In this post, we will discuss the questions from the previous year’s SLST exam on complex numbers with answers. The problems with solutions on complex numbers are given below. Previous Years SLST Questions on Complex Analysis Q1: If a+ib = $\dfrac{c+i}{c-i}$ where a, b,c are real numbers, then a2+b2=? [WB SLST 2016] (A) (c2+1)/(c2-1) (B) … Read more
In this post, we will discuss a few objective questions on definite integrals with answers. This will help us to take preparation for various exams, like board exams, SLST, and many more. Q1: Find $\int_0^\pi$|cosx| dx. [WB SLST 16] Answer: We know that cosx is positive for x∈ [0, π/2] and cosx has negative values … Read more
Definition of orthogonal trajectory Let us consider the two families of curves with the property: every member of either family cuts each member of the other family at right angles. Such two families of curves are called orthogonal trajectories of each other. Method of Finding orthogonal trajectories Question-Answer on orthogonal trajectory Question1: Find the orthogonal … Read more
Beta Function: The beta function B(m,n) = $\int_0^1$ xm-1(1-x)n-1 dx converges when m,n >0. Gamma Function: The gamma function Γ(n) = $\int_0^\infty$ e-xxn-1dx converges when n >0. Properties of Beta and Gamma Functions: The list of the properties of beta and gamma functions is given below: P1: B(m,n) = B(n,m) P2: B(m,n) = 2$\int_0^{\pi/2}$ sin2m-1θ … Read more
In this post, we will learn about Abel’s theorem (also known as Abel-Pringsheim’s Theorem) along with a few questions and answers. Statement of Abel’s Theorem: If {an} is a monotone decreasing sequence of positive terms, then limn→∞ nan= 0 is a necessary condition for the convergence of the series ∑an. Corollary: If {an} is a … Read more
In this post, we will learn about Cauch’s criterion for the convergence of a series. The statement of Cauch’s criterion for series along with some applications will be provided here. Statement of Cauch’s criterion for series Statement: The series $\sum_{n=1}^\infty a_n$ converges if and only if given any ε>0, there exists a positive integer N … Read more
In this post, we will learn about Rolle’s theorem along with examples. We will also discuss some of the related questions of Rolle’s theorem with answers. Rolle’s Theorem Statement Let f(x) be a real-valued function defined on [a, b]. If then there exists at least one element c in (a, b) such that $f'(c)=0$. Examples … Read more