No. of group homomorphism from Z4 to S4
Correct Answer: 16
Solution and Explanation
Top Questions on Symmetric, Skew-Symmetric, Hermitian, Skew-Hermitian, Normal, Orthogonal and Unitary Matrices
- Let \( \mathbb{R}[X] \) denote the ring of polynomials in \( X \) with real coefficients. Then, the quotient ring \( \mathbb{R}[X]/(X^4 + 4) \) is
- GATE MA - 2022
- Linear Algebra
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Questions Asked in GATE MA exam
Consider the relationships among P, Q, R, S, and T:
• P is the brother of Q.
• S is the daughter of Q.
• T is the sister of S.
• R is the mother of Q.
The following statements are made based on the relationships given above.
(1) R is the grandmother of S.
(2) P is the uncle of S and T.
(3) R has only one son.
(4) Q has only one daughter.
Which one of the following options is correct?- GATE MA - 2025
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- Blood Relations
For \( X = (x_1, x_2, x_3)^T \in \mathbb{R}^3 \), consider the quadratic form:
\[ Q(X) = 2x_1^2 + 2x_2^2 + 3x_3^2 + 4x_1x_2 + 2x_1x_3 + 2x_2x_3. \] Let \( M \) be the symmetric matrix associated with the quadratic form \( Q(X) \) with respect to the standard basis of \( \mathbb{R}^3 \).
Let \( Y = (y_1, y_2, y_3)^T \in \mathbb{R}^3 \) be a non-zero vector, and let
\[ a_n = \frac{Y^T(M + I_3)^{n+1}Y}{Y^T(M + I_3)^n Y}, \quad n = 1, 2, 3, \dots \] Then, the value of \( \lim_{n \to \infty} a_n \) is equal to (in integer).- GATE MA - 2025
- Quadratic Equations
- The average marks obtained by a class in an examination were calculated as 30.8. However, while checking the marks entered, the teacher found that the marks of one student were entered incorrectly as 24 instead of 42. After correcting the marks, the average becomes 31.4. How many students does the class have?
- A shop has 4 distinct flavors of ice-cream. One can purchase any number of scoops of any flavor. The order in which the scoops are purchased is inconsequential. If one wants to purchase 3 scoops of ice-cream, in how many ways can one make that purchase?
- GATE MA - 2025
- GATE AG - 2025
- Combinations
Ravi had _________ younger brother who taught at _________ university. He was widely regarded as _________ honorable man.
Select the option with the correct sequence of articles to fill in the blanks.