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Recent questions tagged tifrmaths2010
4
votes
0
answers
1
TIFR2010-Maths-B-15
Which of the following statements is false? The polynomial $x^{2}+x+1$ is irreducible in $\mathbb{Z}/2\mathbb{Z}[x]$. The polynomial $x^{2}-2$ is irreducible in $\mathbb{Q}[x]$. The polynomial $x^{2}+1$ is reducible in $\mathbb{Z}/5\mathbb{Z}[x]$. The polynomial $x^{2}+1$ is reducible in $\mathbb{Z}/7\mathbb{Z}[x]$.
Which of the following statements is false?The polynomial $x^{2}+x+1$ is irreducible in $\mathbb{Z}/2\mathbb{Z}[x]$.The polynomial $x^{2}-2$ is irreducible in $\mathbb{Q}...
Arjun
596
views
Arjun
asked
Nov 14, 2015
Set Theory & Algebra
tifrmaths2010
polynomials
+
–
7
votes
1
answer
2
TIFR2010-Maths-B-14
The equations. $x_{1}+2x_{2}+3x_{3}=1$ $x_{1}+4x_{2}+9x_{3}=1$ $x_{1}+8x_{2}+27x_{3}=1$ have Only one solution Two solutions Infinitely many solutions No solutions
The equations.$x_{1}+2x_{2}+3x_{3}=1$$x_{1}+4x_{2}+9x_{3}=1$$x_{1}+8x_{2}+27x_{3}=1$haveOnly one solutionTwo solutionsInfinitely many solutionsNo solutions
makhdoom ghaya
800
views
makhdoom ghaya
asked
Oct 15, 2015
Linear Algebra
tifrmaths2010
linear-algebra
system-of-equations
+
–
2
votes
1
answer
3
TIFR2010-Maths-B-13
Define $\left \{ x_{n} \right \}$ as $x_{1}=0.1,x_{2}=0.101,x_{3}=0.101001,\dots$ Then the sequence $\left \{ x_{n} \right \}$. Converges to a rational number Converges to a irrational number Does not coverage Oscillates
Define $\left \{ x_{n} \right \}$ as $x_{1}=0.1,x_{2}=0.101,x_{3}=0.101001,\dots$ Then the sequence $\left \{ x_{n} \right \}$.Converges to a rational numberConverges to ...
makhdoom ghaya
1.6k
views
makhdoom ghaya
asked
Oct 15, 2015
Calculus
tifrmaths2010
calculus
convergence
+
–
5
votes
2
answers
4
TIFR2010-Maths-B-12
If $n$ and $m$ are positive integers and $n^{9}=19m+r$, then the possible values for $r$ modulo 19 are. Only 0 Only 0, $\pm$ 1 Only $\pm$ 1 None of the above
If $n$ and $m$ are positive integers and $n^{9}=19m+r$, then the possible values for $r$ modulo 19 are.Only 0Only 0, $\pm$ 1Only $\pm$ 1None of the above
makhdoom ghaya
1.4k
views
makhdoom ghaya
asked
Oct 14, 2015
Quantitative Aptitude
tifrmaths2010
quantitative-aptitude
modular-arithmetic
+
–
2
votes
1
answer
5
TIFR2010-Maths-B-11
Which of the following is true? The matrix $\begin{pmatrix} 1&0 \\ 1&2 \end{pmatrix}$ is not diagonalisable The matrix $\begin{pmatrix} 1&5 \\ 0&2 \end{pmatrix}$ is diagonalisable The matrix $\begin{pmatrix} 1&1 \\ 0&1 \end{pmatrix}$ is diagonalisable None of the above
Which of the following is true?The matrix $\begin{pmatrix}1&0 \\1&2\end{pmatrix}$ is not diagonalisableThe matrix $\begin{pmatrix}1&5 \\0&2\end{pmatrix}$ is diagonalisabl...
