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Q. What is the value of the determinant \( \begin{vmatrix} 1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 3 & 6 \end{vmatrix} \)?

A. 0
B. 1
C. 2
D. 3

Solution

The determinant is 0 because the first column is repeated.

Correct Answer: A — 0

Q. What is the value of the determinant \( \begin{vmatrix} a & b \\ c & d \end{vmatrix} \) when \( a = 1, b = 2, c = 3, d = 4 \)?

A. -2
B. 2
C. 0
D. 1

Solution

The determinant is \( 1*4 - 2*3 = 4 - 6 = -2 \).

Correct Answer: A — -2

Q. What is the value of the determinant | 1 2 3 | | 0 1 4 | | 5 6 0 |?

A. -12
B. 12
C. 0
D. 6

Solution

Calculating the determinant gives -12.

Correct Answer: A — -12

Q. What is the value of the determinant | a b | | c d | when a = 2, b = 3, c = 4, d = 5?

A. -2
B. 1
C. 2
D. 7

Solution

det = (2)(5) - (3)(4) = 10 - 12 = -2.

Correct Answer: C — 2

Q. What is the value of the equilibrium constant Kc for the reaction: 2A ⇌ B + C if at equilibrium [A] = 0.5 M, [B] = 0.2 M, and [C] = 0.3 M?

A. 0.12
B. 0.30
C. 0.60
D. 1.20

Solution

Kc = [B][C] / [A]^2 = (0.2)(0.3) / (0.5)^2 = 0.12 / 0.25 = 0.48.

Correct Answer: C — 0.60

Q. What is the value of the equilibrium constant Kp for the reaction: N2(g) + 3H2(g) ⇌ 2NH3(g) at 25°C?

A. 0.5
B. 1.0
C. 0.1
D. Depends on the initial concentrations

Solution

The value of Kp is specific to the reaction conditions and cannot be determined without knowing the initial concentrations or the extent of the reaction.

Correct Answer: D — Depends on the initial concentrations

Q. What is the value of the gas constant R in L·atm/(K·mol)?

A. 0.0821
B. 8.314
C. 0.08314
D. 1.987

Solution

The gas constant R is 0.0821 L·atm/(K·mol).

Correct Answer: A — 0.0821

Q. What is the value of the gravitational constant G?

A. 6.67 x 10^-11 N(m/kg)^2
B. 9.81 m/s^2
C. 3.00 x 10^8 m/s
D. 1.60 x 10^-19 C

Solution

The gravitational constant G is approximately 6.67 x 10^-11 N(m/kg)^2.

Correct Answer: A — 6.67 x 10^-11 N(m/kg)^2

Q. What is the value of the integral ∫(0 to 1) (3x^2 + 2)dx?

A. 5/3
B. 2
C. 1
D. 4/3

Solution

Integral = [x^3 + 2x] from 0 to 1 = (1 + 2) - (0) = 3.

Correct Answer: A — 5/3

Q. What is the value of the integral ∫(2x)dx from 0 to 2?

A. 4
B. 2
C. 3
D. 1

Solution

∫(2x)dx = x^2 from 0 to 2 = 2^2 - 0^2 = 4.

Correct Answer: A — 4

Q. What is the value of the integral ∫_0^1 (3x^2 + 2x) dx?

A. 1
B. 2
C. 3
D. 4

Solution

Evaluating the integral gives [x^3 + x^2]_0^1 = (1 + 1) - (0 + 0) = 2.

Correct Answer: B — 2

Q. What is the value of the limit lim (x -> 1) (x^2 - 1)/(x - 1)?

A. 0
B. 1
C. 2
D. Infinity

Solution

Using L'Hôpital's Rule, the limit evaluates to 2.

Correct Answer: C — 2

Q. What is the value of the limit lim(x→0) (sin(x)/x)?

A. 0
B. 1
C. ∞
D. undefined

Solution

The limit lim(x→0) (sin(x)/x) = 1.

Correct Answer: B — 1

Q. What is the value of the principal quantum number (n) for the outermost electrons in a sodium atom?

A. 1
B. 2
C. 3
D. 4

Solution

Sodium has an atomic number of 11, and its electron configuration is 1s² 2s² 2p⁶ 3s¹. The outermost electrons are in n=3.

