# 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 1 Explanation:
 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 2 Explanation:
 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 3 Explanation:
 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 4 Explanation:
 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 5 Explanation:
 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 6 Explanation:
 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 7 Explanation:
 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 8 Explanation:
 Question 9
The value of $3^{51} \;mod \;5$ is _____
 A 1 B 2 C 3 D 4
GATE CSE 2019
Question 9 Explanation:
 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
Question 10 Explanation:

There are 10 questions to complete.

### 1 thought on “Engineering Mathematics”

1. Update Q184 as A instead of C