jee-main 2020 Q65

jee-main · India · session1_07jan_shift1 Indefinite & Definite Integrals Integral Equation with Symmetry or Substitution
If $f(a + b + 1 - x) = f(x)$, for all $x$, where $a$ and $b$ are fixed positive real numbers, then $\frac { 1 } { a + b } \int _ { a } ^ { b } x (f(x) + f(x + 1)) d x$ is equal to
(1) $\int _ { a - 1 } ^ { b - 1 } f(x + 1) d x$
(2) $\int _ { a - 1 } ^ { b - 1 } f(x) d x$
(3) $\int _ { a + 1 } ^ { b + 1 } f(x) d x$
(4) $\int _ { a + 1 } ^ { b + 1 } f(x + 1) d x$ 
If $f(a + b + 1 - x) = f(x)$, for all $x$, where $a$ and $b$ are fixed positive real numbers, then $\frac { 1 } { a + b } \int _ { a } ^ { b } x (f(x) + f(x + 1)) d x$ is equal to\\
(1) $\int _ { a - 1 } ^ { b - 1 } f(x + 1) d x$\\
(2) $\int _ { a - 1 } ^ { b - 1 } f(x) d x$\\
(3) $\int _ { a + 1 } ^ { b + 1 } f(x) d x$\\
(4) $\int _ { a + 1 } ^ { b + 1 } f(x + 1) d x$
Paper Questions
Q1 Q2 Q3 Q4 Q5 Q21 Q22 Q23 Q24 Q25 Q51 Q52 Q53 Q54 Q55 Q56 Q57 Q58 Q59 Q60 Q61 Q62 Q63 Q64 Q65 Q66 Q67 Q68 Q69 Q70 Q71 Q72 Q73 Q74 Q75