Q. What is the escape velocity for a satellite to leave the Earth's gravitational field?
A.
7.9 km/s
B.
11.2 km/s
C.
9.8 km/s
D.
5.0 km/s
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Solution
The escape velocity from the Earth's surface is approximately 11.2 km/s.
Correct Answer: B — 11.2 km/s
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Q. What is the escape velocity for a satellite to leave the Earth's gravitational influence?
A.
11.2 km/s
B.
7.9 km/s
C.
9.8 km/s
D.
15.0 km/s
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Solution
The escape velocity from the Earth's surface is approximately 11.2 km/s.
Correct Answer: A — 11.2 km/s
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Q. What is the escape velocity from the surface of a planet with a radius of 3R and mass 4M?
A.
√(8GM/R)
B.
√(6GM/R)
C.
√(4GM/R)
D.
√(10GM/R)
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Solution
Escape velocity v = √(2GM/R); here, v = √(2 * 4GM / 3R) = √(8GM/3R).
Correct Answer: A — √(8GM/R)
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Q. What is the escape velocity from the surface of a planet with a radius of 4,000 km and a mass of 6 × 10^24 kg? (G = 6.67 × 10^-11 N m²/kg²)
A.
10,000 m/s
B.
11,200 m/s
C.
12,000 m/s
D.
13,000 m/s
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Solution
Escape velocity = √(2GM/R) = √(2 * 6.67 × 10^-11 * 6 × 10^24 / 4 × 10^6) = 11,200 m/s
Correct Answer: B — 11,200 m/s
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Q. What is the escape velocity from the surface of a planet with a radius of 4R and mass 2M?
A.
2√(GM/R)
B.
√(8GM/R)
C.
√(2GM/R)
D.
4√(GM/R)
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Solution
Escape velocity v = √(2GM/R) = √(2 * 2M / 4R) = √(8GM/4R) = √(8GM/R)
Correct Answer: B — √(8GM/R)
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Q. What is the escape velocity from the surface of a planet with mass M and radius R?
A.
√(2GM/R)
B.
√(GM/R)
C.
√(2R/G)
D.
√(G/R)
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Solution
Escape velocity is given by v = √(2GM/R).
Correct Answer: A — √(2GM/R)
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Q. What is the escape velocity from the surface of the Earth?
A.
7.9 km/s
B.
11.2 km/s
C.
9.8 km/s
D.
15 km/s
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Solution
The escape velocity from the surface of the Earth is approximately 11.2 km/s.
Correct Answer: B — 11.2 km/s
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Q. What is the escape velocity from the surface of the Earth? (g = 9.8 m/s^2, R = 6.4 x 10^6 m)
A.
7.9 km/s
B.
11.2 km/s
C.
9.8 km/s
D.
5.0 km/s
Show solution
Solution
Escape velocity (v) = sqrt(2gR) = sqrt(2 * 9.8 * 6.4 x 10^6) ≈ 11.2 km/s.
Correct Answer: B — 11.2 km/s
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Q. What is the escape velocity from the surface of the Earth? (g = 9.8 m/s², R = 6.4 × 10^6 m)
A.
11.2 km/s
B.
9.8 km/s
C.
7.9 km/s
D.
15 km/s
Show solution
Solution
Escape velocity (v) = √(2gR) = √(2 * 9.8 * 6.4 × 10^6) ≈ 11.2 km/s
Correct Answer: A — 11.2 km/s
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Q. What is the escape velocity from the surface of the Earth? (R = 6.4 × 10^6 m, g = 9.8 m/s²)
A.
11.2 km/s
B.
9.8 km/s
C.
7.9 km/s
D.
12.0 km/s
Show solution
Solution
Escape velocity v = √(2gR) = √(2 * 9.8 * 6.4 × 10^6) ≈ 11.2 km/s.
Correct Answer: A — 11.2 km/s
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Q. What is the estimated temperature at the Earth's inner core?
A.
4000°C
B.
5000°C
C.
6000°C
D.
7000°C
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Solution
The temperature at the Earth's inner core is estimated to be around 6000°C.
Correct Answer: C — 6000°C
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Q. What is the expansion of (2x - 3y)²?
A.
4x² - 9y²
B.
4x² - 12xy + 9y²
C.
4x² + 9y²
D.
4x² + 12xy + 9y²
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Solution
(2x - 3y)² = 4x² - 12xy + 9y² by applying the square of a binomial.
Correct Answer: B — 4x² - 12xy + 9y²
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Q. What is the expected genotypic ratio in the F2 generation of a dihybrid cross? (2019)
A.
1:2:1
B.
3:1
C.
9:3:3:1
D.
1:1:1:1
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Solution
In a dihybrid cross, the expected genotypic ratio in the F2 generation is 9:3:3:1.
Correct Answer: C — 9:3:3:1
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Q. What is the expected major product when 2-bromobutane undergoes elimination reaction?
A.
But-1-ene
B.
But-2-ene
C.
But-3-ene
D.
Butane
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Solution
The major product of the elimination reaction of 2-bromobutane is But-2-ene due to the formation of the more stable alkene.
Correct Answer: B — But-2-ene
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Q. What is the expected osmotic pressure of a 0.5 M NaCl solution at 25 °C?
A.
12.3 atm
B.
24.6 atm
C.
6.1 atm
D.
