Math
1)Let * be the Binary operation defined by a * b = 3a +4b-2.Find 4 * 5.
  

2)Find the domain for which the functions ƒ(x) = 2x2 - 1 and g(x) = 1 - 3x are equal.
  

3)Write the value of :
  

4)For a 2 x 2 matrix, A = [aij] whose elements are given by aij=i/j , write the value of a12.
  

5)For what value of x, the given matrix is singular ?
  

6)Write A-1 for the given matrix.
  
  

 
 
 
 

7)Write the value of ∫sec x (sec x + tan x) dx.
  

8)Write the value of:
  
  

 
 
 
 

9)For what value of 'a' the given vectors are collinear ?
  

10)Probabilities of solving problem independently by A and B are and respectively. If both try to solve the problem independently, find the probability that the problem is solved.
  

11)Evaluate : ∫( 1og x/x) dx.
  

12)For the given matrix A, what value of α is A an identity matrix?
  

13)What is the principal value of cos-1 (-[√3 /2])
  

14)A matrix in which the Number of rows are equal to Number of columns is .

15)Find dy/dx if x = a (cosθ + θsin 0) and y = a(sin 0 - θcosθ )
  

16)The length x of a rectangle is decreasing at the rate of 3 cm/ mint and the width y is increasing at the rate of 2cm/min. when x = 10cm and y = 6cm, find the ratio of change of the area of the rectangle.
  

17)Find the value of:
  

18)Find the value of:
  

19)Find the area between the curves y = x and y = x2.
  

20)Find the area bounded by the curve y = sinx between x = 0 and x = 2π
  

21)Find the order and degree of the following:
  

22)Solve the differential equation sec2x .tan y dx + sec2y tan x dy = 0
  

23)Complete the magnitude.
  

24)A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of machine time and 3 hours of craftman’s time in its making while a cricket bat takes 3 hour of machine time an 1 hour of craftman’s time. In a day, the factory has the availability of not more than 42 hours of machine time and 24 hours of craftsman’s time.If the profit on a racket and on a bat is Rs 20 and Rs 10 respectively, find the maximum profit of the factory when it works at full capacity.
  

25)Given three identical boxes I, II and III each containing two coins. In box-I both coins are gold coins, in box-II, both are silver coins and in the box-III, there is one gold and one silver coin. A person chooses a box at random and takes out a coin. If the coin is of gold, what is the probability that the other coin in the box is also of gold.
  


  


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