makhdoom ghaya
650
views
makhdoom ghaya
asked
Oct 14, 2015
Linear Algebra
tifrmaths2010
linear-algebra
matrix
+
–
3
votes
1
answer
6
TIFR2010-Maths-B-10
Let $x$ and $y \in \mathbb{R}^{n}$ be non-zero column vectors, from the matrix $A=xy^{T}$, where $y^{T}$ is the transpose of $y$. Then the rank of $A$ is: $2$ $0$ At least $n/2$ None of the above
Let $x$ and $y \in \mathbb{R}^{n}$ be non-zero column vectors, from the matrix $A=xy^{T}$, where $y^{T}$ is the transpose of $y$. Then the rank of $A$ is:$2$$0$At least $...
makhdoom ghaya
2.2k
views
makhdoom ghaya
asked
Oct 14, 2015
Linear Algebra
tifrmaths2010
matrix
+
–
3
votes
1
answer
7
TIFR2010-Maths-B-9
Let $G=\left \{ z \in \mathbb{C} \mid z^n = 1 \text{ for some positive integer } n \right \}$. Then under multiplication of complex numbers, $G$ is a group of finite order $G$ is a group of infinite order, but every element of $G$ has finite order $G$ is a cyclic group None of the above
Let $$G=\left \{ z \in \mathbb{C} \mid z^n = 1 \text{ for some positive integer } n \right \}$$. Then under multiplication of complex numbers,$G$ is a group of finite ord...
makhdoom ghaya
1.7k
views
makhdoom ghaya
asked
Oct 12, 2015
Set Theory & Algebra
tifrmaths2010
set-theory&algebra
group-theory
+
–
3
votes
2
answers
8
TIFR2010-Maths-B-8
The function $f(x)$ defined by $f(x)= \begin{cases} 0 & \text{if x is rational } \\ x & \text{if } x\text{ is irrational } \end{cases}$ is not continuous at any point is continuous at every point is continuous at every rational number is continuous at $x=0$
The function $f(x)$ defined by $$f(x)= \begin{cases} 0 & \text{if x is rational } \\ x & \text{if } x\text{ is irrational } \end{cases}$$is not continuous at any po...
Arjun
1.0k
views
Arjun
asked
Oct 12, 2015
Calculus
tifrmaths2010
calculus
+
–
3
votes
1
answer
9
TIFR2010-Maths-B-7
Number of solutions of the ordinary differential equation. $\frac{d^{2}y}{dx^{2}}-y=0, y(0)=0, y(\pi )=1$ is 0 is 1 is 2 None of the above
Number of solutions of the ordinary differential equation.$\frac{d^{2}y}{dx^{2}}-y=0, y(0)=0, y(\pi )=1$is 0is 1is 2None of the above
makhdoom ghaya
529
views
makhdoom ghaya
asked
Oct 12, 2015
Calculus
tifrmaths2010
calculus
+
–
3
votes
3
answers
10
TIFR2010-Maths-B-6
Let $A, B$ be subsets of $\mathbb{R}$. Define $A + B$ to be the set of all sums $x +y$ with $x \in A$ and $y \in B$. Which of the following statements is false? If $A$ and $B$ are bounded, then $A + B$ is bounded If $A$ and $B$ are open, then $A + B$ is open If $A$ and $B$ are closed, then $A + B$ is closed If $A$ and $B$ are connected, then $A + B$ is connected
Let $A, B$ be subsets of $\mathbb{R}$. Define $A + B$ to be the set of all sums $x +y$ with $x \in A$ and $y \in B$. Which of the following statements is false?If $A$ and...
makhdoom ghaya
933
views
makhdoom ghaya
asked
Oct 12, 2015
Set Theory & Algebra
tifrmaths2010
set-theory&algebra
set-theory
+
–
2
votes
0
answers
11
TIFR2010-Maths-B-5
If $f_{n}(x)$ are continuous functions from [0, 1] to [0, 1], and $f_{n}(x)\rightarrow f(x)$ as $n\rightarrow \infty $, then which of the following statements is true? $f_{n}(x)$ converges to $f(x)$ uniformly on [0, 1] $f_{n}(x)$ converges to $f(x)$ uniformly on (0, 1) $f(x)$ is continuous on [0, 1] None of the above
If $f_{n}(x)$ are continuous functions from [0, 1] to [0, 1], and $f_{n}(x)\rightarrow f(x)$ as $n\rightarrow \infty $, then which of the following statements is true?$f_...
