(c) If Sindhu does not plays to win then she does not gets Bharat Ratna

(d) If Sindhu does not get Bharat Ratna then she does not plays to win
8. Let A and B are non-singular matrices of order 3 such that A  5 and A1B2 + AB = 0, then A2 A 2 
adj (adjB) is equal to
(a) null matrix (b) 25A2 – 5B (c) 25A2 (d) 50A2
9. Number of points of non-differentiability of f(x) = x  1  cos x ; 2 < x < 2 is
(a) 7 (b) 6 (c) 5 (d) 4
2012
10. If C0, C1, ……, C2012 are binomial coefficients in the expansion of (1 + x) and a0, a1, ….., a2012 are
real numbers in arithmetic progression then value of
a0 C0  a1C1  a2C2  a3C3  .....  a2012C2012 is a
(a) Even Number (b) Odd number (c) Natural number (d) Prime number
1
11. In a set of real numbers a relation R is defined as x R y such that x  y  , then relation R is
2
(a) reflexive and symmetric but not transitive (b) symmetric but not transitive and reflexive
(c) transitive but not symmetric and reflexive (d) none of reflexive, symmetric and transitive
   
12. If a, b and c are three mutually perpendicular unit vectors and d is a unit vector which makes
      2
equal angles with a, b and c then the value of a  b  c  d

(a) 4 + 2 2 (b) 4 + 2 3 5
(c) 2 + (d) 3 + 5
2
13. Let the area enclosed by the curve y = 1 – x and the line y = a, where 0  a  1, be represented by
A 0
A(a). If  k, then
1
A 
2
3 3 5 5
(a) 1  k  (b)  k  2 (c) 2  k  (d)  k  3
2 2 2 2
14. If system of linear equations (a – 1) x + z = , x + (b – 1) y =  and y + (c – 1) z =  where a, b, c  I
and , ,   R, does not have a unique solution, then maximum possible value of a  b  c is
(a) 5 (b) 1 (c) 3 (d) 4
15. ABCD is a rectangular field. A vertical lamp post of height 12m stands at the corner A. If the angle of
elevation of its top from B is 60 and from C is 45, then the area of the field is
(a) 48 2 sq. meter (b) 48 3 sq. meter (c) 48 sq. meter (d) 12 2 sq. meter
3 3 3 3
16. Smallest positive x satisfying the equation cos 3x + cos 5x = 8cos 4x  cos x is
(a) 15 (b) 18 (c) 22.5 (d) 30
 x  8 2  x 
17. The set of values of x satisfying simultaneously the inequalities 0
 10 
log 0.3  log2 5  1 
 7 
and 2x 3  31  0 is:
(a) a singleton set (b) an empty set
(c) an infinite set (d) a set consisting of exactly two elements
18. A bag contains 2 white and 4 black balls. A ball is drawn 5 times, each being replaced before
another is drawn. The probability that atleast 4 of the balls drawn are white is:
4 10 11
(a) (b) (c) (d) None
81 243 243
19. The modulus of the complex number z such that z  3  i = 1 and arg(z) =  is equal to
(a) 1 (b) 2 (c) 3 (d) 4
e 1 e
1  x 2  2x  1   x2  2 
20. Let J =  exp.   dx and K =  xn x exp.   dx. The value of (J + K) is equal to
0
x 1  2  l  2 

     
e2  1 e2 1 e2  2
(a) e (b) e (c) 0 (d) e
 SECTION-II: (Maximum Marks: 20)
 This section contains TEN questions. Attempt any 5 questions. First 5 attempted questions will be
considered for marking.
 The answer to each question is a NUMERICAL VALUE.
 For each question, enter the correct numerical value (If the numerical value has more than two
decimal places, truncate/round-off the value to TWO decimal places; e.g. 6.25, 7.00, 0.33, .30,
30.27, 127.30, if answer is 11.36777….. then both 11.36 and 11.37 will be correct) by darken the
corresponding bubbles in the ORS.
For Example: If answer is 77.25, 5.2 then fill the bubbles as follows.
 Answer to each question will be evaluated according to the following marketing scheme: Full
Marks : +4 If ONLY the correct numerical value is entered as answer.
Zero Marks : 0 In all other cases

1. If a, b are odd integers then number of integral root, of equation x 10 + ax9 + b = 0 is equal to
p
2. If the number of distinct positive rational numbers smaller than 1, where p, q  {1, 2, 3 ......,6} is
q
k then k is
3. If two distinct chords of a parabola y2 = 4ax passing through (a, 2a) are bisected on the line x + y =
1, then the sum of integral values of the length of possible latus rectums is equal to
  
sec2  
     2  5x 
4. If the value of Lim sin2   is eA then ‘A’ is
x 0
  2  3x  
5.  
If a, b, c , such that a  a  c  3b  0, if  is the angle between a and c, then cos2  is equal to

2x  1  4x  1
40 5
L
6. If lim  L, then of is
 2x  3
45
x  128

 x
1  sin 2 , x 1

7. If the function f  x    ax  b , 1  x  3 is continuous in the interval
 x
 6 tan , 3 x 6
 12
ab 
  , 6  then value of   is
 8 
1.5

 x  dx is equals to A, then A + √2 = (where [.] denotes greatest integer function)

k
9. If the area bounded by curve x + y = 1 and the y-axis is k, then is equals to
4
       
10. If value of
a  b   a  bc . a  2b  c  is k then k is
a b c  4
 