Q. What is the slope of the line represented by the equation 4x - 2y + 8 = 0? (2021)
Solution
Rearranging gives y = 2x + 4, so slope = 2.
Correct Answer: C — -2
Learn More →
Q. What is the slope of the line represented by the equation y = 3x + 4? (2022)
Solution
The slope of the line in the equation y = mx + b is m. Here, m = 3.
Correct Answer: A — 3
Learn More →
Q. What is the slope of the tangent line to the curve y = x^2 + 2x at x = 1?
Solution
The derivative y' = 2x + 2. At x = 1, y' = 2(1) + 2 = 4.
Correct Answer: A — 3
Learn More →
Q. What is the slope of the tangent line to the curve y = x^2 at the point (1,1)? (2023)
Solution
The derivative y' = 2x; At x = 1, slope = 2(1) = 2.
Correct Answer: B — 2
Learn More →
Q. What is the slope of the tangent line to the curve y = x^2 at the point (2, 4)?
Solution
The derivative y' = 2x. At x = 2, the slope is y'(2) = 2(2) = 4.
Correct Answer: A — 2
Learn More →
Q. What is the slope of the tangent line to the curve y = x^2 at the point (3, 9)? (2020)
Solution
The derivative y' = 2x. At x = 3, y' = 2(3) = 6.
Correct Answer: B — 6
Learn More →
Q. What is the solution of the differential equation dy/dx = y/x?
-
A.
y = Cx
-
B.
y = Cx^2
-
C.
y = C/x
-
D.
y = C ln(x)
Solution
This is separable. Integrating gives y = Cx.
Correct Answer: A — y = Cx
Learn More →
Q. What is the solution to the differential equation dy/dx = xy?
-
A.
y = Ce^(x^2/2)
-
B.
y = Ce^(-x^2/2)
-
C.
y = Cx^2
-
D.
y = C/x
Solution
This is separable. Separating and integrating gives y = Ce^(x^2/2).
Correct Answer: A — y = Ce^(x^2/2)
Learn More →
Q. What is the solution to the initial value problem dy/dx = 4y, y(1) = 2?
-
A.
y = 2e^(4x)
-
B.
y = 2e^(4x-4)
-
C.
y = e^(4x)
-
D.
y = 4e^(x)
Solution
The general solution is y = Ce^(4x). Using y(1) = 2, we find C = 2e^(-4).
Correct Answer: B — y = 2e^(4x-4)
Learn More →
Q. What is the sum of the coefficients in the expansion of (2x - 3)^4?
Solution
To find the sum of the coefficients, substitute x = 1: (2*1 - 3)^4 = (-1)^4 = 1. The sum of coefficients is 81.
Correct Answer: B — 81
Learn More →
Q. What is the sum of the coefficients in the expansion of (x + 1)^4?
Solution
The sum of the coefficients in the expansion of (x + 1)^4 is (1 + 1)^4 = 2^4 = 16.
Correct Answer: C — 16
Learn More →
Q. What is the sum of the coefficients in the expansion of (x + 1)^8?
-
A.
256
-
B.
512
-
C.
128
-
D.
64
Solution
The sum of the coefficients in the expansion of (x + 1)^n is given by (1 + 1)^n = 2^n. Here, n=8, so the sum is 2^8 = 256.
Correct Answer: B — 512
Learn More →
Q. What is the sum of the complex numbers z1 = 2 + 2i and z2 = 3 - 4i?
-
A.
5 - 2i
-
B.
5 + 2i
-
C.
1 - 2i
-
D.
1 + 2i
Solution
To find the sum, we add the real parts and the imaginary parts: (2 + 3) + (2 - 4)i = 5 - 2i.
Correct Answer: A — 5 - 2i
Learn More →
Q. What is the sum of the interior angles of a hexagon? (2022)
-
A.
720 degrees
-
B.
540 degrees
-
C.
360 degrees
-
D.
180 degrees
Solution
Sum of interior angles = (n-2) * 180° = (6-2) * 180° = 720 degrees
Correct Answer: A — 720 degrees
Learn More →
Q. What is the sum of the interior angles of a triangle formed by three intersecting lines?
-
A.
180 degrees
-
B.
360 degrees
-
C.
90 degrees
-
D.
270 degrees
Solution
The sum of the interior angles of any triangle is always 180 degrees.
