Question 1 |
The value of the definite integral \int_{-3}^{3} \int_{-2}^{2} \int_{-1}^{1} (4x^2y-z^3)dzdydx is _____. (Rounded off to the nearest integer)
0 | |
1 | |
2 | |
3 |
Question 1 Explanation:
Question 2 |
Let A be the adjacency matrix of the graph with vertices {1, 2, 3, 4, 5}.

Let \lambda _1,\lambda _2,\lambda _3,\lambda _4,\; and \; \lambda _5 be the five eigenvalues of A. Note that these eigenvalues need not be distinct.
The value of \lambda _1+\lambda _2+\lambda _3+ \lambda _4+ \lambda _5 = _____

Let \lambda _1,\lambda _2,\lambda _3,\lambda _4,\; and \; \lambda _5 be the five eigenvalues of A. Note that these eigenvalues need not be distinct.
The value of \lambda _1+\lambda _2+\lambda _3+ \lambda _4+ \lambda _5 = _____
1 | |
2 | |
3 | |
4 |
Question 2 Explanation:
Question 3 |
Let f(x)=x^3+15x^2-33x-36 be a real-valued function.
Which of the following statements is/are TRUE?
Which of the following statements is/are TRUE?
f(x) does not have a local maximum.
| |
f(x) has a local maximum. | |
f(x) does not have a local minimum. | |
f(x) has a local minimum. |
Question 3 Explanation:
Question 4 |
Let A=\begin{bmatrix}
1 & 2 & 3 &4 \\
4& 1& 2 &3 \\
3& 4 & 1 &2 \\
2 &3 &4 &1
\end{bmatrix} and B=\begin{bmatrix}
3& 4 & 1 &2 \\
4& 1& 2 &3 \\
1 & 2 & 3 &4 \\
2 &3 &4 &1
\end{bmatrix}
Let det(A) and det(B) denote the determinants of the matrices A and B, respectively.
Which one of the options given below is TRUE?
Let det(A) and det(B) denote the determinants of the matrices A and B, respectively.
Which one of the options given below is TRUE?
det(A) = det(B) | |
det(B) = - det(A) | |
det(A)=0 | |
det(AB) = det(A) + det(B) |
Question 4 Explanation:
Question 5 |
Which of the following is/are the eigenvector(s) for the matrix given below?
\begin{pmatrix} -9 &-6 &-2 &-4 \\ -8& -6 & -3 & -1 \\ 20 & 15 & 8 & 5 \\ 32& 21& 7&12 \end{pmatrix}
MSQ
\begin{pmatrix} -9 &-6 &-2 &-4 \\ -8& -6 & -3 & -1 \\ 20 & 15 & 8 & 5 \\ 32& 21& 7&12 \end{pmatrix}
MSQ
\begin{pmatrix}
-1\\
1\\
0\\
1
\end{pmatrix} | |
\begin{pmatrix}
1\\
0\\
-1\\
0
\end{pmatrix} | |
\begin{pmatrix}
-1\\
0\\
2\\
2
\end{pmatrix} | |
\begin{pmatrix}
0\\
1\\
-3\\
0
\end{pmatrix} |
Question 5 Explanation:
There are 5 questions to complete.
Update Q184 as A instead of C
The answer is D
I think Q160 is broken (all options are becoming wrong)