1. Let A and B be two non zero square matrics and AB and BA both are defined. It means

  1. No. of columns of A No. of rows of B
  2. No. of rows of A No. of columns of B
  3. Both matrices (A) and (B) have same order
  4. Both matrices (A) and (B) does not have same order
  

2. If A=[2 3 3 5] , then which of the following statements are correct?

  1. A is a square matrix
  2. A−1 exists
  3. A is a symmetric matrix
  4. |A|=19
  5. A is a null matrix

Choose the correct answer from the options given below.

  1. A, B, C only
  2. A, D, E only
  3. A, B, D only
  4. C, D, E only

 

 

3. The number of all possible matrices of order 2×2 with each entry 0 or 1 is:

  1. 27
  2. 18
  3. 16
  4. 81
  

4. 

  1. 2−1/e
  2. 4−1/e
  3. 1/e
  4. 1−1/e
  

5. The function f(x)=x2−2x is strictly decreasing in the interval

  1. (−∞,−1)
  2. (−1,∞)
  3. (−∞,1)
  4. (−1,∞)
  

6. 

1. 

2. 

3. 

4. 

  

7. 

  

8. 

  1. 7
  2. 5
  3. 4
  4. 6
  

9. If a and b are order and degree of differential equation y''+(y')2+2y=0, then value of 2a+6b, is :

  1. 3
  2. 4
  3. 6
  4. 10
  

10. The solution of the differential equation xdy−ydx=0 represent family of

  1. Circles passing through origin.
  2. Straight line parsing through (−1,6)
  3. Straight line passing through the origin.
  4. Circle whose center is at the origin.
  

11. 

  1. 0
  2. 1
  3. 2
  4. E
  

12. 

  1. 2(e−1−1)
  2. 2(e+1)
  3. e−1
  4. 2(e−1)
  

13. 

  1. 1/2
  2. 1/12
  3. 1/6
  4. 1/3
  

14. The probability distribution of X is :

Then var(X)=

  1. 3/20
  2. 9/4
  3. 141/20
  4. 159/80
  

15. The maximum value of z=4x+2y subject to constraints
2x+3y≤28,
x+y≤10,
x,y≥0 is :

  1. 36
  2. 40
  3. 100/3
  4. 32
  

16. Match List I with List II

Choose the correct answer from the options given below:

  1. A - I, B - IV, C - II, D - III 
  2. A - IV, B - I, C - II, D - II
  3. A - I, B - IV, C - III, D - II
  4. A - IV, B - I, C - II, D - III
  

17. 

  1. π/3
  2. 2π/3
  3. −π/3
  4. π/6
  

18. Match List I with List II

Choose the correct answer from the options given below: 

  1. A-IV, B-III. C-II, D-I 
  2. A-IV. B-I. C-III. D - II 
  3. A-I, BIV. C - II. D - III 
  4. A-IV, B-II, C-I, D - III
  

19. If A=[cosα⁡ sin⁡α −sinα⁡ cosα]⁡ , then:

  1. A'A=I
  2. A'A=0
  3. A'A=2I
  4. A'A=−I
  

20. If A=[2 1 0 3 1 2 0 4 −1] then |adj(A)| is equal to

  1. 11
  2. 12
  3. 225
  4. -225
  

21. Identify the correct option (s)

A. modulus function is continuous at every point in its domain. 

B. modulus function may or may not be continuous at every point in its domain.

C. Every rational function is continuous in its domain.

D. If a function f is differentiable at a point then it is also continuous at that point.

E. If a function f is continuous at a point then it is also differentiable at that point. 

Choose the correct answer from the options given below: 

  1. A and C only 
  2. B and E and A
  3. C and D only 
  4. C and E only
  

22. 

  1. 1
  2. -1
  3. 0
  4. No Value
  

23. 

  

24. 

  

25. Match List I with List II

Choose the correct answer from the options given below:

  1. A-II. B-IV, C-I, D-III 
  2. А-III. В-II. C-IV. D-I 
  3. А-III. В-I, C-IV. D-II 
  4. A-I, B-II.C-III. D-IV
  

26. The order of the differential equation whose general solution is y=ex(acos⁡x+b sin⁡x ), where a and b are arbitrary constants is :

  1. 1
  2. 3
  3. 2
  4. 6
  

27. 

