An angle of rotation of axes so that `[sqrt(3)x-y+1=0` is transformed as `Y=K_(1)` is `(pi)/(K_(2)` then `(K_(2))/(K_(1))=` where `K_(1)`in Q,`K_(2)`in N

The angle of rotation of axes so that sqrt(3)x-y+1=0 transformed as y=k is (i) (pi)/(6)( ii) (pi)/(4)( iii) (pi)/(3)( iv) (pi)/(2)

The angle of rotation of the axes so that the equation where k is a constant is sqrt3x-y+5=0 may be reduced to the form Y=k where k is a constant is

60.A consecutive reaction occurs with two equilibria which co-exist together P(k_(1))/(k_(2) Q (k_(3))/(k_(4) R Where k_(1) , k_(2) , k_(3) and k_(4) are rate constants.Then the equilibrium constant for the reaction P harr R is (1) (k_(1)*k_(2)) / (k_(3)*k_(4) ) (2) (k_(1)*k_(4)) / (k_(2)k_(3) ) (3) k_(1) * k_(2) * k_(3)*k_(4) (4) (k_(1)*k_(3)) / (k_(2)k_(4)) ]]

Let u-=ax+by+a root(3)(b)=0,v-=bx-ay+b root(3)(a)=0,a,b in R be two straight lines.The equations of the bisectors of the angle formed by k_(1)u-k_(2)v=0 and k_(1)u+k_(2)v=0, for nonzero and real k_(1) and k_(2) are u=0 (b) k_(2)u+k_(1)v=0k_(2)u-k_(1)v=0 (d) v=0

A square of area 25 sq.units is formed by taking two sides as 3x+4y=k_(1) and 3x+4y=k_(2) then |k_(1)-k_(2)|=

For a double diferentiable function f(x) if f''(x) ge 0 then f(x) is concave upward and if f''(x) le 0 then f(x) is concave downward if f(x) is a concave upward in [a,b] and alpha , beta in [a,b] the (k_(1)(alpha)+k_(2)f(beta))/(k_(1)+k_(2)) ge f((k_(1) alpha +k_(2)beta)/(k_(1)+k_(2))) where K_(1)+K_(2) in R if f(x) is a concave downward in [a,b] " and "alpha, beta in [a,b] " then "(k_(1)(alpha)+k_(2)f(beta))/(k_(1)+k_(2)) le f((k_(1) alpha +k_(2)beta)/(k_(1)+k_(2))) where k_(1)+k_(2) in R then answer the following : Which of the following is true

A particle moves in the plane x y with constant acceleration a directed along the negative y-axis. The equation of motion of the particle has the form y = k_(1)x-k_(2)x^(2) , where k_(1) and k_(2) are positive constants. Find the velocity of the particle at the origin of coordinates.

The solution of the system of equations sin x sin y=(sqrt(3))/(4),cos x cos y=(sqrt(3))/(4) are x_(1)=(pi)/(3)+(pi)/(2)(2n+k);n,k in Iy_(1)=(pi)/(6)+(pi)/(2)(k-2n);n,k in Ix_(2)=(pi)/(6)+(pi)/(2)(2n+k);n,k in Iy_(2)=(pi)/(3)+(pi)/(2)(k-2n);n,k in I

Find the order of differential equation whose general solution is given by y=(k_(1)+k_(2))tan(x+k_(3))-k_(4)e^(x)+k_(5) where k_(1),k_(2),k_(3),k_(4),k_(5) are arbitrary constants.