Major Competitive Exams

Civil Services Defence Exams Engineering & Architecture Admissions Government Jobs Management Admissions Undergraduate

Q. If Z is seated between A and B, and C is seated to the left of A, who is sitting to the right of B?

A. Z
B. C
C. None
D. A

Solution

None can be determined as there is no information about who is to the right of B.

Correct Answer: C — None

Learn More →

Q. If z1 = 1 + i and z2 = 1 - i, find z1 * z2.

A. 2
B. 0
C. 1
D. -1

Solution

z1 * z2 = (1 + i)(1 - i) = 1 - i^2 = 1 - (-1) = 2.

Correct Answer: A — 2

Learn More →

Q. If z1 = 1 + i and z2 = 2 - 3i, find z1 * z2.

A. 7 - i
B. 7 + i
C. 5 - i
D. 5 + i

Solution

z1 * z2 = (1 + i)(2 - 3i) = 2 - 3i + 2i + 3 = 5 - i.

Correct Answer: A — 7 - i

Learn More →

Q. If z1 = 1 + i and z2 = 2 - 3i, what is z1 * z2?

A. 5 - i
B. 8 - i
C. 7 + i
D. 1 + 5i

Solution

z1 * z2 = (1 + i)(2 - 3i) = 2 - 3i + 2i - 3i^2 = 2 - i + 3 = 5 - i.

Correct Answer: A — 5 - i

Learn More →

Q. If z1 = 1 + i and z2 = 2 - i, find z1 * z2.

A. 3 + i
B. 3 - i
C. 2 + 3i
D. 2 - 3i

Solution

z1 * z2 = (1 + i)(2 - i) = 2 - i + 2i - 1 = 3 + i.

Correct Answer: A — 3 + i

Learn More →

Q. If z1 = 2 + 2i and z2 = 1 - i, find z1 + z2.

A. 3 + i
B. 1 + i
C. 3 - i
D. 1 - i

Solution

z1 + z2 = (2 + 2i) + (1 - i) = 3 + i.

Correct Answer: A — 3 + i

Learn More →

Q. If z1 = 2 + 2i and z2 = 2 - 2i, what is the value of z1 * z2? (2019)

A. 8
B. 0
C. 4
D. 4 + 0i

Solution

z1 * z2 = (2 + 2i)(2 - 2i) = 4 - 4i^2 = 4 + 4 = 8.

Correct Answer: A — 8

Learn More →

Q. If z1 = 2 + 2i and z2 = 3 - i, find z1 + z2. (2023)

A. 5 + i
B. 5 + 3i
C. 1 + i
D. 1 - i

Solution

z1 + z2 = (2 + 2i) + (3 - i) = 5 + i.

Correct Answer: A — 5 + i

Learn More →

Q. If z1 = 2 + 3i and z2 = 4 - 5i, then z1 + z2 is?

A. 6 - 2i
B. 6 + 2i
C. 2 - 2i
D. 2 + 2i

Solution

z1 + z2 = (2 + 3i) + (4 - 5i) = 6 - 2i.

Correct Answer: A — 6 - 2i

Learn More →

Q. If z1 = 2 + 3i and z2 = 4 - i, find z1 + z2.

A. 6 + 2i
B. 6 + 4i
C. 2 + 6i
D. 8 + 2i

Solution

z1 + z2 = (2 + 3i) + (4 - i) = 6 + 2i.

Correct Answer: A — 6 + 2i

Learn More →

Q. If z1 = 2 + 3i and z2 = 4 - i, what is z1 + z2?

A. 6 + 2i
B. 6 + 4i
C. 2 + 4i
D. 2 + 2i

Solution

z1 + z2 = (2 + 3i) + (4 - i) = 6 + 2i.

Correct Answer: A — 6 + 2i

Learn More →

Q. If Z=26, Y=25, what is the value of the word 'BYE'?

A. 52
B. 54
C. 56
D. 58

Solution

B=2, Y=25, E=5; 2+25+5=32.

Correct Answer: B — 54

Learn More →

Q. If Z=26, Y=25, what is the value of the word 'ZOO'?

A. 52
B. 54
C. 56
D. 58

Solution

Z=26, O=15; thus, ZOO = 26 + 15 + 15 = 56.

Correct Answer: B — 54

Learn More →

Q. If \( A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \), find \( |A| \).

A. -2
B. 2
C. 0
D. 1

Solution

The determinant is \( 1*4 - 2*3 = 4 - 6 = -2 \).

Correct Answer: A — -2

Learn More →

Q. If \( A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \), what is \( |2A| \)?

A. -8
B. 8
C. 4
D. 16

Solution

The determinant of \( 2A \) is \( 2^2 * |A| = 4 * (-2) = -8 \).

Correct Answer: B — 8

Learn More →

Q. If \( A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \), what is \( |A| \)?

A. -2
B. 2
C. 0
D. 4

Solution

The determinant is calculated as (1*4) - (2*3) = 4 - 6 = -2.

