Engineering & Architecture Admissions
Q. What is the approximate energy released in MeV during the fission of one uranium-235 nucleus?
A.
0.1 MeV
B.
1 MeV
C.
200 MeV
D.
1000 MeV
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Solution
The fission of one uranium-235 nucleus releases approximately 200 MeV of energy.
Correct Answer: C — 200 MeV
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Q. What is the area between the curves y = x^2 and y = 4 from x = -2 to x = 2?
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Solution
The area between the curves is given by ∫(from -2 to 2) (4 - x^2) dx = [4x - x^3/3] from -2 to 2 = (8 - (8/3)) - (-8 + (8/3)) = 16 - (16/3) = 32/3.
Correct Answer: A — 8
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Q. What is the area of a circle with a radius of 10?
A.
100π
B.
50π
C.
25π
D.
200π
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Solution
The area of a circle is given by A = πr², so A = π(10)² = 100π.
Correct Answer: A — 100π
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Q. What is the area of a circle with a radius of 7?
A.
49π
B.
14π
C.
21π
D.
28π
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Solution
The area of a circle is given by A = πr², so A = π(7)² = 49π.
Correct Answer: A — 49π
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Q. What is the area of a circle with radius r?
A.
πr^2
B.
2πr
C.
πr
D.
r^2
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Solution
The area of a circle is given by the formula A = πr^2.
Correct Answer: A — πr^2
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Q. What is the area of a triangle with base 10 and height 5?
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Solution
Area = (1/2) * base * height = (1/2) * 10 * 5 = 25.
Correct Answer: A — 25
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Q. What is the area of a triangle with vertices at (0,0), (4,0), and (0,3)?
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Solution
The area is calculated as (1/2) * base * height = (1/2) * 4 * 3 = 6.
Correct Answer: A — 6
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Q. What is the area of an ellipse with semi-major axis 7 and semi-minor axis 4?
A.
28π
B.
14π
C.
21π
D.
35π
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Solution
The area of an ellipse is given by A = πab. Here, A = π * 7 * 4 = 28π.
Correct Answer: A — 28π
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Q. What is the area of an equilateral triangle with side length 'a'?
A.
(√3/4)a²
B.
(1/2)a²
C.
(√2/2)a²
D.
(3/2)a²
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Solution
The area of an equilateral triangle is given by the formula (√3/4)a².
Correct Answer: A — (√3/4)a²
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Q. What is the area of the triangle formed by the points (0, 0), (4, 0), and (0, 3)?
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Solution
Area = 1/2 * base * height = 1/2 * 4 * 3 = 6.
Correct Answer: A — 6
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Q. What is the area under the curve y = 1/x from x = 1 to x = 2?
A.
ln(2)
B.
1
C.
ln(2) - 1
D.
0
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Solution
The area is given by the integral from 1 to 2 of 1/x dx. This evaluates to [ln(x)] from 1 to 2 = ln(2) - ln(1) = ln(2).
Correct Answer: A — ln(2)
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Q. What is the area under the curve y = cos(x) from x = 0 to x = π/2?
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Solution
The area is given by the integral from 0 to π/2 of cos(x) dx. This evaluates to [sin(x)] from 0 to π/2 = 1 - 0 = 1.
Correct Answer: A — 1
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Q. What is the area under the curve y = sin(x) from x = 0 to x = π?
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Solution
The area is given by the integral from 0 to π of sin(x) dx. This evaluates to [-cos(x)] from 0 to π = [1 - (-1)] = 2.
Correct Answer: C — π
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Q. What is the area under the curve y = x^2 from x = 0 to x = 3?
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Solution
The area is given by the integral ∫_0^3 x^2 dx = [x^3/3]_0^3 = 27/3 = 9.
Correct Answer: A — 9
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Q. What is the area under the curve y = x^2 from x = 1 to x = 3?
A.
8/3
B.
10/3
C.
9/3
D.
7/3
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Solution
The area is ∫(1 to 3) x^2 dx = [1/3 * x^3] from 1 to 3 = (27/3 - 1/3) = 26/3.
Correct Answer: B — 10/3
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Q. What is the area under the curve y = x^3 from x = 1 to x = 2?
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Solution
The area under the curve y = x^3 from x = 1 to x = 2 is given by ∫(from 1 to 2) x^3 dx = [x^4/4] from 1 to 2 = (16/4) - (1/4) = 4 - 0.25 = 3.75.
