If `abx^2=(a-b)^2(x+1)`, then the value of `1+4/x+4/x^2` is:
a.    `(a+b)/(a-b)`
b.    `(a+b)^2/(a-b)^2`
c.    `(a+b)/(a-b)^2`
d.    `1`

If (xy)/(x+y)=a , (xz)/(x+z)=b and (yz)/(y+z)=c , where a , b and c are other than zero, then x equal a.    (abc)/(ab+bc+ca) b.    (2abc)/(ab+bc+ca) c.    (2abc)/(ab+ac-bc) d.    (2abc)/(ac+bc-ab)

Let the roots of the equation (3x^3-x^2+x-1)/(3x^3-x^2-x+1)=(4x^3+7x^2+x+1)/(4x^3+7x^2-x-1) be x_1 , x_2 and x_3 , then the value of x_1+x_2+x_3 is a.    0 b.    1 c.    -1 d.   None of these

If sin(theta + alpha)=cos(theta+alpha), then the value of tan theta is: a.    1-tan alpha b.    (1-tan alpha)/(1+tan alpha) c.    1+tan alpha d.    None of these

Let y=1/(2+1/(3+1/(2+1/(3+.....)))) the value of y is: a.    +-(sqrt(15)-3)/2 b.    (sqrt(15)-3)/2 c.    (sqrt(15)+3)/2 d.    None of these

In an AP, S_p=q , S_q=p . Then S_(p+q) is equal to: a.     0 b.     -(p+q) c.     (p+q) d.     pq

If a^(1/2)+b^(1/2)-c^(1/2)=0 , then the value of (a+b-c)^2 is: (A)    2ab    (B)    2bc    (C)    4ab    (D)    4ac

If S_1 is the sum of an AP of n odd number of terms and S_2 be the sum of terms of series in odd places of the same AP, then (S_1)/(S_2)= a.     (2n)/(n+1) b.     n/(n+1) c.     (n+1)/(2n) d.     (n+1)/n

The number of integral pairs (x,y) satisfying the equation (x-y)^2+2y^2=27 is: a.    8 b.    7 c.    6 d.    5

If x=3-sqrt(5) , then sqrt(x)/(sqrt(2)+sqrt(3x-2))=_ A.     1/sqrt(5) B.     sqrt(5) C.     sqrt(3) D.     1/sqrt(3)

The number of solutions of z^2+bar z=0 is (a) 1           (b) 2 (c) 3           (d) 4