Correct Answer: A — -2

Learn More →

Q. If \( A = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \), what is the determinant of A?

A. ad - bc
B. bc - ad
C. a + d
D. b + c

Solution

The determinant of matrix A is given by the formula \( ad - bc \).

Correct Answer: A — ad - bc

Learn More →

Q. If \( B = \begin{pmatrix} 1 & 2 & 1 \\ 0 & 1 & 0 \\ 2 & 3 & 1 \end{pmatrix} \), what is \( |B| \)?

A. 1
B. 2
C. 3
D. 4

Solution

The determinant is calculated as 1(1*1 - 0*3) - 2(0*1 - 1*2) + 1(0*3 - 1*2) = 1 - 4 - 2 = -5.

Correct Answer: B — 2

Learn More →

Q. If \( B = \begin{pmatrix} 1 & 2 & 3 \\ 0 & 1 & 4 \\ 5 & 6 & 0 \end{pmatrix} \), what is \( \det(B) \)?

A. -24
B. 24
C. 0
D. 12

Solution

Using the determinant formula, we find \( \det(B) = 1(1*0 - 4*6) - 2(0 - 4*5) + 3(0 - 1*5) = -24 \).

Correct Answer: A — -24

Learn More →

Q. If \( B = \begin{pmatrix} 1 & 2 \\ 2 & 4 \end{pmatrix} \), what is \( |B| \)?

A. 0
B. 1
C. 2
D. 3

Solution

The determinant is 0 because the rows are linearly dependent.

Correct Answer: A — 0

Learn More →

Q. If \( B = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \), what is \( |B| \)?

A. -2
B. 2
C. 0
D. 1

Solution

The determinant is \( 1*4 - 2*3 = 4 - 6 = -2 \).

Correct Answer: A — -2

Learn More →

Q. If \( B = \begin{pmatrix} 1 & 2 \\ 3 & 5 \end{pmatrix} \), what is \( |B| \)?

A. -1
B. 1
C. 2
D. 3

Solution

The determinant is \( 1*5 - 2*3 = 5 - 6 = -1 \).

Correct Answer: B — 1

Learn More →

Q. If \( B = \begin{pmatrix} 2 & 3 \\ 1 & 4 \end{pmatrix} \), find \( |B| \).

A. 5
B. 6
C. 7
D. 8

Solution

The determinant is \( 2*4 - 3*1 = 8 - 3 = 5 \).

Correct Answer: A — 5

Learn More →

Q. If \( B = \begin{pmatrix} 2 & 3 \\ 1 & 4 \end{pmatrix} \), what is \( |B| \)? (2022)

A. 5
B. 10
C. 1
D. 8

Solution

The determinant of \( B \) is \( 2*4 - 3*1 = 8 - 3 = 5 \).

Correct Answer: A — 5

Learn More →

Q. If \( C = \begin{pmatrix} 1 & 0 & 2 \\ 0 & 1 & 3 \\ 0 & 0 & 1 \end{pmatrix} \), what is the determinant of C? (2022)

A. 0
B. 1
C. 2
D. 3

Solution

The determinant of an upper triangular matrix is the product of its diagonal elements: 1 * 1 * 1 = 1.

Correct Answer: B — 1

Learn More →

Q. If \( C = \begin{pmatrix} 1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 3 & 6 \end{pmatrix} \), find \( \det(C) \).

A. 0
B. 1
C. 2
D. 3

Solution

The determinant is 0 because the first column is a linear combination of the other columns.

Correct Answer: A — 0

Learn More →

Q. If \( C = \begin{pmatrix} 1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 3 & 6 \end{pmatrix} \), find \( |C| \).

A. 0
B. 1
C. 2
D. 3

Solution

The determinant is 0 because the first column is a linear combination of the others.

Correct Answer: A — 0

Learn More →

Q. If \( C = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \), what is the determinant of C?

A. ad - bc
B. bc - ad
C. a + d
D. b + c

Solution

The determinant of C is given by the formula \( ad - bc \).

Correct Answer: A — ad - bc

Learn More →

Q. If \( D = \begin{vmatrix} 2 & 3 & 1 \\ 1 & 0 & 2 \\ 4 & 1 & 0 \end{vmatrix} \), find \( D \).

A. -10
B. 10
C. 0
D. 5

Solution

Calculating gives \( 2(0*0 - 2*1) - 3(1*0 - 2*4) + 1(1*1 - 0*4) = -4 + 24 + 1 = 21 \).

Correct Answer: A — -10

Learn More →

Q. If \( E = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix} \), what is \( |E| \)? (2023)

A. 0
B. 1
C. -1
D. 2

Solution

The determinant is calculated as \( 0*0 - 1*1 = 0 - 1 = -1 \).

Correct Answer: C — -1

Learn More →

Showing 12361 to 12390 of 30919 (1031 Pages)

Major Competitive Exams

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?