Page 18 - ISC-12

Single Correct Choice Type Jai Baba Ki15

72. Consider the system of equations
x − 2y + 3z = −1
−x + y − 2z = k
x − 3y + 4z = 1

STATEMENT-1: The system of equations has no solution for k 6= 3.
and

1 3 −1

STATEMENT-2: The determinant −1 −2 k 6= 0, for k 6= 3.

1 4 1

(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for
Statement-1.
(C) Statement-1 is True, Statement-2 is False.
(D) Statement-1 is False, Statement-2 is True.

[JEE 2008]

73. Consider the system of equations
ax + by = 0

cx + dy = 0
where a, b, c, d ∈ {0, 1}.
3
STATEMENT-1: The probability that the system of equations has a unique solution is .
8
and
STATEMENT-2: The probability that the system of equations has a solution is 1.

(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for
Statement-1.
(C) Statement-1 is True, Statement-2 is False.
(D) Statement-1 is False, Statement-2 is True.

[JEE 2008]

74. Let a solution y = y(x) of the differential equation
√ p
2
2
x x − 1 dy − y y − 1 dx = 0
2
satisfy y(2) = √ .
3
π

−1
STATEMENT-1: y(x) = sec sec x − .
6
and √ r
1 2 3 1
STATEMENT-2: y(x) is given by = − 1 − .
y x x 2
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.