3.1 atm
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Solution
Osmotic pressure (π) can be calculated using the formula π = iCRT. For NaCl, i = 2, C = 0.5 M, R = 0.0821 L·atm/(K·mol), and T = 298 K, resulting in approximately 24.6 atm.
Correct Answer: B — 24.6 atm
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Q. What is the expected product of the reaction of 1-chlorobutane with zinc in dry ether?
A.
Butane
B.
Butyne
C.
Butene
D.
No reaction
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Solution
The reaction of 1-chlorobutane with zinc in dry ether leads to the formation of Butane via Wurtz reaction.
Correct Answer: A — Butane
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Q. What is the expected product when 1-chlorobutane reacts with aqueous NaOH?
A.
Butanol
B.
Butene
C.
No reaction
D.
Butyric acid
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Solution
The expected product is Butanol due to nucleophilic substitution with hydroxide ion.
Correct Answer: A — Butanol
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Q. What is the expected ratio of phenotypes in a cross between two purebred parents with contrasting traits? (2019)
A.
1:1
B.
3:1
C.
9:3:3:1
D.
1:2:1
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Solution
The expected ratio of phenotypes in a cross between two purebred parents with contrasting traits is 1:1 in the F1 generation when they are crossed with each other.
Correct Answer: A — 1:1
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Q. What is the expression for the magnetic field at the center of a circular loop of radius R carrying a current I?
A.
B = μ₀I/(2R)
B.
B = μ₀I/(4R)
C.
B = μ₀I/(πR)
D.
B = μ₀I/(2πR)
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Solution
The magnetic field at the center of a circular loop of radius R carrying a current I is given by B = μ₀I/(2πR).
Correct Answer: D — B = μ₀I/(2πR)
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Q. What is the expression for the magnetic field at the center of a circular loop of radius R carrying current I?
A.
μ₀I/(2R)
B.
μ₀I/(4R)
C.
μ₀I/(2πR)
D.
μ₀I/(4πR)
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Solution
The magnetic field at the center of a circular loop is given by B = μ₀I/(2R).
Correct Answer: C — μ₀I/(2πR)
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Q. What is the expression for the magnetic field B at a distance r from a long straight conductor carrying current I?
A.
B = (μ₀I)/(2πr)
B.
B = (μ₀I)/(4πr²)
C.
B = (I)/(2πr)
D.
B = (μ₀I²)/(2πr)
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Solution
The magnetic field B at a distance r from a long straight conductor carrying current I is given by B = (μ₀I)/(2πr).
Correct Answer: A — B = (μ₀I)/(2πr)
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Q. What is the expression for the magnetic field B at a distance r from a long straight wire carrying current I according to the Biot-Savart Law?
A.
B = (μ₀I)/(2πr)
B.
B = (μ₀I)/(4πr²)
C.
B = (I)/(2πr)
D.
B = (μ₀I²)/(2πr)
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Solution
The magnetic field B at a distance r from a long straight wire carrying current I is given by B = (μ₀I)/(2πr).
Correct Answer: A — B = (μ₀I)/(2πr)
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Q. What is the family of curves represented by the equation xy = c?
A.
Hyperbolas
B.
Parabolas
C.
Ellipses
D.
Circles
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Solution
The equation xy = c represents a family of hyperbolas with varying constant c.
Correct Answer: A — Hyperbolas
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Q. What is the family of curves represented by the equation x^2/a^2 + y^2/b^2 = 1?
A.
Ellipses
B.
Hyperbolas
C.
Parabolas
D.
Circles
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Solution
The equation x^2/a^2 + y^2/b^2 = 1 represents a family of ellipses with semi-major axis a and semi-minor axis b.
Correct Answer: A — Ellipses
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Q. What is the family of curves represented by the equation y = a sin(bx + c)?
A.
Sine waves
B.
Cosine waves
C.
Linear functions
D.
Quadratic functions
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Solution
The equation y = a sin(bx + c) represents a family of sine waves with amplitude a and phase shift c.
Correct Answer: A — Sine waves
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Q. What is the family of curves represented by the equation y = e^(kx)?
A.
Linear functions
B.
Exponential functions with varying growth rates
C.
Logarithmic functions
D.
Polynomial functions
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Solution
The equation y = e^(kx) represents a family of exponential functions where 'k' determines the growth rate.
Correct Answer: B — Exponential functions with varying growth rates
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Q. What is the family of curves represented by the equation y = k/x?
A.
Linear functions
B.
Hyperbolas
C.
Parabolas
D.
Circles
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Solution
The equation y = k/x represents a family of hyperbolas with varying asymptotes depending on the value of 'k'.
Correct Answer: B — Hyperbolas
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Q. What is the Faraday's constant value?
A.
96485 C/mol
B.
96500 C/mol
C.
96500 A·s/mol
D.
96480 C/mol
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Solution
Faraday's constant is approximately 96485 C/mol.
Correct Answer: A — 96485 C/mol
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Q. What is the Faraday's constant?
A.
96485 C/mol
B.
96500 C/mol
C.
96500 J/mol
D.
96485 J/mol
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Solution
Faraday's constant is approximately 96485 C/mol.
Correct Answer: A — 96485 C/mol
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Q. What is the female reproductive part of a flower called? (2022)
A.
Stamen
B.
Pistil
C.
Petal
D.
Sepal
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Solution
The pistil is the female reproductive part of the flower, consisting of the ovary, style, and stigma.
Correct Answer: B — Pistil
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