`P(1,1,1) and Q(lamda,lamda,lamda)` are two points in space such that `PQ=sqrt(27)` the value of `lamda` can be (A) -2 (B) -4 (C) 4 (D) 2

If (1,2,4) and (2,-lamda,-3) are the initial and terminal points of the vector hati+5hatj-7hatk then the value lamda is equal to (A) 7 (B) -7 (C) -5 (D) 5

If f (x)= tan ^(-1) (sgn (n ^(2) -lamda x+1)) has exactly one point of discontinuity, then the value of lamda can be:

A plane passing through three points (-lamda^2, 1, 1) (1, -lamda^2, 1),(1, 1, -lamda^2) also passes through (-1,-1,1) then set consisting all the real value of lamda is (A) {-sqrt3,sqrt3} (B) {3,-3} (C) {-1,1} (D) {sqrt3, -sqrt3}

If the straighat lines x=1+s,y=-3-lamdas,z=1+lamdas and x=t/2,y=1+t,z=2-t with parameters s and t respectively, are coplanar, then lamda equals (A) -1/2 (B) -1 (C) -2 (D) 0

If two circles with cenre (1,1) and radius 1 and circle with centre (9,1) and radius 2 lies opposite side of straight line 3x+4y=lamda . The set of values of lamda is (A) [12, 21] (B) [13,22] (C) [10,18] (D) [15,24]

If the vectors veca=2hati-hatj+hatk, vecb=hati+2hatj-hat(3k) and vecc= 3hati+lamda hatj+5hatk are coplanar the value of lamda is (A) -1 (B) 3 (C) -4 (D) -1/4

If ratio of the roots of the quadratic equation 3m^2x^2+m(m-4)x+2=0 is lamda such that lamda+1/lamda=1 then least value of m is (A) -2-2sqrt3 (B) -2+2sqrt3 (C) 4+3sqrt2 (D) 4-3sqrt2

If ratio of the roots of the quadratic equation 3m^2x^2+m(m-4)x+2=0 is lamda such that lamda+1/lamda=1 then least value of m is (A) -2-2sqrt3 (B) -2+2sqrt3 (C) 4+3sqrt2 (D) 4-3sqrt2

Let f (x) = (cos ^(2) x)/(1+ cos x+cos ^(2)x )and g (x) =lamda tan x+(1-lamda) sin x-x, where lamda in R and x in [0, pi//2). The values of 'lamda' such that g '(x) ge 0 for any x in [0, pi//2):

If a and b are positive integers such that a^(2)-b^(4)=2009, then a+b^(2)=lamda^(2). "The value"|lamda| is