Q2.Position vectors of points A, B, C, etc., with respect to the origin O are generally denoted by
Answer : Option BExplaination / Solution: Position vectors of any point in space are usually calculated from the origin, so we write OA−→−,OB−→−,OC−→− three points A ,B,C in space to represent the origin as the initial point.
Q6.Degree of a differential equation, when the equation is polynomial equation in y′ is
Answer : Option BExplaination / Solution:
The power or index of the highest ordered derivative in the polynomial is the degree of the differential equation provided equation is in the standard form.
PQ−→−is a vector joining two points P(x1, y1, z1) and Q(x2, y2, z2).If ∣∣PQ¯¯¯¯¯¯¯¯∣∣=d,Direction cosines of PQ−→−are
Answer : Option AExplaination / Solution: since we know Direction cosines of a line are coefficient of i,j,k of a unit vector along that line,first find a vector PQ−→−=(x2−x1)iˆ+(y2−y1)jˆ+(z2−z1)kˆ then to convert it unit vector divide by its magnitute |PQ−→−| the coefficient of this unit vector will be x2−x1d,y2−y1d,z2−z1d
Q10.Let f be a real valued function defined on (0, 1) ∪(2, 4) such that f ‘ (x) = 0 for every x, then
Answer : Option DExplaination / Solution: f ‘ (x) =0 f (x) is constant in ( 0 , 1 ) and also in ( 2, 4 ). But this does not mean that f ( x) has the same value in both the intervals . However , if f ( c ) =f ( d ) , where c ∈( 0 , 1 ) and d ∈ ( 2, 4) then f ( x ) assumes the same value at all x ∈( 0 ,1 ) U (2, 4 ) and hence f is a constant function.
Total Question/Mark :
Scored Mark :
Mark for Correct Answer : 1
Mark for Wrong Answer : -0.5
Mark for Left Answer : 0