Tricks of Differentiation | Trick 1 & 2 | Supershort cut | Infinite Series | GV sir | Matrix | Dr.Gv

Each question contains statements given in two columns which have to be matched. Statements a,b,c,d in column I have to be matched with statements p,q,r,s in column II. If the correct matches are a-p, q-s, b-q, r c-p, q and d-s, then the correctly bubbled 4x4 matrix should be as follows: Figure Column I, Column II: Differential equation order 1, p. of all parabolas whose axis is the x-axis order 2, q. of family of curves y=a(x+a)^2, whre a is an arbitrary constant degree 1, r. (1+3(dy)/(dx))^(2/3)=(4d^3y)/(dx^3) degree 3, s. of family of curve y^2=2c(x+sqrt(c)), where c >0

A spring of force constant k is cut into lengths of ratio 1 : 2 : 3 . They are connected in series and the new force constant is k'. Then they are connected in parallel and force constant is k'. Then k' : k" is :

A spring of force constant k is cut into lengths of ratio 1 : 2 : 3 . They are connected in series and the new force constant is k'. Then they are connected in parallel and force constant is k'. Then k' : k" is :

Assertion A spring of force constatn k is cut in to two piece having lengths in the ratio 1:2 The force constant of series combination of the two parts is (3k)/(2) The spring connected in series are represented by k=k_(1)+k_(2)

Let y(x) is solution of differential equation (y^2 – x) (dy)/(dx) = 1 and y(0) = 1, then find the value of x where curve cuts the x-axis

A continuous and differentiable function y=f(x) is such that its graph cuts line y=m x+c at n distinct points. Then the minimum number of points at which f''(x)=0 is/are (a) n-1 (b) n-3 (c) n-2 (d) cannot say

A continuous and differentiable function y=f(x) is such that its graph cuts line y=m x+c at n distinct points. Then the minimum number of points at which f^('')(x)=0 is/are n-1 (b) n-3 (c) n-2 (d) cannot say

The 1^(st) , 2^(nd) and 3^(rd) terms of an arithmetic series are a , b and a^(2) where 'a' is negative. The 1^(st) , 2^(nd) and 3^(rd) terms of a geometric series are a , a^(2) and b respectively. The sum of infinite geometric series is

If A is a square matrix of order 2xx2 such that |A|=27 , then sum of the infinite series |A|+|1/2A|+|1/4 A|+|1/8 A|+... is equal to _______ .

Examine the continuity at x =0 of the sum function of the infinite series: x /( 1+x) + x / ((x+1)(2x+1)) + x/((2x+1)(3x+1)) + ........................oo