makhdoom ghaya
532
views
makhdoom ghaya
asked
Oct 11, 2015
Calculus
tifrmaths2010
calculus
convergence
+
–
4
votes
1
answer
12
TIFR2010-Maths-B-4
Which of the following statements is false? There exists a natural number which when divided by 3 leaves remainder 1 and which when divided by 4 leaves remainder 0 There exists a natural number which when divided by 6 leaves remainder 2 and when ... remainder 3 There exists a natural number which when divided by 12 leaves remainder 7 and when divided by 8 leaves remainder 3
Which of the following statements is false?There exists a natural number which when divided by 3 leaves remainder 1 and which when divided by 4 leaves remainder 0There ex...
makhdoom ghaya
690
views
makhdoom ghaya
asked
Oct 11, 2015
Quantitative Aptitude
tifrmaths2010
quantitative-aptitude
modular-arithmetic
+
–
3
votes
1
answer
13
TIFR2010-Maths-B-3
If $f,g:\mathbb{R}\rightarrow \mathbb{R}$ are uniformly continuous functions, then their compositions g ∘ f is. Uniformly continuous Continuous but not uniformly continuous Continuous and bounded None of the above
If $f,g:\mathbb{R}\rightarrow \mathbb{R}$ are uniformly continuous functions, then their compositions g ∘ f is.Uniformly continuousContinuous but not uniformly continuo...
makhdoom ghaya
1.4k
views
makhdoom ghaya
asked
Oct 11, 2015
Set Theory & Algebra
tifrmaths2010
set-theory&algebra
functions
+
–
3
votes
1
answer
14
TIFR2010-Maths-B-2
If $V$ is a vector space over the field $\mathbb{Z}/5\mathbb{Z}$ and $\dim_{Z/5\mathbb{Z}}(V)=3$ then $V$ has. 125 elements 15 elements 243 elements None of the above
If $V$ is a vector space over the field $\mathbb{Z}/5\mathbb{Z}$ and $\dim_{Z/5\mathbb{Z}}(V)=3$ then $V$ has.125 elements15 elements243 elementsNone of the above
makhdoom ghaya
2.1k
views
makhdoom ghaya
asked
Oct 11, 2015
Linear Algebra
tifrmaths2010
vector-space
+
–
2
votes
1
answer
15
TIFR2010-Maths-B-1
Let $U_{n}=\sin(\frac{\pi }{n})$ and consider the series $\sum u_{n}$. Which of the following statements is false? $\sum u_{n}$ is convergent $u_{n}\rightarrow 0$ as $n\rightarrow \infty $ $\sum u_{n}$ is divergent $\sum u_{n}$ is absolutely convergent
Let $U_{n}=\sin(\frac{\pi }{n})$ and consider the series $\sum u_{n}$. Which of the following statements is false?$\sum u_{n}$ is convergent$u_{n}\rightarrow 0$ as $n\rig...
makhdoom ghaya
613
views
makhdoom ghaya
asked
Oct 11, 2015
Calculus
tifrmaths2010
calculus
convergence
+
–
4
votes
2
answers
16
TIFR2010-Maths-A-15
Let G be the set of all 2 x 2 symmetric, invertible matrices with real entries. Then with matrix multiplication, G is. An infinite group A finite group Not a group An abelian group
Let G be the set of all 2 x 2 symmetric, invertible matrices with real entries. Then with matrix multiplication, G is.An infinite groupA finite groupNot a groupAn abelian...
