Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.
Advertisement

 Multiple Choice QuestionsMultiple Choice Questions

1.

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

  • yzy

  • - yxy

  • 2yzy

  • 2yzx


Advertisement

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


B.

27/e2

Let space straight I space equals space limit as straight n stack rightwards arrow infinity with space on top of open parentheses fraction numerator left parenthesis straight n plus 1 right parenthesis. left parenthesis straight n plus 2 right parenthesis..... left parenthesis 3 straight n right parenthesis over denominator straight n to the power of 2 straight n end exponent end fraction close parentheses to the power of 1 over straight n end exponent
space equals space space limit as straight n stack rightwards arrow infinity with space on top of open parentheses fraction numerator left parenthesis straight n plus 1 right parenthesis. left parenthesis straight n plus 2 right parenthesis..... left parenthesis straight n plus 2 straight n right parenthesis over denominator straight n to the power of 2 straight n end exponent end fraction close parentheses to the power of 1 over straight n end exponent

equals space limit as straight n stack rightwards arrow infinity with space on top of open square brackets open parentheses fraction numerator straight n plus 1 over denominator straight n end fraction close parentheses plus open parentheses fraction numerator straight n plus 2 over denominator straight n end fraction close parentheses.... open parentheses fraction numerator straight n plus 2 straight n over denominator straight n end fraction close parentheses close square brackets to the power of 1 over straight n end exponent

taking space log space on space both space sides space comma we space get
log space straight I space equals space limit as straight n stack rightwards arrow infinity with space on top of open square brackets log space open curly brackets open parentheses 1 plus 1 over straight n close parentheses open parentheses 1 plus 2 over straight n close parentheses.... open parentheses 1 plus fraction numerator 2 straight n over denominator straight n end fraction close parentheses close curly brackets close square brackets
rightwards double arrow space log space straight I space equals space limit as straight n stack rightwards arrow infinity with space on top of 1 over straight n open square brackets log open parentheses 1 plus 1 over straight n close parentheses plus space log space open parentheses 1 plus 2 over straight n close parentheses space plus..... plus space log space open parentheses 1 plus fraction numerator 2 straight n over denominator straight n end fraction close parentheses close square brackets
rightwards double arrow space log space straight I space equals limit as straight n stack rightwards arrow infinity with space on top of 1 over straight n sum from straight r space equals 1 to 2 straight n of space log space open parentheses 1 plus straight r over straight n close parentheses
rightwards double arrow space log space straight I space equals space integral subscript 0 superscript 2 space log space left parenthesis 1 plus straight x right parenthesis space dx
rightwards double arrow space log space straight I space equals space open square brackets log space space left parenthesis 1 space plus straight x right parenthesis. straight x space minus space integral fraction numerator 1 over denominator 1 plus straight x end fraction. straight x space dx close square brackets subscript 0 superscript 2
rightwards double arrow space log space space straight I space equals space left square bracket log space left parenthesis 1 space plus straight x right parenthesis. straight x right square bracket subscript 0 superscript 2 space minus integral subscript 0 superscript 2 open parentheses 1 minus fraction numerator 1 over denominator 1 plus straight x end fraction close parentheses dx
rightwards double arrow space log space space straight I space equals space 2. space log space 3 space minus space left square bracket straight x minus log space vertical line 1 plus straight x vertical line subscript 0 superscript 2
rightwards double arrow space log space space straight I space equals space 3. space log space 3 space minus 2
rightwards double arrow space log space space straight I space equals space space log space 27 space minus 2
therefore comma space straight l space equals space straight e to the power of log space 27 minus 2 end exponent space equals space 27. straight e to the power of negative 2 end exponent space equals space 27 over straight e squared
303 Views

Advertisement
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

424 Views

Advertisement
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)

149 Views

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
493 Views

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

154 Views

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
167 Views

Advertisement
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

153 Views

Advertisement