1
GATE EE 2022
MCQ (Single Correct Answer)
+1
-0.33

Consider a 3 $$\times$$ 3 matrix A whose (i, j)-th element, ai,j = (i $$-$$ j)3. Then the matrix A will be

A
symmetric
B
skew-symmetric
C
unitary
D
null
2
GATE EE 2022
MCQ (Single Correct Answer)
+2
-0.67

e4 denotes the exponential of a square matrix A. Suppose $$\lambda$$ is an eigen value and v is the corresponding eigen-vector of matrix A.

Consider the following two statements:

Statement 1 : e$$\lambda$$ is an eigen value of eA.

Statement 2 : v is an eigen-vector of eA.

Which one of the following options is correct?

A
Statement 1 is true and statement 2 is false.
B
Statement 1 is false and statement 2 is true.
C
Both the statements are correct.
D
Both the statements are false.
3
GATE EE 2022
MCQ (Single Correct Answer)
+2
-0.67

Let $$f(x) = \int\limits_0^x {{e^t}(t - 1)(t - 2)dt} $$. Then f(x) decreases in the interval.

A
x $$\in$$ (1, 2)
B
x $$\in$$ (2, 3)
C
x $$\in$$ (0, 1)
D
x $$\in$$ (0.5, 1)
4
GATE EE 2022
MCQ (Single Correct Answer)
+2
-0.67

Consider a matrix $$A = \left[ {\matrix{ 1 & 0 & 0 \cr 0 & 4 & { - 2} \cr 0 & 1 & 1 \cr } } \right]$$. The matrix A satisfies the equation 6A$$-$$1 = A2 + cA + dI, where c and d are scalars and I is the identify matrix. Then (c + d) is equal to

A
5
B
17
C
$$-$$6
D
11
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