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Recent questions in Engineering Mathematics
2
votes
2
answers
8461
Solve : calculate the limit
Calculate the limit $\lim_{x\rightarrow 1^- } \sqrt[3]{x+1}\: ln(x+1)$ (A) $1$ (B) $0$ (C) $2$ (D) Does not exist
Calculate the limit $$\lim_{x\rightarrow 1^- } \sqrt[3]{x+1}\: ln(x+1)$$(A) $1$(B) $0$(C) $2$(D) Does not exist
Riya Roy(Arayana)
751
views
Riya Roy(Arayana)
asked
Dec 21, 2015
Calculus
limits
+
–
2
votes
1
answer
8462
how to find path of length 3 in below graph including V5 ?
what is the issue in the given approach ? Since the path should pass through v5 I am assuming we only include the path in which v5 can be intermediate vertex. And path visited in reverse order is not counted as distinct. Let us ... first vertex we can have total of 16 choices. This gives total paths possible as 16. But answer given is 4C3 .
what is the issue in the given approach ?Since the path should pass through v5 I am assuming we only include the path in which v5 can be intermediate vertex.And path visi...
radha gogia
1.5k
views
radha gogia
asked
Dec 21, 2015
Graph Theory
graph-theory
+
–
5
votes
2
answers
8463
TIFR-2015-Maths-B-5
Let $n \geq 1$ and let $A$ be an $n \times n$ matrix with real entries such that $A^{k}=0$, for some $k \geq 1$. Let $I$ be the identity $n \times n$ matrix. Then. $I+A$ need not be invertible. Det $(I+A)$ can be any non-zero real number. Det $(I+A) = 1$ $A^{n}$ is a non-zero matrix.
Let $n \geq 1$ and let $A$ be an $n \times n$ matrix with real entries such that $A^{k}=0$, for some $k \geq 1$. Let $I$ be the identity $n \times n$ matrix. Then.$I+A$ n...
makhdoom ghaya
950
views
makhdoom ghaya
asked
Dec 20, 2015
Linear Algebra
tifrmaths2015
linear-algebra
matrix
+
–
1
votes
0
answers
8464
TIFR-2015-Maths-B-4
Let $U_{1}\supset U_{2} \supset...$ be a decreasing sequence of open sets in Euclidean $3$-space $\mathbb{R}^{3}$. What can we say about the set $\cap U_{i}$ ? It is infinite. It is open. It is non-empty. None of the above.
Let $U_{1}\supset U_{2} \supset...$ be a decreasing sequence of open sets in Euclidean $3$-space $\mathbb{R}^{3}$. What can we say about the set $\cap U_{i}$ ?It is infin...
makhdoom ghaya
329
views
makhdoom ghaya
asked
Dec 20, 2015
Linear Algebra
tifrmaths2015
linear-algebra
non-gate
+
–
1
votes
0
answers
8465
TIFR-2015-Maths-B-3
Let $f$ be a function from $\left \{ 1, 2,....10 \right \}$ to $\mathbb{R}$ ... statement. There are uncountably many $f$ with this property There are only countably infinitely many $f$ with this property There is exactly one such $f$ There is no such $f$
Let $f$ be a function from $\left \{ 1, 2,....10 \right \}$ to $\mathbb{R}$ such that $ \displaystyle ( \sum_{i=1}^{10}\frac{|f(i)|}{2^{i}})^{2} = (\sum_{i=1}^{10} |f(i)|...
makhdoom ghaya
395
views
makhdoom ghaya
asked
Dec 20, 2015
Set Theory & Algebra
tifrmaths2015
functions
+
–
3
votes
1
answer
8466
TIFR-2015-Maths-B-2
In how many ways can the group $\mathbb{Z}_{5}$ act on the set $\left \{ 1, 2, 3, 4, 5 \right \}$ ? $5$ $24$ $25$ $120$
In how many ways can the group $\mathbb{Z}_{5}$ act on the set $\left \{ 1, 2, 3, 4, 5 \right \}$ ?$5$$24$$25$$120$
makhdoom ghaya
760
views
makhdoom ghaya
asked
Dec 20, 2015
Set Theory & Algebra
tifrmaths2015
combinatory
group-theory
+
–
4
votes
0
answers
8467
TIFR-2015-Maths-B-1
Let $X$ be a proper closed subset of $[0, 1]$. Which of the following statements is always true? The set $X$ is countable. There exists $x \in X$ such that $X$ \ $\left \{ x \right \}$ is closed The set $X$ contains an open interval. None of the above.
