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 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

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

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

The co-ordinates of two fixed points A and B of a triangle ABC are (a,0) and (-a,0) respectively. If variable point C moves such that cot A+ cot B=lamda , (where lamda is a constant) then the locus of point C is:- (1)    y lamda =2a     (2)    y =lamda a     (3)    y a=2lamda     (4)     None of these.

The angle between the lines xcos alpha_1+ysin alpha_1=p_1 and xcos alpha_2+ysin alpha_2=p_2 is (A)    |alpha_1+alpha_2|     (B)    |alpha_1-alpha_2|     (C)    |2alpha_1|     (D)    |2alpha_2|    

The angle between the lines xcos alpha_1+ysin alpha_1=p_1 and xcos alpha_2+ysin alpha_2=p_2 is (A)    |alpha_1+alpha_2|     (B)    |alpha_1-alpha_2|     (C)    |2alpha_1|     (D)    |2alpha_2|    

The simplified form of [((a+1)^2/(a-1)^2+3)/((a-1)^2/(a+1)^2+3)]/((a^3+1)/(a^3-1)-(2a)/(a-1)] is: a.    a-1 b.    1-a c.    -1 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 solutions of z^2+bar z=0 is (a) 1           (b) 2 (c) 3           (d) 4