If `a+c+e=0` and `b+d=0`, then `ax^4+bx^3+cx^2+dx+e` is exactly divisible by
(1)   `x+1`       (2)  `x-1`
(3)   Both (1) & (2)       (4)   None of these

The distance of the point (2,3) from the line x-2y+5=0 measured in a direction parallel to the line x -3y=0 is: (A)   2sqrt(10)     (B)   sqrt(10)     (C)   2sqrt(5)     (D)   None of these

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 int (1+xtanx)^(-2) dx=1/(x+f(x))+c; then value of f(x) is (1)   xtanx    (2)   cotx    (3)   tanx    (4)   tan^2x

A variable takes the values of 0 , 1 , 2 ,....., n with frequencies proportional to the binomial coefficients C_0 , C_1 , C_2 ,......, C_n , then mean of the distribution is (1)   (n(n+1))/4       (2)   n/2       (3)   (n(n-1))/2       (4)   (n(n+1))/2       

If 2^33 is divided by 17 , then the remainder is (1)    15        (2)    2         (3)    4         (4)    9

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.

If the lines ax+y+1=0 , x+by+1=0 and x+y+c=0 , ( a , b , c being distinct and different from 1 ) are concurrent, then 1/(1-a)+1/(1-b)+1/(1-c)= (A)    0    (B)    1    (C)    1/(a+b+c)    (D)   None of these

If the lines ax+y+1=0 , x+by+1=0 and x+y+c=0 , ( a , b , c being distinct and different from 1 ) are concurrent, then 1/(1-a)+1/(1-b)+1/(1-c)= (A)    0    (B)    1    (C)    1/(a+b+c)    (D)   None of these

If p_(n+1)=sqrt(1/2(1+p_n)) , then cos(sqrt(1-p_0^2)/(p_1p_2p_3...to oo)) (a)   1    (b)   -1    (c)   p_0    (d)   1/p_0     (e)  None of these

The measure of the angle between the internal and external bisectors of an angle is: (A)   60°     (B)   70°      (C)   80°      (D)   90°