Let `A=[(0, alpha),(0,0)]` and `(A+I)^(50) A=[(a,b),(c,d)]`. Then the value of `a+b+c+d` is

Let A=[(0, alpha),(0,0)] and (A+I)^(50) -50A=[(a,b),(c,d)] . Then the value of a+b+c+d is

Let A=[(2,1),(0,3)] be a matrix. If A^(10)=[(a,b),(c,d)] then prove that a+d is divisible by 13.

If (21. 4)^a=(0. 00214)^b=100 , then the value of 1/a-1/b is 0 (b) 1 (c) 2 (d) 4

If the points (a, 0), (b,0), (0, c) , and (0, d) are concyclic (a, b, c, d > 0) , then prove that ab = cd .

Let a , b and be the roots of the equation x^2-10 xc -11d =0 and those roots of c and d of x^2-10 a x-11 b=0 ,dot then find the value of a+b+c+d

If an a triangle A B C , b=3ca n d C-B=90^0, then find the value of tanB

Let a,b,c,d and e be positive real numbers such that a+b+c+d+e=15 and ab^2c^3d^4e^5=(120)^3xx50 . Then the value of a^2+b^2+c^2+d^2+e^2 is ___________.

In A B C , if (sinA)/(csinB)+(sinB)/c+(sinC)/b=c/(a b)+b/(a c)+a/(b c), then the value of angle A is 120^0 (b) 90^0 (c) 60^0 (d) 30^0

If A(-2, -1), B(a, 0), C(4, b) and D(1, 2) are the vertices of a parallelogram, find the values of a and b.

For a , b , c in R-{0} , let (a+b)/(1-ab) , b , (b+c)/(1-bc) are in A.P. If alpha , beta are the roots of the quadratic equation 2acx^(2)+2abcx+(a+c)=0 , then the value of (1+alpha)(1+beta) is