Let $X$ be a proper closed subset of $[0, 1]$. Which of the following statements is always true?The set $X$ is countable.There exists $x \in X$ such that $X$ \ $\left \{ ...
makhdoom ghaya
690
views
makhdoom ghaya
asked
Dec 20, 2015
Set Theory & Algebra
tifrmaths2015
set-theory
+
–
3
votes
1
answer
8468
TIFR-2015-Maths-A-15
The series $\sum_{n=1}^{\infty}\frac{\cos (3^{n}x)}{2^{n}}$ Diverges, for all rational $x \in \mathbb{R}$ Diverges, for some irrational $x \in \mathbb{R}$ Converges, for some but not all $x \in \mathbb{R}$ Converges, for all $x \in \mathbb{R}$
The series $\sum_{n=1}^{\infty}\frac{\cos (3^{n}x)}{2^{n}}$Diverges, for all rational $x \in \mathbb{R}$Diverges, for some irrational $x \in \mathbb{R}$Converges, for som...
makhdoom ghaya
350
views
makhdoom ghaya
asked
Dec 20, 2015
Set Theory & Algebra
tifrmaths2015
convergence
non-gate
+
–
3
votes
2
answers
8469
TIFR-2015-Maths-A-13
For a real number $t >0$, let $\sqrt{t}$ denote the positive square root of $t$. For a real number $x > 0$, let $F(x)= \int_{x^{2}}^{4x^{2}} \sin \sqrt{t}$ $dt$. If $F'$ is the derivative of $F$, then $F'(\frac{\pi}{2}) = 0$ $F'(\frac{\pi}{2}) = \pi$ $F'(\frac{\pi}{2}) = - \pi$ $F'(\frac{\pi}{2}) = 2\pi$
For a real number $t >0$, let $\sqrt{t}$ denote the positive square root of $t$. For a real number $x 0$, let $F(x)= \int_{x^{2}}^{4x^{2}} \sin \sqrt{t}$ $dt$. If $F'$ ...
makhdoom ghaya
478
views
makhdoom ghaya
asked
Dec 20, 2015
Calculus
tifrmaths2015
calculus
+
–
2
votes
0
answers
8470
TIFR-2015-Maths-A-12
Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be an infinitely differentiable function that vanishes at $10$ distinct points in $\mathbb{R}$. Suppose $f^{(n)}$ denotes the $n$-th derivative of $f$, for $n \geq 1$. Which of the following statements is always true? $f^{(n)}$ has at ... $f^{(n)}$ has at least $10$ zeros, for $n \geq 10$ $f^{(n)}$ has at least one zero, for $n \geq 9$
Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be an infinitely differentiable function that vanishes at $10$ distinct points in $\mathbb{R}$. Suppose $f^{(n)}$ denotes the $...
makhdoom ghaya
359
views
makhdoom ghaya
asked
Dec 20, 2015
Calculus
tifrmaths2015
functions
calculus
+
–
2
votes
1
answer
8471
TIFR-2015-Maths-A-11
Let $\left\{a_{n}\right\}$ be a sequence of real numbers. Which of the following is true? If $\sum a_{n}$ converges, then so does $\sum a_{n}^{4}$ If $\sum |a_{n}|$ converges, then so does $\sum a_{n}^{2}$ If $\sum a_{n}$ diverges, then so does $\sum a_{n}^{3}$ If $\sum |a_{n}|$ diverges, then so does $\sum a_{n}^{2}$
Let $\left\{a_{n}\right\}$ be a sequence of real numbers. Which of the following is true?If $\sum a_{n}$ converges, then so does $\sum a_{n}^{4}$If $\sum |a_{n}|$ conver...
makhdoom ghaya
363
views
makhdoom ghaya
asked
Dec 20, 2015
Set Theory & Algebra
tifrmaths2015
convergence
non-gate
+
–
0
votes
2
answers
8472
graph theory
nitish
571
views
nitish
asked
Dec 20, 2015
Graph Theory
graph-theory
+
–
1
votes
0
answers
8473
TIFR-2015-Maths-A-10
For a group $G$, let Aut(G) denote the group of automorphisms of $G$. Which of the following statements is true? Aut$(\mathbb{Z})$ is isomorphic to $\mathbb{Z}_{2}$ If $G$ is cyclic, then Aut $(G)$ is cyclic. If Aut (G) is trivial, then $G$ is trivial. Aut $(\mathbb{Z})$ is isomorphic to $\mathbb{Z}$
For a group $G$, let Aut(G) denote the group of automorphisms of $G$. Which of the following statements is true?Aut$(\mathbb{Z})$ is isomorphic to $\mathbb{Z}_{2}$If $G$ ...
makhdoom ghaya
390
views
makhdoom ghaya
asked
Dec 19, 2015
Set Theory & Algebra
tifrmaths2015
group-theory
non-gate
+
–
2
votes
1
answer
8474
MadeEasy Test Series: Calculus - Differentiability
Q.64 A function f (x) is differentiated twice such that its differential equation λ2f (x) – 2λf ′(x) + f ′′(x) = 0 provides two equal value of λ for all x. It f (0) = 1, f′(0) = 2, then f(x) at x = 1 will be _________. Given ans -> 7.39 (7.00 - 7.80)
Q.64A function f (x) is differentiated twice such that its differential equation λ2f (x) – 2λf ′(x) + f ′′(x) = 0 provides two equal value of λ for all x. It f...