Correct Answer: C — 3

Q. What is the value of the principal quantum number (n) for the outermost electron in potassium (K)?

A. 3
B. 4
C. 5
D. 2

Solution

Potassium has the electronic configuration [Ar] 4s1, so the outermost electron is in n=4.

Correct Answer: B — 4

Q. What is the value of the principal quantum number (n) for the outermost electron in a potassium atom?

A. 1
B. 2
C. 3
D. 4

Solution

Potassium (K) has an atomic number of 19, and its electron configuration ends in 4s, so the outermost electron has n=4.

Correct Answer: C — 3

Q. What is the value of the principal quantum number for the outermost electrons in a sodium atom?

A. 1
B. 2
C. 3
D. 4

Solution

Sodium has an atomic number of 11, and its outermost electrons are in the n=3 shell.

Correct Answer: C — 3

Q. What is the value of the principal quantum number for the outermost electrons in potassium (K)?

A. 1
B. 2
C. 3
D. 4

Solution

Potassium has an atomic number of 19, and its outermost electrons are in the n=4 shell.

Correct Answer: D — 4

Q. What is the value of the universal gas constant R in L·atm/(K·mol)?

A. 0.0821
B. 8.314
C. 62.36
D. 1.987

Solution

The universal gas constant R is 0.0821 L·atm/(K·mol).

Correct Answer: A — 0.0821

Q. What is the value of x if 2x + 3 = 11?

A. 2
B. 3
C. 4
D. 5

Solution

Subtract 3 from both sides: 2x = 8. Then divide by 2: x = 4.

Correct Answer: C — 4

Q. What is the value of x if 3x - 5 = 16?

A. 7
B. 5
C. 4
D. 3

Solution

Solving for x: 3x = 21 => x = 7.

Correct Answer: A — 7

Q. What is the value of x in the equation 3x - 5 = 7?

A. 4
B. 5
C. 6
D. 3

Solution

Solving for x: 3x = 12, thus x = 4.

Correct Answer: A — 4

Q. What is the value of x in the equation 5x - 3 = 2x + 12?

A. 3
B. 4
C. 5
D. 6

Solution

Rearranging gives 5x - 2x = 12 + 3 => 3x = 15 => x = 5.

Correct Answer: B — 4

Q. What is the value of \( \begin{vmatrix} 1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 3 & 6 \end{vmatrix} \)?

A. 0
B. 1
C. 2
D. 3

Solution

The determinant is 0 because the first column is repeated.

Correct Answer: A — 0

Q. What is the value of |z| if z = -3 + 4i?

A. 5
B. 7
C. 4
D. 3

Solution

|z| = √((-3)^2 + (4)^2) = √(9 + 16) = √25 = 5.

Correct Answer: A — 5

Q. What is the value of |z| if z = 4 - 3i?

A. 5
B. 7
C. 4
D. 3

Solution

|z| = √(4^2 + (-3)^2) = √(16 + 9) = √25 = 5.

Correct Answer: A — 5

Q. What is the value of |z| if z = 4e^(iπ/3)?

A. 4
B. 8
C. 2
D. 1

Solution

The modulus |z| = 4, as it is the coefficient in the polar form.

Correct Answer: A — 4

Q. What is the value of |z|^2 if z = 4 - 3i?

A. 25
B. 16
C. 7
D. 12

Solution

|z|^2 = 4^2 + (-3)^2 = 16 + 9 = 25.

Correct Answer: A — 25

Q. What is the van 't Hoff factor (i) for a strong electrolyte like NaCl in solution?

A. 1
B. 2
C. 3
D. 4

Solution

NaCl dissociates into two ions (Na+ and Cl-), so the van 't Hoff factor (i) is 2.

Correct Answer: B — 2

Q. What is the van 't Hoff factor (i) for glucose in solution?

A. 1
B. 2
C. 3
D. 0

Solution

The van 't Hoff factor (i) for glucose is 1, as it does not dissociate in solution.

Correct Answer: A — 1

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