# Recent questions tagged engineering-mathematics

The confusion arises as according to the def. continuity exists at a point ‘a’, when LHL, RHL, f(a) is finite and LHL=RHL=f(a).
Hi I need other resource for calculus cause I doing now mitocw David jerison calculus course as I on 10th video I realized this course is way too far for gate exam or psu exams cause this course give detailed proof and solution for every formula for differentiation like ... can follow kreatyrx? Please help me I am very confused ? As I give this week to complete engg maths full please reply fast
i study calculus but now i totally confused in calculus cause what is the exact syllabus of calculus for gate cse in integration , so all types of integration i do like multiple integration etc ? please reply as i stuck in between.
A tree has 14 vertices of degree 1 and degree of each of remaining vertices is 4 or 5. If the tree has ‘n’ vertices then number of vertices with degree 5 is:- (40-2n) (3n-54) (54-2n) (3n-40)
(G,*) is an abelian group .Then, (i). $X$ =$X^{-1}$ for any X belonging to G. (ii). $X$=$X^{2}$ for any X belonging to G. (iii). $(X*Y)^{2}$ = $X^{2}$ * $Y^{2}$ for any X ,Y belonging to G. (iv). G is of finite order
1 vote
The value of $\int_{0}^{inf}$ $e^{-y^{3}}.y^{1/2} dy$ is ? Ans = $\sqrt{\Pi } * 1/3$ How ?
Hi There is 2 book for graph theory so which book is followed because is rosen is short for graph theory and deo is very detailed so for gate which book is followed ? in rosen so there is complete detail for graph theory so if i read rosen so can i make gate related questions or not ? thank you
hi so what is least resource for calculus mainly for gate only, cause mit video is very long it is very time consuming
1 vote
A chair car compartment has 16 chairs in a row and 12 people randomly take up a chair each and the next person comes up with additional luggage which requires him to have two adjacent chairs. The probability that the 13th person is able to sit on the same row is ? A) 11/20 B) 4/7 C) 81/140 D) 17/28
Number of cycles of length 4 that are possible in the complete bipartite graph K(4,6) is
Which of the following number has odd number of divisors? 8762 9993 7568 1147 I tried calculating the numbers but it is very hard Can somehow virtual calculator be used? Is the problem in gate syllabus?
how to solve this?
Consider the first order predicate formula $\varphi$: $\forall x [ ( \forall z \: z \mid x \Rightarrow (( z=x) \vee (z=1))) \rightarrow \exists w ( w > x) \wedge (\forall z \: z \mid w \Rightarrow ((w=z) \vee (z=1)))]$ Here $a \mid b$ ... $S3:$ Set of all integers Which of the above sets satisfy $\varphi$? S1 and S2 S1 and S3 S2 and S3 S1, S2 and S3
Let $G$ be an undirected complete graph on $n$ vertices, where $n > 2$. Then, the number of different Hamiltonian cycles in $G$ is equal to $n!$ $(n-1)!$ $1$ $\frac{(n-1)!}{2}$
Suppose $Y$ is distributed uniformly in the open interval $(1,6)$. The probability that the polynomial $3x^2 +6xY+3Y+6$ has only real roots is (rounded off to $1$ decimal place) _______
Let $G$ be any connected, weighted, undirected graph. $G$ has a unique minimum spanning tree, if no two edges of $G$ have the same weight. $G$ has a unique minimum spanning tree, if, for every cut of $G$, there is a unique minimum-weight edge crossing the cut. Which of the following statements is/are TRUE? I only II only Both I and II Neither I nor II
Consider the following matrix: $R = \begin{bmatrix} 1 & 2 & 4 & 8 \\ 1 & 3 & 9 & 27 \\ 1 & 4 & 16 & 64 \\ 1 & 5 & 25 & 125 \end{bmatrix}$ The absolute value of the product of Eigen values of $R$ is _______
