Golu started from his house towards North. After covering a distance of 8 km. he turned towards left and covered a distance of 6 km. What is the shortest distance now from his house?
Answer: A
Correct answer: 10 km.
He goes 8 km north, then turns left to go 6 km west. The shortest way home is the hypotenuse: \[ \sqrt{8^2+6^2} = \sqrt{100} = \mathbf{10}\text{ km} \]
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A man is facing west. He turns 45 degree in the clockwise direction and then another 180 degree in the same direction and then 270 degree in the anticlockwise direction. Find which direction he is facing now ?
Answer: A
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The man firstly faces the direction OA. On moving 45 degree clockwise[Please check carefully always if clockwise or anticlockwise], he faces the direction OB.
Now again he moved 180 degree clockwise, now he will be facing OC. From here he moved 270 degree anticlockwise, Finally he is facing OD, which is South west.
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Two cars start from the opposite places of a main road, 150 km apart. First car runs for 25 km and takes a right turn and then runs 15 km. It then turns left and then runs for another 25 km and then takes the direction back to reach the main road. In the mean time, due to minor break down the other car has run only 35 km along the main road. What would be the distance between two cars at this point?
Answer: A
Correct answer: 65 km
The two cars set out towards each other from points 150 km apart. The first advances 25 km, steps 15 km aside and returns to the road after a further 25 km, so it has closed 50 km of the gap; allowing for the second car’s run, 65 km separates them.
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Raman is performing yoga with his head down and legs up. His face is towards the west. In which direction, will his left hand be ?
Answer: A
Correct answer: North
Standing upright and facing west, his left hand would point south. Inverting him - head down, legs up - turns his body through 180 degrees about the axis he is facing along, which exchanges left and right while leaving the facing direction alone. His left hand therefore points north. The same reasoning applies to anyone lying face down or hanging inverted: the facing is unchanged, the handedness is reversed.
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The length and breadth of a room are 8 m and 6 m respectively. A cat runs along all the four walls and finally along a diagonal order to catch a rat. How much total distance is covered by the cat?
Answer: C
Correct answer: 38
Running along all four walls covers the perimeter, \( 2(8+6) = 28 \) m, and the diagonal is \[ \sqrt{8^2+6^2} = 10 \text{ m} \] so the cat covers \( 28 + 10 = \mathbf{38} \) metres in all.
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Two cars start from the opposite places of a main road, 150 km apart. First car runs for 25 km and takes a right turn and then runs 15 km. It then turns left and then runs for another 25 km and then takes the direction back to reach the main road. In the mean time, due to minor break down the other car has run only 35 km along the main road. What would be the distance between two cars at this point?
Answer: A
Correct answer: 65 km
The two cars start 150 km apart and move towards each other. The first covers 25 km along the road, steps 15 km aside and back again after another 25 km, so it has advanced 50 km along the road; the second’s progress leaves the gap between them at 65 km.
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Rahul put his timepiece on the table in such a way that at 6 P.M. hour hand points to North. In which direction the minute hand will point at 9.15 P.M. ?
Answer: D
Correct answer: West
At six o’clock the hour hand stands at the 6 on the dial, and that direction is north. At a quarter past nine the minute hand stands at the 3. Going round the dial from 6 to 3 is nine hour-marks, or \( 9 \times 30^\circ = 270^\circ \), which from north brings us to the west.
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I am facing South. I turn right and walk 20 metre. Then I turn right again and walk 10 metre. Then I turn left and walk 10 metre and then turning right walk 20 metre. Then I turn right again and walk 60 metre. In which direction am I from the starting point ?
Answer: A
Correct answer: North-East
Facing south, a right turn brings me west. The legs then come to 20 + 10 = 30 west against 60 east, leaving 30 east, and 10 + 20 = 30 north. Being both east and north of the start, I am to its north-east.
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Rasik walked 20 m towards north. Then he turned right and walks 30 m. Then he turns right and walks 35 m. Then he turns left and walks 15 m. Finally he turns left and walks 15 m. In which direction and how many metres is he from the starting position?
Answer: D
Correct answer: 45 m East
Adding the legs: north 20, then east 30, then south 35, then east 15, then north 15. The northward moves come to \( 20 - 35 + 15 = 0 \) and the eastward to \( 30 + 15 = 45 \). So he finishes 45 m east of his starting point.
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I am facing south. I turn right and walk 20 m. Then I turn right again and walk 10m. Then I turn left and walk 10m and then turning right walk 20m. Then I turn right again and walk 60m. In which direction am I from the starting point?
Answer: C
Correct answer: North-East
Facing south, a right turn is to the west. Taking the start as the origin with east positive: west 20 gives \( (-20,0) \); the next right turn faces north, so 10 north gives \( (-20,10) \); a left turn faces west again, so 10 more gives \( (-30,10) \); a right turn faces north, so 20 gives \( (-30,30) \); and a final right turn faces east, so 60 gives \( (30,30) \). Both coordinates are positive, so he is north-east of the start.
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