Match the column Column-I Column-II
a. If `||x-1|-2|geq3, then x in ` p. `[-2,-1]uu[5,6]`
b. If `||x-1|-2|lt=3,t h e nx in ` q. `[-4,6]`
c. If `2 lt= |x-3|lt=3,t h e nx in ` r. `(-oo,-4]uu[6,oo)`
d. If `2lt=||x-3|-1|lt=3,t h e nx in ` s. `[0,1]uu[5,6]`

Solve 1lt=|x-2|lt=3.

If |x-1|>5, then a. x in (-4,6) b. x in [-4,6] c. x in (-oo,-4)uu(6,oo) d. x in (-oo,-4)uu[6,oo)

If |x+2|lt=9 then x in (-7, 11) b. x in [-11 ,7] c. x in (-oo,7)uu(11 ,oo) d. x in (-oo,-7)uu[11 ,oo)

If x<0,t h e ntan^(-1)x is equal to

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

If domain of f(x) is [1,3] , then the domain of f((log)_2(x^2+3x-2))i s [-5,-4]uu[1,2] b. [-13 ,-2]uu[3/5,5] c. [4,1]uu[2,7] d. {-3,2}

Complete solution set of the inequation (x^2-1)(x^2-6x+8)geq0 is (a) x in [-1,1]uu[2,4] (b) x in (-oo,-1)uu[1,2]uu[4,oo] (c) x in [-1,2]uu[4,oo] (d) none of these

Match the column Column I, Column II If x=3,t h e n(log)_4(2(log)_3(1+(log)_2(1+3Log_3x))) is equal to, p. 3 If x=100 , then 3^((log)_3logsqrt(x))-logx+log^2x is equal to, q. 1 If one of the root of the equation 2((log)_xsqrt(5))^2-3(log)_x(a)+1=0 is sqrt(5) , then the other root is, r. 1/2 If (log)_2(4. 3^x-6)-(log)_2(9^x-6)=1, then x is equal to, s. 5

Solution set of |x^2-4|lt=5-|x^2-9| is [-3,3] (2) [-3,-2]uu[2,3] [-2,2]uu[3,4] (4) [-2,4]

Evaluate the following integral: int_2^4f(x)dx ,\ w h e r e\f(x)={7x+3,\ if\ 1lt=xlt=3 , w h e r e\f(x)=8x \ if\ 3lt=xlt=4