Akash Kanase
491
views
Akash Kanase
asked
Dec 19, 2015
Calculus
made-easy-test-series
calculus
differentiation
+
–
3
votes
0
answers
8475
TIFR-2015-Maths-A-9
Let $\left\{a_{n}\right\}$ be a sequence of real numbers such that $|a_{n+1}-a_{n}|\leq \frac{n^{2}}{2^{n}}$ for all $n \in \mathbb{N}$. Then The sequence $\left\{a_{n}\right\}$ may be unbounded. The sequence $\left\{a_{n}\right\}$ is bounded but may not converge. The sequence $\left\{a_{n}\right\}$ has exactly two limit points. The sequence $\left\{a_{n}\right\}$ is convergent.
Let $\left\{a_{n}\right\}$ be a sequence of real numbers such that $|a_{n+1}-a_{n}|\leq \frac{n^{2}}{2^{n}}$ for all $n \in \mathbb{N}$. ThenThe sequence $\left\{a_{n}\ri...
makhdoom ghaya
390
views
makhdoom ghaya
asked
Dec 19, 2015
Set Theory & Algebra
tifrmaths2015
convergence
non-gate
+
–
3
votes
1
answer
8476
TIFR-2015-Maths-A-8
Let $f(x)=\frac{e^{\frac{-1}{x}}}{x}$, where $x \in (0, 1)$. Then on $(0, 1)$. $f$ is uniformly continuous. $f$ is continuous but not uniformly continuous. $f$ is unbounded. $f$ is not continuous.
Let $f(x)=\frac{e^{\frac{-1}{x}}}{x}$, where $x \in (0, 1)$. Then on $(0, 1)$.$f$ is uniformly continuous.$f$ is continuous but not uniformly continuous.$f$ is unbounded....
makhdoom ghaya
911
views
makhdoom ghaya
asked
Dec 19, 2015
Calculus
tifrmaths2015
calculus
continuity
+
–
2
votes
1
answer
8477
TIFR-2015-Maths-A-7
Let $f$ and $g$ be two functions from $[0, 1]$ to $[0, 1]$ with $f$ strictly increasing. Which of the following statements is always correct? If $g$ is continuous, then $f ∘ g$ is continuous If $f$ is continuous, then $f ∘ g$ is continuous If $f$ and $f ∘ g$ are continuous, then $g$ is continuous If $g$ and $f ∘ g$ are continuous, then $f$ is continuous
Let $f$ and $g$ be two functions from $[0, 1]$ to $[0, 1]$ with $f$ strictly increasing. Which of the following statements is always correct?If $g$ is continuous, then $f...
makhdoom ghaya
571
views
makhdoom ghaya
asked
Dec 19, 2015
Set Theory & Algebra
tifrmaths2015
functions
continuity
+
–
5
votes
2
answers
8478
TIFR-2015-Maths-A-6
Let $A$ be the $2 \times 2$ matrix $\begin{pmatrix} \sin\frac{\pi}{18}&-\sin \frac{4\pi}{9} \\ \sin \frac{4\pi}{9}&\sin \frac {\pi}{18} \end{pmatrix}$. Then the smallest number $n \in \mathbb{N}$ such that $A^{n}=1$ is. $3$ $9$ $18$ $27$
Let $A$ be the $2 \times 2$ matrix $\begin{pmatrix}\sin\frac{\pi}{18}&-\sin \frac{4\pi}{9} \\\sin \frac{4\pi}{9}&\sin \frac {\pi}{18}\end{pmatrix}$. Then the smallest num...
makhdoom ghaya
691
views
makhdoom ghaya
asked
Dec 19, 2015
Linear Algebra
tifrmaths2015
matrix
linear-algebra
+
–
3
votes
1
answer
8479
TIFR-2015-Maths-A-5
Let $f : \mathbb{R} \rightarrow \mathbb{R}$ denote the function defined by $f(x)= (1-x^{2})^{\frac{3}{2}}$ if $|x| < 1$, and $f(x)=0$ if $|x| \geq 1$. Which of the following statements is correct ? $f$ is not continuous $f$ is continuous but not differentiable $f$ is differentiable but $f'$ is not continuous. $f$ is differentiable and $f'$ is continuous.
Let $f : \mathbb{R} \rightarrow \mathbb{R}$ denote the function defined by $f(x)= (1-x^{2})^{\frac{3}{2}}$ if $|x| < 1$, and $f(x)=0$ if $|x| \geq 1$. Which of the follow...
makhdoom ghaya
580
views
makhdoom ghaya
asked
Dec 19, 2015
Calculus
tifrmaths2015
continuity
differentiation
+
–
2
votes
1
answer
8480
TIFR-2015-Maths-A-4
Let $S$ be the collection of (isomorphism classes of) groups $G$ which have the property that every element of $G$ commutes only with the identity element and itself. Then $|S| = 1$ $|S| = 2$ $|S| \geq 3$ and is finite $|S| = \infty$
Let $S$ be the collection of (isomorphism classes of) groups $G$ which have the property that every element of $G$ commutes only with the identity element and itself. The...
makhdoom ghaya
920
views
makhdoom ghaya
asked
Dec 19, 2015
Set Theory & Algebra
tifrmaths2015
group-theory
group-isomorphism
non-gate
+
–
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