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

21. integral subscript negative 3 straight pi divided by 2 end subscript superscript negative straight pi divided by 2 end superscript open square brackets open parentheses straight x plus straight pi close parentheses cubed plus space cos space left parenthesis straight x space plus 3 straight pi right parenthesis close square brackets dx space is space equal space to
  • straight pi to the power of 4 over 32
  • straight pi to the power of 4 over 32 space plus space pi over 2
  • pi over 2
  • pi over 2
101 Views

22. integral space open curly brackets fraction numerator left parenthesis log space straight x minus 1 right parenthesis over denominator 1 plus left parenthesis log space straight x right parenthesis squared end fraction close curly brackets squared space dx space is space equal space to
  • fraction numerator log space straight x over denominator left parenthesis log space straight x right parenthesis squared plus 1 end fraction plus space straight C
  • fraction numerator straight x over denominator straight x plus 1 end fraction space plus straight C
  • fraction numerator xe to the power of straight x over denominator 1 plus straight x squared end fraction plus straight C
  • fraction numerator xe to the power of straight x over denominator 1 plus straight x squared end fraction plus straight C
103 Views

23.

Let f : R → R be a differentiable function having f (2) = 6, f′ (2) =(1/48) . Then limit as straight x space rightwards arrow 2 of space integral subscript 6 superscript straight f left parenthesis straight x right parenthesis end superscript space fraction numerator 4 straight t cubed over denominator straight x minus 2 end fraction dt space equals

  • 24

  • 36

  • 12

  • 12

108 Views

24.

Let f (x) be a non−negative continuous function such that the area bounded by the curve y = f (x), x−axis and the ordinates x = π/4  and x = β >  π/4 open parentheses straight beta space sin space straight beta space plus space straight pi over 4 space cos space straight beta space plus space square root of 2 straight beta close parentheses. Then f (π/2) is

  • open parentheses straight pi over 4 plus square root of 2 minus 1 close parentheses
  • open parentheses straight pi over 4 minus square root of 2 plus 1 close parentheses
  • open parentheses 1 minus straight pi over 4 minus square root of 2 plus 1 close parentheses
  • open parentheses 1 minus straight pi over 4 minus square root of 2 plus 1 close parentheses
117 Views

Advertisement
25.

The value of integral subscript negative straight pi end subscript superscript straight pi space fraction numerator cos squared space straight x over denominator 1 plus space straight a to the power of straight x end fraction space dx comma space straight a greater than 0 space is

  • a π

  • π/2

  • π/a

  • π/a

128 Views

26.

If integral space fraction numerator sin space straight x over denominator sin space left parenthesis straight x minus straight alpha right parenthesis end fraction space dx space equals space Ax space plus space straight B space log space sin space left parenthesis straight x minus straight alpha right parenthesis space plus straight C comma space space then space value space left parenthesis straight A comma space straight B right parenthesis is

  • (sinα, cosα)

  • (cosα, sinα)

  • (- sinα, cosα)

  • (- sinα, cosα)

110 Views

27. integral fraction numerator dx over denominator cos space straight x space minus space sin space straight x end fraction is equal to
  • fraction numerator 1 over denominator square root of 2 end fraction space log space open vertical bar tan open parentheses straight x over 2 minus fraction numerator begin display style straight pi end style over denominator 8 end fraction close parentheses close vertical bar space plus straight C
  • fraction numerator 1 over denominator square root of 2 end fraction space log space open vertical bar cot open parentheses straight x over 2 close parentheses close vertical bar space plus straight C
  • fraction numerator 1 over denominator square root of 2 end fraction space log space open vertical bar tan open parentheses straight x over 2 minus fraction numerator 3 straight pi over denominator 8 end fraction close parentheses close vertical bar space plus straight C
  • fraction numerator 1 over denominator square root of 2 end fraction space log space open vertical bar tan open parentheses straight x over 2 minus fraction numerator 3 straight pi over denominator 8 end fraction close parentheses close vertical bar space plus straight C
108 Views

28.

The value of integral subscript negative 2 end subscript superscript 3 space vertical line 1 minus straight x squared vertical line dx space is

  • 28/7

  • 28/3

  • 7/3

  • 7/3

129 Views

Advertisement
Advertisement

29.

The value of integral subscript 0 superscript pi divided by 2 end superscript fraction numerator left parenthesis sin space x space plus space cos space x right parenthesis squared over denominator square root of 1 plus space sin space 2 x end root end fraction space d x space i s

  • 0

  • 1

  • 2

  • 2


C.

2

integral subscript 0 superscript straight pi divided by 2 end superscript fraction numerator left parenthesis sin space straight x space plus cos space straight x right parenthesis squared over denominator square root of left parenthesis sin space straight x space plus space cos space straight x right parenthesis squared end root end fraction space dx
space equals space integral subscript 0 superscript straight pi divided by 2 end superscript space left parenthesis sin space straight x space plus space cos space straight x right parenthesis space dx
space equals space vertical line minus space cos space straight x space plus space sin space straight x vertical line subscript 0 superscript straight pi divided by 2 end superscript space equals space 2
104 Views

Advertisement
30.

Ifintegral subscript 0 superscript straight pi space xf space left parenthesis sin right parenthesis space dx space equals space straight A space integral subscript 0 superscript straight pi divided by 2 end superscript space straight f space left parenthesis sin space straight x right parenthesis space dx comma space then space straight A space is

  • 0

  • π

  • π/2

  • π/2

101 Views

Advertisement