The population p(t) at time t of a certain mouse species satisfi

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 Multiple Choice QuestionsMultiple Choice Questions

1.

If z = yxsinxy + cos1 + yx  , then xzx is equal to

  • yzy

  • - yxy

  • 2yzy

  • 2yzx


2. limit as straight n rightwards arrow infinity of space open parentheses fraction numerator left parenthesis straight n plus 1 right parenthesis left parenthesis straight n plus 2 right parenthesis....3 straight n over denominator straight n to the power of 2 straight n end exponent end fraction close parentheses to the power of 1 divided by straight n end exponent is equal to
  • 18/e4

  • 27/e2

  • 9/e2

  • 9/e2

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3.

The area (in sq. units) of the regionopen curly brackets left parenthesis straight x comma straight y right parenthesis colon straight y squared space greater or equal than space 2 straight x space and space straight x squared space plus straight y squared space less or equal than 4 straight x comma space straight x space greater or equal than 0 comma space straight y greater or equal than 0 close curly brackets is

  • straight pi minus 4 over 3
  • straight pi minus 8 over 3
  • straight pi minus fraction numerator 4 square root of 2 over denominator 3 end fraction
  • straight pi minus fraction numerator 4 square root of 2 over denominator 3 end fraction
299 Views

4.

If a curve y=f(x) passes through the point (1, −1) and satisfies the differential equation, y(1+xy) dx=x dy, then f(-1/2) is equal to

  • -2/5

  • -4/5

  • 2/5

  • 2/5

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5.

If f and ga re differentiable  functions in (0,1) satisfying f(0) =2= g(1), g(0) = 0 and f(1) = 6, then for some c ε] 0,1[

  • 2f'(c) = g'(c)

  • 2f'(c) = 3g'(c)

  • f'(c) = g'(c)

  • f'(c) = g'(c)

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6.

The population p(t) at time t of a certain mouse species satisfies the differential equation fraction numerator dp space left parenthesis straight t right parenthesis over denominator dt end fraction space equals space 0.5 space left parenthesis straight t right parenthesis space minus 450. if p (0) = 850, then the  time at which the population becomes zero is

  • 2 log 18

  • log 9

  • 1 half space log space 18
  • 1 half space log space 18


A.

2 log 18

fraction numerator straight d left parenthesis straight p left parenthesis straight t right parenthesis right parenthesis over denominator dt end fraction space equals space 1 half straight p left parenthesis straight t right parenthesis space minus 450
fraction numerator begin display style straight d left parenthesis straight p left parenthesis straight t right parenthesis right parenthesis end style over denominator begin display style dt end style end fraction space equals space fraction numerator straight p space left parenthesis straight t right parenthesis minus 900 over denominator 2 end fraction
2 integral fraction numerator straight d left parenthesis straight p left parenthesis straight t right parenthesis right parenthesis over denominator straight p left parenthesis straight t right parenthesis minus 900 end fraction equals integral dt
2 space ln space vertical line straight p left parenthesis straight t right parenthesis minus 900 vertical line space equals space straight t plus straight c
straight t equals 0
rightwards double arrow space 2 space ln space 50 space equals space 0 plus straight c
therefore space 2 space ln space vertical line straight p left parenthesis straight t right parenthesis minus 900 vertical line space equals space straight t space plus space 2 space ln space 50
straight p left parenthesis straight t right parenthesis space equals space 0 space
rightwards double arrow 2 space ln space 900 space equals space straight t plus 2 space ln space 50
straight t space equals space 2 space left parenthesis In space 900 minus In space 50 right parenthesis space equals space 2 space ln space open parentheses 900 over 50 close parentheses space
equals space 2 space ln space 18
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7.

Consider the function f(x) = |x – 2| + |x – 5|, x ∈ R.
Statement 1: f′(4) = 0
Statement 2: f is continuous in [2, 5], differentiable in (2, 5) and f(2) = f(5).

  • Statement 1 is false, statement 2 is true

  • Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1

  • Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1

  • Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1

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8. fraction numerator straight d squared straight x over denominator dy squared end fraction equal to
  • open parentheses fraction numerator straight d squared straight x over denominator dy squared end fraction close parentheses to the power of negative 1 end exponent
  • negative open parentheses fraction numerator straight d squared straight y over denominator dx squared end fraction close parentheses to the power of negative 1 end exponent open parentheses dy over dx close parentheses to the power of negative 3 end exponent
  • open parentheses fraction numerator straight d squared straight y over denominator dx squared end fraction close parentheses open parentheses dy over dx close parentheses to the power of negative 2 end exponent
  • open parentheses fraction numerator straight d squared straight y over denominator dx squared end fraction close parentheses open parentheses dy over dx close parentheses to the power of negative 2 end exponent
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9.

The shortest distance between line y - x = 1 and curve x = y2 is

  • √3/4

  • 3√2 /8

  • 8/3√2

  • 8/3√2

349 Views

10. limit as straight x space rightwards arrow 2 of space open parentheses fraction numerator square root of 1 minus cos space open curly brackets 2 left parenthesis straight x minus 2 right parenthesis close curly brackets end root over denominator straight x minus 2 end fraction close parentheses
  • does not exist

  • equal square root of 2

  • equal negative square root of 2

  • equal negative square root of 2

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