makhdoom ghaya
1.8k
views
makhdoom ghaya
asked
Oct 11, 2015
Set Theory & Algebra
tifrmaths2010
group-theory
+
–
2
votes
1
answer
17
TIFR2010-Maths-A-14
The solution of the ordinary differential equation. $\frac{dy}{dx}=y, y(0)=0$ Is unbounded Is positive Is negative Is zero
The solution of the ordinary differential equation.$$\frac{dy}{dx}=y, y(0)=0$$Is unboundedIs positiveIs negativeIs zero
makhdoom ghaya
601
views
makhdoom ghaya
asked
Oct 11, 2015
Calculus
tifrmaths2010
calculus
+
–
3
votes
3
answers
18
TIFR2010-Maths-A-13
What is the value of $\lim_{x\to 0} \sin{\left (\frac1 x \right )}$ $1$ $0$ $\frac{1}{2}$ Does Not Exist
What is the value of $$\lim_{x\to 0} \sin{\left (\frac1 x \right )}$$$1$$0$$\frac{1}{2}$Does Not Exist
makhdoom ghaya
706
views
makhdoom ghaya
asked
Oct 11, 2015
Calculus
tifrmaths2010
limits
+
–
2
votes
2
answers
19
TIFR2010-Maths-A-12
The sum of the roots of the equation $x^{5}+3x^{2}+7=0$ is. $-3$ $\frac{3}{7}$ $\frac{-1}{7}$ $0$
The sum of the roots of the equation $x^{5}+3x^{2}+7=0$ is.$-3$$\frac{3}{7}$$\frac{-1}{7}$$0$
makhdoom ghaya
494
views
makhdoom ghaya
asked
Oct 11, 2015
Quantitative Aptitude
tifrmaths2010
+
–
2
votes
3
answers
20
TIFR2010-Maths-A-11
The series $\sum ^{\infty }_{n=1}\frac{(-1)^{n+1}}{\sqrt{n}}$ Converges but not absolutely. Converges absolutely. Diverges. None of the above.
The series $$\sum ^{\infty }_{n=1}\frac{(-1)^{n+1}}{\sqrt{n}}$$ Converges but not absolutely. Converges absolutely. Diverges. None of the above.
Arjun
800
views
Arjun
asked
Oct 11, 2015
Quantitative Aptitude
tifrmaths2010
number-series
convergence
+
–
5
votes
2
answers
21
TIFR2010-Maths-A-10
Let $M_{n}(R)$ be the set of n x n matrices with real entries. Which of the following statements is true? Any matrix $A \in M_{4}(R)$ has a real eigenvalue Any matrix $A \in M_{5}(R)$ has a real eigenvalue Any matrix $A \in M_{2}(R)$ has a real eigenvalue None of the above
Let $M_{n}(R)$ be the set of n x n matrices with real entries. Which of the following statements is true?Any matrix $A \in M_{4}(R)$ has a real eigenvalueAny matrix $A \i...
makhdoom ghaya
1.2k
views
makhdoom ghaya
asked
Oct 11, 2015
Linear Algebra
tifrmaths2010
eigen-value
+
–
5
votes
1
answer
22
TIFR2010-Maths-A-9
The total number of subsets of a set of 6 elements is. 720 $6^{6}$ 21 None of the above
The total number of subsets of a set of 6 elements is.720$6^{6}$21None of the above
makhdoom ghaya
1.2k
views
makhdoom ghaya
asked
Oct 11, 2015
Set Theory & Algebra
tifrmaths2010
set-theory&algebra
set-theory
+
–
4
votes
4
answers
23
TIFR2010-Maths-A-8
Let $f(x)= |x|^{3/2}, x \in \mathbb{R}$. Then $f$ is uniformly continuous. $f$ is continuous, but not differentiable at $x=0$. $f$ is differentiable and $f ' $ is continuous. $f$ is differentiable, but $f ' $ is discontinuous at $x=0$.
Let $f(x)= |x|^{3/2}, x \in \mathbb{R}$. Then$f$ is uniformly continuous.$f$ is continuous, but not differentiable at $x=0$.$f$ is differentiable and $f ' $ is continuous...
makhdoom ghaya
1.4k
views
makhdoom ghaya
asked
Oct 11, 2015
Calculus
tifrmaths2010
calculus
differentiation
continuity
+
–
2
votes
1
answer
24
TIFR2010-Maths-A-7
The sequence $\sqrt{7},\sqrt{7+\sqrt{7}},{\sqrt{7+\sqrt{7+\sqrt{7}}}},....$ converges to. $\frac{1+\sqrt{33}}{2}$ $\frac{1+\sqrt{32}}{2}$ $\frac{1+\sqrt{30}}{2}$ $\frac{1+\sqrt{29}}{2}$
The sequence $\sqrt{7},\sqrt{7+\sqrt{7}},{\sqrt{7+\sqrt{7+\sqrt{7}}}},....$ converges to.$\frac{1+\sqrt{33}}{2}$$\frac{1+\sqrt{32}}{2}$$\frac{1+\sqrt{30}}{2}$$\frac{1+\sq...
