Column I, Column II `y=(x^2-2x+4)/(x^2+2x+4),x in R ,t h e ny c a nb e` , p. `1` `y=(x^2-3x-2)/(2x-3),x in R ,t h e ny c a nb e` , q. `4` `y=(2x^2-2x+4)/(x^2-4x+3),x in R ,t h e ny c a nb e` , r. `-3` `x^2-(a-3)x+2<0,AA,x in (-2,3),t h a nac a nb e` , s. `-10`

y=4x^2 + e^(3x) find y'

Let f: R->R \ w h e r e \ f(x)=(x^2+4x+7)/(x^2+x+1) . Is f(x) \ on e \ on e ?

Let (x , y) be such that sin^(-1)(a x)+cos^(-1)(y)+cos^(-1)(b x y)=pi/2dot Match the statements in column I with statements in column II Ifa=1a n db=0,t h e n(x , y) , (p) lies on the circle x^2+y^2=1 Ifa=1a n db=1,t h e n(x , y) , (q) l i e son(x^2-1)(y^2-1)=0 Ifa=1a n db=2,t h e n(x , y) , (r) lies on y=x Ifa=2a n db=2,t h e n(x , y) , (s) lies on (4x^2-1)(y^2-1)=0

int e^(x^4) (x + x^3 +2x^5) e^(x^2) dx is equal to

Solve the equation x^2-x+1=1/2+sqrt(x-3/4), w h e r e xgeq3/4

If f: R^+ to R , f(x) + 3x f(1/x)= 2(x+1),t h e n find f(x)

f: R->R is defined by f(x)=(e^(x^2)-e^(-x^2))/(e^(x^2)+e^(-x^2)) is :

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 match are a-p, a-s, b-r, c-p, c-q, and d-s, then the correctly bubbled 4 x 4 matrix should be as follows: fig Column I, Column II If L=""("lim")_(xvec-1)((7-x)^(1/3)-2)/((x+1)),t h e n12 L= , p. -2 If L=""("lim")_(xvecpi/4)(tan^3x-tanx)/(cos(x+pi/4)),t h e n-L/4= , q. 2 If L=""("lim")_(xvec1)((2x-3)(sqrt(x)-1))/(2x^2+x-3),t h e n20 L= , r. 1 If L=""("lim")_(xvecoo)(logx^n-[x])/([x]),w h e r en in N ,([x] denotes greatest integer less than or equal to x),t h e n-2L= , s. -1

Let a=int_0^(log2) (2e^(3x)+e^(2x)-1)/(e^(3x)+e^(2x)-e^x+1)dx , then 4e^a =

Column I, Column II Area enclosed , q. 1. sq. units The smaller area included between the curves sqrt(x)+sqrt(|y|)=1 and |x|+|y|=1 , r. 4 sq. units Area bounded by the curves y=[(x^2)/(64)+2](w h e r e[dot]d e not e s the greatest integer function), y=x-1a n dx=0 above the x-axis., s. 2/3 sq. units