Page 68 - ISC-12

10Jai Baba Ki ISC Mathematics – Class XII by Gupta–Bansal

Matching-Matrix Type

In this section, each question contains statements given in two columns, which
have to be matched. The statements in Column I are labelled (A), (B), (C) and
(D), while the statements in Column II are labelled (p), (q), (r), (s) and (t). Any
given statement in Column I can have correct matching with ONE OR MORE
statement(s) in Column II. The appropriate bubbles corresponding to the answers
to these questions have to be darkened.

10. Match the following two lists:

List-I List-II

ˆ
ˆ
2
(A) In R , if the magnitude of the projection vector of the vector αi + βj (p) 1
√ √ √
ˆ
ˆ
on 3 i + j is 3 and if α = 2 + 3 β, then possible value(s) of |α|
is(are)
(B) Let a and b be real numbers such that the function (q) 2

−3ax − 2 if x < 1
 2
f(x) =
bx + a if x ≥ 1
 2
is differentiable for all x ∈ R. Then possible value(s) of a is(are)

(C) Let ω 6= 1 be a complex cube root of unity. If (r) 3
2 4n+3
2 4n+3
2 4n+3
(3 − 3ω + 2ω ) + (2 + 3ω − 3ω ) + (−3 + 2ω + 3ω ) = 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 (s) 4

is a positive real number such that a, 5, q, b is an arithmetic
progression, then the value(s) of |q − a| is(are)

(t) 5

(p) (q) (r) (s) (t)

(A) p q r s t

(B) p q r s t

(C) p q r s t

(D) p q r s t

[JEE 2015]