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 P , Q be the A.M., G.M. respectively between any two rational numbers a and b , then P-Q is equal to (A)   (a-b)/a   (B)   (a+b)/2   (C)   (2ab)/(a+b)   (D)   ((sqrt(a)-sqrt(b))/sqrt(2))^2

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

Let vec a and vec b be unit vectors that are perpendicular to each other then [vec a+(vec a×vecb),vec b+(vec a×vec b), vec a × vec b] is equal to- (1)    1    (2)    0    (3)    -1    (4)    2

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

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

If alpha , beta gamma are the roots of the equation x^3+px^2+qx+r=0 , then (1-alpha^2)(1-beta^2)(1-gamma^2) is equal to (a)    (1+q)^2-(p-r)^2    (b)    (1+q)^2+(p+r)^2 (c)    (1-q)^2+(p-r)^2    (d)   none of these

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)

int (px^(p+2q-1)-qx^(q-1))/(x^(2p+2q)+2x^(p+q)+1) dx is equal to (1)    -x^p/(x^(p+q)+1)+C     (2)    x^q/(x^(p+q)+1)+C     (3)    -x^q/(x^(p+q)+1)+C     (4)    x^p/(x^(p+q)+1)+C