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.

Integrals

Short Answer Type

241.

If space straight f left parenthesis straight x right parenthesis space equals space integral subscript 0 superscript straight x straight t space sint space dt comma space write space the space value space of space straight f apostrophe left parenthesis straight x right parenthesis

170 Views

242.

If $integral subscript 0 superscript straight a fraction numerator 1 over denominator 4 plus straight x squared end fraction dx equals straight pi over 8$ , find the value of a.

157 Views

243.

Evaluate colon integral subscript 0 superscript straight pi fraction numerator 4 straight x space sinx over denominator 1 plus cos squared straight x end fraction dx

151 Views

244.

Evaluate:
$integral fraction numerator straight x plus 2 over denominator square root of straight x squared plus 5 straight x plus 6 end root end fraction dx$

140 Views

Long Answer Type

245.

Evaluate:
$integral fraction numerator 1 over denominator sin to the power of 4 straight x plus sin squared xcos squared straight x plus cos to the power of 4 straight x end fraction dx$

164 Views

Short Answer Type

246.

Evaluate: $integral fraction numerator sin left parenthesis straight x minus straight a right parenthesis over denominator sin left parenthesis straight x plus straight a right parenthesis end fraction dx$

191 Views

247.

Evaluate:
$integral fraction numerator 5 straight x minus 2 over denominator left parenthesis 1 plus 2 straight x plus 3 straight x squared end fraction dx$

181 Views

248.
Evaluate:
$integral fraction numerator straight x squared over denominator left parenthesis straight x squared plus 4 right parenthesis left parenthesis straight x squared plus 9 right parenthesis end fraction dx$

Let space straight x squared equals straight y fraction numerator straight x squared over denominator open parentheses straight x squared plus 4 close parentheses space left parenthesis straight x squared plus 9 right parenthesis end fraction space equals space fraction numerator straight y over denominator left parenthesis straight y plus 4 right parenthesis left parenthesis straight y plus 9 right parenthesis end fraction equals fraction numerator straight A over denominator straight y plus 4 end fraction plus fraction numerator straight B over denominator straight y plus 9 end fraction straight y space equals space straight A left parenthesis straight y plus 9 right parenthesis plus straight B left parenthesis straight y plus 4 right parenthesis Comparing space both space sides comma straight A plus straight B equals 1 space and space 9 straight A plus 4 straight B space equals space 0 Solving comma space We space get space straight A equals fraction numerator negative 4 over denominator 5 end fraction space and space straight B space equals 9 over 5 therefore space space straight I space equals space integral open square brackets fraction numerator negative 4 over denominator 5 left parenthesis straight x squared plus 4 right parenthesis end fraction plus fraction numerator 9 over denominator 5 left parenthesis straight x squared plus 9 right parenthesis end fraction close square brackets dx space space space space space equals negative 4 over 5 cross times 1 half tan to the power of negative 1 end exponent open parentheses straight x over 2 close parentheses plus 9 over 5 cross times 1 third tan to the power of negative 1 end exponent open parentheses straight x over 3 close parentheses plus straight C space space space space space equals negative 2 over 5 tan to the power of negative 1 end exponent straight x over 2 plus 3 over 5 tan to the power of negative 1 end exponent straight x over 3 plus straight C

188 Views

249.

Evaluate: $integral subscript 0 superscript 4 open parentheses open vertical bar straight x close vertical bar plus open vertical bar straight x minus 2 close vertical bar plus open vertical bar straight x minus 4 close vertical bar close parentheses dx$