Major Competitive Exams

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Q. Which of the following relations on the set of integers is not a function?
  • A. R1 = {(1, 2), (1, 3)}
  • B. R2 = {(2, 3), (3, 4)}
  • C. R3 = {(4, 5)}
  • D. R4 = {(5, 6), (6, 7)}
Q. Which of the following represents a family of circles with varying radii?
  • A. (x - h)^2 + (y - k)^2 = r^2
  • B. (x - h)^2 + (y - k) = r
  • C. x^2 + y^2 = r
  • D. x^2 + y^2 = kx
Q. Which of the following represents a family of curves for the equation y = a sin(bx)?
  • A. Linear functions
  • B. Exponential functions
  • C. Sine waves with varying amplitudes and frequencies
  • D. Quadratic functions
Q. Which of the following represents a family of curves for the equation y = ax^2 + bx + c?
  • A. Linear functions
  • B. Quadratic functions
  • C. Cubic functions
  • D. Exponential functions
Q. Which of the following represents a family of exponential curves?
  • A. y = ae^(bx)
  • B. y = ax^2 + bx + c
  • C. y = a sin(bx)
  • D. y = a log(bx)
Q. Which of the following represents a family of straight lines?
  • A. y = mx + c
  • B. y = ax^2 + bx + c
  • C. y = e^x
  • D. y = sin(x)
Q. Which of the following represents a homozygous dominant genotype? (2021)
  • A. AA
  • B. Aa
  • C. aa
  • D. A
Q. Which of the following represents a hyperbola with transverse axis along the x-axis?
  • A. x^2/a^2 - y^2/b^2 = 1
  • B. y^2/a^2 - x^2/b^2 = 1
  • C. x^2/b^2 - y^2/a^2 = 1
  • D. y^2/b^2 - x^2/a^2 = 1
Q. Which of the following represents a phenotype? (2021)
  • A. BB
  • B. Bb
  • C. bb
  • D. Brown eyes
Q. Which of the following represents a physical change?
  • A. Burning wood
  • B. Dissolving sugar in water
  • C. Rusting of iron
  • D. Cooking an egg
Q. Which of the following represents a systematic error? (2020)
  • A. Calibration error
  • B. Random fluctuations
  • C. Environmental changes
  • D. Human error
Q. Which of the following represents a test cross? (2020)
  • A. AA x aa
  • B. Aa x Aa
  • C. AA x Aa
  • D. aa x aa
Q. Which of the following represents an endothermic reaction?
  • A. Combustion of gasoline
  • B. Dissolving ammonium nitrate in water
  • C. Respiration
  • D. Rusting of iron
Q. Which of the following represents the concept of significant figures? (2023)
  • A. All digits in a number
  • B. Only the non-zero digits
  • C. All digits except leading zeros
  • D. All digits except trailing zeros
Q. Which of the following represents the correct relationship between moles and mass?
  • A. Moles = Mass / Molar Mass
  • B. Mass = Moles x Molar Mass
  • C. Molar Mass = Mass / Moles
  • D. All of the above
Q. Which of the following represents the correct relationship between moles, mass, and molar mass?
  • A. moles = mass × molar mass
  • B. mass = moles × molar mass
  • C. molar mass = mass / moles
  • D. mass = moles / molar mass
Q. Which of the following represents the enthalpy change for a reaction at constant pressure?
  • A. ΔU
  • B. ΔH
  • C. ΔS
  • D. ΔG
Q. Which of the following represents the ideal gas constant? (2022)
  • A. R = 0.0821 L·atm/(K·mol)
  • B. R = 8.314 J/(K·mol)
  • C. Both A and B
  • D. None of the above
Q. Which of the following represents the number of particles in one mole of a substance?
  • A. 6.022 x 10^23
  • B. 3.14 x 10^22
  • C. 1.6 x 10^19
  • D. 9.11 x 10^28
Q. Which of the following represents the slope of the line represented by the equation y = mx + b?
  • A. m
  • B. b
  • C. x
  • D. y
Q. Which of the following represents the solution to the inequality 4 - x < 1?
  • A. x > 3
  • B. x < 3
  • C. x > 4
  • D. x < 4
Q. Which of the following represents the solution to the inequality 4 - x < 2?
  • A. x < 2
  • B. x > 2
  • C. x < 4
  • D. x > 4
Q. Which of the following represents the solution to the inequality 6x - 4 ≤ 2x + 8?
  • A. x ≤ 3
  • B. x ≥ 3
  • C. x < 3
  • D. x > 3
Q. Which of the following represents the solution to the inequality 7x - 4 < 10?
  • A. x < 2
  • B. x > 2
  • C. x < 3
  • D. x > 3
Q. Which of the following represents the solution to the inequality x/3 + 2 < 5?
  • A. x < 9
  • B. x > 9
  • C. x < 6
  • D. x > 6
Q. Which of the following represents the solution to the inequality x/3 - 2 < 1?
  • A. x < 9
  • B. x > 9
  • C. x ≤ 9
  • D. x ≥ 9
Q. Which of the following revolutions is associated with the establishment of constitutional governance in England?
  • A. Glorious Revolution
  • B. American Revolution
  • C. French Revolution
  • D. Industrial Revolution
Q. Which of the following revolutions is associated with the phrase 'Liberty, Equality, Fraternity'?
  • A. American Revolution
  • B. French Revolution
  • C. Russian Revolution
  • D. Industrial Revolution
Q. Which of the following revolutions is associated with the rise of industrial capitalism in the 18th century?
  • A. American Revolution
  • B. French Revolution
  • C. Industrial Revolution
  • D. Russian Revolution
Q. Which of the following revolutions is known for the phrase 'Liberty, Equality, Fraternity'?
  • A. The American Revolution.
  • B. The French Revolution.
  • C. The Russian Revolution.
  • D. The Industrial Revolution.
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