Correct Answer: B — 4
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Q. What is the area under the curve y = x^4 from x = 0 to x = 1?
A.
1/5
B.
1/4
C.
1/3
D.
1/2
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Solution
The area under the curve y = x^4 from x = 0 to x = 1 is given by ∫(from 0 to 1) x^4 dx = [x^5/5] from 0 to 1 = 1/5.
Correct Answer: A — 1/5
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Q. What is the argument of the complex number z = -1 + 0i?
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Solution
The argument of z = -1 + 0i is arg(z) = π.
Correct Answer: A — π
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Q. What is the argument of the complex number z = -1 - i?
A.
-3π/4
B.
3π/4
C.
-π/4
D.
π/4
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Solution
The argument of z = -1 - i is θ = tan^(-1)(-1/-1) = -3π/4.
Correct Answer: A — -3π/4
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Q. What is the arithmetic mean of the first five prime numbers?
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Solution
Mean = (2 + 3 + 5 + 7 + 11) / 5 = 28 / 5 = 5.6.
Correct Answer: B — 6
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Q. What is the atomic number of the element with the symbol 'Na'?
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Solution
Sodium (Na) has an atomic number of 11.
Correct Answer: A — 11
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Q. What is the average kinetic energy of a gas molecule at temperature T?
A.
(3/2)kT
B.
(1/2)kT
C.
(3/2)RT
D.
(1/2)RT
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Solution
The average kinetic energy of a gas molecule is given by the formula KE_avg = (3/2)kT, where k is the Boltzmann constant.
Correct Answer: A — (3/2)kT
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Q. What is the average kinetic energy of one mole of an ideal gas at temperature T?
A.
(3/2)RT
B.
(5/2)RT
C.
(1/2)RT
D.
(2/3)RT
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Solution
The average kinetic energy of one mole of an ideal gas is given by the formula KE = (3/2)RT, where R is the gas constant and T is the temperature in Kelvin.
Correct Answer: A — (3/2)RT
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Q. What is the average power consumed in an AC circuit with a power factor of 0.8 and an RMS voltage of 100 V with a current of 5 A?
A.
200 W
B.
400 W
C.
300 W
D.
500 W
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Solution
Average power (P) is given by P = V_rms * I_rms * PF. Therefore, P = 100 V * 5 A * 0.8 = 400 W.
Correct Answer: C — 300 W
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Q. What is the average power consumed in an AC circuit with a power factor of 0.8 and a maximum power of 100 W?
A.
80 W
B.
100 W
C.
120 W
D.
160 W
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Solution
Average power (P_avg) is given by P_avg = P_max × power factor. Therefore, P_avg = 100 W × 0.8 = 80 W.
Correct Answer: A — 80 W
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Q. What is the axis of symmetry for the parabola defined by the equation y^2 = -12x?
A.
x = 0
B.
y = 0
C.
y = -6
D.
x = -6
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Solution
The axis of symmetry for a parabola in the form y^2 = 4px is the x-axis, which is x = 0.
Correct Answer: A — x = 0
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Q. What is the axis of symmetry for the parabola given by the equation y = -2x^2 + 4x + 1?
A.
x = 1
B.
y = 1
C.
x = 2
D.
y = 2
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Solution
The axis of symmetry for a parabola in the form y = ax^2 + bx + c is given by x = -b/(2a). Here, a = -2, b = 4, so x = -4/(2*-2) = 1.
Correct Answer: A — x = 1
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Q. What is the axis of symmetry for the parabola given by the equation y = 3x^2 + 6x + 2?
A.
x = -1
B.
y = -1
C.
x = 1
D.
y = 1
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Solution
The axis of symmetry for a parabola in the form y = ax^2 + bx + c is given by x = -b/(2a). Here, a = 3 and b = 6, so x = -6/(2*3) = -1.
Correct Answer: A — x = -1
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Q. What is the band gap energy of a typical semiconductor?
A.
0 eV
B.
1-3 eV
C.
5 eV
D.
10 eV
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Solution
Typical semiconductors have a band gap energy in the range of 1-3 eV.
Correct Answer: B — 1-3 eV
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Q. What is the band gap energy of a typical silicon semiconductor?
A.
0.1 eV
B.
1.1 eV
C.
2.0 eV
D.
3.5 eV
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Solution
Silicon has a band gap energy of approximately 1.1 eV, which is suitable for many electronic applications.
Correct Answer: B — 1.1 eV
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