KCET 2017 Question Paper Maths

COMMON ENTRANCE TEST – 2017
DATE SUBJECT TIME
02-05-2017 MATHEMATICS 2.30 pm to 3.50 pm

MAXIMUM MARKS TOTAL DURATION MAXIMUM TIME FOR ANSWERING
60 80 Minutes 70 Minutes

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Page: 1

1. If A and B are finite sets and , then 1. A  B     
(A) ) = n(A) (B) ) = n(B) (A) ) = n(A) (B) ) = n(B)
(C) ) = n(B) (D) )=φ (C) ) = n(B) (D) )=φ
Question Id : 1 Question Id : 1

2. The value of 2.  
is (A) (B)
(A) (B)

(C) (D)
(C) (D)

Question Id : 2

Question Id : 2

3. 3 + 5 +7 + …. to n term is 3. 3 + 5 +7 + ….  n   
(A) n(n + 2) (B) (A) n(n + 2) (B)

(C) (D) (C) (D)

Question Id : 3 Question Id : 3

4. 4.
= 1, then the least positive integral = 1  m    
value of m is 
(A) 2 (B) 3 (A) 2 (B) 3
(C) 4 (D) 1 (C) 4 (D) 1
Question Id : 4 Question Id : 4

5. If ≤ 1, then 5. ≤ 1 
(A) (B) (A) (B)
(C) (D) (C) (D)
Question Id : 5 Question Id : 5

6. If = then n is equal to 6. =  n  
(A) 26 (B) 12 (A) 26 (B) 12
(C) 6 (D) 20 (C) 6 (D) 20
Question Id : 6 Question Id : 6

7. The total number of terms in the expansion of 7.    
after simplification is   
(A) 24 (B) 47 (A) 24 (B) 47
(C) 48 (D) 96 (C) 48 (D) 96
Question Id : 7 Question Id : 7

Page: 2

8. Equation of line passing through the point 8.    
and perpendicular to the line     
is 
(A) (B) (A) (B)
(C) (D) (C) (D)
Question Id : 8
Question Id : 8

9. 9.
The eccentricity of the ellipse +  +  
is (A) (B)
(A) (B)

(C) (D)
(C) (D)

Question Id : 9

Question Id : 9

10. The perpendicular distance of the point 10. XY    
from XY-plane is (A) 8 (B) 7
(A) 8 (B) 7 (C) 6 (D) 5
(C) 6 (D) 5 Question Id : 10

Question Id : 10

11. 11.
The value of is  
(A) 4/9 (B) 9/4 (A) 4/9 (B) 9/4
(C) 9/3 (D) 3/4 (C) 9/3 (D) 3/4
Question Id : 11 Question Id : 11

12. The contrapositive statement of the statement 12. “       
“If is prime number, then is odd” is ”     
(A) I f is not a prime number, then is not (A)     
odd

(B) If is a prime number, then is not odd. (B)     

(C) If is not a prime number, then is odd.     
(C)
(D) I f is not odd, then is not a prime 
number. (D)     

Question Id : 12

Question Id : 12

Page: 3

13. If coefficient of variation is 60 and standard 13.     6 0  
deviation is 24, then Arithmetic mean is  24    
(A) 40 (B) 7/20 (A) 40 (B) 7/20
(C) 20/7 (D) 1/40 (C) 20/7 (D) 1/40
Question Id : 13 Question Id : 13

14. The range of the function )= is 14. )=  
(A) (0, 3) (B) [0, 3] (A) (0, 3) (B) [0, 3]
(C) (0, 3] (D) [0, 3) (C) (0, 3] (D) [0, 3)
Question Id : 14 Question Id : 14

15. Let be defined by = , then 15.  = 
(A) f is one-one and onto 
(B) f may be one-one and onto (A) f -   

(C) f is one-one but not onto (B) f -   

(D) f is neither one-one nor onto (C) f -   
Question Id : 15
(D) f -    
Question Id : 15

16. The range of is 16.  
(A) (B) (A) (B)

(C) (D) (C) (D)

Question Id : 16 Question Id : 16

17. If , then 17.  
is equal to 
(A) π (B) (A) π (B)

(C) (D) (C) (D)

Question Id : 17 Question Id : 17

18. If , , then is 18. ,   
(A) (B) (A) (B)

(C) (D) (C) (D)
Question Id : 18 Question Id : 18

Page: 4

19. 19.

