Engineering Mathematics

Question 1
For two n-dimensional real vectors P and Q, the operation s(P,Q) is defined as follows:

s(P,Q) = \displaystyle \sum_{i=1}^n (P[i] \cdot Q[i])

Let \mathcal{L} be a set of 10-dimensional non-zero real vectors such that for every pair of distinct vectors P,Q \in \mathcal{L}, s(P,Q)=0. What is the maximum cardinality possible for the set \mathcal{L}?
A
9
B
10
C
11
D
100
GATE CSE 2021 SET-2      Calculus
Question 2
Suppose that P is a 4x5 matrix such that every solution of the equation Px=0 is a scalar multiple of \begin{bmatrix} 2 & 5 & 4 &3 & 1 \end{bmatrix}^T. The rank of P is _______
A
1
B
2
C
3
D
4
GATE CSE 2021 SET-2      Linear Algebra
Question 3
Consider the following matrix.
\begin{pmatrix} 0 & 1 & 1 & 1\\ 1& 0& 1 & 1\\ 1& 1 & 0 & 1 \\1 & 1 & 1 & 0 \end{pmatrix}
The largest eigenvalue of the above matrix is __________.
A
1
B
3
C
4
D
6
GATE CSE 2021 SET-1      Linear Algebra
Question 4
Consider the following expression.
\lim_{x\rightarrow-3}\frac{\sqrt{2x+22}-4}{x+3}
The value of the above expression (rounded to 2 decimal places) is ___________.
A
0.25
B
0.45
C
0.75
D
0.85
GATE CSE 2021 SET-1      Calculus
Question 5
If x+2 y=30,then \left(\frac{2 y}{5}+\frac{x}{3}\right)+\left(\frac{x}{5}+\frac{2 y}{3}\right) will be equal to
A
8
B
16
C
18
D
20
ISRO CSE 2020      Linear Algebra
Question 6
Let A and B be two nxn matrices over real numbers. Let rank(M) and det(M) denote the rank and determinant of a matrix M, respectively. Consider the following statements.

I. rank(AB)=rank (A)rank (B)
II. det(AB)=det(A)det(B)
III. rank(A+B) \leq rank (A) + rank (B)
IV. det(A+B) \leq det(A) + det(B)

Which of the above statements are TRUE?
A
I and II only
B
I and IV only
C
II and III only
D
III and IV only
GATE CSE 2020      Linear Algebra
Question 7
Consider the functions

I. e^{-x}
II. x^2-\sin x
III. \sqrt{x^3+1}

Which of the above functions is/are increasing everywhere in [0,1] ?
A
III only
B
II only
C
II and III only
D
I and III only
GATE CSE 2020      Calculus
Question 8
Consider the following matrix:
\begin{bmatrix} 1 & 2 & 4 & 8\\ 1& 3 & 9 &27 \\ 1 & 4 & 16 &64 \\ 1 & 5 & 25 &125 \end{bmatrix}
The absolute value of the product of Eigenvalues of R is _________ .
A
10
B
12
C
25
D
125
GATE CSE 2019      Linear Algebra
Question 9
The value of 3^{51} \;mod \;5 is _____
A
1
B
2
C
3
D
4
GATE CSE 2019      
Question 10
Compute \lim_{x \to 3}\frac{x^4-81}{2x^2-5x-3}
A
1
B
53/12
C
108/7
D
Limit does not exist
GATE CSE 2019      Calculus


There are 10 questions to complete.

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