As you are looking for IIA Entrance Exam paper of last year so on your demand I am providing same for you :

1. Black-body radiation, at temperature Ti fills a volume V . The system expands adiabatically and
reversibly to a volume 8 V . The final temperature Tf = xTi, where the factor x is equal to
(a) 0.5 (b) 2.8 (c) 0.25 (d) 1
2. A particle of mass m, constrained to move along the x-axis. The potential energy is given by, V (x) =
a + bx + cx2, where a, b and c are positive constants. If the particle is disturbed slightly from its
equilibrium position, then it follows that
(a) it performs simple harmonic motion with period 2π
√
(m/2c)
(b) it performs simple harmonic motion with period 2π
√
(ma/2b2)
(c) it moves with constant velocity
(d) it moves with constant acceleration
3. Consider a square ABCD, of side a, with charges +q,−q,+q,−q placed at the vertices, A, B, C, D
respectively in a clockwise manner. The electrostatic potential at some point located at a distance r
(where r ≫ a) is proportional to
(a) a constant (b) 1/r (c) 1/r2
(d) 1/r3
4. The general solution of dy/dx − y = 2ex is (where C is an arbitrary constant)
(a)
e2x + Cex
(b) 2xex + Cex
(c) 2xex + C (d) ex2
+ C
5. The value of lim
θ→0
(ln(1 + sinθ)
sinθ
)
is
(a)
∞ (b) −∞ (c) 1 (d) 0

IIA Entrance Exam paper