RAMAKRISHNA MISSION RECIDENTIAL COLLEGE (AUTONOMOUS)
Department of Statistics
Sample questions for UG admission test
1.
Objective type questions
I.
2
3
æ
If f(x) = x(x − 1)(x − 2) (x − 3) , then f (2) =_________________________________
100
II.
1
2
n=1 4n −1
lim
x2
x
=
= ______________________________________________________
__________________
lim
III.
xd0−
IV.
9
If [x] denotes the greatest integer ≤ x ,then
xd0+
x2
x
=
_______________________
¶ [ x ]dx =
0
_________________________
x2
V. The maximum area bounded by the ellipse m
y2
+ 1−m =1,0<m<1,
is
______________
VI.
e ,e ?
Which one is larger :
VII.
The maximum value of f(x) = e
VIII.
lim
nd∞
1
n
(1 +
1
2
+
1
3
+ ....... +
_________________________________________
−{xxx+xx−1x+xx−2x}
1
n
)=
is _________________________
____________________________________
IX. The number of factors of 360 is____________________________________
2
2
2
X. The number of roots of the equation : (x − 1) + (x − 2) + (x − 3) = 0 is
¶ max(sinx, cosx)dx=
XI.
_________________________________________________
0
3 2
The coefficient x yz
XII.
6
in the expansion of (x + y + z) is ____________________
2. Short answer type questions
I.
Consider a sequence of independent events A 1 , A 2 . . . .A n . . . . . with respective
probabilities p 1 , p 2 , . . .p n . . Find the probability (q n ) that at least one of the events will
qn .
occur. Hence, find lim
nd∞
II.
Draw the graph of y = x and sketch the area bounded by the curve y = x between the
lines x=1 and x=n+1. Hence, using an approximation to the area, show that
1
1+
1
2
+
1
3
+ . .. +
1
n
1
> log e (n + 1).
III.
Give an example of a function which is continuous everywhere but not differentiable
at three points.
IV.
Find the maximum area of a rectangle that can be inscribed in a circle of radius r.
V.
VI.
Is f(x) = sinx one-to-one mapping on R? How do you define sin-1x? Explain clearly.
A box contains tickets numbered 1 to 20. 3 tickets are drawn from the box with
replacement. Find the probability that the largest number on the tickets drawn is 7.