JEE Advanced 2015 Paper 1 Mathematics Q19

Mathematics

Problem

Match each problem in Column I with every possible value in Column II. Column I — A: In

\mathbb R^2

, if the magnitude of the projection vector of

\alpha\hat i+\beta\hat j

\sqrt3\hat i+\hat j

\sqrt3

and if

\alpha=2+\sqrt3\beta

, then possible value(s) of

|\alpha|

is (are); B: Let

a

and

b

be real numbers such that

f(x)=\begin{cases}-3ax^2-2,&x<1,\\bx+a^2,&x\ge1\end{cases}

is differentiable for all

x\in\mathbb R

. Then possible value(s) of

a

is (are); C: Let

\omega\ne1

be a complex cube root of unity. If

(3-3\omega+2\omega^2)^{4n+3}+(2+3\omega-3\omega^2)^{4n+3}+(-3+2\omega+3\omega^2)^{4n+3}=0

, then possible value(s) of

n

is (are); D: Let the harmonic mean of two positive real numbers

a

and

b

be 4. If

q

is a positive real number such that

a,5,q,b

is an arithmetic progression, then the value(s) of

|q-a|

is (are) Column Ii — P: 1; Q: 2; R: 3; S: 4; T: 5