Model test paper
 M.Sc.(Statistics) Entrance test 

Note:    1.      Each question carries 2 marks.
                2.      There will be no negative marking.
                3.      Each question has four possible answers out of which one is 
                          correct.
4.	    Candidates are required to darken the corresponding circle in 
         the OMR answer-sheet supplied separately.

1.      The sequence {0, 1, 0, 1/2, 0, 1/3, …}has the nth term
         (a)                                      (b)             
         (c)                                        (d)  none of these.

2.       The sequence {1, 0, 1, 0, 1, 0 …} is 
          (a) increasing	                                   (b) decreasing           
          (c) monotone	                                  (d) none of these.

3.       The series  2 + 4 + 6 + 8 + … .. is 
           (a) divergent	                                   (b) convergent 	       
           (c) unbounded                                     (d) none of these

4.       The function y = | log x |  is
           (a) discontinuous at x = 1	            (b) differentiable at  x =1
           (c) not differentiable at x =1                (d) none of these

5.       The difference and the quotient of complex numbers are
         (a)  -1+5i,                               (b) -5+i,  
         (c)  -1+5i,                               (d) none of these

6.        For  z = 4+3i, the value of  is
           (a)  44                                                        (b)  - 44                     
           (c)  33                                                        (d)  - 33
        
7.        The set S is closed if  
           (a)  it does not contain its boundary points (b) it have no boundary points
           (c) it contains its boundary points 	        (d)  none of these

8.         The diagonal (1,1,1,……..,1) is   
           (a) idempotent matrix                                (b)  rectangular matrix
           (c) non-symmetric matrix                          (d)  none of these
9.         The rank of the matrix  A= is
         (a) 1                                                              (b)  2                         
         (c)  3                                                             (d)  4

10.       The value of the determinant   is
           (a)  zero                                                      (b)  2                                                           
           (c)  9                                                           (d)  none of these

11.	The Binominal distribution have the mean 
            (a)  n2p		                                    (b)  np	
            (c)  npq	                                    (d) None of these

12.	The variance of Poisson distribution is given by 
           (a)  l		                                (b)  1/l		
           (c) 1/l2	                                            (d) None of these

13.	The normal distribution have number of parameters 
            (a)  One		                   (b) Two 	
            (c) Three	                               (d) Four

14	What is the probability that one-leap year have 53 Sundays ?
            (a)  1/6                                             (b)  1/5	
            (c)  1/4		                                (d)  1/7

15.	The mean and variance of a standardized random variable are 
            (a)  (1,0) 	                                (b)   (0,1)	
            (c)  ( 0,0 )		                    (d) (1,1 )

16        For the constants   a     and b  , E ( aX + b ) is 
           (a)  aE(X)+b	                                         (b)  E(X)		
           (c)  a E (X)	                                         (d)  None of thes
                
17.       In a sample survey, the chances of young professionals courses MBA degree, MCA   
           degree or both are 0.86, 0.35 and 0.29 respectively. What is the probability of owing   
           either or both degrees?
            (a)  0.82                                                     (b)  0.92                  
            (c)  0.08                                                     (d)  0.18

18.       If random variable X has the probability function f(x) = k/x! (x=0,1,2,3,…..), the 
            value of k is 
            (a)  1/e                                                       (b)  e                       
            (c)  1-1/e                                                    (d)  none of these

19.      The random variable X takes the values 0,1, 2 and 3 with probabilities 1/125, 123/125, 
           48/125, and 64/125, the value of E(X) is 
         
           (a)  12/4                                                      (b)  12/7                    
           (c)  12/5                                                      (d)  none of these

20.       In Physics ‘mean’ represents 
           (a)  centre of gravity                                    (b) moment of inertia
           (c)  gravitational forces                               (d)  none of these

21.    A plane passes through (1,-2,1) and is perpendicular to two planes 2x - 2y + z = 0 
         and x – y + 2z = 4. The distance of the plane from the point (1,2,2) is 
         (a)  0                                                               (b)  1   
         (c)                                                            (d)  2  

22.       When , the Binomial distribution can be approximated by 
            (a)  Bernoulli distribution	                    (b)  Uniform distribution	
            (c)  Poisson distribution	                    (d)  none of these

23.       What is the probability of getting two ‘six’ in rolling a die four times?
            (a)  179/1296                                              (b)  170/1296           
            (c)  2/1296                                                  (d)  171/1296

24.       In normal distribution, the curve of f(x) is symmetric with respect to 
            (a)                                                     (b)            
            (c)                                                 (d)  none of these

25.       The range of the Bernoulli random variable is the set 
            (a)                                                      (b)  set of real numbers  
            (c)  set of integers                                      (d)  none of these

26.     The value of the variable corresponding to the highest point of a frequency
    distribution curve represents:
          (a) mean                                                  (b)  median          
          (c)  mode                                                 (d)  none of these

