# Recent questions tagged algebra 1
Let $\mathbb{N}=\{1,2,3, \dots\}$ be the set of natural numbers. For each $n \in \mathbb{N}$, define $A_n=\{(n+1)k, \: k \in \mathbb{N} \}$. Then $A_1 \cap A_2$ equals $A_3$ $A_4$ $A_5$ $A_6$
2
If p(n+1)+p(n-1)=p(n) for every natural number ‘n’then for what values of natural number ‘a’ will p(n+a)=-p(n) a)3 b)2 c)4 d)6
3
If $a/b=c/d$, then which of the following does not hold good? $(a+b)/b=(c+d)/d$ $(a+c)/(b+d)=(a-c)/(b-d)$ $(a+b)/(a-b)=(c+d)/(c-d)$ $(a+c)/(b-d)=(a-c)(b+d)$
4
If $x=cy+bz, \: y=az+cx, \: z=bx+ay,$ where $x,y,z$ are not all zero, then $a^2+b^2+c^2=$ $1+2abc$ $1-2abc$ $1+abc$ $abc-1$
5
What is the maximal order of an element in S7? The symbol Sn will stand for the set of all permutations of the symbols {1,2,···,n}, which is a group under composition.
1 vote
6
For what values of $\lambda$ the system of equations will have $2$ linear independent solutions - $x + y + z = 0$ $(\lambda + 1) y + (\lambda + 1) z = 0$ ($\lambda^{2}- 1) z = 0$ Now the problem i'm facing is if there is $2$ Linear ... rank of matrix will be $1$. Can anyone please explain in simple why the rank of matrix should be $1$ if we need $2$ Linear Independent solution. Thankyou.
7
$\underbrace{a+a+a+ \dots +a}_{\text{n times}}=a^2b$ and $\underbrace{b+b+b+ \dots +b}_{\text{m times}} = ab^2$, where $a, b, n, m$ are natural numbers. What is the value of $\Bigg( \underbrace{m+m+m+ \dots +m}_{\text{n times}} \Bigg) \Bigg( \underbrace{n+ n+ n+ \dots + n}_{\text{m times}} \Bigg)?$ $2a^{2}b^{2}$ $a^{4}b^{4}$ $ab(a+b)$ $a^{2}+b^{2}$
8
Standard books required for linear algebra and calculus for gate syllabus ?
1 vote
9
Let f and g be the functions from the set of integers defined by $f(x) = 2x+3$ and $g(x) =3x+2$. Then the composition of f and g and g and f is given as 6x+7, 6x+11 6x+11, 6x+7 5x+5, 5x+5 None of the above
If $\dfrac{(2y+1)}{(y+2)} < 1,$ then which of the following alternatives gives the CORRECT range of $y$ ? $- 2 < y < 2$ $- 2 < y < 1$ $- 3 < y < 1$ $- 4 < y < 1$
A tiled floor of a room has dimensions $m \times m$ Sq.m. Dimensions of the tiles used are $n \times n$ Sq.m. All tiles used are green tiles except diagonal tiles which are red. After some years some green tiles are replaced by red tiles to form an alternate red and green tile pattern. How many green tiles are removed? ... $(m^2 - 4mn - n^2) / 2n^2$ D) $(m^2 -4mn - 2n^2) / 2n^2$
Given $\displaystyle \cfrac{\;\cfrac{a}{b} + \cfrac{b}{a}\;}{\cfrac{a}{b} - \cfrac{b}{a}} = 1$ If $a$ and $c$ are positive integers, then how many ordered pairs are possible for $(a,c)$, where: $a + 4b^2 + c \leq 8$? 45 28 17 18