  1. 2a
  2. ∫(sin⁡2a)
  3. ∫(cos⁡2a)
  4. 0
  

28. ∫tan⁡x(sec⁡x−tan⁡x)dx=

  1. sec⁡x−tan⁡x+x−C
  2. sec⁡x−tan2⁡x+C
  3. sec⁡x+tan⁡x+x+C
  4. sec⁡x−tan⁡x+C
  

29. If cosα⁡,cosβ⁡,cos⁡γ are the direction cosines of vector a, then value of cos⁡2α+cos⁡2β+cos⁡2γ is equal to:

  1. 3
  2. 0
  3. 2
  4. -1
  

30. The value of i.(jˆkˆ)+j.(iˆkˆ)+k⋅(iˆjˆ) is

  1. 0
  2. -1
  3. 1
  4. 3
  

31. The corner points of the feasible region for an L.P.P are (2,0), (7,0), (4, 5) and (0,3) and z = 2x+3y is the objective function. The difference of the maximum and minimum values of z is-

  1. 19
  2. 4
  3. 23
  4. 14
  

32. The area of the parallelogram whose adjacent sides are iˆ+kˆ and 2iˆ+jˆ+kˆ is

  1. 3
  2. √2
  3. 4
  4. √3
  

33. If x(iˆ+jˆ+kˆ) is a unit vector then value of x is :

  1. ±√3
  2. ±1/3
  3. ±3
  4. ±1/√3

 

 34. 

  1. (1,1,1)
  2. (1,−1,−1)
  3. (−1,1,−1)
  4. (−1,−1,−1)
  

 35. The distance between the point (3,4,5) and the point where the line x−3/1=y−4/2=z−5/2 meets the plane x+y+z=17, is

    1. 3
    2. 2
    3. 1
    4. 0
  

 36. If events A and B are independent, then identify the correct statements 

(A) A and B must be mutually exclusive 

(B) The sum of their probabilities must be equal to 1 

(C) P(A) . P(B) =P(A Ո B) 

(D) A'and B' are also independent 

Choose the correct answer from the options given below 

  1. A and B only 
  2. B and C only 
  3. C and D only 
  4. A and D only

 

 37. The equation of plane passing through the point (0,7,−7) and containing the line x+1/−3=y−3/2=z+2/1, is:

    1. x−y−z=0
    2. 4x+y+z=0
    3. x+y+z=0
    4. 3x+2y+2z=0

 

 38. If A and B are two independent events with P(A)=35 and P(B)=4/9, then P(A'∩B') is equal to

  1. 4/15
  2. 8/45
  3. 1/3
  4. 2/9
  

39. A line L:x−2/1=y−3/2=z−1/−1 is perpendicular to a plane (P), which passing through the point (4,3,9). If the mirror image of point ' S ' on the line (L) in the given plane (P) is (2,3,1), then co-ordinates of point S, is :

  1. (1,0,3)
  2. (0, -1, 3)
  3. (-2, -3, -1)
  4. (4, 7, -1)
  

40. A biased dice is thrown once. If X denotes the number appearing on it and have probability distribution :

where k>0. Then consider the following statements :
A. P(X=3).
B. P(X≤2 ).
C. P(X≥5 ).
D. P(X=4).
E. P(X=1)+P(X=5).

Choose the correct answer from the options given below:

  1. C > D > B > A > E 
  2. E > C > D > A > B 
  3. E > C > A > B > D 
  4. C > E > A > B > D
  

In a school, a auditorium was used for its cultural activities. The shape of the floor of the auditorium is rectangular with dimensions x and y(x>y), has fixed parameter p .

 

Based on the above information answer the following questions.

 

41. If x and y represent the length and breadth of the rectangular region, then:

    1. p=x+y
    2. p2=x2+y2
    3. p=2(x+y)
    4. p=x+2y

 

42. The area (A) of the floor, as a function of x can be expressed as:

  

 43. The value of x, for which area of floor of auditorium is maximum is:

    1. p/4
    2. p/2
    3. p
    4. p/3
  

44. The value of y, for which the area of the floor of auditorium is maximum is :

    1. p/2
    2. p/3
    3. p/4
    4. p/16

 

45. Maximum area of floor is:

  1. p2/4
  2. p2/16
  3. p2/28
  4. p2/64
  

 A ball is thrown upwards from the plane surface of the ground. Suppose the plane surface from which the ball is thrown also consists of the points A(1, 0, 2) B(3, - 1, 1) and C(1, 2, 1) on it. The highest point of the ball takes, is D(2, 3, 1) as shown in the figure. Using this information answer the question

46. The equation of the plane passing through the points A,B and C is:

  1. 3x−2y+4z=−11
  2. 3x+2y+4z=11
  3. 3x−2y−4z=11
  4. −3x+2y+4z=−11
  

47. The maximum height of the ball from the ground is

  

48. The equation of the perpendicular line drawn from the maximum height of the ball to the ground, is :

  

49. The co-ordinates of the foot of the perpendicular drawn from the maximum height of the ball to the ground are

  
50. The Area of ΔABC is