makhdoom ghaya
753
views
makhdoom ghaya
asked
Oct 11, 2015
Quantitative Aptitude
tifrmaths2010
quantitative-aptitude
+
–
3
votes
1
answer
25
TIFR2010-Maths-A-6
The maximum value of $f(x)=x^{n}(1 - x)^{n}$ for a natural numbers $n\geq 1$ and $0\leq x\leq 1$ is $\frac{1}{2^{n}}$ $\frac{1}{3^{n}}$ $\frac{1}{5^{n}}$ $\frac{1}{4^{n}}$
The maximum value of $f(x)=x^{n}(1 - x)^{n}$ for a natural numbers $n\geq 1$ and $0\leq x\leq 1$ is$\frac{1}{2^{n}}$$\frac{1}{3^{n}}$$\frac{1}{5^{n}}$$\frac{1}{4^{n}}$
makhdoom ghaya
712
views
makhdoom ghaya
asked
Oct 11, 2015
Calculus
tifrmaths2010
calculus
maxima-minima
+
–
4
votes
2
answers
26
TIFR2010-Maths-A-5
Let $f$ be an one to one function from the closed interval [0, 1] to the set of real numbers $R$, then. $f$ must be onto Range of $f$ must contain a rational number Range of $f$ must contain an irrational number Range of $f$ must contain both rational and irrational numbers
Let $f$ be an one to one function from the closed interval [0, 1] to the set of real numbers $R$, then.$f$ must be ontoRange of $f$ must contain a rational numberRange of...
makhdoom ghaya
3.0k
views
makhdoom ghaya
asked
Oct 11, 2015
Set Theory & Algebra
tifrmaths2010
set-theory&algebra
functions
+
–
2
votes
2
answers
27
TIFR2010-Maths-A-4
The sum of the series $\frac{1}{1 \cdot 2}+ \frac{1}{2 \cdot 3}+ \frac{1}{3 \cdot 4} + \dots +\frac{1}{100 \cdot 101}$ $\frac{99}{101}$ $\frac{98}{101}$ $\frac{99}{100}$ None of the above
The sum of the series $$\frac{1}{1 \cdot 2}+ \frac{1}{2 \cdot 3}+ \frac{1}{3 \cdot 4} + \dots +\frac{1}{100 \cdot 101}$$$\frac{99}{101}$$\frac{98}{101}$$\frac{99}{100}$No...
makhdoom ghaya
779
views
makhdoom ghaya
asked
Oct 11, 2015
Set Theory & Algebra
tifrmaths2010
number-series
+
–
3
votes
3
answers
28
TIFR2010-Maths-A-3
The last digit of $2^{80}$ is.. 2 4 6 8
The last digit of $2^{80}$ is..2468
makhdoom ghaya
612
views
makhdoom ghaya
asked
Oct 11, 2015
Quantitative Aptitude
tifrmaths2010
quantitative-aptitude
+
–
4
votes
1
answer
29
TIFR2010-Maths-A-2
Which of the following is false? Any abelian group of order 27 is cyclic Any abelian group of order 14 is cyclic Any abelian group of order 21 is cyclic Any abelian group of order 30 is cyclic
Which of the following is false?Any abelian group of order 27 is cyclicAny abelian group of order 14 is cyclicAny abelian group of order 21 is cyclicAny abelian group of ...
makhdoom ghaya
2.2k
views
makhdoom ghaya
asked
Oct 11, 2015
Set Theory & Algebra
tifrmaths2010
set-theory&algebra
group-theory
+
–
3
votes
2
answers
30
TIFR2010-Maths-A-1
A cyclic group of order 60 has 12 Generators 15 Generators 16 Generators 20 Generators
A cyclic group of order 60 has12 Generators15 Generators16 Generators20 Generators
makhdoom ghaya
4.4k
views
makhdoom ghaya
asked
Oct 11, 2015
Set Theory & Algebra
tifrmaths2010
group-theory
+
–
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