# Recent questions tagged algebra

1 vote
1
If $x_{1} = \;– 1$ and $x_{m} = x_{m+1} + (m + 1)$ for every positive integer $m,$ then $x_{100}$ equals $– 5151$ $– 5150$ $– 5051$ $– 5050$
1 vote
2
If $\text{a,b,c}$ are non-zero and $14^{a} = 36^{b} = 84^{c},$ then $6b \left( \frac{1}{c} \;– \frac{1}{a} \right)$ is equal to
3
How many pairs $(a,b)$ of positive integers are there such that $a \leq b$ and $ab = 4^{2017} \; ?$ $2017$ $2019$ $2020$ $2018$
4
If $\textsf{x}$ and $\textsf{y}$ are positive real numbers satisfying $\textsf{x+y = 102},$ then the minimum possible value of $\textsf{2601} \left( 1 + \frac{1}{\textsf{x}} \right) \left( 1 + \frac{1}{\textsf{y}} \right)$ is
5
For real $\textsf{x}$ , the maximum possible value of $\frac{x}{\sqrt{1+x^{4}}}$ is $\frac{1}{\sqrt{3}}$ $1$ $\frac{1}{\sqrt{2}}$ $\frac{1}{2}$
6
The number of integers that satisfy the equality $\left( x^{2} – 5x + 7 \right)^{x+1} = 1$ is $2$ $3$ $5$ $4$
1 vote
7
The number of real$-$valued of the equation $2^{x}+2^{-x}=2-(x-2)^{2}$ is infinite $1$ $0$ $2$
1 vote
8
How many distinct positive integer-valued solutions exist to the equation $\left ( x^{2}-7x+11 \right )^{(x^{2}-13x+42)} =1$? $6$ $8$ $2$ $4$
9
If $x=\left ( 4096 \right )^{7+4\sqrt{3}}$, then which of the following equals $64$? $\frac{x^{7}}{x^{2\sqrt{3}}}$ $\frac{x^{7}}{x^{4\sqrt{3}}}$ $\frac{x\frac{7}{2}}{x\frac{4}{\sqrt{3}}}$ $\frac{x\frac{7}{2}}{x^{2\sqrt{3}}}$
1 vote
10
If $a, b$ and $c$ are positive integers such that $ab=432, bc=96$ and $c<9,$ then the smallest possible value of $a+b+c$ is $56$ $59$ $49$ $46$
1 vote
11
A gentleman decided to treat a few children in the following manner. He gives half of his total stock of toffees and one extra to the first child, and then the half of the remaining stock along with one extra to the second and continues giving away in this fashion. His total stock exhausts after he takes care of $5$ children. How many toffees were there in his stock initially?
1 vote
12
The number of distinct real roots of the equation $\left ( x+\frac{1}{x}\right )^{2}-3\left ( x+\frac{1}{x} \right )+2= 0$ equals
1 vote
13
A certain number when added to $50\%$ of itself is $27$. What is the number? $7$ $9$ $11$ $18$
14
Twelve less than $4$ times a number is $20$. What is the number? $2$ $4$ $6$ $8$
1 vote
15
The sum of a number and its double is $69$. What is the number? $46.6$ $34.5$ $23$ $20$
16
A school has $378$ girls and $675$ boys. All the students divided into strictly boys and strictly girls students sections. All the sections in the school has same number of students. What is the number of sections in the school? $27$ $36$ $39$ $23$
17
A dog at point $A$ goes in pursuit of a fox $30$ $m$ away. The dog makes $2$ $m$ and the fox, $1$ m long leaps. If the dog makes two leaps to the fox’s three, at what distance from $A$ will the dog catch up with the fox ? $100$ $m$ $110$ $m$ $105$ $m$ $120$ $m$
18
If $5$ spiders can catch $5$ files in $5$ minutes. How many files can $100$ spiders catch in $100$ minutes : $100$ $1000$ $500$ $2000$
19
The expression $(11.98\times 11.98 + 11.98 \times x +0.02 \times 0.02)$ will be a perfect square for $x$ equal to: $2.02$ $0.17$ $0.04$ $1.4$
20
The value of $\large\frac{(0.96)^3-(0.1)^3}{(0.96)^2+0.096+(0.1)^2}$ is : $0.86$ $0.95$ $0.97$ $1.06$
21
