Statement-1 : If `|x+3|+5=|x+8|` then `xgeq-3` Statement-2 : `|a|+|b|=|a+b|adotbdotgeq0`

Statement 1: If |x+3|+5=|x+8|t h e nxgeq-3 Statement 2: |a|+|b|=|a+b| a bgeq0

Statement -1 : lim_( x to 0) (sin x)/x exists ,. Statement -2 : |x| is differentiable at x=0 Statement -3 : If lim_(x to 0) (tan kx)/(sin 5x) = 3 , then k = 15

lim_(x to 0) (A "sin" x + B log (1 + x^(2)) + C (1 - cos x))/(x^(2)) = 2 then Statement-1 : A = 1 Statement-2 : 2B + C = 4 Statement-3 A + B + C = 0

Let a, b R be such that the function f given by f(x)""=""ln""|x|""+""b x^2+""a x ,""x!=0 has extreme values at x""=""1 and x""=""2 . Statement 1: f has local maximum at x""=""1 and at x""=""2 . Statement 2: a""=1/2"and"b=(-1)/4 (1) Statement 1 is false, statement 2 is true (2) Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1 (3) Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1 (4) Statement 1 is true, statement 2 is false

Consider the determinant Delta = |[a_1+b_1x^2,a_1x^2+b_1,c_1],[a_2+b_2x^2,a_2x^2+b_2,c_2],[a_3+b_3x^2,a_3x^2+b_3,c_3]| = 0 , \ w h e r e \ a_i ,b_i , c_i in R \ (i = 1,2,3) \ a n d \ x in R . Statement 1: The value of x satisfying Delta=0 are x=1,-1. Statement 2: If |[a_1,b_1,c_1],[a_2,b_2,c_2],[a_3,b_3,c_3]|=0,t h e n \ Delta=0.

Statement 1: If 27 a+9b+3c+d=0, then the equation f(x)=4a x^3+3b x^2+2c x+d=0 has at least one real root lying between (0,3)dot Statement 2: If f(x) is continuous in [a,b], derivable in (a , b) such that f(a)=f(b), then there exists at least one point c in (a , b) such that f^(prime)(c)=0.

Statement 1 is True: Statement 2 is True; Statement 2 is a correct explanation for statement 1 Statement 1 is true, Statement 2 is true;2 Statement 2 not a correct explanation for statement 1. Statement 1 is true, statement 2 is false Statement 1 is false, statement 2 is true Statement I: If a=y^2,\ b=z^2, c=x^2,\ t h e n8(log)_a x^3dot(log)_b y^3dot(log)_c z^3=27 Statement II: (log)_b adot(log)_c b=(log)_c a ,\ also (log)_b a=1/("log"_a b) a. A b. \ B c. \ C d. D

Statement - 1 : If x gt 1 then log_(10)x lt log_(3)x lt log_(e )x lt log_(2)x . Statement - 2 : If 0 lt x lt 1 , then log_(x)a gt log_(x)b implies a lt b .

Each question has four choice: a, b, c and d, out of which only one is correct. Each question contains Statement 1 and Statement 2. Find the correct answer. Both the Statements are true but Statement 2 is the correct explanation of Statement 1. Both the Statement are True but Statement 2 is not the correct explanation of Statement 1. Statement 1 is True and Statement 2 is False. Statement 1 is False and Statement 2 is True Statement 1: The lines (a+b)x+(a-2b)y=a are con-current at the point (2/3,1/3)dot Statement 2: The lines x+y-1=0 and x-2y=0 intersect at the point (2/3,1/3)dot

Statement 1 is True: Statement 2 is True; Statement 2 is a correct explanation for statement 1 Statement 1 is true, Statement 2 is true;2 Statement 2 not a correct explanation for statement 1. Statement 1 is true, statement 2 is false Statement 1 is false, statement 2 is true Statement I: If (log)_(((log)_5x))5=2,\ t h n\ x=5^(sqrt(5)) Statement II: (log)_x a=b ,\ if\ a >0,\ t h e n\ x=a^(1//b) a. A b. \ B c. \ C d. D