Engineering & Architecture Admissions
Q. Which of the following represents a family of curves for the equation y = ax^2 + bx + c?
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A.
Linear functions
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B.
Quadratic functions
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C.
Cubic functions
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D.
Exponential functions
Solution
The equation y = ax^2 + bx + c represents a family of quadratic functions where 'a', 'b', and 'c' are constants.
Correct Answer: B — Quadratic functions
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Q. Which of the following represents a family of exponential curves?
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A.
y = ae^(bx)
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B.
y = ax^2 + bx + c
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C.
y = a sin(bx)
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D.
y = a log(bx)
Solution
The equation y = ae^(bx) represents a family of exponential curves where a and b are constants.
Correct Answer: A — y = ae^(bx)
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Q. Which of the following represents a family of straight lines?
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A.
y = mx + c
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B.
y = ax^2 + bx + c
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C.
y = e^x
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D.
y = sin(x)
Solution
The equation y = mx + c represents a family of straight lines for different values of m and c.
Correct Answer: A — y = mx + c
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Q. Which of the following represents a hyperbola with transverse axis along the x-axis?
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A.
x^2/a^2 - y^2/b^2 = 1
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B.
y^2/a^2 - x^2/b^2 = 1
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C.
x^2/b^2 - y^2/a^2 = 1
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D.
y^2/b^2 - x^2/a^2 = 1
Solution
The equation x^2/a^2 - y^2/b^2 = 1 represents a hyperbola with transverse axis along the x-axis.
Correct Answer: A — x^2/a^2 - y^2/b^2 = 1
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Q. Which of the following represents a physical change?
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A.
Burning wood
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B.
Dissolving sugar in water
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C.
Rusting of iron
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D.
Cooking an egg
Solution
Dissolving sugar in water is a physical change as it does not alter the chemical composition of sugar.
Correct Answer: B — Dissolving sugar in water
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Q. Which of the following represents an endothermic reaction?
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A.
Combustion of gasoline
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B.
Dissolving ammonium nitrate in water
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C.
Respiration
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D.
Rusting of iron
Solution
Dissolving ammonium nitrate in water absorbs heat, making it an endothermic reaction.
Correct Answer: B — Dissolving ammonium nitrate in water
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Q. Which of the following represents the correct relationship between moles and mass?
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A.
Moles = Mass / Molar Mass
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B.
Mass = Moles x Molar Mass
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C.
Molar Mass = Mass / Moles
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D.
All of the above
Solution
All the given relationships are correct and represent the conversion between moles, mass, and molar mass.
Correct Answer: D — All of the above
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Q. Which of the following represents the correct relationship between moles, mass, and molar mass?
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A.
moles = mass × molar mass
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B.
mass = moles × molar mass
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C.
molar mass = mass / moles
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D.
mass = moles / molar mass
Solution
The correct relationship is mass = moles × molar mass.
Correct Answer: B — mass = moles × molar mass
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Q. Which of the following represents the enthalpy change for a reaction at constant pressure?
Solution
The enthalpy change for a reaction at constant pressure is represented by ΔH.
Correct Answer: B — ΔH
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Q. Which of the following represents the number of particles in one mole of a substance?
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A.
6.022 x 10^23
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B.
3.14 x 10^22
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C.
1.6 x 10^19
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D.
9.11 x 10^28
Solution
Avogadro's number is 6.022 x 10^23, which represents the number of particles in one mole.
Correct Answer: A — 6.022 x 10^23
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Q. Which of the following represents the solution to the inequality 4 - x < 1?
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A.
x > 3
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B.
x < 3
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C.
x > 4
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D.
x < 4
Solution
4 - x < 1 => -x < -3 => x > 3
Correct Answer: A — x > 3
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Q. Which of the following represents the solution to the inequality 4 - x < 2?
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A.
x < 2
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B.
x > 2
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C.
x < 4
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D.
x > 4
Solution
4 - x < 2 => -x < -2 => x > 2.
Correct Answer: B — x > 2
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Q. Which of the following represents the solution to the inequality 6x - 4 ≤ 2x + 8?
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A.
x ≤ 3
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B.
x ≥ 3
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C.
x < 3
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D.
x > 3
Solution
6x - 4 ≤ 2x + 8 => 4x ≤ 12 => x ≤ 3.
Correct Answer: B — x ≥ 3
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Q. Which of the following represents the solution to the inequality 7x - 4 < 10?
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A.
x < 2
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B.
x > 2
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C.
x < 3
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D.
x > 3
Solution
7x - 4 < 10 => 7x < 14 => x < 2.
Correct Answer: C — x < 3
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Q. Which of the following represents the solution to the inequality x/3 + 2 < 5?