If

B = then A − B is B= , A − B 

equal to 
(A) I (B) 0 (A) I (B) 0
(C) 2I (D) (C) 2I (D)

Question Id : 19 Question Id : 19

20. If a matrix A is both symmetric and skew 20. A      
symmetric, then  A 
(A) A is diagonal matrix (A) A   (B) A  
(B) A is a zero matrix (C) A   (D) A  
(C) A is scalar matrix (D) A is square matrix Question Id : 20

Question Id : 20

21. 21.
If , then the value   y
of and y are  
(A) (A) (B)

(B) (C)

(C) (D)

Question Id : 21
(D)

Question Id : 21

22. Binary operation * on R − {−1} defined by 22.
R − {−1 }  , = 
= is
  
(A) * is associative and commutative (A)   
(B) * is associative but not commutative
(B)  
(C) * is neither associative nor commutative
(C)    
(D) * is commutative but not associative
Question Id : 22 (D)   
Question Id : 22

Page: 5

23. 23.
If then is equal to   
(A) 2 (B) 4 (A) 2 (B) 4
(C) 8 (D) (C) 8 (D)
Question Id : 23 Question Id : 23

24. If A is a square matrix of order 3 × 3, then |KA| 24. A   3 × 3    |KA|
is equal to  
(A) K|A| (B) (A) K|A| (B)

(C) (D) 3K|A| (C) (D) 3K|A|
Question Id : 24
Question Id : 24

25. The area of triangle with vertices (K, 0), 25. (K, 0), (4, 0), (0, 2)   
, (0, 2) is 4 square units, then value of K   4   K  
(A) 0  8 (B) 0  − 8
is
(A) 0 or 8 (B) 0 or − 8 (C) 0 (D) 8
(C) 0 (D) 8 Question Id : 25

Question Id : 25

26. 26.



then 

(A) =−Δ (B) =Δ (A) =−Δ (B) =Δ
(C) (D) =2Δ (C) (D) =2Δ
Question Id : 26 Question Id : 26

27. 27.
If = is continuous at =  
, then the value of K is   K  
(A) 3 (B) 4 (A) 3 (B) 4
(C) 3/4 (D) 4/3 (C) 3/4 (D) 4/3
Question Id : 27 Question Id : 27

Page: 6

28. The value of C in Mean value theorem for the 28.  [2, 4]  
function in [2, 4] is   C  
(A) 3 (B) 2 (A) 3 (B) 2
(C) 4 (D) 7/2 (C) 4 (D) 7/2
Question Id : 28 Question Id : 28

29. The point on the curve where the 29.     
tangent makes an angle of π /4 with X-axis is  X    π /4
(A) (B) .
(A) (B)

(C) (4, 2) (D) (1, 1)
Question Id : 29 (C) (4, 2) (D) (1, 1)
Question Id : 29

30. The function is strictly 30.   
increasing in the interval 
(A) (B) (A) (B)

(C) (D) (C) (D)
Question Id : 30 Question Id : 30

31. The rate of change of volume of a sphere with 31.   4 cm    
respect to its surface area when the radius is     
is (A) (B)
(A) (B) (C) (D)
(C) (D) Question Id : 31

Question Id : 31

32. 32.
, then is equal   
to (A) 1/2 (B) π /4
(A) 1/2 (B) π /4 (C) 0 (D) 1
(C) 0 (D) 1 Question Id : 32

Question Id : 32

Page: 7

33. 33.

If y = , then is equal y=  

to (A)
(A)

(B)
(B)

(C)
(C)

(D)
(D)

Question Id : 33

Question Id : 33

34. then is 34.   
equal to (A) 1 (B) 0
(A) 1 (B) 0 (C) (D) 2
(C) − 1 (D) 2 Question Id : 34

Question Id : 34

35. The derivative of w.r.t 35.    
is (A) 2 (B)
(A) 2 (B)

(C) (D)
(C) (D)
Question Id : 35

Question Id : 35

Page: 8

36. 36.
If ) then is equal to )   
(A) (B) (A) (B)

(C) (D) (C) (D)

Question Id : 36 Question Id : 36

37. 37.
is equal to  
(A) (B) (A) (B)

(C) (D) (C) (D)

Question Id : 37 Question Id : 37

38. 38.
is equal to  
(A) (A)

(B) (B)

(C) (C)

(D) (D)
Question Id : 38 Question Id : 38

Page: 9

39. 39.
is equal to  
(A) (A)

+C +C
(B) (B)

+C +C
(C) (C)

+C +C
(D) (D)

+C +C
Question Id : 39 Question Id : 39

40. 40.
is equal to  
(A) (B) (A) (B)

(C) (D) (C) (D)

Question Id : 40 Question Id : 40

41. 41.
is equal to  

(A) 29 (B) 28 (A) 29 (B) 28
(C) 27 (D) 30 (C) 27 (D) 30
Question Id : 41 Question Id : 41

42. 42.
is equal to  
(A) 0 (B) 1 (A) 0 (B) 1
(C) (D) (C) (D)

Question Id : 42 Question Id : 42

Page: 10

43. 43.
is equal to  
(A) (B) (A) (B)

(C) (D) (C) (D)

Question Id : 43 Question Id : 43

44. The area of the region bounded by the curve 44.  y = 16   
and the line y = 16 is 
(A) sq. units (B) sq. units (A)   (B)  

(C) sq. units (D) sq. units (C)   (D)  

