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a. | The number of polynomials f(x) with non-negative integer coefficients of degree \[\le \] 2, satisfying\[f(0)=0\,\,and\,\,\int\limits_{0}^{1}{f(x)\,\,dx=1}\]is _____. | p. | 8 |
b. | The number of points in the interval \[\left[ -\sqrt{13},\sqrt{13} \right]\] at which \[f(x)=sin({{x}^{2}})+cos({{x}^{2}})\] attains, its maximum value is ________. | q. | 2 |
c. | \[\int\limits_{-2}^{2}{\left( \frac{3{{x}^{2}}}{1+{{e}^{x}}} \right)}\,\,dx\] equals to ______. | r. | 4 |
d. | \[\frac{\int\limits_{-1/2}^{1/2}{\cos 2x\,\,\log \left( \frac{1+x}{1-x} \right)\,\,dx}}{\int\limits_{0}^{1/2}{\cos 2x\,\,\log \left( \frac{1+x}{1-x} \right)}\,\,dx}\] equals to _______. | s. | 0 |
A) \[a-p,\,\,b-r,\,\,c-q,\,\,d-s\]
B) \[a-q,\,\,b-r,\,\,c-s,\,\,d-p\]
C) \[a-r,\,\,b-q,\,\,c-s,\,\,d-p\]
D) \[a-r,\,\,b-q,\,\,c-p,\,\,d-s\]
E) None of these
Correct Answer: E
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