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 complex numbers z1 = 2 + 3i and z2 = 4 - 2i?
-
A.
6 + i
-
B.
6 + i
-
C.
2 + 5i
-
D.
8 + i
Solution
The sum of two complex numbers z1 + z2 = (2 + 3i) + (4 - 2i) = (2 + 4) + (3 - 2)i = 6 + i.
Correct Answer:
A
— 6 + i
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 interior angles of a triangle? (2019)
-
A.
90 degrees
-
B.
180 degrees
-
C.
270 degrees
-
D.
360 degrees
Solution
The sum of the interior angles of any triangle is always 180 degrees.
Correct Answer:
B
— 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 2x2 matrix [[a, b], [c, d]]? (2019)
-
A.
a + b
-
B.
b + c
-
C.
a + d
-
D.
c + d
Solution
The trace of a matrix is the sum of its diagonal elements. For the matrix [[a, b], [c, d]], the trace is a + d.
Correct Answer:
C
— a + d
Learn More →
Q. What is the trace of a matrix?
-
A.
Sum of all elements
-
B.
Sum of diagonal elements
-
C.
Product of diagonal elements
-
D.
None of the above
Solution
The trace of a matrix is defined as the sum of the elements on the main diagonal.
Correct Answer:
B
— Sum of diagonal elements
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 unit vector in the direction of vector A = 4i + 3j?
-
A.
(4/5)i + (3/5)j
-
B.
(3/4)i + (4/3)j
-
C.
(4/3)i + (3/4)j
-
D.
(3/5)i + (4/5)j
Solution
Unit vector = A / |A| = (4i + 3j) / √(4^2 + 3^2) = (4i + 3j) / 5 = (4/5)i + (3/5)j.
Correct Answer:
A
— (4/5)i + (3/5)j
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 (1 + i)²?
-
A.
2i
-
B.
2
-
C.
0
-
D.
1 + 2i
Solution
(1 + i)² = 1² + 2(1)(i) + i² = 1 + 2i - 1 = 2i.
Correct Answer:
B
— 2
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 →
Q. What is the value of (3x + 4)(3x - 4)?
-
A.
9x² - 16
-
B.
9x² + 16
-
C.
12x² - 16
-
D.
12x² + 16
Solution
(3x + 4)(3x - 4) = (3x)² - 4² = 9x² - 16.
Correct Answer:
A
— 9x² - 16
Learn More →
Q. What is the value of (a + b)² - (a² + b²)?
-
A.
2ab
-
B.
a² + b²
-
C.
0
-
D.
a + b
Solution
(a + b)² - (a² + b²) = 2ab.
Correct Answer:
A
— 2ab
Learn More →
Q. What is the value of (a + b)²?
-
A.
a² + b²
-
B.
a² + 2ab + b²
-
C.
2ab
-
D.
a² - b²
Solution
(a + b)² = a² + 2ab + b² by the expansion of the square of a binomial.
Correct Answer:
B
— a² + 2ab + b²
Learn More →
Showing 1411 to 1440 of 1593 (54 Pages)