Major Competitive Exams

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Q. If x ≡ 4 (mod 7) and y ≡ 3 (mod 7), what is the value of (x + y) mod 7?
  • A. 0
  • B. 1
  • C. 2
  • D. 3
Q. If x ≡ 4 (mod 7), which of the following could be a possible value of x?
  • A. 11
  • B. 10
  • C. 9
  • D. 8
Q. If x ≤ 4, which of the following must be true?
  • A. x + 1 ≤ 5
  • B. x - 2 ≥ 2
  • C. 2x ≤ 8
  • D. x + 3 > 8
Q. If x^2 + 2x + 1 = 0, what is the value of x?
  • A. -1
  • B. 0
  • C. 1
  • D. 2
Q. If x^2 - 5x + 6 = 0, what are the values of x? (2019)
  • A. 2, 3
  • B. 1, 6
  • C. 3, 2
  • D. 0, 6
Q. If x^2 - 6x + 9 = 0, what is the value of x?
  • A. 3
  • B. 6
  • C. 9
  • D. 0
Q. If x^3 - 8 = 0, what is the value of x?
  • A. 2
  • B. 3
  • C. 4
  • D. 1
Q. If x^3 = 8, then the value of x is?
  • A. 2
  • B. 4
  • C. 1
  • D. 0
Q. If x^4 = 81, what is the value of x?
  • A. 3
  • B. 4
  • C. 9
  • D. 16
Q. If y < 2 and y + 3 > 0, which of the following is true?
  • A. y < -3
  • B. y > -3
  • C. y < 0
  • D. y > 0
Q. If y = cos^(-1)(1/2), what is the value of y?
  • A. π/3
  • B. π/4
  • C. π/6
  • D. π/2
Q. If y = cos^(-1)(x), then dy/dx is:
  • A. -1/√(1-x^2)
  • B. 1/√(1-x^2)
  • C. 0
  • D. 1
Q. If y = cos^(-1)(x), then what is dy/dx?
  • A. -1/√(1-x^2)
  • B. 1/√(1-x^2)
  • C. 1/x
  • D. -1/x
Q. If y = cos^(-1)(x), what is dy/dx?
  • A. -1/√(1-x^2)
  • B. 1/√(1-x^2)
  • C. 0
  • D. 1
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 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
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