l) – (400 + l) = 400 m.
Speed → 400/40 m/sec. = 10 m/s
Distance covered in 60 sec = 10 × 60 = 600 meter
So, 400 + l = 600
⇒ l = 200 meter
S8. Ans.(b)
Sol. Speed =D/T=125/30 m/sec
=(125/30)×(18/5) km/hr
= 15 km/hr
S9. Ans.(a)
Sol. Speed =120/10 m/sec = 12 m/sec
S10. Ans.(c)
Sol. T=D/S=(75 × 18)/(20 ×5 )=27/2 sec
= 13.5 sec