Correct Answer: A — 180 degrees
Learn More →
Q. What is the sum of the roots of the equation 2x^2 - 8x + 6 = 0? (2022)
Solution
Using Vieta's formulas, the sum of the roots is -(-8)/2 = 4.
Correct Answer: A — 4
Learn More →
Q. What is the sum of the roots of the equation x² - 5x + 6 = 0? (2022)
Solution
The sum of the roots is given by -b/a = 5/1 = 5.
Correct Answer: A — 5
Learn More →
Q. What is the sum of the squares of the roots of the equation x^2 - 5x + 6 = 0?
Solution
The sum of the squares of the roots is given by (sum of roots)^2 - 2(product of roots). Here, sum = 5, product = 6. So, 5^2 - 2*6 = 25 - 12 = 13.
Correct Answer: B — 19
Learn More →
Q. What is the trace of a 2x2 matrix A = [[3, 2], [1, 4]]? (2022)
Solution
The trace of a matrix is the sum of its diagonal elements. For matrix A, the trace is 3 + 4 = 7.
Correct Answer: B — 6
Learn More →
Q. What is the trace of a 2x2 matrix A = [[a, b], [c, d]]? (2022)
-
A.
a + b + c + d
-
B.
a + d
-
C.
b + c
-
D.
a * d
Solution
The trace of a matrix is the sum of its diagonal elements. For matrix A, the trace is a + d.
Correct Answer: B — a + d
Learn More →
Q. What is the trace of a square matrix? (2022)
-
A.
Sum of all elements
-
B.
Product of diagonal elements
-
C.
Sum of diagonal elements
-
D.
Difference of diagonal elements
Solution
The trace of a square matrix is defined as the sum of the elements on its main diagonal.
Correct Answer: C — Sum of diagonal elements
Learn More →
Q. What is the trace of the matrix H = [[2, 0, 1], [0, 3, 0], [1, 0, 4]]? (2019)
Solution
The trace of a matrix is the sum of its diagonal elements. Here, trace(H) = 2 + 3 + 4 = 9.
Correct Answer: C — 7
Learn More →
Q. What is the trace of the matrix H = [[2, 1], [1, 3]]?
Solution
The trace of a matrix is the sum of its diagonal elements. Here, trace(H) = 2 + 3 = 5.
Correct Answer: B — 4
Learn More →
Q. What is the trace of the matrix I = [[3, 2], [1, 4]]? (2023)
Solution
The trace of a matrix is the sum of its diagonal elements. Here, trace(I) = 3 + 4 = 7.
Correct Answer: B — 6
Learn More →
Q. What is the trace of the matrix I = [[5, 2], [3, 4]]? (2022)
Solution
The trace of a matrix is the sum of its diagonal elements. Thus, trace(I) = 5 + 4 = 9.
Correct Answer: C — 9
Learn More →
Q. What is the value of (1 + 2)^5 using the binomial theorem?
-
A.
32
-
B.
64
-
C.
128
-
D.
256
Solution
Using the binomial theorem, (1 + 2)^5 = 3^5 = 243.
Correct Answer: B — 64
Learn More →
Q. What is the value of (2 + 3i) + (4 - 2i)?
-
A.
6 + i
-
B.
6 + i
-
C.
2 + 5i
-
D.
8 + i
Solution
To add the complex numbers, we combine the real parts and the imaginary parts: (2 + 4) + (3 - 2)i = 6 + 1i = 6 + i.
Correct Answer: A — 6 + i
Learn More →
Q. What is the value of (2x + 3)(2x - 3)?
-
A.
4x² - 9
-
B.
4x² + 9
-
C.
4x² - 6x + 9
-
D.
4x² + 6x - 9
Solution
(2x + 3)(2x - 3) = 4x² - 9.
Correct Answer: A — 4x² - 9
Learn More →
Q. What is the value of (2x + 3)²?
-
A.
4x² + 9
-
B.
4x² + 12x + 9
-
C.
4x² + 6x + 9
-
D.
2x² + 6x + 9
Solution
(2x + 3)² = 4x² + 12x + 9 by expanding the square of a binomial.
Correct Answer: B — 4x² + 12x + 9
Learn More →
Q. What is the value of (3/4) + (1/2)?
-
A.
1
-
B.
5/4
-
C.
3/2
-
D.
7/4
Solution
Convert 1/2 to 2/4, then (3/4) + (2/4) = 5/4.
Correct Answer: B — 5/4
Learn More →
Showing 991 to 1020 of 1137 (38 Pages)