Question Id : 44 Question Id : 44

45. Area of the region bounded by the curve 45.   
and is    
(A) 2 sq. units (B) 4 sq. units (A) 2   (B) 4  
(C) 3 sq. units (D) 1 sq. unit (C) 3   (D) 1  
Question Id : 45 Question Id : 45

46. The degree of the differential equation 46.
=  
= is
 
(A) 1 (B) 2 (A) 1 (B) 2
(C) 3 (D) 4 (C) 3 (D) 4
Question Id : 46 Question Id : 46

47. General solution of differential equation 47.
  
is

(A) (B) (A) (B)

(C) (C)

(D) (D)

Question Id : 47 Question Id : 47

Page: 11

48. The integrating factor of the differential 48.  
equation is
 
(A) (B) (A) (B)

(C) (D) (C) (D)

Question Id : 48 Question Id : 48

49. and are 49.  
orthogonal, then value of λ is  λ 
(A) 0 (B) 1 (A) 0 (B) 1
(C) (D) (C) (D)

Question Id : 49 Question Id : 49

50. , , are unit vectors such that 50. , ,    
, then the value of   
is equal to (A) 1 (B) 3
(A) 1 (B) 3 (C) (D)
(C) (D)
Question Id : 50

Question Id : 50

51. If & are unit vectors, then angle between 51.     
for to be unit vector is       
(A) 30 ° (B) 45 ° 
(C) 60 ° (D) 90 ° (A) 30 ° (B) 45 °
Question Id : 51
(C) 60 ° (D) 90 °
Question Id : 51

52. Reflexion of the point ( α , β , γ ) in XY plane is 52. X Y   ( α , β , γ )  
(A) ( α , β , 0) (B) (0, 0, γ ) (A) ( α , β , 0) (B) (0, 0, γ )
(C) (− α , − β , γ ) (D) ( α , β , − γ ) (C) (− α , − β , γ ) (D) ( α , β , − γ )
Question Id : 52 Question Id : 52

Page: 12

53. The plane − 3y + 6z − 11 = 0 makes an 53. X   − 3y + 6z − 11 = 0  
angle ( α ) with X-axis. The value of α is  ( α )  α  
equal to (A) (B)
(A) (B)

(C) (D)
(C) (D)
Question Id : 53

Question Id : 53

54. The distance of the point (−2, 4, −5) from the 54.
= =   (−2,
line = = is
4, −5)  
(A) (B) (A) (B)

(C) (D) (C) (D)

Question Id : 54 Question Id : 54

55. A box has 100 pens of which 10 are defective. 55.   100         10
The probability that out of a sample of 5 pens          . 5  
drawn one by one with replacement and atmost     
one is defective is     
(A) (B) (A) (B)

(C) (C)

(D) (D)

Question Id : 55 Question Id : 55

56. Two events A and B will be independent if 56. A  B    
(A) A and B are mutually exclusive (A) A  B    
(B) P(A' B') = (1 − P(A)) (1 − P(B)) (B) P(A' B') = (1 − P(A)) (1 − P(B))
(C) P(A) = P(B) (D) P(A) + P(B) = 1 (C) P(A) = P(B) (D) P(A) + P(B) = 1
Question Id : 56 Question Id : 56

Page: 13

57. The probability distribution of X is 57. X   

The value of k is  k  
(A) 0.14 (B) 0.3 (A) 0.14 (B) 0.3
(C) 0.7 (D) 1 (C) 0.7 (D) 1
Question Id : 57 Question Id : 57

58. The shaded region in the figure is the solution 58.      
set of the inequations  .

(A) (A)

(B) (B)
(C) (C)
(D) (D)
Question Id : 58 Question Id : 58

59. If an LPP admits optimal solution at two 59. LPP      
consecutive vertices of a feasible region, then   
(A) the required optimal solution is at the (A)       
midpoint of the line joining two points.     .
(B) the optimal solution occurs at every point (B)      
on the line joining these two points     
(C) the LPP under consideration is not
.
solvable (C)  LPP  .
(D) the LPP under consideration must be (D)  LPP   .
reconstructed Question Id : 59

Question Id : 59

60. 60.
is equal to  
(A) 4 (B) 4.5 (A) 4 (B) 4.5
(C) 3.5 (D) 3 (C) 3.5 (D) 3
Question Id : 60 Question Id : 60

Page: 14

Space For Rough Work

Page: 15

   – 2017
  
02-05-2017  . 2.30  3.50  
        
60 80  70 

      / 
0
 :
1.    ...       
.
2.      2   ,  . 2.30   .
3.    /  ...      
.
4. ...       .
 :
1. ...     /  / .
2.   . 2.40  . ,
·     .
·      .
· ...   .
  
1.   60 ,   4    .
2.    . 2.40           
           ,  
     .  ...   .
3.  70  :
·    .
·            .
·      ...      
           .
...      :
4.  ...          .  ...
   .
5.       . ...   .
6.    . 3.50    .       .
7. ...     .
8.      (KEA copy)      (
)      .
9.       .
10.             
 .

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