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A.
x < 9
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B.
x > 9
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C.
x < 6
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D.
x > 6
Solution
x/3 + 2 < 5 => x/3 < 3 => x < 9.
Correct Answer: A — x < 9
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Q. Which of the following represents the solution to the inequality x/3 - 2 < 1?
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A.
x < 9
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B.
x > 9
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C.
x ≤ 9
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D.
x ≥ 9
Solution
x/3 - 2 < 1 => x/3 < 3 => x < 9.
Correct Answer: A — x < 9
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Q. Which of the following s-block elements has the highest melting point?
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A.
Lithium
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B.
Sodium
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C.
Potassium
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D.
Rubidium
Solution
Lithium has the highest melting point among the alkali metals due to its small size and strong metallic bonding.
Correct Answer: A — Lithium
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Q. Which of the following s-block elements is a liquid at room temperature?
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A.
Lithium
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B.
Sodium
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C.
Potassium
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D.
Mercury
Solution
Mercury is a liquid at room temperature, but it is not an s-block element; however, among the options, it is the only liquid.
Correct Answer: D — Mercury
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Q. Which of the following s-block elements is essential for human health?
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A.
Sodium
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B.
Calcium
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C.
Potassium
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D.
All of the above
Solution
Sodium, calcium, and potassium are all essential s-block elements for human health, playing vital roles in various physiological processes.
Correct Answer: D — All of the above
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Q. Which of the following s-block elements is known for forming a protective oxide layer?
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A.
Sodium
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B.
Potassium
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C.
Calcium
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D.
Magnesium
Solution
Magnesium forms a protective oxide layer that prevents further oxidation.
Correct Answer: D — Magnesium
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Q. Which of the following s-block elements is known for its use in batteries?
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A.
Lithium
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B.
Sodium
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C.
Potassium
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D.
Calcium
Solution
Lithium is widely used in batteries, especially in rechargeable lithium-ion batteries.
Correct Answer: A — Lithium
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Q. Which of the following s-block elements is least reactive?
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A.
Lithium
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B.
Sodium
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C.
Potassium
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D.
Rubidium
Solution
Lithium is the least reactive among the alkali metals.
Correct Answer: A — Lithium
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Q. Which of the following s-block elements is most reactive?
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A.
Lithium
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B.
Sodium
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C.
Potassium
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D.
Rubidium
Solution
Rubidium is the most reactive among the s-block elements listed.
Correct Answer: D — Rubidium
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Q. Which of the following s-block elements is the least reactive?
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A.
Lithium
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B.
Sodium
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C.
Potassium
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D.
Rubidium
Solution
Lithium is the least reactive among the alkali metals.
Correct Answer: A — Lithium
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Q. Which of the following s-block elements is used in fireworks for its bright red color?
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A.
Lithium
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B.
Sodium
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C.
Potassium
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D.
Barium
Solution
Lithium is used in fireworks to produce a bright red color.
Correct Answer: A — Lithium
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Q. Which of the following s-block elements is used in fireworks for producing a bright red color?
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A.
Lithium
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B.
Sodium
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C.
Potassium
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D.
Calcium
Solution
Lithium (Li) is used in fireworks to produce a bright red color.
Correct Answer: A — Lithium
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Q. Which of the following s-block elements is used in fireworks?
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A.
Lithium
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B.
Beryllium
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C.
Sodium
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D.
Magnesium
Solution
Sodium is commonly used in fireworks for its bright yellow color.
Correct Answer: C — Sodium
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Q. Which of the following salts will produce a basic solution when dissolved in water?
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A.
NaCl
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B.
KNO3
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C.
NH4Cl
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D.
Na2CO3
Solution
Na2CO3 is a salt of a weak acid (H2CO3) and a strong base (NaOH), thus it will produce a basic solution.
Correct Answer: D — Na2CO3
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Q. Which of the following sets is a power set of F = {1, 2}?
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A.
{{1}, {2}}
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B.
{{}, {1}, {2}, {1, 2}}
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C.
{{1, 2}}
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D.
{{1, 2}, {1}}
Solution
The power set of F = {1, 2} is {{}, {1}, {2}, {1, 2}}.
Correct Answer: B — {{}, {1}, {2}, {1, 2}}
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Q. Which of the following sets is a power set of F = {a, b}?
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A.
{∅, {a}, {b}}
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B.
{∅, {a}, {b}, {a, b}}
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C.
{a, b}
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D.
{a, b, ∅}
Solution
The power set of F = {a, b} is {∅, {a}, {b}, {a, b}}.
Correct Answer: B — {∅, {a}, {b}, {a, b}}
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