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Given : A circle, 2x^2+""2y^2=""5 and a ...

Given : A circle, `2x^2+""2y^2=""5` and a parabola, `y^2=""4sqrt(5)""x` . Statement - I : An equation of a common tangent to these curves is `y="x+"sqrt(5)` Statement - II : If the line, `y=m x+(sqrt(5))/m(m!=0)` is their common tangent, then m satisfies `m^4-3m^2+""2""=0.` (1) Statement - I is True; Statement -II is true; Statement-II is not a correct explanation for Statement-I (2) Statement -I is True; Statement -II is False. (3) Statement -I is False; Statement -II is True (4) Statement -I is True; Statement -II is True; Statement-II is a correct explanation for Statement-I

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Given : a circle 2x^(2)+2y^(2)=5 and a parabola y^(2)=4sqrt(5)x . Statement-I : An equation of a common tangent to these curves is y=x+sqrt(5) . Statement-II : If the line y=mx+(sqrt(5))/(m)(m ne 0) is their common tangent, then m satisfies m^(4)-3m^(2)+2=0 .

Given :A circle 2x^(2) +2y^(2) =5 and a parabola y^(2) =4 sqrt5 x. Statement -I : an equation of a common tangent to these curves is y=x+sqrt5. Statement -II - If the line, y= mx+ ( sqrt5)/( m ) (mne0) is their common tangent ,then m satisfies m^(4) -3m ^(2) +2=0

Statement - I : The value of the integral int_(pi//6)^(pi//3)(dx)/(1+sqrt(tanx)) is equal to pi/6 . Statement - II : int_a^bf(x)dx=int_a^bf(a+b-x)dxdot (1) Statement - I is True; Statement -II is true; Statement-II is not a correct explanation for Statement-I (2) Statement -I is True; Statement -II is False. (3) Statement -I is False; Statement -II is True (4) Statement -I is True; Statement -II is True; Statement-II is a correct explanation for Statement-I

Consider : Statement I : (phat~""q)hat(~""phatq) is a fallacy. Statement II : (pvecq)harr(~""qvec~""p) is a tautology. (1) Statement - I is True; Statement -II is true; Statement-II is not a correct explanation for Statement-I (2) Statement -I is True; Statement -II is False. (3) Statement -I is False; Statement -II is True (4) Statement -I is True; Statement -II is True; Statement-II is a correct explanation for Statement-I

If A is 2 x 2 invertible matrix such that A=adjA-A^-1 Statement-I 2A^2+I=O(null matrix) Statement-II: 2|A|=1 (i) Statement-I is true, Statement-II is true; Statement-II is a correct explanation for Statement-I (2) Statement-I is true, Statement-II is true; Statement-II is not a correct explanation for Statement-I. 3) Statement-I is true, Statement-II is false. (4) Statement-I is false, Statement-II is true.

Statement-1: The point A(3, 1, 6) is the mirror image of the point B(1, 3, 4) in the plane x""""y""+""z""=""5 . Statement-2: The plane x x""""y""+""z""=""5 bisects the line segment joining A(3, 1, 6) and B(1, 3, 4). (1) Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation for Statement-1 (2) Statement-1 is true, Statement-2 is false (3) Statement-1 is false, Statement-2 is true (4) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1

Statement-I int_0^9[sqrtx]dx=13, Statement-II int_0^(n^2) [sqrt x]dx=(n(n-1)(4n+1))/6, n in N (where [.] denotes greatest integer function) (1) Statement-I is true, Statement-II is true Statement-II is a correct explanation for Statement-I (2) Statement-I is true, Statement-II is true Statement-II is not a correct explanation for Statement-I, (3) Statement-I is true, Statement-II is false. (4) Statment-I is false, Statement-II is true.