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Recent questions tagged tifrmaths2011
+2
votes
1
answer
1
TIFR2011MathsB15
A gardener throws $18$ seeds onto an equilateral triangle shaped plot of land with sides of length one metre. Then at least two seeds are within a distance of $25$ centimetres. TRUE/FALSE
asked
Dec 10, 2015
in
Numerical Ability
by
makhdoom ghaya
Boss
(
40k
points)

129
views
tifrmaths2011
numericalability
geometry
+1
vote
0
answers
2
TIFR2011MathsB14
Let $f$ be a continuous integrable function of $\mathbb{R}$ such that either $f(x) > 0$ or $f(x) + f(x + 1) > 0$ for all $x \in \mathbb{R}$. Then $\int_{\infty}^{\infty} f(x) \text{d}x > 0$.
asked
Dec 10, 2015
in
Linear Algebra
by
makhdoom ghaya
Boss
(
40k
points)

69
views
tifrmaths2011
integration
+2
votes
1
answer
3
TIFR2011MathsB13
Any nonsingular $k \times k$matrix with real entries can be made singular by changing exactly one entry.
asked
Dec 10, 2015
in
Linear Algebra
by
makhdoom ghaya
Boss
(
40k
points)

135
views
tifrmaths2011
linearalgebra
matrices
+1
vote
0
answers
4
TIFR2011MathsB12
Let $S$ be a finite subset of $\mathbb{R}^{3}$ such that any three elements in $S$ span a two dimensional subspace. Then $S$ spans a two dimensional space.
asked
Dec 10, 2015
in
Linear Algebra
by
makhdoom ghaya
Boss
(
40k
points)

57
views
tifrmaths2011
vectorspace
nongate
+1
vote
1
answer
5
TIFR2011MathsB11
There exists a set $A \subset \left\{1, 2,....,100\right\}$ with $65$ elements, such that $65$ cannot be expressed as a sum of two elements in $A$.
asked
Dec 10, 2015
in
Numerical Ability
by
makhdoom ghaya
Boss
(
40k
points)

151
views
tifrmaths2011
numericalability
pigeonholeprinciple
+1
vote
2
answers
6
TIFR2011MathsB10
Suppose a box contains three cards, one with both sides white, one with both sides black, and one with one side white and the other side black. If you pick a card at random, and the side facing you is white, then the probability that the other side is white is $1/2$.
asked
Dec 10, 2015
in
Probability
by
makhdoom ghaya
Boss
(
40k
points)

150
views
tifrmaths2011
probability
conditionalprobability
+1
vote
1
answer
7
TIFR2011MathsB9
Let $P$ be a degree $3$ polynomial with complex coefficients such that the constant term is $2010$. Then $P$ has a root $\alpha$ with $\alpha > 10$.
asked
Dec 10, 2015
in
Set Theory & Algebra
by
makhdoom ghaya
Boss
(
40k
points)

63
views
tifrmaths2011
polynomials
+2
votes
1
answer
8
TIFR2011MathsB8
If $A$ and $B$ are $3 \times 3$ matrices and $A$ is invertible, then there exists an integer $n$ such that $A + nB$ is invertible.
asked
Dec 9, 2015
in
Linear Algebra
by
makhdoom ghaya
Boss
(
40k
points)

152
views
tifrmaths2011
linearalgebra
matrices
+1
vote
0
answers
9
TIFR2011MathsB7
There is a nontrivial group homomorphism from $S_{3}$ to $\mathbb{Z}/3\mathbb{Z}$.
asked
Dec 9, 2015
in
Set Theory & Algebra
by
makhdoom ghaya
Boss
(
40k
points)

88
views
tifrmaths2011
groups
groupisomorphism
nongate
+1
vote
0
answers
10
TIFR2011MathsB6
Suppose $f_{n}(x)$ is a sequence of continuous functions on the closed interval $[0, 1]$ converging to $0$ point wise. Then the integral $\int_{0}^{1} f_{n}(x) \text{d}x$ converges to 0.
asked
Dec 9, 2015
in
Calculus
by
makhdoom ghaya
Boss
(
40k
points)

47
views
tifrmaths2011
functions
convergence
+1
vote
1
answer
11
TIFR2011MathsB5
The symmetric group $S_{5}$ consisting of permutations on $5$ symbols has an element of order $6$.
asked
Dec 9, 2015
in
Set Theory & Algebra
by
makhdoom ghaya
Boss
(
40k
points)

90
views
tifrmaths2011
groups
+1
vote
0
answers
12
TIFR2011MathsB4
A bounded continuous function on $\mathbb{R}$ is uniformly continuous.
asked
Dec 9, 2015
in
Calculus
by
makhdoom ghaya
Boss
(
40k
points)

63
views
tifrmaths2011
calculus
continuity
+1
vote
0
answers
13
TIFR2011MathsB3
There are n homomorphisms from the group $\mathbb{Z}/n\mathbb{Z}$ to the additive group of rationals $\mathbb{Q}$.
asked
Dec 9, 2015
in
Set Theory & Algebra
by
makhdoom ghaya
Boss
(
40k
points)

64
views
tifrmaths2011
groups
groupisomorphism
nongate
+1
vote
1
answer
14
TIFR2011MathsB2
In the ring $\mathbb{Z}/8\mathbb{Z}$, the equation $x^{2}=1$ has exactly $2$ solutions.
asked
Dec 9, 2015
in
Set Theory & Algebra
by
makhdoom ghaya
Boss
(
40k
points)

