Question 21 (Differential Equation)
Let $y_1$ and $y_2$ are two solutions of the differential equation $y'' + P(x)y' + Q(x)y = 0$ for all $x \in I$, w…
Let $y_1$ and $y_2$ are two solutions of the differential equation $y'' + P(x)y' + Q(x)y = 0$ for all $x \in I$, w…
Let $G=M_{3\times 3}(\mathbb{Z})$, let $*$ denote componentwise multiplication of matrices, then- (a) $(G,*)$ is a group (b…
Let $y(x)$ is the solution of the D.E. $y' = y(y-2); y(0)=\alpha,$ then- (a) $y(x)$ is increasing for all $\alpha$ (b) …
Let $f$ be a holomorphic function on $0 < |z| < \epsilon$, $\epsilon > 0$ given by a convergent Laurent Series $\sum_…
Let $A$ is $2 \times 2$ matrix with $\det(A) \neq 0$, then under what condition $Ch(A) - Ch(A^{-1})$ is constant- (a) $\det…
Consider the vector space $P_n$ of real polynomials in $x$ of degree $\le n$. Define $T: P_2 \to P_3$ by $T(f(x)) = \int_0^x f…
Let $g_n(x) = \frac{nx}{1+n^2x^2}$, $x \in [0, \infty)$, let $n \to \infty$, then- (a) $g_n \to 0$ pointwise but not uniform…
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Ok