Recent questions tagged isi2019-mma

Consider the function $h$ defined on $\{0,1,…….10\}$ with $h(0)=0, \: h(10)=10 $ and$$2[h(i)-h(i-1)] = h(i+1) – h(i) \: \text{ for } i = 1,2, \dots ,9.$$Then the val...

If $t = \begin{pmatrix} 200 \\ 100 \end{pmatrix}/4^{100} $, then$t < \frac{1}{3}$$\frac{1}{3} < t < \frac{1}{2}$$\frac{1}{2} < t < \frac{2}{3}$$\frac{2}{3} < t < 1$

Let $a,b,c$ be non-zero real numbers such that $\int_{0}^{1} (1 + \cos^8x)(ax^2 + bx +c)dx = \int_{0}^{2}(1+ \cos^8x)(ax^2 + bx + c) dx =0$Then the quadratic equation $ax...

Let $f:\mathbb{R} \rightarrow \mathbb{R}$ be a continuous function such that $\lim _{n\rightarrow \infty} f^n(x)$ exists for every $x \in \mathbb{R}$, where $f^n(x) = f ...

A coin with probability $p (0 < p < 1)$ of getting head, is tossed until a head appears for the first time. If the probability that the number of tosses required is even ...

Let $G =\{a_1,a_2, \dots ,a_{12}\}$ be an Abelian group of order $12$ . Then the order of the element $ ( \prod_{i=1}^{12} a_i)$ is$1$$2$$6$$12$

The reflection of the point $(1,2)$ with respect to the line $x + 2y =15$ is$(3,6)$$(6,3)$$(5,10)$$(10,5)$

The rank of the matrix $\begin{bmatrix} 0 &1 &t \\ 2& t & -1\\ 2& 2 & 0 \end{bmatrix}$ equals $3$ for any real number $t$$2$ for any real number $t$$2$ or $3$ depending o...

Let $V$ be the vector space of all $4 \times 4$ matrices such that the sum of the elements in any row or any column is the same. Then the dimension of $V$ is$8$$10$$12$$1...

The chance of a student getting admitted to colleges $A$ and $B$ are $60\%$ and $40\%$, respectively. Assume that the colleges admit students independently. If the studen...

The solution of the differential equation $$\frac{dy}{dx} = \frac{2xy}{x^2-y^2}$$is$x^2 + y^2 = cy$, where $c$ is a constant$x^2 + y^2 = cx$, where $c$ is a constant$x^2 ...

If $f(a)=2, \: f’(a) = 1, \: g(a) =-1$ and $g’(a) =2$, then the value of $$\lim _{x\rightarrow a}\frac{g(x) f(a) – f(x) g(a)}{x-a}$$ i...