27.     In a class test, 40 students out of 50 passed with mean marks 6.0 and the overall       
           average of the class marks was 5.5. The average marks of the students who failed  
           were  
           (a)  2.5                                                   (b)  3.0                    
           (c)  4.8                                                   (d)  3.5

28.      Sum of the absolute deviations about median is 
           (a)  zero                                                (b)  maximum           
           (c)  minimum                                       (d)  one  

29.       In case of a positive skewed distribution, the relation between mean, median and  
            mode that holds is 
           (a)  median > mean > mode                  (b)  mean >median > mode
           (c)  mean = median = mode                  (d)  none of these

30.      If the coefficient of kurtosis of a distribution is zero, the frequency curve is 
           (a)  leptokurtic                                      (b)  platykurtic         
           (c)  mesokurtic                                      (d)  any of these

31.      If  A  is a square matrix , then A-1 exist iff 
            (a)    |A|  = 0	                                    (b)  |A|  ¹  0 		
            (c)    |A|  >  0                           	(d)   |A|  < 0
		 
32.	y = x (dy/dx ) + x /(dy/dx) is of degree 
	(a) zero 	                                    (b) two 
	(c) three                                   	(d) one

33.        If  an = which of the following is true about the progression 	             
             a1 , a2 , a3 , ………., a n  ?
	  (a) A.P. Only                                     (b) A.P. as well as G.P.
             (c) A.P.  G.P. & H.P                       . (d) G. P. Only

34.        If radius of the incircle of a triangle with sides 5k , 6 k and 5k is 6 then k =
              (a) 4	                                                 (b)  5               
              (c) 6                                                    (d)  7  
                                               
              2
35.        ò  | 1-x2| dx =
	 -2	
            (a)	4	                                           (b)  2	
            (c)  -2		                                           (d)  0
					  
36.         =
 (a) 0		                                         (b)  3/8	
             (c)  8/3	                                   	     (d)  p

37.	The sum of the series 20C 0  + 20C 1  + 20C2  + ….. + 20C10   is

           ( a)   220                                                                             (b)   219	
                (c)  219+ (1/2)  20C10                                                (d) 219 – (1/2)  20C10 

38.       The lines 3x – 4y + 7 = 0 and ax + 6y +1 = 0  are perpendicular than ‘a’is 
(a)      4	                                        (b) 5	
	(c)   10 		                           (d) 8
        
39.	The distance between the lines 3x+4y = 6 and 6x+ 8y = 15 is 
(a)  3/2	                                                    (b) 3/10
(c)  6		                                        (d) none of these.                          

40.	The domain of the function y =    1/ Ö {  x  - |x| }                                                                        
          
           (a)  ( -¥ ,0 )	                                           (b)  ( - ¥ , 0] 
           (c)  ( - ¥ , - 1 ] 	                                           (d)  ( - ¥ , ¥ )

41.       If the lines of regression of y on x and x on y are respectively y = kx + 4 and                    
             x = 4y + 5, then
            (a) 0  k  4		                               (b) 0  k  ¼ 
	(c) k> ¼	                                           (d) none of these 

42.	If A & B are two events, then P (neither A nor B) equals 
             (a) 1- P(AB)	                                (b) P(A) + P(B)   
             (c) 1 - P(A) - P(B)                                      (d) none of these

43.	The expected value of the constant b is
	(a) 0		                                             (b) 1
            (c) 	                                                         (d) b
44.	In a triangle ABC , c=150 , b=50 & B=30 then major of c is
             (a) 60		                                (b) 130	
             (c) 90		                                (d) none of these

45.	If t=ex & y=t2 – 1 then  is
           (a) 	                                            (b) 	
           (c) 2		                                            (d) 2e2	

46.       An integer is chosen at random from two hundred digits. What is the probability 
           that the integer is divisible by 6 or 8?
           (a)  0.30                                                        (b)  0.10  
           (c)  0.25                                                        (d)  none of these

47.    The circumference of the circle is :
a.	Both boundary and extreme points
b.	Boundary Points only
c.	Extreme points only
d.	Interior point

48. 	If the mean of the set of numbers x1, x2, ……, xn is
, the mean of the 
 number of   xi + 2i , 1 i  n  is
            (a) + 2n		                              (b)	 + n +1	
            (c)	+ 2	                                          (d)+ n
49.      If ,  and  the coefficient of correlation between X 
           and Y is 
           (a)  1                                                                 (b)  1/4   
           (c)  1/2                                                              (d)  5/6  

50.      Given that P(A) = 1/3, P(B) = 1/4,  P(A/B) =1/6, then P(B/A) is equal to
(a)  1/4                                                            (b) 3/4 		
(c) 1/8		                                               (d) none of these