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Recent questions tagged isi2004
5
votes
1
answer
1
ISI2004-MIII: 23
If $\textit{f}(x)=x^{2}$ and $g(x)=x \sin x +\cos x$ then $f$ and $g$ agree at no point $f$ and $g$ agree at exactly one point $f$ and $g$ agree at exactly two point $f$ and $g$ agree at more then two point
Tesla!
asked
in
Calculus
Apr 5, 2017
by
Tesla!
1.4k
views
isi2004
engineering-mathematics
functions
6
votes
1
answer
2
ISI2004-MIII: 22
If $\textit{f}(x)=\frac{\sqrt{3}\sin x}{2+\cos x}$ then the range of $\textit{f}(x)$ is the interval $\left[-1,\frac{\sqrt{3}}{2}\right]$ the interval $\left[\frac{-\sqrt{3}}{2},1\right]$ the interval $\left[-1,1\right]$ none of the above
Tesla!
asked
in
Calculus
Apr 5, 2017
by
Tesla!
696
views
isi2004
engineering-mathematics
functions
2
votes
2
answers
3
ISI 2004 MIII
Let $X$ be a nonempty set and let $\mathcal{P}(X)$ denote the collection of all subsets of $X.$ Define $\textit{f}:\textit{X$\times$ $\mathcal{P}$(X)}\rightarrow \mathbb{R}$ by $f(x,A) = \begin{cases} 1 \text{ if } x \in A & \\ 0 \text{ if } x \notin A & \end{cases}$ ... $f(x,A)+f(x,B) - f(x,A) \cdot f(x,B)$ $f(x,A)+ \mid f(x,A) - f(x,B) \mid$
Tesla!
asked
in
Set Theory & Algebra
Apr 5, 2017
by
Tesla!
658
views
isi2004
functions
1
vote
2
answers
4
ISI 2004 MIII
The inequality $\frac{2-gx+x^{2}}{1-x+x^{2}}\leq 3$ is true for all the value of $x$ if and only if $1\leq g\leq 7$ $-1\leq g\leq 1$ $-6\leq g\leq 7$ $-1\leq g\leq 7$
Tesla!
asked
in
Set Theory & Algebra
Apr 4, 2017
by
Tesla!
876
views
isi2004
inequality
5
votes
3
answers
5
ISI2004-MIII: 13
Let $X =\frac{1}{1001}+\frac{1}{1002}+\frac{1}{1003}+\ldots+\frac{1}{3001}$. Then $X< 1$ $X>\frac{3}{2}$ $1< X< \frac{3}{2}$ none of the above
Tesla!
asked
in
Calculus
Apr 4, 2017
by
Tesla!
2.5k
views
isi2004
engineering-mathematics
integration
9
votes
2
answers
6
ISI2004-MIII: 12
The maximum possible value of $xy^2z^3$ subjected to condition $x,y,z \geq 0$ and $x+y+z=3$ is $1$ $\frac{9}{8}$ $\frac{9}{4}$ $\frac{27}{16}$
Tesla!
asked
in
Calculus
Apr 4, 2017
by
Tesla!
1.1k
views
isi2004
engineering-mathematics
maxima-minima
7
votes
1
answer
7
ISI2004-MIII: 11
If $\alpha 1,\alpha 2,\dots,\alpha n$ are the positive numbers then $\frac{a1}{a2}+\frac{a2}{a3}+\dots+\frac{an-1}{an}+\frac{an}{a1}$ is always $\geq n$ $\leq n$ $\leq n^{\frac{1}{2}}$ None of the above
Tesla!
asked
in
Set Theory & Algebra
Apr 4, 2017
by
Tesla!
850
views
isi2004
set-theory&algebra
number-theory
2
votes
1
answer
8
ISI 2004 MIII
$Q10$ The equation $p\left ( x \right ) = \alpha$ where $p\left ( x \right ) = x^{4}+4x^{3}-2x^{2}-12x$ has four distinct real root if and only if $p\left ( -3 \right )<\alpha$ $p\left ( -1 \right )>\alpha$ $p\left ( -1 \right )<\alpha$ $p\left ( -3 \right )<\alpha <p\left ( -1 \right )$
Tesla!
asked
in
Set Theory & Algebra
Apr 3, 2017
by
Tesla!
