Mathematics
Q. What is the radius of a circle if the area is 154 square units? (2023)
-
A.
7 units
-
B.
14 units
-
C.
11 units
-
D.
10 units
Solution
Area = πr²; 154 = 22/7 * r²; r² = 154 * 7/22 = 49; r = 7 units.
Correct Answer: A — 7 units
Learn More →
Q. What is the radius of a circle if the diameter is 14 cm? (2021)
-
A.
7 cm
-
B.
14 cm
-
C.
21 cm
-
D.
28 cm
Solution
Radius is half of the diameter. Therefore, radius = 14 cm / 2 = 7 cm.
Correct Answer: A — 7 cm
Learn More →
Q. What is the real part of the complex number 4 + 5i? (2023)
Solution
The real part of the complex number 4 + 5i is 4.
Correct Answer: A — 4
Learn More →
Q. What is the real part of the complex number 7 - 4i? (2023)
Solution
The real part of the complex number 7 - 4i is 7.
Correct Answer: A — 7
Learn More →
Q. What is the slope of the line passing through the points (1, 2) and (3, 6)? (2020) 2020
Solution
Slope = (6-2)/(3-1) = 4/2 = 2.
Correct Answer: A — 2
Learn More →
Q. What is the slope of the line perpendicular to the line 3x + 4y = 12?
-
A.
-3/4
-
B.
4/3
-
C.
3/4
-
D.
-4/3
Solution
The slope of the line 3x + 4y = 12 is -3/4. The slope of the perpendicular line is the negative reciprocal, which is 4/3.
Correct Answer: B — 4/3
Learn More →
Q. What is the slope of the line perpendicular to the line 5x + 2y = 10?
-
A.
-2/5
-
B.
5/2
-
C.
2/5
-
D.
-5/2
Solution
The slope of the line is -5/2. The slope of the perpendicular line is the negative reciprocal, which is 2/5.
Correct Answer: A — -2/5
Learn More →
Q. What is the slope of the line perpendicular to the line 7x - 2y + 3 = 0?
-
A.
1/2
-
B.
-1/2
-
C.
2
-
D.
-2
Solution
The slope of the line is 7/2. The slope of the perpendicular line is the negative reciprocal, which is -2/7.
Correct Answer: B — -1/2
Learn More →
Q. What is the slope of the line perpendicular to the line 7x - 2y = 14?
-
A.
1/7
-
B.
-1/7
-
C.
2/7
-
D.
-2/7
Solution
The slope of the line is 7/2. The slope of the perpendicular line is the negative reciprocal, which is -2/7.
Correct Answer: B — -1/7
Learn More →
Q. What is the slope of the tangent line to f(x) = x^2 + 2x at x = 1? (2023)
Solution
f'(x) = 2x + 2. At x = 1, f'(1) = 2(1) + 2 = 4.
Correct Answer: B — 3
Learn More →
Q. What is the slope of the tangent to the curve y = x^2 + 2x at x = 1? (2023)
Solution
f'(x) = 2x + 2. At x = 1, f'(1) = 2(1) + 2 = 4.
Correct Answer: B — 3
Learn More →
Q. What is the solution of the differential equation y' = 2y + 3?
-
A.
y = Ce^(2x) - 3/2
-
B.
y = Ce^(2x) + 3/2
-
C.
y = 3e^(2x)
-
D.
y = 2e^(x) + C
Solution
The integrating factor is e^(-2x). Solving gives y = Ce^(2x) + 3/2.
Correct Answer: B — y = Ce^(2x) + 3/2
Learn More →
Q. What is the solution of the equation dy/dx = 3x^2?
-
A.
y = x^3 + C
-
B.
y = 3x^3 + C
-
C.
y = x^2 + C
-
D.
y = 3x^2 + C
Solution
Integrating both sides gives y = ∫3x^2 dx = x^3 + C.
Correct Answer: A — y = x^3 + C
Learn More →
Q. What is the solution of the equation dy/dx = 4y + 2? (2021)
-
A.
y = Ce^(4x) - 1/2
-
B.
y = Ce^(-4x) + 1/2
-
C.
y = 2e^(4x) + C
-
D.
y = 4e^(4x) + C
Solution
Using an integrating factor, the solution is y = Ce^(4x) - 1/2.
Correct Answer: A — y = Ce^(4x) - 1/2
Learn More →
Q. What is the solution of the equation dy/dx = 6 - 2y? (2021)
-
A.
y = 3 - Ce^(-2x)
-
B.
y = 3 + Ce^(-2x)
-
C.
y = 2 - Ce^(2x)
-
D.
y = 6 - Ce^(2x)
Solution
Rearranging gives dy/(6 - 2y) = dx. Integrating both sides leads to y = 3 - Ce^(-2x).
