Major Competitive Exams

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Q. If y = sin^(-1)(x), then what is the derivative dy/dx?
  • A. 1/√(1-x^2)
  • B. 1/(1-x^2)
  • C. √(1-x^2)
  • D. 1/x
Q. If y = sin^(-1)(x), then x = sin(y) implies:
  • A. y = x
  • B. y = -x
  • C. y = 1-x
  • D. y = 1+x
Q. If y = sin^(-1)(x), what is dy/dx?
  • A. 1/sqrt(1-x^2)
  • B. 1/(1-x^2)
  • C. sqrt(1-x^2)
  • D. 1/x
Q. If y = sin^(-1)(x), what is the second derivative d^2y/dx^2?
  • A. 0
  • B. 1/√(1-x^2)^3
  • C. -1/√(1-x^2)^3
  • D. undefined
Q. If y = tan^(-1)(x), then the range of y is:
  • A. (-π/2, π/2)
  • B. (0, π)
  • C. (-π, π)
  • D. [0, 1]
Q. If y = tan^(-1)(x), then what is the second derivative d^2y/dx^2?
  • A. 0
  • B. -2/(1+x^2)^2
  • C. 2/(1+x^2)^2
  • D. 1/(1+x^2)
Q. If Y is the sister of Z and A is the mother of Z, how is Y related to A? (2023)
  • A. Daughter
  • B. Sister
  • C. Niece
  • D. Cousin
Q. If you add 12.11 and 0.3, how many decimal places should the answer have?
  • A. 1
  • B. 2
  • C. 3
  • D. 4
Q. If you are at point A and move 2 km north, then 2 km west, where are you relative to point A?
  • A. 2 km North-West
  • B. 2 km South-East
  • C. 2 km South-West
  • D. 2 km North-East
Q. If you are at point A and move 2 miles south, then 2 miles west, which direction is point A from your current location?
  • A. North-East
  • B. South-West
  • C. North-West
  • D. South-East
Q. If you are at point A and move 2 miles south, then 2 miles west, which direction is point A from your current position?
  • A. Northeast
  • B. Southwest
  • C. Southeast
  • D. Northwest
Q. If you are at point A and move 2 miles west, then 3 miles south, which direction is point A from your current position?
  • A. North-East
  • B. South-West
  • C. North-West
  • D. South-East
Q. If you are at point A and move 3 km east to point B, then 4 km south to point C, what is the direction from A to C?
  • A. North-East
  • B. South-East
  • C. South-West
  • D. North-West
Q. If you are at point A and move 3 km east, then 4 km north, where are you relative to point A?
  • A. 3 km North-East
  • B. 4 km North-West
  • C. 5 km North-East
  • D. 7 km South-East
Q. If you are at point A and move 3 km north, then 4 km west, what is your final position relative to point A?
  • A. 3 km North
  • B. 4 km West
  • C. 5 km North-West
  • D. 7 km South-East
Q. If you are at point A and move 3 km south, then 4 km west, where are you relative to point A?
  • A. 3 km North-East
  • B. 4 km South-West
  • C. 5 km South-West
  • D. 7 km East
Q. If you are at point A and move 3 miles east, then 4 miles north, what is your final position relative to point A?
  • A. 3 miles east
  • B. 4 miles north
  • C. 5 miles northeast
  • D. 7 miles northwest
Q. If you are at point A and move 3 miles north, then 4 miles east, what is your final position relative to point A?
  • A. 3 miles north
  • B. 4 miles east
  • C. 5 miles north-east
  • D. 7 miles from A
Q. If you are at point A and move 3 miles north, then 4 miles west, what is your final position relative to point A?
  • A. 3 miles north
  • B. 4 miles west
  • C. 5 miles northwest
  • D. 7 miles away
Q. If you are at point A and move 3 units east and 4 units north, what is your new position relative to point A?
  • A. 3 units east
  • B. 4 units north
  • C. 5 units northeast
  • D. 7 units northwest
Q. If you are at point B and move 3 miles east, then 4 miles north, what is your final position relative to point B?
  • A. 3 miles east
  • B. 4 miles north
  • C. 5 miles north-east
  • D. 7 miles away
Q. If you are at point B and move 6 miles south, then 8 miles west, how far are you from point B?
  • A. 10 miles
  • B. 14 miles
  • C. 8 miles
  • D. 6 miles
Q. If you are at the center of a compass and move towards the southeast, which two directions are you between?
  • A. North and East
  • B. South and East
  • C. South and West
  • D. North and West
Q. If you are facing east and turn 180 degrees, which direction are you facing now?
  • A. West
  • B. North
  • C. South
  • D. East
Q. If you are facing east and turn 270 degrees to your right, which direction will you be facing?
  • A. North
  • B. South
  • C. East
  • D. West
Q. If you are facing east and you turn 90 degrees to your left, which direction will you be facing?
  • A. North
  • B. South
  • C. East
  • D. West
Q. If you are facing North and turn 90 degrees to your right, which direction are you facing? (2020)
  • A. East
  • B. West
  • C. South
  • D. North-East
Q. If you are facing north and turn 90 degrees to your right, which direction are you now facing?
  • A. East
  • B. West
  • C. South
  • D. North
Q. If you are facing south and turn 180 degrees, which direction are you facing now?
  • A. North
  • B. East
  • C. West
  • D. South
Q. If you are facing south and turn 180 degrees, which direction will you be facing?
  • A. North
  • B. East
  • C. West
  • D. South
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