36. Match the items in columns I and II.
    Column I
    P. Gauss-Seidel method
    Q. Forward Newton-Gauss method
    R. Runge-Kutta method
    S. Trapezoidal Rule
    Column II
    1. Interpolation
    2. Non-linear differential equations
    3. Numerical integration
    4. Linear algebraic equations
    

1. 1. P-1, Q-4, R-3, S-2
      

   
   
   

   2. P-1, Q-4, R-2, S-3
      

   
   
   

   3. P-1, Q-3, R-2, S-4
      

   
   
   

   4. P-4, Q-1, R-2, S-3

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: D

   NA

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37. The derivative of f(x) = cos(x) can be estimated using the approximation
    

    f '(x) =	f(x + h) - f(x - h)
    	2h

    
    The percentage error is calculated as
    

    	Exact value - Approximation value		× 100
    	Exact value

    
    The percentage error in the derivative of f(x) at x = π / 6 radian, choosing h = 0.1 radian, is
    

1. 1. < 0.1%
      

   
   
   

   2. > 1% and < 5%
      

   
   
   

   3. > 0.1% and < 1%
      

   
   
   

   4. > 5%

   
   
   

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1. View Hint View Answer Discuss in Forum

   f(x) = cos(x)
   

   at x =	π	rad =	π	×	180	= 30°
   	6		6		π

   
   

   [f '(x)]2 = -sin30° =	-1	.......(1)
   	2

   
   

   f '(x)=	cos(x + h) - cos(x - h)
   	2h

   
   

   ∵ x =	π	= 30°
   	6

   
   

   h = 0.1 =	28°
   	π

   
   

   [f '(x)]2 =	cosx . cosh - sinx . sinh - cosx.cosh - sinx.sinh
   	2h

   
   

   =	- 2sinx . sinh	=	- 2sin30° × sin(18/ π)	= -0.499
   	2h		2 × 0.1

   
   

   % error =	[f '(x)]1 - [f '(x)]2
   	[f '(x)]1

   
   = 0.166% (> 0.1% and < 1%)

   Correct Option: C

   f(x) = cos(x)
   

   at x =	π	rad =	π	×	180	= 30°
   	6		6		π

   
   

   [f '(x)]2 = -sin30° =	-1	.......(1)
   	2

   
   

   f '(x)=	cos(x + h) - cos(x - h)
   	2h

   
   

   ∵ x =	π	= 30°
   	6

   
   

   h = 0.1 =	28°
   	π

   
   

   [f '(x)]2 =	cosx . cosh - sinx . sinh - cosx.cosh - sinx.sinh
   	2h

   
   

   =	- 2sinx . sinh	=	- 2sin30° × sin(18/ π)	= -0.499
   	2h		2 × 0.1

   
   

   % error =	[f '(x)]1 - [f '(x)]2
   	[f '(x)]1

   
   = 0.166% (> 0.1% and < 1%)

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38. Three cards were drawn from a pack of 52 cards. The probability that they are a king, a queen, and a jack is
    

1. 1. 16

      5525

      
      

   
   
   

   2. 64

      2197

      
      

   
   
   

   3. 3

      13

      
      

   
   
   

   4. 8

      16575

   
   
   

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1. View Hint View Answer Discuss in Forum

   ρ =	4C1 × 4C1 × 4C1
   	52C3

   
   

   ρ =	16
   	5525

   
   

   Correct Option: A

   ρ =	4C1 × 4C1 × 4C1
   	52C3

   
   

   ρ =	16
   	5525

   
   

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39. The probability that a screw manufactured by a company is defective is 0.1. The company sells screws in packets containing 5 screws and gives a guarantee of replacement if one or more screws in the packet are found to be defective. The probability that a packet would have to be replaced is ___.

1. 1. 1.41

   
   
   

   2. 0.141

   
   
   

   3. 0.41

   
   
   

   4. 10.41

   
   
   

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1. View Hint View Answer Discuss in Forum

   we require P(x ≥ 1) = 1 – P(x = 0)
   = 1 – ⁵C₀ (0.1)⁰ (0.9)⁵
   = 0.4095 ≈ 0.41

   Correct Option: C

   we require P(x ≥ 1) = 1 – P(x = 0)
   = 1 – ⁵C₀ (0.1)⁰ (0.9)⁵
   = 0.4095 ≈ 0.41

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40. The probability of obtaining at least two "SIX" in throwing a fair dice 4 times is
    

1. 1. 425

      432

      
      

   
   
   

   2. 19

      144

      
      

   
   
   

   3. 13

      144

      
      

   
   
   

   4. 125

      432

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let P be the probability that six happens in a fair dice,
   

   ∴ p =	1	, q =	5
   	6		6

   
   Let X, be the number of times ‘six’ happens Probability of obtaining atleast two ‘six’ in throwing a fair dice 4 times is
   = 1 – {P (X = O) + P (X = 1)}
   = 1 – {⁴C₀ P°q⁴ + ⁴C₁, P’q³}

   Correct Option: B

   Let P be the probability that six happens in a fair dice,
   

   ∴ p =	1	, q =	5
   	6		6

   
   Let X, be the number of times ‘six’ happens Probability of obtaining atleast two ‘six’ in throwing a fair dice 4 times is
   = 1 – {P (X = O) + P (X = 1)}
   = 1 – {⁴C₀ P°q⁴ + ⁴C₁, P’q³}

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