The simplified form of $\left[ \left ( \left( \dfrac{a+1}{a-1}\right)^2+3 \right)\div \left( \left( \dfrac{a+1}{a-1}\right)^2+3\right) \right] \div \left [\left( \dfrac{a^{3}+1}{a^{3}-1}\right)-\dfrac{2a}{a-1} \right]$ is: $a-1$ $1-a$ $-1$ $1$
22
$₹6500/-$ were divided among a certain number of persons. If there had been $15$ more persons, each would have got $₹30/-$ less. Find the original number of persons. $50$ $60$ $45$ $55$
23
A charitable trust donates $28$ different books of Maths, $16$ different books of science and $12$ different books of social science to poor students. Each student is given maximum number of books of only one subject of their interest and each student got equal number of books. Find the total number of students who got books. $14$ $10$ $12$ $15$
24
The factors of $(x^{2}+4y^{2}+4y-4xy-2x-8)$ are: $(x-2y-4)(x-2y+2)$ $(x-y+2)(x-4y-4)$ $(x+2y-4)(x+2y+2)$ None of these
1 vote
25
If $a^{x}=b, b^{y}=c$ and $c^{z}=a$, then $xyz$ equals: $abc$ $\dfrac{1}{abc}$ $1$ None
1 vote
26
What is the largest positive integer $n$ such that $\frac{n^{2}+7n+12}{n^{2}-n-12}$ is also a positive integer? $8$ $12$ $16$ $6$
1 vote
27
If $5^{x}-3^{y}=13438$ and $5^{x-1}+3^{y+1}=9686$, then $x+y$ equals _______
28
Given that $x^{2018}y^{2017}=1/2$ and $x^{2016}y^{2019}=8$, the value of $x^2+y^3$ is $35/4$ $37/4$ $31/4$ $33/4$
29
If $u^2+(u-2v-1)^2=-4v(u+v)$, then what is the value of $u+3v$ ? $1/4$ $0$ $1/2$ $-1/4$
1 vote
30
How many different pairs $(a,b)$ of positive integers are there such that $a\leq b$ and $1/a+1/b=1/9$ None of these $2$ $0$ $1$
1 vote
31
If $9^{\left ( x-1/2 \right )}-2^{\left ( 2x-2 \right )}=4^{x}-3^{\left (2x-3 \right )}$, then $x$ is $3/2$ $2/5$ $3/4$ $4/9$
1 vote
32
If $9^{2x-1}-81^{x-1}= 1944$ then $x$ is $3$ $9/4$ $4/9$ $1/3$
1 vote
33
If $x+1= x^{2}$ and $x> 0$, then $2x^{4}$ is $6+4\sqrt{5}$ $3+5\sqrt{5}$ $5+3\sqrt{5}$ $7+3\sqrt{5}$
1 vote
34
If $a, b, c$ and $d$ are integers such that $a+b+c+d=30$ , then the minimum possible value of $( a-b )^{2}+( a-c )^{2}+( a-d)^{2}$ is $1$ $2$ $5$ $6$
1 vote
35
If three positive real numbers $x,y,z$ satisfy $y–x=z–y$ and $xyz = 4$, then what is the minimum possible value of $y$? $2^{(1/3)}$ $2^{(2/3)}$ $2^{(1/4)}$ $2^{(3/4)}$
36
Let $x<0,\:0<y<1,\:z>1$. Which of the following may be false? $\left (x ^{2} -z^{2}\right )$ has to be positive. $yz$ can be less than one. $xy$ can never be zero. $\left (y ^{2} -z^{2}\right )$ is always negative.
If $(5.55)^{x}=(0.555)^{y}=1000$, then the value of $\frac{1}{x}-\frac{1}{y}$ is $3$ $1$ $\frac{1}{3}$ $\frac{2}{3}$
Consider the following operators defined below [email protected]$: gives the positive difference of$x$and$y.x\$y$: gives the sum of squares of $x$ and $y.$ $x₤y$: gives the positive difference of the squares of $x$ and $y.$ $x\&y$:gives the product of $x$ and $...$ will be equal to $x₤y$ $x\$y(x₤y)([email protected])$Cannot be determined 0 votes 0 answers 39 Consider the following operators defined below [email protected]$: gives the positive difference of $x$ and $y.$ $x\$y$: gives the sum of squares of$x$and$y.x₤y$: gives the positive difference of the squares of$x$and$y.x\&y$:gives the product of$x$and$y.$Also,$x,y\:\in ... $, then find$(x\$y)+(x₤y)$. $2x^2$ $2y^2$ $2(x^2+y^2)$ Cannot be determined
Given $a$ and $b = a-b$; $a$ and $b$ but $c=a+c-b$; $a$ or $b=b-a$; $a$ but not $b= a+b$; find $1$ or $(2$ but not $(3$ or $(4$ and $5$ but $(6$ but not $(7$ and $(8$ or $9) ) ) ) ) ).$ $9$ $-8$ $-11$ $17$