490
views
isi2004
polynomials
6
votes
2
answers
9
ISI2004-MIII
The equation $\frac{1}{3}+\frac{1}{2}s^{2}+\frac{1}{6}s^{3}=s$ has exactly three solution in $[0.1]$ exactly one solution in $[0,1]$ exactly two solution in $[0,1]$ no solution in $[0,1]$
Tesla!
asked
in
Set Theory & Algebra
Apr 3, 2017
by
Tesla!
622
views
isi2004
polynomials
2
votes
1
answer
10
ISI 2004 MIII
$Q8$ If $\alpha_{1},\alpha_{2},\alpha_{3}, \dots , \alpha_{n}$ be the roots of $x^{n}+1=0$, then $\left ( 1-\alpha_{1} \right )\left ( 1-\alpha_{2} \right ) \dots \left ( 1-\alpha_{n} \right )$ is equal to $1$ $0$ $n$ $2$
Tesla!
asked
in
Set Theory & Algebra
Apr 3, 2017
by
Tesla!
438
views
isi2004
polynomials
5
votes
2
answers
11
ISI2004-MIII: 7
The equation $x^{6}-5x^{4}+16x^{2}-72x+9=0$ has exactly two distinct real roots exactly three distinct real roots exactly four distinct real roots six different real roots
Tesla!
asked
in
Set Theory & Algebra
Apr 3, 2017
by
Tesla!
1.7k
views
isi2004
polynomials
maxima-minima
1
vote
1
answer
12
ISI 2004 MIII
If the equation $x^{4}+ax^{3}+bx^{2}+cx+1=0$ (where $a,b,c$ are real number) has no real roots and if at least one of the root is of modulus one, then $b=c$ $a=c$ $a=b$ none of this
Tesla!
asked
in
Set Theory & Algebra
Apr 3, 2017
by
Tesla!
343
views
isi2004
polynomials
0
votes
1
answer
13
ISI 2004 MIII
$x^{2}+x+1$ is a factor of $\left ( x+1 \right )^{n}-x^{n}-1$ whenever $n$ is odd $n$ is odd and multiple of $3$ $n$ is an even multiple of $3$ $n$ is odd and not a multiple of $3$
Tesla!
asked
in
Set Theory & Algebra
Apr 3, 2017
by
Tesla!
519
views
factors
isi2004
engineering-mathematics
19
votes
5
answers
14
ISI 2004 MIII
In how many ways can three person, each throwing a single die once, make a score of $11$ $22$ $27$ $24$ $38$
Tesla!
asked
in
Combinatory
Apr 3, 2017
by
Tesla!
2.8k
views
combinatory
isi2004
19
votes
4
answers
15
ISI 2004 MIII
A subset $S$ of set of numbers $\{2,3,4,5,6,7,8,9,10\}$ is said to be good if has exactly $4$ elements and their $gcd=1$, Then number of good subset is $126$ $125$ $123$ $121$
Tesla!
asked
in
Combinatory
Apr 3, 2017
by
Tesla!
2.7k
views
combinatory
isi2004
discrete-mathematics
normal
13
votes
3
answers
16
ISI 2004 MIII
A club with $x$ members is organized into four committees such that each member is in exactly two committees, any two committees have exactly one member in common . Then $x$ has exactly two values both between $4$ and $8$. exactly one value and this lies between $4$ and $8$. exactly two values both between $8$ and $16$. exactly one value and this lies between $8$ and $16$.
Tesla!
asked
in
Combinatory
Apr 3, 2017
by
Tesla!
1.6k
views
combinatory
isi2004
14
votes
5
answers
17
ISI 2004 MIII
The number of permutation of $\{1,2,3,4,5\}$ that keep at least one integer fixed is. $81$ $76$ $120$ $60$
Tesla!
asked
in
Combinatory
Apr 3, 2017
by
Tesla!
3.1k
views
combinatory
isi2004
discrete-mathematics
normal
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