Let fR→R be a function we say that f has
property 1 if h→0lim∣h∣f(h)−f(0) exist and is finite.
Property 2 if h→0limh2f(h)−f(0) exist and is finite. Then which of the following options is/are correct?
Which of the following values of αsatisfying the equation ∣∣(1+α)2(1+2α)2(1+3α)2(2+α)2(2+2α)2(2+3α)2(3+α)2(3+2α)2(3+3α)2∣∣=−648α?−4b. 9c. −9d. 4
Let a,b,xandy be real numbers such that a−b=1andy=0. If the complex number z=x+iy satisfies Im(z+1az+b)=y , then which of the following is (are) possible value9s) of x? (a)−1−1−y2 (b) 1+1+y2(c)−1+1−y2 (d) −1−1+y2
Football teams T1 and T2 have to play two games against each other. It is assumed that theoutcomes of the two games are independent. The probabilities of T1 winning, drawing andlosing a game against T2 are1/ 2,and1/6,1/3respectively. Each team gets 3 points for a win,1 point for a draw and 0 point for a loss in a game. Let X and Y denote the total pointsscored by teams T1 and T2, respectively, after two gamesP (X=Y) is
Â·If the normals of the parabola y2=4x drawn at the end points of its latus rectum are tangents to the circle (x−3)2(y+2)2=r2 , then the value of r2 is
Let f:R→Rbe a differentiable function with f(0)=0. If y=f(x)satisfies the differential equation dxdy=(2+5x)(5x−2)1, then the value of (lim)x→∞f(x)is ______