# Questions by kvkumar

1
1 vote
2
1 vote
3
4
Number of words of 4 letters that can be formed with the letters of the word IITJEE is a) 42 b) 82 c)102 d) 142
5
how to Solve Any 3rd Degree Polynomial Equation ax3 + bx2 + cx + d = 0
1 vote
6
L = {an bam|n,m ≥ 0 and n = m mod 5} is regular
1 vote
7
The regular expression corresponding to the finite automata given below is (ab*(a+b)+ϵ)* (ϵ+a(a+b)b*a)* ((ϵ+(a+b)ab*)a)* (ab*(a+b)a+a)*(ab*(a+b)+ε)
8
How many states are there in a minimum state deterministic finite automaton accepting the language $L = \{w \mid w \in \{0,1\}^*,$ number of 0's is divisible by 2 and number of 1's is divisible by 5, respectively $\}$? 7 9 10 11
9
Which of the following is not a maturity level as per Capability Maturity Model? Initial Measurable Repeatable Optimized
1 vote
10
The dynamic allocation of storage areas with VSAM files is accomplished by Hashing Control splits Overflow areas Relative recoding
11
#include<stdio.h> int main(){ int a; if(a=printf("hello")) printf("gatecse%d",a); }
1 vote
12
Let $x_1, x_2, x_3, x_4, y_1, y_2, y_3$ and $y_4$ be fixed real numbers, not all of them equal to zero. Define 4 $\times$ ... Then rank(A) equals 1 or 2 0 4 2 or 3
1 vote
13
Let $f(x,y) = \begin{cases} 1, & \quad if \: xy=0, \\ xy, & \quad xy \neq 0. \end{cases}$ Then $f$ is continuous at $(0,0)$ and $\frac{\partial f}{ \partial x} (0,0)$ exists $f$ is not continuous at $(0,0)$ and $\frac{\partial f}{ \partial x} (0,0)$ exists ... $f$ is not continuous at $(0,0)$ and $\frac{\partial f}{ \partial x} (0,0)$ does not exist
14
15
16
1 vote
Let $\lambda_1, \lambda_2, \lambda_3$ denote the eigenvalues of the matrix $A = \begin{pmatrix} 1 & 0 & 0 \\ 0 & \cos t & \sin t \\ 0 & -\sin t & \cos t \end{pmatrix}$. If $\lambda_1+ \lambda_2+\lambda_3=\sqrt{2} +1$ then the set of possible values of $t, - \pi \leq t < \pi$, is Empty set $\{ \frac{\pi}{4} \}$ $\{ - \frac{\pi}{4}, \frac{\pi}{4} \}$ $\{ - \frac{\pi}{3}, \frac{\pi}{3} \}$
Consider the function $f(x)=\begin{cases} \int_0^x \{5+ \mid 1-y \mid \} dy & \quad if \: x>2 \\ 5x+2 & \quad if \: x \leq 2 \end{cases}$ Then $f$ is not continuous at x=2 $f$ is continuous and differentiable everywhere $f$ is continuous everywhere but not differentiable at x=1 $f$ is continuous everywhere but not differentiable at x=2