If the characteristic polynomial of a 3 $\times$ 3 matrix $M$ over $\mathbb{R}$ (the set of real numbers) is $\lambda^3 – 4 \lambda^2 + a \lambda +30, \quad a \in \mathbb{R}$, and one eigenvalue of $M$ is 2, then the largest among the absolute values of the eigenvalues of $M$ is _______
Let $G$ be an arbitrary group. Consider the following relations on $G$: $R_1: \forall a , b \in G, \: a R_1 b \text{ if and only if } \exists g \in G \text{ such that } a = g^{-1}bg$ $R_2: \forall a , b \in G, \: a R_2 b \text{ if and only if } a= b^{-1}$ Which of the above is/are equivalence relation/relations? $R_1$ and $R_2$ $R_1$ only $R_2$ only Neither $R_1$ nor $R_2$
Let $U = \{1, 2, \dots , n\}$ Let $A=\{(x, X) \mid x \in X, X \subseteq U \}$. Consider the following two statements on $\mid A \mid$. $\mid A \mid = n2^{n-1}$ $\mid A \mid = \Sigma_{k=1}^{n} k \begin{pmatrix} n \\ k \end{pmatrix}$ Which of the above statements is/are TRUE? Only I Only II Both I and II Neither I nor II
If $f(x) = R \: \sin ( \frac{\pi x}{2}) + S, f’\left(\frac{1}{2}\right) = \sqrt{2}$ and $\int_0^1 f(x) dx = \frac{2R}{\pi}$, then the constants $R$ and $S$ are $\frac{2}{\pi}$ and $\frac{16}{\pi}$ $\frac{2}{\pi}$ and 0 $\frac{4}{\pi}$ and 0 $\frac{4}{\pi}$ and $\frac{16}{\pi}$
Let $X$ be a square matrix. Consider the following two statements on $X$. $X$ is invertible Determinant of $X$ is non-zero Which one of the following is TRUE? I implies II; II does not imply I II implies I; I does not imply II I does not imply II; II does not imply I I and II are equivalent statements
Compute $\displaystyle \lim_{x \rightarrow 3} \frac{x^4-81}{2x^2-5x-3}$ $1$ $53/12$ $108/7$ Limit does not exist
Which one of the following predicate formulae is NOT logically valid? Note that $W$ is a predicate formula without any free occurrence of $x$. $\forall x (p(x) \vee W) \equiv \forall x \: ( px) \vee W$ $\exists x(p(x) \wedge W) \equiv \exists x \: p(x) \wedge W$ ... $\exists x(p(x) \rightarrow W) \equiv \forall x \: p(x) \rightarrow W$
Consider the functions $e^{-x}$ $x^{2}-\sin x$ $\sqrt{x^{3}+1}$ Which of the above functions is/are increasing everywhere in $[ 0,1]$? Ⅲ only Ⅱ only Ⅱ and Ⅲ only Ⅰ and Ⅲ only
The number of permutations of the characters in LILAC so that no character appears in its original position, if the two L’s are indistinguishable, is ______.
The function $y=|2 - 3x|$​ is continuous $∀ x ∈ R$ and differentiable $∀ x ∈ R$ is continuous $∀ x ∈ R$ and differentiable $∀ x ∈ R$ except at $x=\frac{3}{2}$ is continuous $∀ x ∈ R$ and differentiable $∀ x ∈ R$ except at $x=\frac{2}{3}$ is continuous $∀ x ∈ R$ except $x=3$ and differentiable $∀ x ∈ R$
1 vote
Let $G$ be a group of $35$ elements. Then the largest possible size of a subgroup of $G$ other than $G$ itself is _______.
Let $A$ and $B$ be two $n \times n$ matrices over real numbers. Let rank($M$) and $\text{det}(M)$ denote the rank and determinant of a matrix $M$, respectively. Consider the following statements. $\text{rank}(AB) = \text{rank }(A) \text{rank }(B)$ ... Which of the above statements are TRUE? I and II only I and IV only II and III only III and IV only
The value of ‘x’ for which all the eigen values of the matrix given below are real is 10 5+j 4 x 20 2 4 2 -10 5+j b. 5-j c.1-5j d.1+5j
Which one of the following descries the relationship among the three vectors, i+j+k ,2i+3j+k ,5i+6j+4k ? The vectors are mutually perpendicular The vectors are linearly dependent The vectors are linearly independent The vectors are unit vectors Anyone please clarify.
In the expansion of $(v+w+x+y+z)^{16}$, the coefficient of $wxy^{13}z$ is $?$ How to solve these types of problems?
38.