Correct Answer: A — y = 3 - Ce^(-2x)
Learn More →
Q. What is the solution to the differential equation dy/dx = -y/x?
-
A.
y = Cx
-
B.
y = C/x
-
C.
y = Cx^2
-
D.
y = Cx^(-1)
Solution
This is a separable equation. Separating variables and integrating gives y = C/x.
Correct Answer: B — y = C/x
Learn More →
Q. What is the solution to the equation dy/dx = -5y?
-
A.
y = Ce^(-5x)
-
B.
y = -5Ce^x
-
C.
y = Ce^(5x)
-
D.
y = 5Ce^(-x)
Solution
This is a separable differential equation. The solution is y = Ce^(-5x), where C is a constant.
Correct Answer: A — y = Ce^(-5x)
Learn More →
Q. What is the solution to the equation dy/dx = y^2? (2022)
-
A.
y = 1/(C - x)
-
B.
y = C/(x - 1)
-
C.
y = Cx^2
-
D.
y = ln(Cx)
Solution
This is a separable equation. Integrating gives y = 1/(C - x).
Correct Answer: A — y = 1/(C - x)
Learn More →
Q. What is the solution to the equation y' + 2y = 0?
-
A.
y = Ce^(-2x)
-
B.
y = Ce^(2x)
-
C.
y = 2Ce^x
-
D.
y = Ce^x
Solution
This is a separable equation. The solution is y = Ce^(-2x).
Correct Answer: A — y = Ce^(-2x)
Learn More →
Q. What is the solution to the equation y' + 3y = 0?
-
A.
y = Ce^(-3x)
-
B.
y = Ce^(3x)
-
C.
y = 3Ce^(-x)
-
D.
y = Ce^(-x/3)
Solution
This is a first-order linear differential equation. The solution is y = Ce^(-3x).
Correct Answer: A — y = Ce^(-3x)
Learn More →
Q. What is the solution to the equation y' = 3y + 6?
-
A.
y = Ce^(3x) - 2
-
B.
y = Ce^(3x) + 2
-
C.
y = 2e^(3x)
-
D.
y = 3Ce^(x)
Solution
This is a first-order linear equation. The integrating factor is e^(3x), leading to the solution y = Ce^(3x) + 2.
Correct Answer: B — y = Ce^(3x) + 2
Learn More →
Q. What is the solution to the equation y'' + 4y = 0?
-
A.
y = C1 cos(2x) + C2 sin(2x)
-
B.
y = C1 e^(2x) + C2 e^(-2x)
-
C.
y = C1 e^(4x) + C2 e^(-4x)
-
D.
y = C1 sin(4x) + C2 cos(4x)
Solution
The characteristic equation is r^2 + 4 = 0, giving complex roots. The general solution is y = C1 cos(2x) + C2 sin(2x).
Correct Answer: A — y = C1 cos(2x) + C2 sin(2x)
Learn More →
Q. What is the square of the modulus of the complex number 1 + 2i? (2014)
Solution
The modulus is √(1^2 + 2^2) = √(1 + 4) = √5. The square of the modulus is 5.
Correct Answer: A — 5
Learn More →
Q. What is the square of the modulus of the complex number 1 + i? (2020)
Solution
The modulus is √(1^2 + 1^2) = √2, and the square of the modulus is 2.
Correct Answer: A — 2
Learn More →
Q. What is the square root of 64? (2020)
Solution
The square root of 64 is 8.
Correct Answer: C — 8
Learn More →
Q. What is the sum of the complex numbers 3 + 2i and 1 - 4i? (2023)
-
A.
4 - 2i
-
B.
2 - 2i
-
C.
4 + 2i
-
D.
2 + 2i
Solution
(3 + 2i) + (1 - 4i) = (3 + 1) + (2 - 4)i = 4 - 2i.
Correct Answer: A — 4 - 2i
Learn More →
Q. What is the sum of the roots of the equation 2x² - 4x + 1 = 0? (2023)
Solution
The sum of the roots is given by -b/a = 4/2 = 2.
Correct Answer: A — 2
Learn More →
Q. What is the term containing x^2 in the expansion of (x + 4)^6?
-
A.
240
-
B.
360
-
C.
480
-
D.
600
Solution
The term containing x^2 is given by C(6,2) * (4)^4 * (x)^2 = 15 * 256 * x^2 = 3840.
Correct Answer: C — 480
Learn More →
Q. What is the value of (1 + i)(1 - i)? (2019)
Solution
(1 + i)(1 - i) = 1^2 - i^2 = 1 - (-1) = 1 + 1 = 2.
Correct Answer: A — 2
Learn More →
Q. What is the value of (2 + 3) × (4 - 1)? (2023)
Solution
Using BODMAS: (2 + 3) = 5 and (4 - 1) = 3, so 5 × 3 = 15.
Correct Answer: C — 10
Learn More →
Showing 421 to 450 of 493 (17 Pages)
