Recent questions tagged tifrmaths2010

7 votes
1 answer
2
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
2 votes
1 answer
3
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 ...
5 votes
2 answers
4
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
3 votes
1 answer
6
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$$0$At least $...
3 votes
2 answers
8
The function $f(x)$ defined by $$f(x)= \begin{cases} 0 & \text{if x is rational } \\ x & \text{if } x\text{ is irrational } \end{cases}$$is not continuous at any po...
3 votes
1 answer
9
Number of solutions of the ordinary differential equation.$\frac{d^{2}y}{dx^{2}}-y=0, y(0)=0, y(\pi )=1$is 0is 1is 2None of the above
3 votes
1 answer
13
If $f,g:\mathbb{R}\rightarrow \mathbb{R}$ are uniformly continuous functions, then their compositions g ∘ f is.Uniformly continuousContinuous but not uniformly continuo...
3 votes
1 answer
14
If $V$ is a vector space over the field $\mathbb{Z}/5\mathbb{Z}$ and $\dim_{Z/5\mathbb{Z}}(V)=3$ then $V$ has.125 elements15 elements243 elementsNone of the above
2 votes
1 answer
15
4 votes
2 answers
16
Let G be the set of all 2 x 2 symmetric, invertible matrices with real entries. Then with matrix multiplication, G is.An infinite groupA finite groupNot a groupAn abelian...
2 votes
1 answer
17
The solution of the ordinary differential equation.$$\frac{dy}{dx}=y, y(0)=0$$Is unboundedIs positiveIs negativeIs zero
3 votes
3 answers
18
What is the value of $$\lim_{x\to 0} \sin{\left (\frac1 x \right )}$$$1$$0$$\frac{1}{2}$Does Not Exist
2 votes
2 answers
19
The sum of the roots of the equation $x^{5}+3x^{2}+7=0$ is.$-3$$\frac{3}{7}$$\frac{-1}{7}$$0$
2 votes
3 answers
20
The series $$\sum ^{\infty }_{n=1}\frac{(-1)^{n+1}}{\sqrt{n}}$$ Converges but not absolutely. Converges absolutely. Diverges. None of the above.
5 votes
1 answer
22
4 votes
4 answers
23
2 votes
1 answer
24
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}$$\frac{1+\sq...
3 votes
1 answer
25
The maximum value of $f(x)=x^{n}(1 - x)^{n}$ for a natural numbers $n\geq 1$ and $0\leq x\leq 1$ is$\frac{1}{2^{n}}$$\frac{1}{3^{n}}$$\frac{1}{5^{n}}$$\frac{1}{4^{n}}$
2 votes
2 answers
27
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...
3 votes
3 answers
28
4 votes
1 answer
29
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 ...
3 votes
2 answers
30
A cyclic group of order 60 has12 Generators15 Generators16 Generators20 Generators
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