62
views
tifrmaths2011
settheory&algebra
+1
vote
0
answers
15
TIFR2011MathsB1
Let $A$ be a $2 \times 2$matrix with complex entries. The number of $2 \times 2$matrices $A$ with complex entries satisfying the equation $A^{3}$ is infinite.
asked
Dec 9, 2015
in
Linear Algebra
by
makhdoom ghaya
Boss
(
40k
points)

77
views
tifrmaths2011
linearalgebra
matrices
+3
votes
1
answer
16
TIFR2011MathsA25
The function $f(x) = \begin{cases} 0 & \text{if x is rational} \\ x& \text{if x is irrational} \end{cases}$ is not continuous anywhere on the real line.
asked
Dec 9, 2015
in
Calculus
by
makhdoom ghaya
Boss
(
40k
points)

105
views
tifrmaths2011
calculus
continuity
+1
vote
0
answers
17
TIFR2011MathsA24
The series $\sum_{n=1}^{\infty}\frac{\sqrt{n+1}\sqrt{n}}{n}$ diverges.
asked
Dec 9, 2015
in
Set Theory & Algebra
by
makhdoom ghaya
Boss
(
40k
points)

47
views
tifrmaths2011
convergence
+1
vote
0
answers
18
TIFR2011MathsA23
The space of solutions of infinitely differentiable functions satisfying the equation $y" + y = 0$ is infinite dimensional.
asked
Dec 9, 2015
in
Linear Algebra
by
makhdoom ghaya
Boss
(
40k
points)

50
views
tifrmaths2011
vectorspace
nongate
+1
vote
0
answers
19
TIFR2011MathsA22
There exists a group with a proper subgroup isomorphic to itself.
asked
Dec 9, 2015
in
Set Theory & Algebra
by
makhdoom ghaya
Boss
(
40k
points)

73
views
tifrmaths2011
groups
groupisomorphism
+1
vote
0
answers
20
TIFR2011MathsA21
Any continuous function from the open unit interval $(0, 1)$ to itself has a fixed point.
asked
Dec 9, 2015
in
Calculus
by
makhdoom ghaya
Boss
(
40k
points)

65
views
tifrmaths2011
continuity
+1
vote
1
answer
21
TIFR2011Maths20
The equation $63x + 70y + 15z = 2010$ has an integral solution.
asked
Dec 9, 2015
in
Numerical Ability
by
makhdoom ghaya
Boss
(
40k
points)

94
views
tifrmaths2011
numericalability
+1
vote
0
answers
22
TIFR2011MathsA19
The derivative of the function $\int_{0}^{\sqrt{x}} e^{t^{2}}dt$ at $x = 1$ is $e^{1}$ .
asked
Dec 9, 2015
in
Calculus
by
makhdoom ghaya
Boss
(
40k
points)

94
views
tifrmaths2011
calculus
differentiability
+1
vote
0
answers
23
TIFR2011MathsA18
Consider the map $T$ from the vector space of polynomials of degree at most $5$ over the reals to $R \times R$, given by sending a polynomial $P$ to the pair $(P(3), P' (3))$ where $P'$ is the derivative of $P$. Then the dimension of the kernel is $3$.
asked
Dec 9, 2015
in
Linear Algebra
by
makhdoom ghaya
Boss
(
40k
points)

45
views
tifrmaths2011
vectorspace
nongate
+1
vote
1
answer
24
TIFR2011MathsA17
The value of the infinite product $\prod_{n=2}^{\infty} (1\frac{1}{n^{2}})$ is 1.
asked
Dec 9, 2015
in
Numerical Ability
by
makhdoom ghaya
Boss
(
40k
points)

79
views
tifrmaths2011
numericalability
+1
vote
1
answer
25
TIFR2011MathsA16
The polynomial $x^{4}+7x^{3}13x^{2}+11x$ has exactly one real root.
asked
Dec 9, 2015
in
Set Theory & Algebra
by
makhdoom ghaya
Boss
(
40k
points)

90
views
tifrmaths2011
polynomials
+1
vote
1
answer
26
TIFR2011MathsA15
If $A, B$ are closed subsets of $[0,\infty)$, then $A + B = \left\{x + y  x \in A, y \in B\right\}$ is closed in $[0,\infty)$
asked
Dec 9, 2015
in
Calculus
by
makhdoom ghaya
Boss
(
40k
points)

56
views
tifrmaths2011
calculus
+1
vote
1
answer
27
TIFR2011MathsA14
$\log x$ is uniformly continuous on $( \frac{1}{2}, \infty)$.
asked
Dec 9, 2015
in
Calculus
by
makhdoom ghaya
Boss
(
40k
points)

108
views
tifrmaths2011
continuity
+1
vote
1
answer
28
TIFR2011MathsA13
$A$ is $3 \times 4$matrix of rank $3$. Then the system of equations, $Ax = b$ has exactly one solution.
asked
Dec 9, 2015
in
Linear Algebra
by
makhdoom ghaya
Boss
(
40k
points)

109
views
tifrmaths2011
linearalgebra
systemofequations
+1
vote
1
answer
29
TIFR2011MathsA12
$e^{\sqrt{2}}> 3$
asked
Dec 9, 2015
in
Numerical Ability
by
makhdoom ghaya
Boss
(
40k
points)

110
views
tifrmaths2011
numericalability
+1
vote
1
answer
30
TIFR2011MathsA11
For any real number $c$, the polynomial $x^{3}+x+c$ has exactly one real root.
asked
Dec 9, 2015
in
Set Theory & Algebra
by
makhdoom ghaya
Boss
(
40k
points)

73
views
tifrmaths2011
polynomials
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