2. Sample Papers
  3. JEE Main & Advanced

JEE Main & Advanced Sample Paper JEE Main Sample Paper-42

  • question_answer
    The expression \[{{\{x+{{({{x}^{3}}-1)}^{1/2}}\}}^{5}}+\]\[{{\{x-{{({{x}^{3}}-1)}^{1/2}}\}}^{5}}\] polynomial of degree

    A)  5                                

    B)  6   

    C)  7                                

    D)  8

    Correct Answer: C

    Solution :

    We know that,\[{{(a+b)}^{5}}+{{(a-b)}^{5}}\] \[=2{{[}^{5}}{{C}_{0}}{{a}^{5}}{{+}^{5}}{{C}_{2}}{{a}^{3}}{{b}^{2}}{{+}^{5}}{{C}_{4}}a{{b}^{4}}]\] \[=2[{{a}^{5}}+10{{a}^{3}}{{b}^{2}}+5a{{b}^{4}}]\] \[\therefore \]\[{{[x+{{({{x}^{3}}-1)}^{1/2}}]}^{5}}+{{[x-{{({{x}^{3}}-1)}^{1/2}}]}^{5}}\] \[=2[{{x}^{5}}+10{{x}^{3}}({{x}^{3}}-1)+5x{{({{x}^{3}}-1)}^{2}}]\] \[=2[{{x}^{5}}+10{{x}^{6}}-10{{x}^{3}}+5{{x}^{7}}+5x-10{{x}^{4}}]\] Therefore, the given expression is a polynomial of degree 7.


You need to login to perform this action.
You will be redirected in 3 sec spinner